JP6497494B1 - Shape correction apparatus and shape correction method for figure pattern - Google Patents

Abstract

A simulation for forming an actual pattern on the actual substrate is performed by lithography based on the unit graphic (10). First, the unit graphic (10) is divided into polygons (FIG. (A)), and vectors (Va1 to Vd4) are defined on individual sides of the polygon (FIG. (B)). The vector arranged overlappingly in the same section is removed, and the vectors (V1 to V10) along the contour line of the unit graphic (10) are left (FIG. (C)). A normal end point (A to J) is defined at the start point position of each vector (V1 to V10), and a contour line segment (line segment AB or the like) having the adjacent normal end points as both ends is defined (FIG. (D)). An evaluation point is defined at the midpoint of each contour line segment, and a deviation amount of each evaluation point is calculated by simulation. A supplementary end point is additionally defined at the position of the intermediate normal end point (B, C, D, G, H, I) that is not the apex, and a separate end point is secured for each of the left and right contour segments, and according to the amount of deviation. Then, correction is performed by moving each contour line segment in a direction orthogonal to the contour line.

Description

  The present invention relates to a figure pattern shape correction apparatus and a shape correction method, and more particularly to a technique for correcting the shape of a figure pattern formed on a substrate through a lithography process.

  In fields that require fine patterning of specific material layers, such as semiconductor device manufacturing processes, a fine pattern is formed on a physical substrate through a lithography process that involves drawing using light or an electron beam. The technique to form is taken. Usually, a fine mask pattern is designed using a computer, and the resist layer formed on the substrate is exposed based on the obtained mask pattern data. After developing this, the remaining resist layer is masked. Etching is performed to form a fine pattern on the substrate.

  However, there is a slight discrepancy between the actual graphic pattern actually obtained on the substrate through such a lithography process and the original graphic pattern designed on the computer. This is because the lithography process includes steps of exposure, development, and etching, so that the actual graphic pattern finally formed on the substrate does not exactly match the original graphic pattern used in the exposure process. Because. In particular, in the exposure process, the resist layer is drawn with light or an electron beam. At that time, the exposure area actually drawn on the resist layer by the proximity effect (PE) is the original figure. It is known that the area is slightly wider than the pattern. In addition, since an etching loading phenomenon occurs in the etching process, the pattern after development and the pattern after etching differ in shape. It is known that the effect of the etching loading phenomenon varies depending on the area exposed from the resist layer on the surface of the actual substrate. The proximity effect in the drawing process and the loading phenomenon in the etching process are all phenomena that cause a difference between the shape of the original graphic pattern and the shape of the actual graphic pattern. The range (scale size) is different for each phenomenon.

  Under these circumstances, in a semiconductor device manufacturing process including a lithography process, a desired original figure pattern is designed on a computer, and then the lithography process using the original figure pattern is simulated on a computer, and an actual substrate is obtained. A procedure is performed to estimate the shape of the actual graphic pattern that will be formed above. Based on the shape (dimension) of the actual figure pattern obtained as a result of the simulation, the shape (dimension) of the original figure pattern is corrected if necessary, and the actual figure pattern is obtained using the corrected figure pattern obtained by this correction. The actual lithography process is performed to manufacture an actual semiconductor device.

  Therefore, in order to produce a final product with a precise pattern as designed, the actual figure pattern shape is accurately estimated by simulation before the lithography process is actually performed, and the original figure pattern is appropriately corrected. It is necessary to apply. Therefore, for example, in Patent Document 1 below, a feature factor that characterizes the layout of the original graphic pattern and a control factor that affects the size of the resist pattern formed on the substrate by the lithography process are used as an input layer. A method of performing a highly accurate simulation using a neural network is disclosed. Patent Document 2 discloses a method for improving the accuracy of simulation using two sets of neural networks, and Patent Document 3 discloses an appropriate method for extracting feature values from a photomask pattern. A method for improving the accuracy of simulation by setting various extraction parameters is disclosed.

JP 2008-122929 A JP 2010-044101 A JP 2010-156866 A

  As described above, when a real graphic pattern is formed on a real substrate by a lithography process based on the original graphic pattern, it will be formed on the real substrate when a simulation is performed in advance and the original graphic pattern is used as it is. A process of estimating the shape of the actual graphic pattern and performing a necessary correction on the original graphic pattern based on the estimation result to obtain a corrected graphic pattern is performed. In order to perform such estimation and correction, various shape correction devices have been proposed, including the devices described in the aforementioned patent documents.

  In a general shape correction device, an evaluation point is set at a predetermined position on an original graphic pattern, and based on a feature amount indicating a feature around the evaluation point, a deviation amount on the actual graphic pattern about the evaluation point A corrected graphic pattern is created by obtaining (process bias) by simulation and performing correction according to the amount of deviation. Therefore, it is very important to set an appropriate number of evaluation points at appropriate positions on the original graphic pattern. Of course, if the evaluation point density is increased and a large number of evaluation points are set, the accuracy of the simulation is improved and more accurate correction can be performed. However, as the number of evaluation points increases, the computation load of the simulation increases and the time until the simulation is completed increases. For this reason, it is desired to perform efficient evaluation point setting that can reduce the calculation burden as much as possible while maintaining practically sufficient simulation accuracy.

  Therefore, the present invention provides a graphic pattern capable of performing efficient evaluation point setting capable of reducing the calculation burden as much as possible while maintaining a practically sufficient simulation accuracy when performing a simulation necessary for correcting the original graphic pattern. An object of the present invention is to provide a shape correction apparatus.

(1) In the first aspect of the present invention, when a real graphic pattern is formed on a real substrate by a lithography process based on the original graphic pattern, the original graphic pattern is matched with the original graphic pattern. In the figure pattern shape correction apparatus that corrects the shape and creates a correction figure pattern that is actually used in the lithography process,
An evaluation point setting unit for setting an evaluation point at a predetermined position on the contour line indicating the boundary between the inside and the outside for each unit figure constituting the original figure pattern,
A feature quantity extraction unit that extracts a feature quantity indicating features around the evaluation point for the original graphic pattern;
A bias estimation unit that estimates a process bias indicating the amount of deviation between the position of the evaluation point on the original graphic pattern and the position on the actual graphic pattern based on the feature amount;
A pattern correction unit that creates a corrected graphic pattern by correcting the original graphic pattern based on the estimated value of the process bias output from the bias estimation unit;
Provided,
Evaluation point setting unit
A unit graphic input unit for inputting individual unit graphics made of polygons;
A unit graphic dividing unit for dividing a unit graphic by a linear dividing line to form a divided graphic consisting of a plurality of polygons;
For each divided figure, a divided figure vector definition unit that defines a divided figure vector on each side of the polygon so as to go around the predetermined forward direction along the outline of the polygon constituting the divided figure. When,
Search for overlapping vector pairs that are arranged on overlapping sides of a pair of adjacent polygons that are adjacent to each other from a set of divided graphic vectors, and whose directions are opposite to each other, and an overlapping section portion of the searched overlapping vector pairs And a unit graphic vector definition unit that defines a plurality of unit graphic vectors arranged along the outline of the unit graphic by the remaining vector,
A normal end point definition section for defining normal end points at the start position of each unit graphic vector,
An evaluation point definition unit that defines an evaluation point between two normal end points arranged adjacent to each other on the contour line of each unit graphic;
For each unit graphic, a supplementary endpoint definition unit that searches for a regular normal endpoint that is a regular endpoint that does not constitute a vertex of the polygon, and additionally defines a supplementary endpoint at the same position as the searched regular intermediate point;
And have
The pattern correction unit
For each evaluation point, the normal end point or supplement end point adjacent to one side of the evaluation point along the outline of the unit graphic is the first end point, and the normal end point or supplement end point adjacent to the other side is the second end point. A process of defining a contour line segment that is the end point of each of the evaluation points, and moving the contour line segment of each evaluation point in a direction orthogonal to the contour line segment by a correction amount according to the estimated value of the process bias of the evaluation point An outline segment movement processing unit for performing
If the intermediate normal end point and the replenishment end point that were in the same position before the moving process are separated into two different positions after the moving process, an additional process for adding a new contour segment that connects the positions after the moving process. Contour line addition processing unit for performing,
If the corner normal end point, which is the normal end point that formed the vertex of the polygon before the movement process, is separated into two different positions after the movement process, the two corner normal end points after the separation are merged to form a new one. A contour line segment expansion / contraction processing unit that performs expansion / contraction processing to expand / contract each contour line segment including the corner normal end point after separation so as to be a corner normal end point,
The correction figure pattern comprised by the unit figure which makes the outline the assembly of the outline line segment after performing a movement process, an addition process, and an expansion / contraction process is created.

(2) According to a second aspect of the present invention, in the shape correction apparatus for graphic patterns according to the first aspect described above,
The unit graphic dividing unit divides the unit graphic to form a divided graphic consisting of trapezoids.

(3) According to a third aspect of the present invention, in the shape correction apparatus for graphic patterns according to the first or second aspect described above,
When the unit figure input unit inputs an elongated strip-like unit figure that extends along a predetermined longitudinal axis and has straight upper and lower sides parallel to each other,
The unit graphic dividing unit divides the band-shaped unit graphic by a plurality of dividing lines arranged at predetermined intervals along the longitudinal axis, so that a plurality of divided graphics arranged one-dimensionally along the longitudinal axis Is formed.

(4) According to a fourth aspect of the present invention, in the shape correction apparatus for graphic patterns according to the first or second aspect described above,
When the unit graphic input unit inputs a unit graphic defined on the XY plane,
The unit figure dividing unit arranges a plurality of horizontal dividing lines parallel to the X axis at predetermined intervals in the Y axis direction, and divides the unit figure by the plurality of horizontal dividing lines, thereby extending a plurality of elongated plurality of lines extending in the X axis direction. A plurality of two-dimensionally arranged strips by dividing each of the plurality of strip-shaped figures by a plurality of vertical dividing lines arranged at predetermined intervals along the X-axis and parallel to the Y-axis. The divided figure is formed.

(5) According to a fifth aspect of the present invention, in the shape correction apparatus for graphic patterns according to the first to fourth aspects described above,
The unit graphic division unit has a function to set the maximum beam forming size of the drawing device used in the lithography process, and the arrangement interval of the dividing lines used for dividing the unit graphic is set to be equal to or less than the maximum beam forming size. is there.

(6) According to a sixth aspect of the present invention, in the shape correction apparatus for graphic patterns according to the first to fifth aspects described above,
The divided graphic vector definition unit assigns numbers to the vertices of the K-shaped divided graphic in the order of the first vertex to the Kth vertex in the clockwise or counterclockwise order along the contour line, and the k-th vertex. By repeating the process of defining the k-th divided figure vector starting at (k + 1) and ending at the (k + 1) -th vertex (if k = K, the first vertex) from k = 1 to K A divided graphic vector for the divided graphic is defined.

(7) According to a seventh aspect of the present invention, in the shape correction apparatus for graphic patterns according to the first to sixth aspects described above,
The evaluation point definition unit defines an evaluation point at the midpoint position of two normal end points arranged adjacent to each other on the contour line of the unit graphic.

(8) According to an eighth aspect of the present invention, in the shape correction apparatus for graphic patterns according to the first to seventh aspects described above,
The replenishment endpoint definition unit defines a total of N normal endpoints defined for one contour line in the order along the contour line, respectively, from the first normal endpoint T (1) to the Nth normal endpoint T (N ), When paying attention to the n-th normal end point T (n), the (n-1) -th normal end point T (n-1) (where n = 1, the N-th normal end point T (N)), the nth normal end point T (n), and the (n + 1) th normal end point T (n + 1) (where n = N, the first normal end point T (1)) When it is on a straight line, the nth normal end point T (n) is determined as the intermediate normal end point, and the process of additionally defining the supplementary end point at the same position as the intermediate normal end point is repeatedly executed from n = 1 to N. It is what I did.

(9) According to a ninth aspect of the present invention, in the shape correction apparatus for graphic patterns according to the first to eighth aspects described above,
When the contour line segment expansion / contraction processing unit separates one corner normal end point into the first moving end point and the second moving end point by the moving process, the first moving end point is set as the first end point. The intersection of the straight line including the post-movement contour line segment and the straight line including the second post-movement contour line segment having the second moving end point as one end point is obtained, and the intersection point is set as a new corner normal end point. Expansion and contraction processing is performed such that one end point becomes the new corner normal end point with respect to one post-movement contour line segment and the second post-movement contour line segment.

(10) According to a tenth aspect of the present invention, in the shape correction apparatus for graphic patterns according to the first to ninth aspects described above,
The evaluation point setting unit further includes an end point reconstructing unit that performs reconstruction to correct the number or position of the normal end points defined on the contour line of the unit graphic by the normal end point defining unit,
The evaluation point definition unit is configured to define evaluation points based on the normal end points obtained by the above reconstruction.

(11) An eleventh aspect of the present invention is the figure pattern shape correcting apparatus according to the tenth aspect described above,
The end point reconstructing unit reconstructs normal end points by performing end point removal processing for removing some or all of the intermediate normal end points for some or all of the unit graphics.

(12) A twelfth aspect of the present invention is the figure pattern shape correcting apparatus according to the eleventh aspect described above,
The end point reconstructing unit sets a total of N normal end points defined for one contour line of one unit graphic in the order along the contour line, respectively, in the order of the first normal end points T (1) to Nth. Focusing on the nth normal end point T (n), the nth normal end point T (n) and the normal end point T (n) that is not to be removed immediately before the normal end point T (n) n−m) (where m is a natural number, and when n−m <1, T (n−m + N)) is L1, and the nth normal endpoint T (n) and (n + 1) ) Of the normal end point T (n + 1) (where n = N, the first normal end point T (1): the same applies hereinafter) is defined as L2.
At least one of L1 and L2 is equal to or less than a predetermined reference value Wmerge, and normal end point T (n-1) (where N = 1, Nth normal end point T (N)), T (n) , T (n + 1) are on a straight line, the determination process for removing the n-th normal end point T (n) is repeatedly executed from n = 1 to N, and the normal that has been removed An end point removal process for removing the end points is performed.

(13) A thirteenth aspect of the present invention is the figure pattern shape correcting apparatus according to the eleventh aspect described above,
The end point reconstructing unit sets a total of N normal end points defined for one contour line of one unit graphic in the order along the contour line, respectively, in the order of the first normal end points T (1) to Nth. Normal end point T (N), n-th normal end point T (n), and normal end point T (n−m) that is not to be removed immediately before it (where m is a natural number, When n−m <1, the distance from T (n−m + N)) is L1, and the nth normal end point T (n) and the (n + 1) th normal end point T (n + 1) (where n = N In this case, the distance between the first normal end point T (1) (the same applies hereinafter) is L2, and the (n + 1) th normal end point T (n + 1) and the (n + 2) th normal end point T (n + 2) (however, , N = N−1, the distance from the first normal end point T (1), and when n = N, the distance from the second normal end point T (2): When 3 and it was,
L2 is equal to or less than a predetermined reference value Wmerge, and normal end point T (n-1) (where n = 1, Nth normal end point T (N): the same applies hereinafter), T (n), T When the four points (n + 1) and T (n + 2) are on a straight line, if L1 <L3, the normal end point T (n) is to be removed, and if L1> L3, the normal end point T (n + 1) is selected. If it is a removal target, and L1 = L3, either the normal end point T (n) or the normal end point T (n + 1) is the removal target,
L2 is equal to or less than a predetermined reference value Wmerge, and the three normal end points T (n−1), T (n), and T (n + 1) are on a straight line, but the normal end point T (n + 2) is the straight line. If it is not on the line, the normal endpoint T (n) is the removal target,
L2 is equal to or less than a predetermined reference value Wmerge, and the three normal end points T (n), T (n + 1), and T (n + 2) are on a straight line, but the normal end point T (n-1) is the straight line. If it is not on the line, the normal end point T (n + 1) is to be removed,
This process is repeatedly executed while increasing n by 1 until n ≧ N is satisfied, thereby performing an end point removal process for removing the normal end point to be removed.

(14) According to a fourteenth aspect of the present invention, in the shape correction apparatus for graphic patterns according to the tenth aspect described above,
The end point reconstruction unit temporarily removes the intermediate normal end points for a part of the contour lines, and reconstructs the normal end points by the end point rearrangement process in which new intermediate normal end points are arranged on each side of the part of the contour lines. Is to do.

(15) According to a fifteenth aspect of the present invention, in the shape correction apparatus for graphic patterns according to the fourteenth aspect described above,
After the end point reconstruction unit removes the intermediate normal end point for the specific contour line, the end point relocation processing is performed by rearranging the intermediate normal end point at predetermined intervals on each side of the specific contour line. It is a thing.

(16) According to a sixteenth aspect of the present invention, in the shape correction apparatus for a graphic pattern according to the tenth aspect described above,
The end point reconstruction unit performs the end point removal processing by the graphic pattern shape correction device according to the above-described eleventh to thirteenth aspects, and the end point rearrangement by the graphic pattern shape correction device according to the fourteenth or fifteenth aspect described above. And a function to selectively execute the processing for each contour line of the unit graphic,
For normal endpoints on a regular figure surrounded by unit graphic vectors around the forward direction, the endpoints are reconstructed by the above endpoint removal processing, and are surrounded by unit graphic vectors around the opposite direction to the forward direction. For normal end points on the opposite figure, end point reconstruction is performed by the end point rearrangement process.

(17) According to a seventeenth aspect of the present invention, in the shape correction apparatus for graphic patterns according to the first to sixteenth aspects described above,
The feature amount extraction unit has a function of extracting a feature amount indicating a feature around an evaluation point on the corrected graphic pattern for the corrected graphic pattern created by the pattern correction unit,
The bias estimation unit has a function of estimating a process bias indicating an amount of deviation between the position of the evaluation point on the corrected graphic pattern and the position on the actual graphic pattern based on the feature amount;
The pattern correction unit has a function of creating a new corrected graphic pattern by performing further correction on the corrected graphic pattern based on the estimated value of the process bias output from the bias estimation unit,
The correction for the corrected figure pattern is repeatedly executed.

(18) According to an eighteenth aspect of the present invention, in the shape correction apparatus for a graphic pattern according to the seventeenth aspect described above,
The contour line segment expansion / contraction processing unit performs a process of correcting the position of the evaluation point for the contour line segment after the expansion / contraction process after performing the process of expanding / contracting the contour line segment.

  (19) According to a nineteenth aspect of the present invention, there is provided an evaluation point setting unit or a pattern correction unit included in the graphic pattern shape correction device or the graphic pattern shape correction device according to the first to eighteenth aspects described above. It is configured by incorporating a program into a computer.

(20) In the twentieth aspect of the present invention, when a real graphic pattern is formed on a real substrate by a lithography process based on the original graphic pattern, the original graphic pattern is matched with the original graphic pattern. In the shape correction method of a graphic pattern that corrects the shape and creates a corrected graphic pattern that is actually used in the lithography process,
An evaluation point setting stage in which the computer sets an evaluation point at a predetermined position on the contour line indicating the boundary between the inside and the outside for each unit figure constituting the original figure pattern;
A feature amount extraction stage in which the computer extracts a feature amount indicating features around the evaluation point for the original graphic pattern;
A bias estimation stage in which a computer estimates a process bias indicating an amount of deviation between the position of the evaluation point on the original graphic pattern and the position on the actual graphic pattern based on the feature amount;
A pattern correction stage in which a computer creates a corrected figure pattern by correcting the original figure pattern based on the estimated value of the process bias obtained by the bias estimation stage;
Have
The evaluation point setting stage
A unit figure input step for inputting individual unit figures consisting of polygons;
A unit graphic dividing step of dividing the unit graphic by a linear dividing line to form a divided graphic consisting of a plurality of polygons;
A divided graphic vector defining step for defining a divided graphic vector on each side of the polygon so that each divided graphic makes a round around a predetermined forward direction along the outline of the polygon constituting the divided graphic. When,
Search for overlapping vector pairs that are arranged on overlapping sides of a pair of adjacent polygons that are adjacent to each other from a set of divided graphic vectors, and whose directions are opposite to each other, and an overlapping section portion of the searched overlapping vector pairs A unit graphic vector defining step for defining a plurality of unit graphic vectors arranged along the outline of the unit graphic by the remaining vector,
A normal endpoint definition step for defining normal endpoints at the start position of each unit graphic vector,
An evaluation point defining step for defining an evaluation point between two normal end points arranged adjacent to each other on the outline of the unit graphic;
For each unit figure, a supplementary endpoint definition step of searching for a regular normal endpoint that is a regular endpoint that does not constitute a vertex of the polygon, and additionally defining a supplementary endpoint at the same position as the searched regular intermediate point;
Have
The pattern correction stage
For each evaluation point, the normal end point or supplement end point adjacent to one side of the evaluation point along the outline of the unit graphic is the first end point, and the normal end point or supplement end point adjacent to the other side is the second end point. A process of defining a contour line segment that is the end point of each of the evaluation points, and moving the contour line segment of each evaluation point in a direction orthogonal to the contour line segment by a correction amount according to the estimated value of the process bias of the evaluation point A contour segment moving step for performing
If the intermediate normal end point and the replenishment end point that were in the same position before the moving process are separated into two different positions after the moving process, an additional process for adding a new contour segment that connects the positions after the moving process. An outline segment adding step for performing
If the corner normal end point, which is the normal end point that formed the vertex of the polygon before the movement process, is separated into two different positions after the movement process, the two corner normal end points after the separation are merged to form a new one. Contour line segment expansion / contraction step for performing expansion / contraction processing to expand / contract each contour line segment including the corner normal end point after separation so as to be a corner normal end point,
The correction figure pattern comprised by the unit figure which makes the outline the assembly of the outline line segment after performing a movement process, an addition process, and an expansion / contraction process is created.

(21) According to a twenty-first aspect of the present invention, in the shape correction method for a graphic pattern according to the twentieth aspect described above,
The evaluation point setting stage further includes an end point restructuring step for performing a restructuring to correct the number or position with respect to the normal end point defined by the normal end point defining step,
In the evaluation point definition step, evaluation points are defined based on the normal end points obtained by the reconstruction.

  According to the shape correction apparatus and shape correction method for a graphic pattern according to the present invention, after the unit graphic constituting the original graphic pattern is divided into polygons, the end points are defined with reference to the vertex positions of the polygons, An evaluation point is defined for each contour segment connecting two adjacent end points, and the position can be corrected for each contour segment. For this reason, when correcting the original graphic pattern, it is possible to perform efficient evaluation point setting that can reduce the calculation burden as much as possible while maintaining practically sufficient simulation accuracy. In addition, if an embodiment in which the end point reconstruction is further performed on the end point defined with respect to the vertex position of the polygon is adopted, the number and positions of the end points are corrected, so that more efficient evaluation point setting is performed. It becomes possible.

It is a block diagram which shows the structure of the shape correction apparatus 100 of the figure pattern which concerns on prior invention and basic embodiment of this invention. It is a top view which shows an example in which the difference in shape produced between the original figure pattern and the real figure pattern. In the example shown in FIG. 2, it is a top view which shows the example of a setting of each evaluation point, and the process bias which arises in each evaluation point. It is a flowchart which shows the design / manufacturing process of a product using the shape correction apparatus 100 of the graphic pattern shown in FIG. It is a top view which shows the concept which grasps | ascertains the surrounding characteristic about the evaluation point defined on the outline of a figure pattern. It is a figure which shows the outline | summary of the process performed in the feature-value extraction unit 120 and the bias estimation unit 130 shown in FIG. It is a flowchart which shows the process sequence performed in the feature-value extraction unit 120 shown in FIG. It is a top view which shows the specific example of the original figure pattern 10 given to the shape correction apparatus 100 of the figure pattern shown in FIG. It is a top view which shows the state in which the process which superimposes the original figure pattern 10 on the mesh which consists of a two-dimensional arrangement | sequence of a pixel was performed in the original image creation part 121 shown in FIG. It is a figure which shows the area density map M1 produced based on the original figure pattern 10 shown in FIG. It is a figure which shows the edge length density map M2 produced based on the original figure pattern 10 shown in FIG. It is a top view which shows the original figure pattern 10 containing the information of dose amount. It is a figure which shows the dose density map M3 produced based on the original figure pattern 10 with a dose amount shown in FIG. It is a top view which shows the procedure which produces the kth hierarchy image Pk by performing the filter process which used the Gaussian filter GF33 to the kth preparation image Qk. It is a top view which shows the kth hierarchy image Pk obtained by the filter process shown in FIG. It is a top view which shows the example of the image processing filter utilized for the filter process shown in FIG. It is a top view which shows another example of the image processing filter utilized for the filter process shown in FIG. It is a top view which shows the procedure which produces the (k + 1) th preparation image Q (k + 1) by performing an average pooling process with respect to the kth hierarchy image Pk. It is a top view which shows the procedure which produces the (k + 1) th preparation image Q (k + 1) by performing a max pooling process with respect to the kth hierarchy image Pk. It is a top view which shows the procedure which produces the image pyramid PP which consists of n kinds of hierarchy images P1-Pn in the image pyramid creation part 122 shown in FIG. FIG. 7 is a plan view showing a procedure for calculating a feature value for an evaluation point E from each hierarchical image in the feature value calculation unit 123 shown in FIG. 1. It is a figure which shows the specific calculating method used with the feature-value calculation procedure shown in FIG. It is a top view which shows the procedure which produces image pyramid PD which consists of n types of difference images D1-Dn in the image pyramid preparation part 122 shown in FIG. It is a block diagram which shows the Example using a neural network as the estimation calculating part 132 shown in FIG. FIG. 25 is a diagram showing a specific calculation process executed by the neural network shown in FIG. 24. FIG. FIG. 26 is a diagram illustrating an arithmetic expression for obtaining each value of the first hidden layer in the diagram illustrated in FIG. 25. It is a figure which shows the specific example of the activation function f (ξ) shown in FIG. It is a figure which shows the computing equation which calculates | requires each value of the 2nd hidden layer-the Nth hidden layer in the diagram shown in FIG. FIG. 26 is a diagram illustrating an arithmetic expression for obtaining a value y of an output layer in the diagram illustrated in FIG. 25. It is a flowchart which shows the procedure of the learning step for obtaining the learning information L which the neural network shown in FIG. 24 uses. It is a flowchart which shows the detailed procedure of the estimation calculating part learning of step S84 in the flowchart shown in FIG. It is a block diagram which shows the structure of the evaluation point setting unit 110 in the shape correction apparatus 100 (refer FIG. 1) of the figure pattern which concerns on fundamental embodiment of this invention. It is a top view which shows the example of the specific division process performed by the unit figure division part 112 shown in FIG. FIG. 33 is a plan view illustrating an example of a specific division process performed on the parallelogram unit graphic 10 by the unit graphic division unit 112 illustrated in FIG. 32. It is a top view which shows the example of the trapezoid-shaped division | segmentation figure obtained by the division | segmentation process by the unit figure division part 112 shown in FIG. FIG. 35 is a plan view showing a state in which shape correction is performed on each divided figure shown in FIG. It is a top view which shows an example of the exposure process based on the unit figure 15 after correction | amendment shown in FIG. An example in which processing by the divided graphic vector defining unit 113, the unit graphic vector defining unit 114, and the normal end point defining unit 115 shown in FIG. 32 is performed on the parallelogram unit graphic 10 shown in FIG. 34 (c). FIG. A plane showing an example in which the L-shaped unit graphic 10 is processed by the unit graphic dividing unit 112, the divided graphic vector defining unit 113, the unit graphic vector defining unit 114, and the normal end point defining unit 115 shown in FIG. FIG. An example is shown in which the unit graphic dividing unit 112, the divided graphic vector defining unit 113, the unit graphic vector defining unit 114, and the normal end point defining unit 115 shown in FIG. It is a top view. FIG. 33 is a schematic diagram (FIG. (A)) and a flow diagram (FIG. (B)) showing a procedure when a three-point endpoint removal process is adopted as the endpoint reconstruction process by the endpoint rebuilding unit 116 shown in FIG. An example in which the end points are reconstructed by applying the three-point end point removal processing shown in FIG. 41 to the normal end points A to J on the parallelogram unit graphic 10 shown in FIG. 38 (d). FIG. An example is shown in which the end points are reconstructed by applying the three-point end point removal processing shown in FIG. 41 to the normal end points A to I on the L-shaped unit graphic 10 shown in FIG. 39 (f). It is a top view. FIG. 33 is a schematic diagram (FIG. (A)) and a flow chart (FIG. (B)) showing a procedure when a four-point type endpoint removal process is adopted as the endpoint reconstruction process by the endpoint reconstruction unit 116 shown in FIG. It is a schematic diagram which shows the procedure at the time of employ | adopting an endpoint rearrangement process as an endpoint reconstruction process by the endpoint reconstruction part 116 shown in FIG. It is a flowchart which shows the procedure at the time of employ | adopting an endpoint rearrangement process as an endpoint reconstruction process by the endpoint reconstruction part 116 shown in FIG. The top view which shows the example which applied the end-point rearrangement process shown in FIG. 46 to the end-point rearrangement processing on the normal end points M to T on the square-shaped unit graphic 10 shown in FIG. It is. FIG. 43 is a plan view showing an example in which evaluation points 1 to 8 are defined on the parallelogram type unit graphic 10 after the end point reconstruction shown in FIG. 42B by the evaluation point definition unit 117 shown in FIG. 32. It is a top view which shows the example which defined the evaluation points 1-8 on the L-shaped unit figure 10 after the end point reconstruction shown in FIG.43 (b) by the evaluation point definition part 117 shown in FIG. FIG. 47 is a plan view showing an example in which evaluation points 1 to 18 are defined on the square-shaped unit graphic 10 after the end point reconstruction shown in FIG. 47 (b) by the evaluation point definition unit 117 shown in FIG. FIG. 49 is a plan view showing an example in which replenishment end points are defined on each unit graphic shown in FIGS. 48 (b), 49 (b), and 50 (b) by the replenishment end point defining unit 118 shown in FIG. FIG. 33 is a schematic diagram (FIGS. (A) and (b)) and a flowchart (FIG. (C)) showing a specific procedure of a supplementary endpoint definition process performed by the supplementary endpoint definition unit 118 shown in FIG. It is a block diagram which shows the pattern correction unit 140 in the shape correction apparatus 100 (refer FIG. 1) of the figure pattern which concerns on fundamental embodiment of this invention, and the component related to this. FIG. 52 is an enlarged plan view showing each end point and each evaluation point defined on the L-shaped unit graphic shown in FIG. 51 (b). It is a figure which shows an example of the data format showing the mutual relationship of each end point and each evaluation point shown in FIG. FIG. 55 is a plan view showing a state in which the contour line segment movement processing is performed on the L-shaped unit graphic 10 illustrated in FIG. 54 by the contour line segment movement processing unit 141 illustrated in FIG. 53; FIG. 57 is a plan view showing a state in which contour line segment addition processing is performed on the L-shaped unit graphic after the movement processing shown in FIG. 56 by the contour line segment addition processing unit 142 shown in FIG. 53; FIG. 58 is a plan view showing a state where the contour line segment expansion / contraction processing is performed on the L-shaped unit graphic after the addition processing illustrated in FIG. 57 by the contour line segment expansion / contraction processing unit 143 illustrated in FIG. 53; FIG. 57 is a plan view showing a state where the contour line segment expansion / contraction processing unit 143 illustrated in FIG. 53 performs processing for correcting the position of the evaluation point for the contour line segment of the L-shaped unit graphic after the expansion / contraction processing illustrated in FIG. is there. It is a top view which shows the procedure of the conventional method of defining an end point with a predetermined space | interval for every edge | side of a unit figure. In this invention, it is a top view which shows the merit which divides | segments a unit figure into a polygon and defines an end point on the basis of the vertex position of this polygon. It is a top view which shows the merit which defines a supplement end point. In this invention, it is a top view which shows the merit which moves a supplementary end point in the direction orthogonal to an outline. It is a top view which shows the demerit at the time of moving an intermediate | middle normal endpoint and a supplementary endpoint in arbitrary directions. In the example shown in FIG. 58, it is a top view which shows the demerit when not performing an endpoint reconstruction.

  Hereinafter, the present invention will be described based on the illustrated embodiments. The technology according to the present invention is applied to the invention (hereinafter referred to as the prior application) described in International Application No. PCT / JP2018 / 022100 (hereinafter referred to as the prior application) based on the Patent Cooperation Treaty. It has been developed. Therefore, here, for convenience of explanation, in the following §1 to §4, the invention of the prior application will first be explained, and the features of the present invention will be explained in §5 and thereafter. Therefore, the contents described in the following §1 to §4 (contents shown in FIGS. 1 to 31) are substantially the same as the basic embodiments described in the prior application.

<<< §1. Basic configuration of shape correction apparatus according to invention of prior application >>>
Here, the configuration of the figure pattern shape correcting apparatus 100 according to the basic embodiment of the invention of the prior application will be described with reference to the block diagram of FIG. As shown in the figure, the figure pattern shape correction apparatus 100 includes an evaluation point setting unit 110, a feature amount extraction unit 120, a bias estimation unit 130, and a pattern correction unit 140. Here, the figure pattern shape estimation device 100 ′ according to the prior application invention is configured by the three units of the evaluation point setting unit 110, the feature amount extraction unit 120, and the bias estimation unit 130. The pattern shape correcting apparatus 100 is configured by further adding a pattern correcting unit 140 as a fourth unit to the figure pattern shape estimating apparatus 100 ′.

<1.1 Shape Estimation Device for Graphic Pattern>
First, the configuration and function of the figure pattern shape estimation apparatus 100 ′ will be described. The figure pattern shape estimation apparatus 100 ′ serves to estimate the shape of the actual figure pattern 20 formed on the actual substrate S by simulating a lithography process using the original figure pattern 10. In the upper part of FIG. 1, an alternate long and short dash line arrow from the original graphic pattern 10 is shown, and an actual substrate S having a real graphic pattern 20 is drawn at the tip of the arrow. This dashed-dotted arrow indicates a physical lithography process.

  The original graphic pattern 10 shown in the figure is graphic pattern data created by design work using a computer, and the alternate long and short dash line arrow indicates a lithography process such as physical exposure, development, and etching based on this data. It is shown that the actual substrate S is manufactured by carrying out. On the actual substrate S, an actual graphic pattern 20 corresponding to the original graphic pattern 10 is formed. However, when such a lithography process is performed, there is a slight discrepancy between the original graphic pattern 10 and the actual graphic pattern 20. This is because, as described above, it is difficult to form an accurate figure on the actual substrate S according to the various conditions of the steps of exposure, development, and etching included in the lithography process.

  FIG. 2 is a plan view showing a specific example in which a difference in shape occurs between the original graphic pattern 10 and the actual graphic pattern 20. In a semiconductor device or the like, it is actually necessary to form a very fine and complicated figure pattern on the surface of an actual substrate S such as silicon. Here, for the sake of convenience of explanation, a simple pattern as shown in FIG. A case where a simple figure is given as the original figure pattern 10 will be described. The illustrated original figure pattern 10 is a pattern composed of one rectangle, for example, original figure data indicating that a material layer corresponding to the hatched rectangular inner region is formed on the actual substrate S. Become.

  In an actual lithography process, a resist layer is formed on the upper surface of the material layer on the actual substrate S, and exposure to light or an electron beam is performed to perform drawing on the resist layer. For example, if the resist layer is exposed to the inner area (hatched portion) of the original graphic pattern 10 shown in FIG. 2A, the resist layer is developed to remove the non-exposed portion. The exposed portion remains as a remaining resist layer (hatched portion). Furthermore, if the remaining resist layer is used as a mask and the material layer is etched, theoretically, the inner region (hatched portion) of the original figure pattern 10 can be left also for the material layer. On the actual substrate S, the same actual graphic pattern as the original graphic pattern 10 shown in FIG.

  However, actually, the actual graphic pattern 20 obtained on the actual substrate S does not exactly match the original graphic pattern 10. This is because the conditions of the steps of exposure, development, and etching included in the lithography process affect the shape of the actual figure pattern 20 finally obtained. For example, in the exposure process, the resist layer is drawn with light or an electron beam. At that time, the exposure area actually drawn on the resist layer by the proximity effect (PE) is the original figure. It is known that the area is slightly wider than the pattern 10. Under the influence of such a proximity effect, the actual graphic pattern 20 obtained on the actual substrate S is an area wider than the original graphic pattern 10 (indicated by a broken line), as in the example shown in FIG. become.

  In addition, conditions such as the characteristics of the developer used in the development process, the characteristics of the etchant and plasma used in the etching process, the time of the development process and the etching process, and the like are factors that affect the shape of the actual figure pattern 20. Therefore, when actually manufacturing a semiconductor device or the like, after designing a desired original figure pattern 10 on a computer, a lithography process using the original figure pattern 10 is simulated on the computer, and the actual substrate S is formed. The procedure for estimating the shape of the actual graphic pattern 20 that will be formed in the next step is executed. The figure pattern shape estimation apparatus 100 'shown in FIG. 1 is an apparatus having a function of performing such estimation, and does not actually perform a lithography process (exposure, development, etching process) for creating an actual substrate S. In addition, it has a function of estimating the shape of the actual figure pattern 20 that will be formed on the actual substrate S by simulation.

  In the figure pattern shape estimation apparatus 100 ′ shown in FIG. 1, an evaluation point E is set on the original figure pattern 10 by the evaluation point setting unit 110. Specifically, the shape estimation apparatus 100 ′ is provided with graphic data including contour information indicating the boundary between the inside and the outside of the figure as the original figure pattern 10, and the evaluation point setting unit 110 performs such processing. Based on the original graphic pattern 10, a process for setting an evaluation point at a predetermined position on the contour line is performed.

  FIG. 3 is a plan view showing an example in which several evaluation points are set for the original figure pattern 10 shown in FIG. 2A and a process bias (dimensional error) occurring at each evaluation point. First, FIG. 3A is a plan view showing an example in which evaluation points E11, E12, E13 are set on the contour line of the original figure pattern 10 (rectangular figure) shown in FIG. FIG. 3 shows a simple example in which three evaluation points E11, E12, and E13 are set for convenience of explanation, but actually, a larger number of evaluation points are set on each side of the rectangle. The For example, if it is determined that the evaluation points are set continuously at a predetermined pitch along the contour line, a large number of evaluation points can be automatically set. The present invention proposes a new method for setting the evaluation points, and the specific contents thereof will be described in §5 and later.

  Here, let us consider a case where an actual graphic pattern 20 as shown in FIG. 2B is obtained based on the original graphic pattern 10 shown in FIG. FIG. 3B is a plan view showing the contour (solid line) of the actual graphic pattern 20 shown in FIG. 2B in contrast to the contour (broken line) of the original graphic pattern 10 shown in FIG. There is shown a state in which the contour line of the real graphic pattern 20 indicated by a solid line extends outward by a dimension y as compared to the contour line of the original graphic pattern 10 indicated by a broken line. For this reason, the horizontal width a of the original graphic pattern 10 extends to the horizontal width b in the actual graphic pattern 20. Similarly, the vertical width slightly expands.

  In FIG. 3B, the evaluation points E21, E22, E23 on the actual graphic pattern 20 are evaluation points defined as points corresponding to the evaluation points E11, E12, E13 on the original graphic pattern 10. Here, the evaluation point E21 is defined as a point shifted from the evaluation point E11 by a predetermined dimension y11 toward the outer side in the normal direction of the contour line indicated by a broken line. Similarly, the evaluation point E22 is defined as a point shifted from the evaluation point E12 by a predetermined dimension y12 toward the outside in the normal direction of the contour line indicated by a broken line, and the evaluation point E23 is a contour line indicating the evaluation point E13 by a broken line. Is defined as a point shifted by a predetermined dimension y13 toward the outside in the normal direction.

  As in the example shown in FIG. 3, here, in order to quantitatively indicate the shape change of the actual graphic pattern 20 with respect to the original graphic pattern 10, the deviation amount y in the normal direction of the contour line generated for each evaluation point E is set. I will use it. Further, this deviation amount y is referred to as “process bias y” because it is a bias amount caused by the lithography process. The process bias y is a value having a positive / negative sign, and in the embodiment described below, the direction in which the figure exposure part (drawing part) is fattened is defined as a positive value, and the direction in which the figure is thinned is defined as a negative value. In the example shown in the figure, the inside of the figure surrounded by the contour line is the exposure part (drawing part), so if it is shifted in the outer direction of the contour line, it is a positive value, and it shifts in the inner direction of the contour line. Is negative. In the case of the example shown in FIG. 3, since each evaluation point E is shifted in the outward direction, the process bias y11, y12, y13 takes a positive value.

  In FIG. 3, only three evaluation points E11, E12, and E13 are shown for convenience of explanation, but actually, more evaluation points E are defined on the contour line of the original graphic pattern 10. The Therefore, if the process bias y can be estimated for each evaluation point E, the position of each evaluation point E after the lithography process is shifted by shifting each evaluation point E by the process bias y in the normal direction of the contour line. The contour position of the actual graphic pattern 20 can be estimated.

  However, the value of the process bias y at each evaluation point E is different for each evaluation point. For example, in the case of the example shown in FIG. 3B, the values of the process biases y11, y12, and y13 are individual values. This is because the relative positions of the evaluation points E11, E12, and E13 with respect to the original graphic pattern 10 are different, so that the influence of the lithography process is also different, and the amount of deviation that occurs is also different. Therefore, in order to improve the estimation accuracy when the shape of the actual graphic pattern 20 is estimated by simulation based on the original graphic pattern 10, the influence of the lithography process is appropriately predicted for each evaluation point, and an appropriate process bias is determined. It is important to obtain y.

  Therefore, in the figure pattern shape estimation apparatus 100 ′ shown in FIG. 1, first, an evaluation point is set on the original figure pattern 10 by the evaluation point setting unit 110. Specifically, each evaluation point E may be set at a predetermined position on the contour line based on the contour line information indicating the boundary between the inside and the outside of the figure included in the original figure pattern 10. For example, evaluation points can be set continuously at predetermined intervals along the contour line (an evaluation point setting method unique to the present invention will be described in §5 and later).

  Subsequently, the feature amount extraction unit 120 extracts a feature amount indicating features around each evaluation point E for the original graphic pattern 10. The feature amount x for one evaluation point E is a value indicating the features around the evaluation point E. In order to perform the process of extracting the feature quantity x, the feature quantity extraction unit 120 includes an original image creation unit 121, an image pyramid creation unit 122, and a feature quantity calculation unit 123, as shown in FIG.

  The original image creating unit 121 creates an original image composed of a collection of pixels each having a predetermined pixel value based on the given original graphic pattern 10. For example, when the original figure pattern 10 as shown in FIG. 2A is given, the pixel value is 1 for pixels inside the rectangle (the hatched portion in the figure), and the pixel value is 0 for pixels outside the rectangle. Is added, an original image composed of binary images is created.

  The image pyramid creation unit 122 performs an image pyramid creation process including a reduction process for creating a reduced image by reducing the original image, and creates an image pyramid including a plurality of n hierarchical images. Each of the n layer images constituting each layer of the image pyramid is an image obtained by performing predetermined image processing on the original image created by the original image creation unit 121, and has different sizes. Yes. Such a set of hierarchical images is called an “image pyramid” because each layered image is stacked in order from the largest to the smallest to form a hierarchical structure, as if a pyramid is formed. This is because it can be seen.

  The feature amount calculation unit 123 calculates a feature amount based on the pixel values of pixels in the vicinity of the evaluation point E for each of the n layer images constituting the layer of the image pyramid. Specifically, the feature amount x1 is calculated based on the pixel value of the pixel near the evaluation point E in the first hierarchical image, and the pixel value of the pixel near the evaluation point E in the second hierarchical image is calculated. On the basis of the feature amount x2, similarly, the feature amount xn is calculated based on the pixel value of the pixel in the vicinity of the evaluation point E in the nth hierarchical image. n feature amounts x1 to xn are extracted. For example, in the example shown in FIG. 3A, n feature values x1 (E11) to xn (E11) are extracted for the evaluation point E11, and n feature values x1 (E12) for the evaluation point E12. -Xn (E12) are extracted, and n feature values x1 (E13) -xn (E13) are extracted for the evaluation point E13.

  On the other hand, the bias estimation unit 130 is a process that indicates the amount of deviation between the position of the evaluation point E on the original graphic pattern 10 and the position on the actual graphic pattern 20 based on the feature value x extracted by the feature value extraction unit 120. A process for estimating the bias y is performed. In order to perform such estimation processing, the bias estimation unit 130 includes a feature amount input unit 131 and an estimation calculation unit 132. The feature amount input unit 131 is a component that inputs the feature amounts x1 to xn calculated for the evaluation point E by the feature amount calculation unit 123, and the estimation calculation unit 132 performs learning obtained by a learning stage performed in advance. Based on the information L, an estimated value corresponding to the feature amounts x1 to xn is obtained, and the obtained estimated value is output as the estimated value y of the process bias for the evaluation point E.

  More specifically, the estimation calculating unit 132 estimates the process bias for each evaluation point E located on the contour line of the graphic constituting the original graphic pattern 10 as a deviation amount in the normal direction of the contour line. y is output. For example, for the original figure pattern 10 shown in FIG. 3A, as shown in FIG. 3B, the process bias y11 for the evaluation point E11, the process bias y12 for the evaluation point E12, and the process bias y13 for the evaluation point E13. , Respectively, are output from the estimation calculation unit 132 as estimated values. Thus, if the estimated value y of the process bias for each evaluation point E is obtained, a new position of each evaluation point E (a position shifted by the process bias y in the normal direction of the contour line) can be determined. Therefore, as shown in FIG. 3B, the shape of the actual graphic pattern 20 can be estimated.

  The above is the basic configuration and basic operation of the figure pattern shape estimation apparatus 100 ′ according to the prior invention. The specific operation of the feature quantity extraction unit 120 will be described in detail in §2, and the specific operation of the bias estimation unit 130 will be described in detail in §3.

<1.2 Shape Pattern Correction Device>
Next, the configuration and function of the figure pattern shape correcting apparatus 100 according to the invention of the prior application will be described. The figure pattern shape correction apparatus 100 is an apparatus that corrects the shape of the original figure pattern 10 using the figure pattern shape estimation apparatus 100 'described above. As shown in FIG. 1, the figure pattern shape estimation apparatus 100' is used. In addition to the evaluation point setting unit 110, the feature amount extraction unit 120, and the bias estimation unit 130 which are constituent elements of the above, a pattern correction unit 140 is further provided. The pattern correction unit 140 is a component that corrects the original graphic pattern 10 based on the estimated value y of the process bias output from the bias estimation unit 130, and the corrected graphic pattern obtained by the correction by the pattern correction unit 140 15 is the final output of the shape correction apparatus 100 for this graphic pattern.

  The correction by the pattern correction unit 140 is performed by moving each evaluation point E on the original graphic pattern 10 in a direction to cancel the process bias y, and correcting the boundary line of each graphic to the position of each evaluation point E after the movement. It can be carried out. For example, let us consider a case where an actual graphic pattern 20 as shown in FIG. 3B is estimated for the original graphic pattern 10 shown in FIG. In this case, the horizontal width “a” of the rectangle included in the original graphic pattern 10 increases to the horizontal width “b” on the actual graphic pattern 20, and if (b−a) / 2 = y, the positions of the left and right sides of the rectangle If both are moved inward by y, a rectangle having the same horizontal width a as that of the original graphic pattern 10 is obtained. Therefore, basically, if correction is performed to reduce the width a of the original graphic pattern 10 by 2y, and a lithography process is executed based on the corrected graphic pattern, the actual graphic pattern 20 is formed on the actual substrate S. A rectangle having a width a as originally designed can be obtained.

  In the case of the original graphic pattern 10 shown in FIG. 3A, the evaluation point E11 is moved to the left (inside the rectangle) by the process bias y11, and the evaluation point E12 is moved to the left (inside the rectangle) by the process bias y12. Then, the correction may be performed by moving the evaluation point E13 upward (inside the rectangle) by the process bias y13. Of course, since more evaluation points are actually defined, correction is performed to move all the evaluation points to the inside of the rectangle by a dimension corresponding to the process bias, and new evaluation points are connected. If a simple contour line is defined, a corrected graphic pattern 15 including a graphic defined by the contour line is obtained. Since such correction processing itself is a known technique, detailed description thereof is omitted here.

  However, actually, even if a lithography process is executed using the corrected graphic pattern 15 obtained in this way and a real graphic pattern 25 (not shown) is formed on the real substrate S, the actual graphic pattern 25 obtained is It does not exactly match the original figure pattern 10 at the beginning of the design (for example, the lateral width of the rectangle formed on the actual substrate S is not exactly a). This is because the graphic included in the original graphic pattern 10 and the graphic included in the corrected graphic pattern 15 are different in size and shape, so that there is a difference in the influence such as the proximity effect when the lithography process is executed.

  In other words, even if it is found that a process bias y occurs as a result of simulation for a specific evaluation point E, simply moving the position of the evaluation point E in the reverse direction by the process bias y Accurate correction cannot be performed.

  Of course, compared to the actual figure pattern 20 obtained as a result of executing the lithography process using the original figure pattern 10, the actual figure pattern 25 obtained as a result of executing the lithography process using the corrected figure pattern 15 is Since the pattern becomes closer to the original figure pattern 10, the actual lithography process is performed using the corrected figure pattern 15 obtained by the correction by the pattern correction unit 140, rather than executing the actual lithography process using the original figure pattern 10 as it is. The more accurate figure pattern can be obtained on the actual substrate S by executing the above. That is, if correction is performed by the pattern correction unit 140, it is certain that the error is reduced.

  Therefore, in practice, as shown in FIG. 1, the process of giving the corrected figure pattern 15 output from the pattern correction unit 140 to the figure pattern shape correcting apparatus 100 is repeated. That is, the corrected figure pattern 15 is given as a new original figure pattern to the figure pattern shape estimation apparatus 100 ', and this new original figure pattern (corrected figure pattern 15) is described in §1.1. Processing is executed. Specifically, each evaluation point E is set on the corrected graphic pattern 15 by the evaluation point setting unit 110, the feature amount for each evaluation point E is extracted by the feature amount extraction unit 120, and the bias estimation unit 130 performs the setting. An estimated process bias value y for each evaluation point E is calculated. Then, the correction process is performed again in the pattern correction unit 140 using the calculated process bias estimated value y.

  The graphic pattern shape correction apparatus 100 shown in FIG. 1 has a function of repeatedly executing correction on a graphic pattern as described above. In other words, a first corrected graphic pattern 15 is obtained based on the original graphic pattern 10, a second corrected graphic pattern is obtained based on the first corrected graphic pattern 15, and based on the second corrected graphic pattern. Thus, the third corrected graphic pattern is obtained, and the correction process of... Is repeated. Each time correction processing is performed, the shape error between the original graphic pattern and the graphic pattern obtained by the simulation is reduced.

  Therefore, for example, when the shape error between the original figure pattern and the figure pattern obtained by simulation converges within a predetermined tolerance, the correction is completed, and the actual lithography process is executed using the last obtained figure pattern Then, a real graphic pattern close to the original graphic pattern 10 at the initial design can be formed on the real substrate S. Thus, if the figure pattern shape correcting apparatus 100 according to the invention of the prior application is used, the shape of the original figure pattern can be accurately corrected.

  The evaluation point setting unit 110, the feature amount extraction unit 120, the bias estimation unit 130, and the pattern correction unit 140 shown in FIG. 1 are all configured by incorporating a predetermined program into a computer. Therefore, the figure pattern shape estimation apparatus 100 'and the figure pattern shape correction apparatus 100 according to the prior invention are actually realized by incorporating a dedicated program into a general-purpose computer.

  FIG. 4 is a flowchart showing a product design / manufacturing process using the figure pattern shape correcting apparatus 100 shown in FIG. First, in step S1, a product design stage is performed. This product design stage is a process of creating a graphic pattern for configuring a semiconductor device or the like, and the original graphic pattern 10 shown in FIG. 1 is created at this product design stage. An apparatus for designing a product such as a semiconductor device and creating a graphic pattern is already a known apparatus, and therefore detailed description thereof is omitted here.

  The next evaluation point setting stage of step S2 is a stage executed in the evaluation point setting unit 110 shown in FIG. For example, when the original figure pattern 10 as shown in FIG. 2 (a) is given, evaluation points E11, E12, E13 and the like as shown in FIG. 3 (a) are set. The subsequent feature quantity extraction stage of step S3 is a stage executed in the feature quantity extraction unit 120 shown in FIG. 1. As described above, n kinds of feature quantities x1 to xn are extracted for one evaluation point E. (The detailed extraction procedure is described in §2). Then, the process bias estimation stage of step S4 is a stage executed in the bias estimation unit 130 shown in FIG. 1, and as described above, the process is performed using n feature quantities x1 to xn for one evaluation point E. The estimated bias value y is obtained (the detailed calculation procedure is described in §3).

  Then, the pattern shape correction stage in step S5 is a stage executed in the pattern correction unit 140 shown in FIG. 1, and as described above, using the process bias estimated value y obtained for each evaluation point E, the original figure A corrected graphic pattern 15 is obtained by correcting the pattern 10. Since such correction is not sufficient once, the process of returning to step S2 is repeated until it is determined that “correction is completed” in step S6. That is, by treating the corrected graphic pattern 15 obtained in step S5 as a new original graphic pattern 10, the processes in steps S2 to S5 are repeatedly executed.

  If it is determined in step S6 that “correction is complete” as a result of such repeated processing, the process proceeds to step S7, and a lithography process is executed. The determination of “correction completion” is, for example, “the error between the position on the original graphic pattern and the position on the graphic pattern obtained by the simulation is equal to or less than a predetermined reference value for a certain percentage of evaluation points E”. This can be done by satisfying certain specific conditions. In the lithography process in step S7, actual processes such as exposure, development, and etching are performed based on the finally obtained corrected graphic pattern, and the actual substrate S is manufactured.

  In the flowchart shown in FIG. 4, steps S1 to S6 are processes executed on a computer (computer), and step S7 is a process executed on an actual substrate S.

<1.3 Basic Concept of Feature Extraction in Prior Invention>
So far, the basic configuration and basic operation of the figure pattern shape estimation apparatus 100 ′ and the figure pattern shape correction apparatus 100 shown in FIG. 1 have been described. In each of these devices, the most characteristic component as the prior invention is the feature quantity extraction unit 120. The prior application invention has the effect of extracting an accurate feature amount from the original graphic pattern 10 and performing an accurate simulation to accurately estimate the shape of the actual graphic pattern 20 formed on the actual substrate S. However, the component that plays the most important role in obtaining such an effect is the feature quantity extraction unit 120. In other words, an important feature of the prior invention is that feature values are extracted from the original graphic pattern 10 by a very unique method. Therefore, here, the basic concept of feature quantity extraction in the prior application invention will be described.

  FIG. 5 is a plan view showing the concept of grasping the surrounding features of each of the evaluation points E11, E12, E13 defined on the outline of the graphic pattern 10 made of a rectangle. FIG. 5A shows a state in which the features inside the reference circle C1 and the inside of the reference circle C2 are extracted for the evaluation point E11 set at the center of the right side of the rectangle. The reference circles C1 and C2 are both circles centered on the evaluation point E11, but the reference circle C2 is larger than the reference circle C1. Similarly, FIG. 5 (b) shows two reference circles C1, 2 for the evaluation point E12 set below the right side of the rectangle, and FIG. 5 (c) shows the evaluation point E13 set for the center of the lower side of the rectangle. The state where the internal features of C2 are extracted is shown.

  Here, when the internal features of the reference circle C1 are compared for each evaluation point, for the evaluation points E11 and E12, the left half is inside the figure (hatching area) and the right half is outside the figure (blank area). There is no difference in the internal features of the reference circle C1. On the other hand, the internal features of the reference circle C1 for the evaluation point E13 are such that the upper half is inside the figure (hatched area) and the lower half is outside the figure (blank area), and the inside of the reference circle C1 of the evaluation points E11 and E12 However, there is no difference in the occupation ratio of the hatched area. On the other hand, comparing the internal features of the reference circle C2 with respect to the respective evaluation points E11, E12, E13, it can be seen that the distributions of the hatched regions are different and have different features.

  As described above, for each evaluation point E11, E12, E13 on the graphic pattern 10, even if the features of the neighborhood are grasped, the feature of the narrow neighborhood region such as the reference circle C1 is extracted or the reference circle C2 Thus, the extracted features differ depending on whether or not features in a slightly wide neighboring region are extracted. Therefore, when a feature of a neighboring region is quantitatively extracted as some feature amount x with respect to a certain evaluation point E, the feature amount can be extracted by various methods by changing the range of the neighboring region stepwise. You can see that

  Further, as described above, when the lithography process is executed based on the original graphic pattern 10, the actual graphic pattern 20 obtained on the substrate has a dimensional error (process bias) with respect to the original graphic pattern 10 due to the proximity effect in the exposure process. ) Will occur. In particular, the proximity effect in electron beam exposure includes various effects such as an effect caused by forward scattering having a narrow influence range and an effect caused by back scattering having a wide influence range. For example, forward scattering is explained as a phenomenon in which, when an electron beam is irradiated onto a molding layer composed of a resist layer or the like, electrons having a small mass spread while being scattered by molecules in the resist, It is described as a phenomenon in which electrons scattered and bounced near the surface of a metal substrate or the like under the resist layer are diffused in the resist layer. In addition, a process bias is also generated by the etching process, and the magnitude of the process bias varies depending on a loading phenomenon during etching. Similar to the proximity effect in the exposure process described above, this loading phenomenon is also caused by combining various components such as a component having a narrow influence range and a component having a wide influence range.

  After all, the value of the process bias y for a certain evaluation point E becomes a value determined by fusing phenomena having various scale feelings. Therefore, extracting various feature values from feature values related to a narrow range to feature values related to a wide range is different from the various phenomena in each process that affect the process bias that have different influence ranges. This is important for accurate simulation. Accordingly, in the invention of the prior application, for one evaluation point E, feature quantities for various regions around it are extracted from the vicinity to the distance. As described above, in order to extract a plurality of feature amounts for one evaluation point E, the invention of the prior application employs a method of creating an “image pyramid” composed of a plurality of hierarchical images each having a different size. This image pyramid includes information obtained by multiplexing various phenomena having different influence ranges.

  FIG. 6 is a diagram showing an outline of processing executed in the feature amount extraction unit 120 and the bias estimation unit 130 shown in FIG. An original image Q1 shown in the upper part of the figure is an image created by the original image creating unit 121 shown in FIG. 1 and is an image corresponding to the given original figure pattern 10. As described above, the original graphic pattern 10 is data created by a semiconductor device design apparatus or the like, and is data indicating a graphic as shown in FIG. It is given as vector data (data indicating the coordinate value of each vertex and the connection relationship between each vertex).

  The original image creation unit 121 executes a process of creating an original image Q1 composed of a collection of pixels each having a predetermined pixel value based on the data of the given original graphic pattern 10. For example, if a pixel having a pixel value of 1 is arranged inside a graphic constituting the original graphic pattern 10 and a pixel having a pixel value of 0 is arranged outside, the original image Q1 composed of an aggregate of a large number of pixels U Can be created. An original image Q1 shown in FIG. 6 is an image composed of such an assembly of pixels U, and has a rectangular figure included in the original figure pattern 10 as image information, as indicated by a broken line. The evaluation point E is set on the contour line of the figure by the evaluation point setting unit 110. In FIG. 6, only one evaluation point E is drawn for convenience, but actually, a large number of evaluation points are set along the contour line of the figure.

  The image pyramid creation unit 122 shown in FIG. 1 creates an image pyramid PP based on the original image Q1. The image pyramid PP is composed of a plurality of hierarchical images having different sizes. In the figure, an image pyramid PP composed of a plurality of n (n ≧ 2) hierarchical images P1 to Pn is shown. The specific procedure for creating the hierarchical images P1 to Pn from the original image Q1 will be described in Section 2. Basically, the hierarchical images P1 to Pn are created by a reduction process for reducing the number of pixels. For example, in the illustrated example, the hierarchical image P1 is an image having the same size as the original image Q1 (an image having the same number of vertical and horizontal pixels), whereas the hierarchical image P2 is reduced to a small size image. The hierarchical image P3 is an image having a smaller size obtained by further reducing the hierarchical image P2.

  Thus, in the prior application invention, hierarchical images P1 to Pn whose image size is gradually reduced are created based on the original image Q1. In this way, the state in which a plurality of hierarchical images having different sizes are arranged one above the other is in the form of a pyramid as illustrated. Therefore, in the prior application, an aggregate of these plurality of hierarchical images P1 to Pn is referred to as an image pyramid PP. I'm calling. Since each of the hierarchical images P1 to Pn is created based on the original image Q1, the hierarchical images P1 to Pn have information of the original graphic pattern 10, and the position of the evaluation point E can be defined for each. In the figure, a rectangular figure is drawn on each of the hierarchical images P1 to Pn, and an evaluation point E is arranged on the contour line.

  The feature amount calculation unit 123 illustrated in FIG. 1 performs a process of calculating a feature amount for each hierarchical image constituting the image pyramid based on the pixel values of pixels near the evaluation point. FIG. 6 shows a state in which feature amounts x1 to xn of the evaluation points E are extracted from n layer images P1 to Pn constituting the image pyramid PP, respectively. The illustrated feature amounts x1 to xn are values indicating features around the same evaluation point E, but the feature amount x1 is a pixel value of a neighboring pixel of the evaluation point E on the first hierarchical image P1. The feature amount x2 is a value calculated based on the pixel values of the neighboring pixels of the evaluation point E on the second hierarchical image P2, and the feature amount x3 is the third value. This is a value calculated based on the pixel values of the neighboring pixels of the evaluation point E on the hierarchical image P3. A specific calculation procedure of each feature amount x1 to xn will be described in §2.

  Although only one evaluation point E is drawn in FIG. 6 for convenience, in practice, n feature amounts x1 to xn are calculated for each of a large number of evaluation points. Each of the individual feature amounts x1 to xn is a predetermined scalar value, but n feature amounts x1 to xn are obtained for each evaluation point E, respectively. Therefore, if the n feature quantities x1 to xn are grasped as n-dimensional vectors, the feature quantity extraction unit 120 performs a process of extracting feature quantities composed of n-dimensional vectors for one evaluation point E. .

  The feature amount (n-dimensional vector) for each evaluation point extracted in this way is input by the feature amount input unit 131 in the bias estimation unit 130 and is given to the estimation calculation unit 132. In the case of the embodiment shown here, the estimation calculation unit 132 is configured by a neural network, and based on the learning information L obtained in advance by the learning stage, the estimation calculation unit 132 applies the feature amounts x1 to xn given as n-dimensional vectors. Accordingly, an operation for calculating an estimated value y (scalar value) of the process bias for the evaluation point E is performed. A specific calculation procedure will be described in §3.

  As described above, according to the invention of the prior application, even if a physical / experimental simulation model is not constructed for an actual lithography process, an accurate feature amount is extracted for every original figure pattern 10. be able to. In addition, since it is not necessary to construct a physical / experimental simulation model in the first place, it is not necessary to consider various set values of material properties and process conditions in the learning stage of the neural network described later in §3.2.

  As described above, the example in which the figure pattern shape estimation apparatus 100 ′ and the shape correction apparatus 100 according to the invention of the prior application are used in a lithography process for manufacturing a semiconductor device has been described. The present invention is not limited to use in the manufacturing process, and can be used in various product manufacturing processes including lithography processes. For example, the invention of the prior application or the present invention can be used in the manufacturing process of various products including lithography processes such as NIL (Nano Imprint Lithography) and EUV (Extreme UltraViolet Lithography). In particular, in the NIL, the original graphic pattern may be corrected so that the actual graphic pattern on the master template produced from the original graphic pattern through exposure lithography matches the original graphic pattern. Or you may correct | amend an original figure pattern so that the real figure pattern on the replica template produced through the imprint from the master template may correspond with the original figure pattern. In addition, the invention of the prior application and the present invention are all product fields including lithography processes such as MEMS (Micro Electro Mechanical Systems), LSPM (Large-size Photomask), lead frames, metal masks, metal mesh sensors, color filters, etc. It is applicable to.

<<< §2. Details of feature extraction unit >>
Next, a detailed processing operation of the feature amount extraction unit 120 will be described. As shown in FIG. 1, the feature amount extraction unit 120 includes an original image creation unit 121, an image pyramid creation unit 122, and a feature amount calculation unit 123, and performs the feature amount extraction process in step S3 in the flowchart of FIG. Has the function to execute. This feature amount extraction processing is actually executed by each procedure shown in FIG. Here, steps S31 and S32 are procedures executed by the original image creation unit 121, steps S33 to S36 are procedures executed by the image pyramid creation unit 122, and step S37 is a feature amount calculation unit 123. The procedure executed by Hereinafter, a procedure executed by each unit will be described in detail with a specific example.

<2.1 Processing Procedure by Original Image Creation Unit 121>
The original image creation unit 121 performs a function of creating an original image composed of a collection of pixels each having a predetermined pixel value based on the given original graphic pattern 10, and performs steps S31 and S32 in the flowchart of FIG. Run. First, in step S31, the process of inputting the original graphic pattern 10 is performed, and in the subsequent step S32, the original image creation process is performed.

  In §1, for convenience of explanation, as an example of the original figure pattern 10 input in step S31, a simple pattern including only one rectangular figure as shown in FIG. Here, in order to explain in more detail, let us consider a case where an original graphic pattern 10 including five graphics F1 to F5 (rectangles) as shown in FIG. 8 is given. As described above, the original figure pattern 10 given to the figure pattern shape correction apparatus 100 is usually vector data indicating the outline of the figure. Therefore, in FIG. 8, hatching is shown inside each of the figures F1 to F5. However, in actuality, the original figure pattern 10 includes the coordinate values of the vertices of the five rectangles F1 to F5 and the vertices. Is given as vector data indicating the connection relationship.

  The original image creation process of step S32 is a process of creating data (raster data) of the original image Q1 composed of a collection of pixels based on the original graphic pattern 10 given as such vector data. Specifically, the original image creation unit 121 defines a mesh composed of a two-dimensional array of pixels U, overlays the original graphic pattern 10 on this mesh, and configures the position of each pixel U and the original graphic pattern 10. The pixel value of each pixel U is determined based on the relationship with the positions of the contour lines of the graphics F1 to F5 to be performed.

  FIG. 9 is a plan view showing a state in which processing for superimposing the original graphic pattern 10 on the mesh composed of the two-dimensional array of pixels U is performed in the original image creation unit 121. In this example, a mesh is defined in which pixels U having pixel dimensions u both vertically and horizontally are two-dimensionally arranged, and a large number of pixels U are arranged at a pitch u both vertically and horizontally. The pixel dimension u is set to an appropriate value that can represent the shapes of the figures F1 to F5 with sufficient resolution. The smaller the pixel size u is set, the higher the resolution of shape expression, but the later processing load becomes heavier. In general, since the original figure pattern 10 used for manufacturing a semiconductor device is a very fine pattern, the pixel dimension u is preferably set to a value of about u = 5 to 20 nm, for example.

  Thus, when the two-dimensional array of the pixels U is defined, pixel values are defined for the individual pixels U based on the relationship with the positions of the contour lines of the graphics F1 to F5. There are several methods for defining pixel values.

  The most basic definition method recognizes the internal area and external area of each graphic F1 to F5 based on the original graphic pattern 10, and uses the occupation rate of the internal area in each pixel U as the pixel value of the pixel. Is the method. In FIG. 8, hatched areas are internal areas of the figures F1 to F5, and white areas are external areas. Therefore, when this method is adopted, the pixel value of each pixel is defined as the occupation ratio (0 to 1) of the internal area (hatched area) in the pixel in the overlapped state as shown in FIG. An image in which pixel values are defined by such a method is generally called an “area density map”.

  FIG. 10 is a diagram showing an area density map M1 created based on the “original graphic pattern 10 + two-dimensional array of pixels” shown in FIG. Here, each cell is each pixel defined in FIG. 9, and the numbers in the cell are pixel values defined for each pixel. A blank cell is a pixel having a pixel value of 0 (illustration of the pixel value of 0 is omitted). In this area density map M1, for example, a pixel having a pixel value of 1.0 is a pixel whose occupancy ratio of the hatching area in FIG. 9 is 100%, and a pixel having a pixel value of 0.5 is the hatching area in FIG. This is a pixel with an occupation ratio of 50%. This area density map M1 is basically a binary image in which the inside of the figure is represented by a pixel value of 1 and the outside of the figure is represented by a pixel value of 0. However, for the pixel where the outline of the figure is located, Since the value indicating the ratio is given as the pixel value, the whole image is a monochrome gradation image.

  As another definition method of the pixel value, a method of recognizing the contour lines of the graphics F1 to F5 based on the original graphic pattern 10 and setting the length of the contour line existing in each pixel U as the pixel value of the pixel. Can also be taken. When this method is adopted, the pixel value of each pixel is defined as the total sum of the lengths of the contour lines existing in the pixel in the superimposed state as shown in FIG. An image in which pixel values are defined by such a method is generally called an “edge length density map”. As a unit of the length of the contour line, for example, a unit in which the pixel dimension u is 1 may be used.

  FIG. 11 is a diagram showing an edge length density map M2 created based on the “original graphic pattern 10 + two-dimensional array of pixels” shown in FIG. Again, each cell is each pixel defined in FIG. 9, and the numbers in the cell are defined as the sum of the lengths of the contour lines existing in each pixel (the length when the pixel dimension u is 1). Pixel value. A blank cell is a pixel having a pixel value of 0 (illustration of the pixel value of 0 is omitted). In the edge length density map M2, for example, a pixel having a pixel value of 1.0 is a pixel having a length u of the contour line existing in the pixel in FIG. Since the edge length density map M2 is basically a monochrome gradation image showing the density distribution of the contour line, the image is considerably different from the area density map M1 described above. However, it is a very useful image in extracting the feature amount for the evaluation point E defined on the contour line.

  As described above, the method for defining the pixel value of each pixel based on the original graphic pattern 10 shown in FIG. 8 has been described. However, the original graphic pattern 10 used in the lithography process shows the boundary between the inside and the outside of the graphic. In addition to the geometric information of the contour line, information on a dose amount for each figure may be further added. FIG. 12 is a plan view showing the original graphic pattern 10 including information on such a dose amount. The original figure pattern 10 with a dose amount shown in FIG. 12 includes information on the outlines of the figures F1 to F5, similarly to the original figure pattern 10 shown in FIG. For each of F5, information defining the dose amount is included.

  Specifically, in the illustrated example, a dose amount of 100% is defined for the graphics F1 to F3, a dose amount of 50% is defined for the graphics F4, and a dose amount of 10% is defined for the graphics F5. . These dose amounts indicate the intensity of light or electron beam to be irradiated (including the case where the total energy amount is controlled by the number of exposures) in the exposure process of the lithography process. In the case of the illustrated example, when exposing the internal area of the figures F1 to F3, light or an electron beam is irradiated with an intensity of 100%, but when exposing the internal area of the figure F4, 50% of the figure F5 When the internal region is exposed, light or an electron beam is irradiated with an intensity of 10%. As described above, when the dose is controlled for each figure during the exposure process, the dimensions of the actual figure pattern 20 formed on the actual substrate S can be further finely adjusted.

  In the case of controlling the dose amount in the exposure process of the lithography process, it is necessary to consider the dose amount in the simulation. In such a case, when determining the pixel value of the original image, it is necessary to adopt a method that takes the dose amount into consideration. That is, when an original graphic pattern 10 including information on a contour line indicating the boundary between the inside and the outside of the graphic and information on a dose amount for each graphic in the lithography process is given, Based on this, the internal area and external area of each figure are recognized, the dose amount for each figure is recognized, and for each figure existing in each pixel, the occupancy rate of the internal area and the dose amount of the figure are determined. What is necessary is just to take the method which calculates | requires "a product" and makes the sum total of the said product the pixel value of the said pixel.

  When this method is adopted, the pixel value of each pixel in the state of being overlapped as shown in FIG. 9 is determined based on the occupation ratio (0 to 1) of the internal area (hatched area) of the specific figure in the pixel and the specific value. It is defined as the sum of products of doses related to figures. An image in which pixel values are defined by such a method is generally called a “dose density map”. This dose density map also becomes a monochrome gradation image as a whole.

  FIG. 13 is a diagram showing a dose density map M3 created based on the original figure pattern 10 with dose shown in FIG. Here, each cell is each pixel defined in FIG. 9, and the numbers in the cell are pixel values defined for each pixel. A blank cell is a pixel having a pixel value of 0 (illustration of the pixel value of 0 is omitted). When this dose density map M3 is compared with the area density map M1 shown in FIG. 10, there is no change in the pixel value for the pixels where the figures F1 to F3 to which the dose amount 100% is given are arranged, but the dose amount 50%. It can be seen that the pixel value of the pixel in which the figure F4 to which the figure is given and the figure F5 to which the dose amount is 10% is arranged is reduced by an amount corresponding to the dose quantity. This shows a phenomenon in which light or an electron beam with reduced intensity is irradiated to the inside of the figures F4 and F5 in the actual exposure process.

  As described above, an example in which three images (an aggregate of pixels U having a predetermined pixel value), that is, the area density map M1, the edge length density map M2, and the dose density map M3 are created based on the original figure pattern 10 has been shown. . In the original image creation process in step S32 in the flowchart of FIG. 7, any of these three images may be created and used as the original image. FIG. 7 shows an example in which the area density map M1 is the original image Q1. Of course, it is also possible to create the original image Q1 by a method other than the three methods described above.

  The original image Q1 created in step S32 is used as the first preparation image Q1 in the filtering process in step S33. As will be described later, the filtering process in step S33 is a process of creating a kth hierarchical image Pk by applying an image processing filter to the kth preparation image Qk. Therefore, it can be said that the procedure of step S32 is a process of setting the parameter k (k = 1, 2, 3,...) To the initial value k = 1 and creating the first preparation image Q1. . The first preparation image Q1 is an original image that is first created based on the original graphic pattern 10, and is a reference image that is first used in an image pyramid creation process described later.

<2.2 Processing Procedure by Image Pyramid Creation Unit 122>
Subsequently, a procedure of image pyramid creation processing by the image pyramid creation unit 122 will be described. The image pyramid creation unit 122 has a function of performing a reduction process for reducing the number of pixels based on the original image Q1 created in step S32 of FIG. 7 (for example, the area density map M1 shown in FIG. 10). An image pyramid creation process is performed to create an image pyramid composed of a plurality of hierarchical images having different sizes. In the case of the embodiment described here, this image pyramid creation process is executed by the procedure shown in steps S33 to S36 in the flowchart of FIG.

  Here, in step S31, an original graphic pattern 10 as shown in FIG. 8 is input, and in step S32, a specific image is taken as an example where the area density map M1 shown in FIG. 10 is created as the original image Q1. The procedure of the pyramid creation process will be described.

  First, in step S33, a filter process for creating a kth hierarchical image Pk by applying an image processing filter to the kth preparation image Qk is executed. Specifically, this filter processing is executed, for example, as a convolution operation using a Gaussian filter as an image processing filter. FIG. 14 is a plan view showing a procedure for creating the k-th hierarchical image Pk by performing the filtering process using the Gaussian filter GF33 on the preparation image Qk. The kth preparation image Qk shown in FIG. 14 is actually the same as the area density map M1 shown in FIG.

  That is, the area density map M1 shown in FIG. 10 is shown as an 8 × 8 pixel array for convenience, and the description of the pixel value 0 is omitted, whereas the preparation image Qk shown in FIG. Although shown as a pixel array of 10 and a pixel value of 0 is also shown, they are substantially the same image. In short, in FIG. 14, for the convenience of executing the filtering process, pixels having a pixel value of 0 are arranged around the area density map M1 including the 8 × 8 pixel array shown in FIG. It is only doing. At this stage, the parameter k has an initial value of 1, and the preparation image Qk shown in FIG. 14 is the first preparation image Q1. As described above, the first preparation image Q1 is nothing but the original image created by the original image creation process in step S32.

  In the filter processing shown in FIG. 14, a convolution operation using the Gaussian filter GF33 is executed. The Gaussian filter GF33 has a 3 × 3 pixel array as shown in the figure. The Gaussian filter GF33 is superposed on a predetermined position of the k-th preparation image Qk to perform a product-sum operation process, thereby performing the k-th operation. Layer image Pk (filtered image). FIG. 15 is a plan view showing the k-th hierarchical image Pk obtained by the filtering process shown in FIG. This k-th hierarchical image Pk has a 10 × 10 pixel array as in the k-th preparation image Qk, and the pixel value of each pixel is obtained by a product-sum operation using the Gaussian filter GF33. Value.

  For example, in the k-th hierarchical image Pk shown in FIG. 15, when attention is paid to a pixel surrounded by a thick frame (pixel in the fourth row and third column), a pixel value of 0.375 is given to the target pixel. . The pixel value is obtained by superimposing the illustrated Gaussian filter GF33 on the 3 × 3 pixel array (9 pixels centered on the pixel in the fourth row and third column) surrounded by a thick frame in FIG. , The product of the pixel values of pixels superposed at the same position is obtained, and the product is obtained as the sum of nine products. Specifically, the pixel value 0.375 of the target pixel is “(1/16 × 0) + (2/16 × 0.25) + (1/16 × 0.5) + (2/16 × 0). ) + (4/16 × 0.5) + (2/16 × 1.0) + (1/16 × 0) + (2/16 × 0.25) + (1/16 × 0.5) ” Is obtained as a product-sum operation value. Such filter processing by product-sum operation is generally known as convolution operation processing for an image, and thus detailed description thereof is omitted here.

  In the filter processing shown in FIG. 14, a convolution operation is performed using a Gaussian filter GF33 having a 3 × 3 pixel array as shown in FIG. 16A as an image processing filter. A convolution operation using a Laplacian filter LF33 having a 3 × 3 pixel array as shown in b) may be performed. In general, it is known that filter processing using a Gaussian filter gives an effect of blurring the contour of an image, and filter processing using a Laplacian filter gives an effect of enhancing the contour of an image. Regardless of which filter processing is employed, the k-th hierarchical image Pk having slightly different characteristics from the k-th prepared image Qk can be obtained, and thus includes a plurality of hierarchical images each having different characteristics. It is effective in creating an image pyramid.

  Of course, the image processing filter used for the filter processing in step S33 is not limited to the Gaussian filter GF33 shown in FIG. 16 (a) or the Laplacian filter LF33 shown in FIG. 16 (b). Processing filters can be used. Further, the size of the image processing filter to be used is not limited to the 3 × 3 pixel array, and an image processing filter of an arbitrary size can be used. For example, a Gaussian filter GF55 having a 5 × 5 pixel array as shown in FIG. 17A or a Laplacian filter LF55 having a 5 × 5 pixel array as shown in FIG. 17B may be used. .

  Thus, when the filtering process in step S33 in the procedure of FIG. 7 is completed, it is determined in step S34 whether or not the parameter k has reached a predetermined set value n. If k <n, the reduction in step S35 is performed. Processing is executed. This reduction processing is processing for creating an image having a smaller number of pixels than the target image based on the predetermined target image. In the case of the example shown here, the (k + 1) th preparation image Q (k + 1) is created by executing the reduction process on the kth hierarchical image Pk created by the filtering process of step S33. Processing is executed. Therefore, the preparation image Q (k + 1) is an image having a smaller size than the hierarchical image Pk (an image having a small number of vertical and horizontal pixels in the pixel array).

  Such reduction processing for an image is also referred to as “pooling processing”, and for example, “average pooling processing” can be adopted as the reduction processing performed in step S35. FIG. 18 is a plan view showing a procedure for creating an (k + 1) th preparation image Q (k + 1) as a reduced image by performing an average pooling process on the kth hierarchical image Pk. . Specifically, by applying an average pooling process (reduction process) to the hierarchical image Pk having the 4 × 4 pixel array shown in FIG. 18A, a 2 × 2 pixel as shown in FIG. A preparation image Q (k + 1) having a pixel array is created as a reduced image.

  The average pooling process shown in FIG. 18 is a process of converting (reducing) four pixels having a 2 × 2 pixel array into one pixel, and an average value of pixel values of the original four pixels is expressed as follows: By using the pixel value of one pixel after conversion, a reduced image is created. For example, four pixels (pixels within a thick frame) having a 2 × 2 pixel arrangement arranged on the upper left of the hierarchical image Pk shown in FIG. 18A are prepared images Q (in FIG. 18B). On (k + 1), it is converted (reduced) to one pixel indicated by a thick frame. The pixel value 0.5 of the thick frame pixel after this conversion (reduction) is an average value of the pixel values of the original four pixels.

  On the other hand, FIG. 19 is a plan view showing a procedure for creating a (k + 1) th preparation image Q (k + 1) as a reduced image by performing a max pooling process on the kth hierarchical image Pk. It is. Specifically, by performing a max pooling process (reduction process) on the hierarchical image Pk having the 4 × 4 pixel array shown in FIG. 19A, a 2 × 2 pixel as shown in FIG. 19B is obtained. A preparation image Q (k + 1) having a pixel array is created as a reduced image.

  The maximum pooling process shown in FIG. 19 is a process for converting (reducing) four pixels having a 2 × 2 pixel array into one pixel, similar to the average pooling process shown in FIG. By using the maximum value of the pixel values of the four pixels as the pixel value of one pixel after conversion, a reduced image is created. For example, four pixels (pixels within a thick frame) having a 2 × 2 pixel arrangement arranged at the upper left of the hierarchical image Pk shown in FIG. 19A are prepared images Q (in FIG. 19B). On (k + 1), it is converted (reduced) to one pixel indicated by a thick frame. The pixel value 1.0 of the thick frame pixel after this conversion (reduction) is the maximum value of the pixel values of the original four pixels.

  Each of the pooling processes shown in FIGS. 18 and 19 is a reduction process for converting four pixels having a 2 × 2 pixel array into a single pixel, but of course, having a 3 × 3 pixel array. It is also possible to perform a reduction process for converting nine pixels into a single pixel, and it is also possible to perform a reduction process for converting six pixels having a 3 × 2 pixel array into a single pixel. It is.

  After all, the image pyramid creation unit 122 replaces the plurality of m adjacent pixels with a single pixel having an average value of the pixel values of the plurality of m adjacent pixels as a pixel value as the reduction processing in step S35. It is also possible to create a reduced image by executing the pooling process, and to replace a plurality of m adjacent pixels with a single pixel having the maximum pixel value of the plurality of m adjacent pixels as a pixel value. -It is also possible to create a reduced image by executing a pooling process. Of course, other reduction processing can be performed as the reduction processing in step S35. In short, a process that can create a small-sized preparation image Q (k + 1) by performing conversion that reduces the number of pixels on the hierarchical image Pk, in other words, “the number of pixels has decreased. As long as it is a process for creating a “reduced image”, any reduction process may be executed in step S35.

  Thus, when the reduction process of step S35 is completed, the parameter k is increased by 1 in step S36, and the filter process of step S33 is executed again. Eventually, as described above, k = 1 and the first preparation image Q1 (original image) is filtered in step S33 to create the first hierarchical image P1, and then step S35. Thus, the second preparation image Q2 is created by performing the reduction process on the hierarchical image P1, and is updated to k = 2 in step S36. By performing the process, the second hierarchical image P2 is created.

  Such an iterative procedure is repeatedly executed until it is determined in step S34 that k = n. Here, as the value of n, an appropriate value may be set in advance as the number of layers of the image pyramid (that is, the total number of layer images constituting the image pyramid). As the value of n is set larger, the number n of feature quantities extracted for one evaluation point E increases, so that more accurate simulation becomes possible, but the calculation burden increases. Further, as the reduction process in step S35 is repeated, the size of the image becomes smaller. Therefore, if the value of n is set too large, the reduction process in step S35 cannot be performed. Therefore, in practice, the value of n may be set appropriately in consideration of the size of the original image Q1 and the calculation burden.

  Thus, when it is determined in step S34 that k = n, the processing by the image pyramid creation unit 122 is completed. At this time, as shown in FIG. 6, an image pyramid PP composed of a plurality of n hierarchical images P1 to Pn is created. Therefore, the process proceeds from step S34 to step S37, and a feature amount calculation process is executed.

  FIG. 20 is a plan view showing a procedure (steps S33 to S36 in FIG. 7) for creating an image pyramid PP including n hierarchical images P1 to Pn in the image pyramid creation unit 122. The first preparation image Q1 shown in the upper left of the figure is an original image created with k = 1 in the original image creation processing in step S32. The area density map M1 shown in FIG. The pixel value is defined as follows. As described above, in step S33, the filter process is performed on the first preparation image Q1. Specifically, for example, a first hierarchical image P1 as shown in the upper right of FIG. 20 is created by a convolution operation using a Gaussian filter GF33 having a 3 × 3 pixel array. The size of the first hierarchical image P1 is the same as the size of the first preparation image Q1.

  Subsequently, in the reduction process in step S35, a reduction process (for example, average pooling process) is performed on the first hierarchical image P1, and a second preparation image Q2 shown in the middle left of FIG. 20 is created. The size of the second preparation image Q2 is smaller than the size of the first hierarchical image P1. Subsequently, in step S36, the value of the parameter k is updated to 2, and the filtering process of step S33 is executed again. That is, the second hierarchical image P2 as shown in the middle right of FIG. 20 is created by the convolution operation using the Gaussian filter GF33 having a 3 × 3 pixel array. The size of the second hierarchical image P2 is the same as the size of the second preparation image Q2.

  Then, the reduction process in step S35 is executed again. That is, reduction processing (for example, average pooling processing) is performed on the second hierarchical image P2, and a third preparation image Q3 shown on the lower left of FIG. 20 is created. The size of the third preparation image Q3 is smaller than the size of the second hierarchical image P2. Subsequently, in step S36, the value of the parameter k is updated to 3, and the filtering process of step S33 is executed again. That is, a third layer image P3 as shown in the lower right of FIG. 20 is created by a convolution operation using a Gaussian filter GF33 having a 3 × 3 pixel array. The size of the third layer image P3 is the same as the size of the third preparation image Q3.

  Such processing is repeatedly executed until the parameter k = n, and finally, the n-th preparation image Qn and the n-th layer image are obtained. In this way, the image pyramid PP is constituted by n hierarchical images having different sizes from the first hierarchical image P1 to the nth hierarchical image Pn.

  After all, in the case of the embodiment shown in the procedure of FIG. 7, the image pyramid creation unit 122 has a function of performing a filter process using a predetermined image processing filter on the original image Q1 or the reduced image Q (k + 1). By alternately executing the filter process and the reduction process, an image pyramid PP composed of a plurality of hierarchical images P1 to Pn is created.

  More specifically, the image pyramid creation unit 122 uses the original image created by the original image creation unit 121 as the first preparation image Q1, and performs a filtering process on the kth preparation image Qk (where k is a natural number). The obtained image is set as the k-th hierarchical image Pk, the image obtained by the reduction process for the k-th hierarchical image Pk is set as the (k + 1) -th prepared image Q (k + 1), and the filter is performed until the n-th hierarchical image Pn is obtained. By alternately executing the processing and the reduction processing, an image pyramid PP composed of a plurality of n hierarchical images including the first hierarchical image P1 to the nth hierarchical image Pn is created.

  Since the image pyramid PP in the prior application invention only needs to be composed of a plurality of hierarchical images having different sizes, the reduction process in step S35 is an essential process in the procedure shown in the flowchart of FIG. However, the filtering process in step S33 is not necessarily a necessary process. However, when the filter process is performed, the influence of the pixel values of the surrounding pixels can be applied to the pixel values of the individual pixels. For this reason, by adding filter processing, it is possible to create a plurality of hierarchical images rich in variations, and it is possible to extract feature quantities including more diverse information, resulting in more accurate results. Simulation becomes possible. Therefore, in practice, it is preferable to alternately perform the reduction process and the filter process as in the procedure shown in the flowchart of FIG.

<2.3 Processing Procedure by Feature Quantity Calculation Unit 123>
Next, a procedure of feature amount calculation processing by the feature amount calculation unit 123 will be described. As shown in step S37 of FIG. 7, the feature amount calculation unit 123 performs a process of calculating the feature amounts x1 to xn for each evaluation point E based on the hierarchical images P1 to Pn that form the image pyramid PP. Here, the procedure of calculation processing of the feature amounts x1 to xn will be specifically described.

  FIG. 21 is a plan view showing a procedure for calculating feature amounts x1 to xn for a specific evaluation point E from the hierarchical images P1 to Pn in the feature amount calculation unit 123. FIG. Specifically, on the left side of FIGS. 21A to 21C, the original graphic pattern 10 is arranged in each pixel arrangement of the first hierarchical image P1, the second hierarchical image P2, and the third hierarchical image P3, respectively. A rectangle (indicated by a thick frame) is formed on the right side of FIGS. 21 (a) to 21 (c), and specific evaluation points are shown on the right side based on the hierarchical images P1, P2, and P3. The principle of calculating feature amounts x1, x2, and x3 for E is shown.

  Each hierarchical image P1, P2, P3 shown in FIG. 21 is a part of an image constituting each hierarchy of the image pyramid PP. Actually, n hierarchical images from P1 to Pn are prepared and n sets of feature values x1 to xn are extracted. In FIG. 21, for convenience of explanation, three hierarchical images P1, P1 and Pn are extracted. A state in which three sets of feature values x1, x2, and x3 are extracted from P2 and P3 is shown.

  Here, the first hierarchical image P1 is an image obtained by performing a filtering process on the original image Q1 (first preparation image). In the illustrated example, the first hierarchical image P1 has a 16 × 16 pixel array. doing. In contrast, the second hierarchical image P2 is an image obtained by performing reduction processing and filtering processing on the first hierarchical image P1, and in the illustrated example, an 8 × 8 pixel array is formed. Have. The third hierarchical image P3 is an image obtained by performing reduction processing and filtering processing on the second hierarchical image P2, and has a 4 × 4 pixel array in the illustrated example. Yes.

  In FIG. 21, since each of the hierarchical images P1, P2, and P3 is drawn so that the outline thereof becomes a square having the same size, the images are all the same size, but the pixel arrangement is 16 The image size is gradually reduced to x16, 8x8, and 4x4, and the image size is gradually reduced. However, in FIG. 21, the outer frame of each hierarchical image P1, P2, P3 is drawn as a square of the same size, so the size of the pixels gradually increases. In other words, the resolution of the image decreases in the order of the hierarchical images P1, P2, and P3, and gradually becomes a coarse image.

  As described above, in the figure, the rectangles constituting the original graphic pattern 10 are drawn with a thick frame. Since each of the hierarchical images P1, P2, and P3 is a raster image made up of a collection of pixels, the rectangular outline drawn with a thick frame in the figure is actually included as information on the outline itself. However, it is included as information on pixel values of individual pixels. However, in FIG. 21, for the convenience of explanation, the positions of the rectangles on the hierarchical images P1, P2, and P3 are indicated by bold lines. Here, a process of extracting feature amounts x1 to xn for a specific evaluation point E defined on the rectangular outline will be described.

  As can be seen from FIGS. 21 (a) to 21 (c), the rectangles indicated by the thick frames are arranged at the same relative positions with respect to the respective hierarchical images P1, P2, and P3, and the specific evaluation points E are also at the same relative positions. Placed in position. In the case of the embodiment shown here, the feature amount for one evaluation point E is calculated based on the pixel values of the neighboring pixels.

  First, as shown in FIG. 21A, a feature quantity x1 for the evaluation point E is extracted based on the first hierarchical image P1. Specifically, as shown on the right side of FIG. 21A, the feature amount calculation unit 123 includes four pixels (see FIG. 5) located in the vicinity of the evaluation point E from the pixels constituting the first hierarchical image P1. Are extracted as the target pixel, and the feature amount x1 is calculated by the calculation using the pixel values of these four target pixels. Similarly, as shown on the right side of FIG. 21 (b), attention is paid to four pixels (hatched pixels in the figure) located in the vicinity of the evaluation point E from the pixels constituting the second hierarchical image P2. Extracted as pixels, the feature amount x2 is calculated by calculation using the pixel values of these four target pixels. Further, as shown on the right side of FIG. 21 (c), four pixels located in the vicinity of the evaluation point E (pixels hatched in the drawing) from the pixels constituting the third hierarchical image P3 are focused pixels. And the feature amount x3 is calculated by calculation using the pixel values of these four target pixels.

  If such processing is also performed for the fourth hierarchical image P4 to the nth hierarchical image Pn, n sets of feature quantities x1 to xn can be extracted for a specific evaluation point E. These n sets of feature amounts x1 to xn are parameters indicating the surrounding features of the same evaluation point E on the original graphic pattern 10, but the ranges affected by the original graphic pattern 10 are different from each other. . For example, the feature quantity x1 extracted from the first hierarchical image P1 is a value indicating the feature in the narrow area hatched in the diagram on the right side of FIG. 21 (a), but the second hierarchical image P2 The feature value x2 extracted from FIG. 21B is a value indicating a feature in a wider area hatched in the diagram on the right side of FIG. 21B, and the feature value x3 extracted from the third hierarchical image P3 is The value on the right side of FIG. 21 (c) is a value indicating a characteristic in a wider area where hatching is performed.

  As described above, the value of the process bias y for a certain evaluation point E is a value determined by fusing phenomena having various scale feelings such as forward scattering and back scattering. Therefore, if various feature quantities x1 to xn are extracted from the feature quantity x1 related to a very narrow range to the feature quantity xn related to a wider range as the feature quantity for the same evaluation point E, the influence range is extracted. It is possible to perform an accurate simulation in consideration of various phenomena different from each other. FIG. 21 shows a process of extracting n sets of feature amounts x1 to xn for one evaluation point E. Actually, each of a large number of evaluation points defined on the original graphic pattern 10 is shown. N sets of feature quantities x1 to xn are extracted by the same procedure.

  As a method for calculating the feature amount x based on the pixel value of the target pixel near the evaluation point E, a simple method in which the simple average of the pixel values of the target pixel is the feature amount x can be employed. For example, as shown in FIG. 21 (a), in order to extract the feature quantity x1 for the evaluation point E from the first hierarchical image P1, the pixel of interest (in the vicinity of the evaluation point E) indicated by hatching in the figure is shown. A simple average of the pixel values of (four pixels) may be the feature amount x1. However, in order to calculate a more accurate feature quantity, it is preferable to obtain a weighted average that takes into account the weight according to the distance between the evaluation point E and each pixel of interest, and to use the weighted average value as the feature quantity x1. .

  FIG. 22 is a diagram showing a specific calculation method (calculation method using a weighted average value as a feature value) used in the feature value calculation procedure shown in FIG. Here, an example is shown in which four pixels A, B, C, and D are selected as the pixel of interest located in the vicinity of a specific evaluation point E. Specifically, the target pixels A, B, C, and D can be determined by performing a process of selecting a total of four pixels in order from the evaluation point E on the hierarchical image P to be processed. Therefore, for the pixel values of the four target pixels A, B, C, and D, a calculation may be performed using a weighted average considering the weight according to the distance between the evaluation point E and each pixel as the feature amount x.

  In FIG. 22A, an x mark is displayed at the center point of each pixel of interest A, B, C, D, and a broken line connecting these x marks is drawn. The pixel size of each pixel of interest A, B, C, and D is u both vertically and horizontally, and the broken line is a dividing line that divides the pixel having the pixel size u in half. In the embodiment shown here, the distance between the evaluation point E and each pixel of interest A, B, C, D is the lateral distance between the evaluation point E and the center point of each pixel of interest A, B, C, D, and The vertical distance is adopted. Specifically, in the example shown in FIG. 22 (a), the target pixel A has a horizontal distance a and a vertical distance c, and the target pixel B has a horizontal distance b and a vertical distance c. Thus, the pixel of interest C has a horizontal distance a and a vertical distance d, and the pixel of interest D has a horizontal distance b and a vertical distance d.

In this case, if the feature value x of the evaluation point E is represented by the same reference symbols A, B, C, and D as the pixel values of the respective target pixels A, B, C, and D, and the pixel size u (pixel pitch) is 1, As shown in FIG. 22 (b),
G = (A · b + B · a) / 2
H = (C · b + D · a) / 2
x = (G · d + H · c) / 2
Can be obtained by the following calculation.

  Of course, the method of calculating the feature amount x from the pixel values of the four target pixels A, B, C, and D is not limited to the method illustrated in FIG. Various other calculation methods can be employed as long as the feature value x reflecting the pixel value can be calculated. In the calculation methods illustrated in FIGS. 21 and 22, four pixels located in the vicinity of the evaluation point E are selected as the target pixels. However, the number of target pixels used for calculating the feature amount x is as follows. It is not limited to four. For example, nine pixels constituting a 3 × 3 pixel array located in the vicinity of the evaluation point E are selected as the target pixels, and the pixel values of these nine target pixels are set according to the distance from the evaluation point E. It is also possible to obtain a weighted average in consideration of the weight and use this as the feature quantity x for the evaluation point E.

  In general terms, when calculating the feature value x for a specific evaluation point E on the specific hierarchical image P, the feature value calculating unit 123 calculates the specific evaluation from the pixels constituting the specific hierarchical image P. A total of j pixels are extracted as the target pixel in the order close to the point E, and the weight of the extracted pixel values of the j target pixels in consideration of the weight according to the distance between the specific evaluation point E and each target pixel An arithmetic operation for obtaining an average is performed, and the obtained weighted average value can be used as the feature amount x.

<2.4 Modification of Feature Extraction Process>
Here, some modified examples of the procedure of the feature amount extraction processing described so far will be described.

(1) Modified Example Using Difference Image Dk as Hierarchical Image In §2.2, the processing of steps S33 to S36 shown in the flowchart of FIG. 7 is exemplified as the image pyramid PP creation processing procedure by the image pyramid creation unit 122. In this process, starting from the original image Q1 (first preparation image), the filtering process and the reduction process are executed alternately, and n images (by the procedure shown in FIG. (Hereinafter referred to as “filtered image”) is adopted as the hierarchical images P1 to Pn as they are to create the image pyramid PP.

  On the other hand, the modified example described here is based on the processing of steps S33 to S36 shown in the flowchart of FIG. 7, and further, when the filtering processing of step S33 is completed, the k-th obtained by the filtering processing. The difference calculation “Pk−Qk” is performed by subtracting the kth preparation image Qk from the filtered image Pk (image called the kth hierarchical image Pk in §2.2) to obtain the kth difference image Dk. The required processing is added. In other words, in the modification described here, the processing of steps S33 to S36 shown in the flowchart of FIG. 7 is executed as it is, and further, from the kth filtered image Pk to the kth prepared image Qk. The difference calculation “Pk−Qk” is reduced.

  Here, the difference calculation “Pk−Qk” defines pixels arranged at the same position on the pixel array as corresponding pixels for the k-th filtered image Pk and the k-th preparation image Qk. This is a process for subtracting the pixel value of the corresponding pixel on the image Qk from the pixel value of each pixel to obtain a difference, and obtaining a difference image Dk composed of a new pixel aggregate with the obtained difference as the pixel value.

  FIG. 23 is a plan view showing a procedure for creating an image pyramid PD including n difference images D1 to Dn by such a difference calculation “Pk−Qk”. Here, the first hierarchical image D1 shown on the upper right side is a difference image obtained by the difference calculation “P1-Q1”. Specifically, the first filtered image P1 ( In FIG. 20, the difference is calculated by subtracting the first preparation image Q1 shown on the upper left side (referred to as the first hierarchical image P1) (subtraction of pixel values of pixels at corresponding positions).

  Similarly, the second hierarchical image D2 shown on the right side of the middle stage in FIG. 23 is a difference image obtained by the difference calculation “P2-Q2”. Specifically, the second filter processing shown on the right side of the middle stage in FIG. The difference is calculated by subtracting the second preparation image Q2 shown on the left side of the middle stage from the image P2 (referred to as the second hierarchical image P2 in FIG. 20). Also, the third hierarchical image D3 shown on the lower right side of FIG. 23 is a difference image obtained by the difference calculation “P3-Q3”. Specifically, the third filtered image shown on the lower right side of FIG. The difference is calculated by subtracting the third preparation image Q3 shown on the left side of the lower stage from P3 (referred to as the third hierarchical image P3 in FIG. 20). Hereinafter, the same difference calculation is performed, and the difference image finally obtained by the difference calculation “Pn−Qn” is the n-th layer image Dn.

  In the embodiment described in §2.2, as shown in FIG. 20, the image pyramid PP is generated by the first hierarchical image (first filtered image) P1 to the nth hierarchical image (nth filtered image) Pn. In the modification described here, as shown in FIG. 23, the image pyramid is formed by the first layer image (first difference image) D1 to the nth layer image (nth difference image) Dn. The PD is configured.

  As described above, in order to implement the modification described here, a difference calculation procedure may be added to the procedure of the embodiment described in §2.2. Specifically, the image pyramid creation unit 122 uses the original image created by the original image creation unit 121 as the first preparation image Q1, and obtains it by filtering the kth preparation image Qk (where k is a natural number). The difference image Dk between the filtered image Pk and the kth preparation image Qk is obtained, the difference image Dk is set as the kth hierarchical image Dk, and the image obtained by the reduction processing on the kth filtered image Pk is the ( As the preparation image Q (k + 1) of (k + 1), the first hierarchical image D1 to the nth hierarchical image Dn are included by alternately executing the filtering process and the reduction process until the nth hierarchical image Dn is obtained. An image pyramid PD composed of a plurality of n hierarchical images may be created.

  After all, in this modification, the k-th layer image Dk constituting the k-th layer of the image pyramid PD is an image after the filter process (filtered image Pk) and an image before the filter process (prepared image Qk). This is a difference image, and the pixel value of each pixel corresponds to the difference between the pixel values before and after the filtering process. That is, the k-th hierarchical image Pk in the embodiment described in §2.2 shows the image after the filtering process, whereas the k-th hierarchical image Dk in the modification described here is a filter. It shows the difference caused by the process. As described above, the image pyramid PP created in the embodiment described in §2.2 and the image pyramid PD created in the modification described here are significantly different in the meaning of the hierarchical image as a component. As a matter of course, there is no change in the points that are images showing some characteristics about the evaluation point E. Therefore, it is possible to extract feature amounts from each of the hierarchical images D1 to Dn created in the modified example described here, and the feature amount calculating unit 123 in this modified example has the hierarchical images D1 to Dn. Thus, the process of extracting the feature amounts x1 to xn is performed.

(2) Modified Example of Creating Plural Image Pyramids Using Plural Algorithms In the embodiment described in §2.2, as shown in FIG. 20, the original image (first prepared image Q1) is filtered. The image pyramid PP is created by the algorithm that obtains the filter processed images P1 to Pn by alternately executing the reduction processing and the filter processed images P1 to Pn as n hierarchical images P1 to Pn as they are. Yes. On the other hand, in the modified example in which the difference image Dk described in §2.4 (1) is a hierarchical image, as shown in FIG. 23, each difference operation between the filtered image Pk and the preparation image Qk is performed. Difference images D1 to Dn are obtained, and an image pyramid PD is created by an algorithm that uses these difference images D1 to Dn as n hierarchical images D1 to Dn.

  Further, there are various types of image filters used for the filter processing as shown in FIGS. 16 and 17, and there are various types of reduction processing (pooling processing) methods as shown in FIGS. is there. Thus, even if the starting point is the same original image (first preparation image Q1), the contents of the hierarchical images constituting the obtained image pyramid differ depending on the algorithm employed. Moreover, it is not always necessary to use one image pyramid for executing the invention of the prior application. A plurality of image pyramids are created by a plurality of algorithms, and feature amounts are extracted from the individual image pyramids. Is also possible.

  That is, the image pyramid creation unit 122 has a function of performing image pyramid creation processing based on a plurality of different algorithms for one original image (first preparation image Q1), thereby creating a plurality of image pyramids. You may be made to do. In this case, the feature amount calculation unit 123, for each hierarchical image constituting each of the plurality of image pyramids, based on the pixel value of a pixel (a pixel located around the evaluation point) corresponding to the evaluation point position. What is necessary is just to perform the process which calculates a feature-value.

  For example, when the image pyramid creation unit 122 performs the image pyramid creation process, if the algorithm of the embodiment described in §2.2 is adopted as the main algorithm, as shown in FIG. A main image pyramid PP composed of P1 to Pn (filtered images) can be created, and as a sub-algorithm, an algorithm of a modified example in which the difference image Dk described in §2.4 (1) is a hierarchical image is used. If it employ | adopts, as shown in FIG. 23, the subimage pyramid PD comprised by n types of subhierarchical images D1-Dn (difference image) can be created. Therefore, if the image pyramid creation unit 122 performs image pyramid creation processing using the above two algorithms, it is possible to create two types of image pyramids, the main image pyramid PP and the sub image pyramid PD. .

  Here, the main image pyramid PP created by the filter processing using the Gaussian filter illustrated in FIG. 14 can be called a Gaussian pyramid. Further, the sub-image pyramid PD configured using the difference image can be called a Laplacian pyramid. Since the Gaussian pyramid and the Laplacian pyramid are image pyramids that are greatly different from each other, they are adopted as the main image pyramid PP and the sub image pyramid PD, and feature amounts are extracted using two image pyramids. This makes it possible to extract feature values with more diversity.

  On the other hand, the feature quantity calculation unit 123 sets the pixel values of the pixels near the evaluation point E for the main layer images P1 to Pn constituting the main image pyramid PP and the sub layer images D1 to Dn constituting the sub image pyramid PD, respectively. If the process for calculating the feature amount is performed based on the feature amounts, the feature amounts xp1 to xpn calculated from the main layer images P1 to Pn and the feature amounts xd1 to xdn calculated from the sub layer images D1 to Dn are obtained. . That is, a total of 2n feature amounts are extracted for one evaluation point E. In this case, since the feature amount for one evaluation point E is given to the estimation calculation unit 132 as a 2n-dimensional vector, more accurate estimation calculation can be performed.

  Eventually, in order to implement the above-described modification, the image pyramid creation unit 122 sets the original image created by the original image creation unit 121 as the first preparation image Q1, and the kth preparation image Qk (where k is The image obtained by the filtering process for (natural number) is the k-th main layer image Pk, the image obtained by the reduction process for the k-th main layer image Pk is the (k + 1) th preparation image Q (k + 1), and the nth By alternately executing filter processing and reduction processing until the main hierarchy image Pn is obtained, a main image pyramid including a plurality of n types of hierarchy images including the first main hierarchy image P1 to the nth main hierarchy image Pn. And the difference image Dk between the k-th main layer image Pk and the k-th preparation image Qk is obtained, and the difference image Dk is used as the k-th sub-layer image Dk. It is sufficient to create a sub image pyramid consisting of hierarchy images of a plurality n as including a sub-hierarchy image Dn image D1~ the n.

  The feature amount calculation unit 123 may calculate the feature amount based on the pixel values of the pixels near the evaluation point E for each hierarchical image constituting the main image pyramid PP and the sub image pyramid PD. . If it does so, it will become possible to extract a 2n-dimensional vector as a feature-value about one evaluation point E, and it will become possible to perform a more exact estimation calculation.

(3) Modified example of creating multiple image pyramids by creating multiple image originals In §2.4 (2) above, multiple algorithms are applied to the same original image. A modification of creating multiple image pyramids was described. Here, a modified example in which a plurality of original images are created to create a plurality of image pyramids will be described.

  In the figure pattern shape estimation apparatus 100 ′ according to the prior application invention, as shown in FIG. 1, the original image creation unit 121 performs a process of creating an original image based on the given original figure pattern 10. As the original image created here, as described in §2.1, the area density map M1 (FIG. 10), the edge length density map M2 (FIG. 11), the dose density map M3 (FIG. 13), etc. Various forms of images can be employed.

  In other words, the original image creation unit 121 can employ various creation algorithms when creating an original image based on the original graphic pattern 10, and the contents differ depending on which algorithm is employed. Various original images can be created. For example, the area density map M1 shown in FIG. 10, the edge length density map M2 shown in FIG. 11, and the dose density map M3 shown in FIG. 13 are all images created based on the same original figure pattern 10. The pixel values of the individual pixels are different from each other, and each has a different image. Alternatively, based on the same original figure pattern 10, a plurality of density maps (in other words, a plurality of maps having different resolutions) having different pixel sizes (dimensions of one pixel) and map sizes (numbers of pixels arranged vertically and horizontally) are prepared. Then, a plurality of image pyramids may be created using each of the plurality of density maps as an original image. Of course, theoretically, it is ideal to use a density map with a small pixel size and a large map size (high-resolution density map) as the original image. However, since the memory of a computer is limited, it is practically used. Preferably, a plurality of density maps having different pixel sizes and map sizes are used as the original image.

  Therefore, the original image creation unit 121 has a function of performing original image creation processing based on a plurality of different algorithms to create a plurality of types of original images, and the image pyramid creation unit 122 has a plurality of types of original images. A plurality of image pyramids can be created by providing a function of performing processing for creating separate image pyramids based on images. Then, if the feature amount calculation unit 123 has a function of calculating the feature amount based on the pixel values of the pixels in the vicinity of the evaluation point E for each hierarchical image constituting each of the plurality of image pyramids, It is possible to extract a feature amount composed of a higher-dimensional vector, and it is possible to perform a more accurate estimation calculation.

  For example, the original image creation unit 121 performs a first original image composed of the area density map M1 shown in FIG. 10, a second original image composed of the edge length density map M2 shown in FIG. 11, and a dose density shown in FIG. If the function of creating the third original image composed of the map M3 is provided, the image pyramid creation unit 122 creates three sets of independent image pyramids based on the three original images. Can do. All of the image pyramids are image pyramids created based on the same original graphic pattern 10. The feature amount calculation unit 123 can perform a process of calculating a feature amount based on the pixel values of pixels in the vicinity of the evaluation point E for each hierarchical image constituting each of the three image pyramids. If n feature amounts x1 to xn are extracted from one image pyramid, a total of 3n feature amounts can be extracted for the same evaluation point E. That is, since a 3n-dimensional vector can be given as a feature amount for one evaluation point E, more accurate estimation calculation can be performed.

  Of course, the above-described modification of §2.4 (2) can be combined with the modification described above. As described in §2.4 (2), if the image pyramid creation unit 122 employs two different types of algorithms when creating the image pyramid, the main image pyramid PP and the sub-image pyramid PD An image pyramid can be created. Therefore, if two image pyramids of the main image pyramid PP and the sub image pyramid PD are created based on each of the above three original images, a total of six image pyramids based on the same original graphic pattern 10 are created. Therefore, a 6n-dimensional vector can be given as a feature amount for one evaluation point E.

<<< §3. Bias estimation unit details >>
Here, a detailed processing operation of the bias estimation unit 130 will be described. As shown in FIG. 1, the bias estimation unit 130 includes a feature amount input unit 131 and an estimation calculation unit 132, and has a function of executing the process bias estimation process in step S4 in the flowchart of FIG. . In the case of the embodiment shown in FIG. 6, for one evaluation point E, feature quantities (n-dimensional vectors) x1 to xn are input to the feature quantity input unit 131, and an estimation calculation by the estimation calculation unit 132 is executed. An estimate y of the process bias for E is determined. In the embodiment shown in FIG. 6, a neural network is used as the estimation calculation unit 132. Therefore, the detailed configuration and operation of this neural network will be described below.

<3.1 Estimate calculation by neural network>
In recent years, neural networks have attracted attention as a technology that forms the basis of artificial intelligence, and are used in various fields including image processing. This neural network is a computer-like structure that mimics the structure of a biological brain, and is composed of neurons and edges that connect them.

  FIG. 24 is a block diagram showing an embodiment using a neural network as the estimation calculation unit 132 shown in FIG. As shown in the figure, an input layer, an intermediate layer (hidden layer), and an output layer are defined in the neural network, and predetermined information processing is performed on the information given to the input layer in the intermediate layer (hidden layer). The result is output to the output layer. In the case of the prior application invention, as shown in the figure, feature quantities x1 to xn for one evaluation point E are given to the input layer as n-dimensional vectors, and the process layer is estimated for the evaluation point E in the output layer. The value y is output. Here, the estimated value y of the process bias is an estimated value indicating the amount of deviation in the normal direction of the contour line for the evaluation point E located on the contour line of the predetermined graphic as described in §1. .

  In the case of the embodiment shown in FIG. 24, the estimation calculation unit 132 has a neural network having the feature amounts x1 to xn input by the feature amount input unit 131 as input layers and the process bias estimate y as an output layer. The intermediate layer of the neural network is composed of N hidden layers which are a first hidden layer, a second hidden layer,..., An Nth hidden layer. These hidden layers have a large number of neurons (nodes), and edges connecting these neurons are defined.

  The feature amounts x1 to xn given to the input layer are transmitted as signals to the neurons via the edges. Finally, a signal corresponding to the estimated value y of the process bias is output from the output layer. A signal in the neural network is transmitted from one hidden layer neuron to the next hidden layer neuron through computation via an edge. The calculation via the edge is performed using learning information L (specifically, parameters W and b described later) obtained in the learning stage.

  FIG. 25 is a diagram showing a specific calculation process executed by the neural network shown in FIG. The parts shown in bold lines in the figure indicate the first hidden layer, the second hidden layer,..., The Nth hidden layer, and each circle in each hidden layer is a neuron (node) and connects each circle. Lines indicate edges. As described above, feature values x1 to xn for one evaluation point E are given to the input layer as n-dimensional vectors, and an estimated value y of the process bias for the evaluation point E is scalar in the output layer. It is output as a value (a dimension value indicating the amount of deviation in the normal direction of the outline).

  In the illustrated example, the first hidden layer is an M (1) -dimensional layer, and is configured by a total of M (1) neurons h (1,1) to h (1, M (1)). The second hidden layer is an M (2) -dimensional layer and is configured by a total of M (2) neurons h (2,1) to h (2, M (2)), and the Nth hidden layer is M (N ) Dimension layer, which is composed of a total of M (N) neurons h (N, 1) to h (N, M (N)).

  Here, the calculation values of signals transmitted to the neurons h (1,1) to h (1, M (1)) of the first hidden layer are respectively calculated using the same symbols. ˜h (1, M (1)), the values of these calculated values h (1,1) to h (1, M (1)) are given by the matrix equation shown in the upper part of FIG. It is done. As the function f (ξ) on the right side of this equation, a sigmoid function shown in FIG. 27A, a normalized linear function ReLU shown in FIG. 27B, a normalized linear function Leakey ReLU shown in FIG. The activation function can be used.

  Further, ξ described as an argument of the function f (ξ) is a matrix [W] and a matrix [x1 to xn] (features given to the input layer as n-dimensional vectors, as shown in the middle of FIG. ) And the product of the matrix [b]. Here, the contents of the matrix [W] and the matrix [b] are as shown in the lower part of FIG. 26, and each component of the matrix (weight parameter W (u, v) and bias parameter b (u, v)). Is learning information L obtained by a learning stage described later. That is, the values of the individual components (parameters W (u, v), b (u, v)) constituting the matrix [W] and the matrix [b] are given as learning information L, and are shown in FIG. Using the calculated calculation formula, the calculation values h (1, 1) to h (1, M (1)) of the first hidden layer are calculated based on the feature amounts x1 to xn given to the input layer. Can do.

  On the other hand, FIG. 28 is a diagram showing an arithmetic expression for obtaining each value of the second hidden layer to the Nth hidden layer in the diagram shown in FIG. Specifically, the same sign is used for the operation value of the signal transmitted to the neurons (i + 1, 1) to h (i + 1, M (i + 1)) in the (i + 1) th hidden layer (1 ≦ i ≦ N). Thus, if expressed as operation values h (i + 1, 1) to h (i + 1, M (i + 1)), the values of these operation values h (i + 1, 1) to h (i + 1, M (i + 1)) are It is given by the matrix equation shown in the upper part of FIG. As the function f (ξ) on the right side of this equation, as described above, each function shown in FIG. 27 can be used.

  Further, ξ described as an argument of the function f (ξ) is a matrix [W] and a matrix [h (i, 1) to h (i, M (i))] as shown in the middle part of FIG. It is a value obtained by adding the matrix [b] to the product of (the calculated value of the neuron h (i, 1) to h (i, M (i)) of the previous i-th hidden layer). Here, the contents of the matrix [W] and the matrix [b] are as shown in the lower part of FIG. 28, and the individual components of the matrix (parameters W (u, v), b (u, v)) are This is learning information L obtained by a learning stage described later.

  Again, the values of the individual components (parameters W (u, v), b (u, v)) constituting the matrix [W] and the matrix [b] are given as learning information L, and are shown in FIG. Using the arithmetic expression shown, based on the arithmetic values [h (i, 1) to h (i, M (i))] obtained in the i-th hidden layer, the arithmetic values in the (i + 1) -th hidden layer h (i + 1, 1) to h (i + 1, M (i + 1)) can be calculated. Therefore, each value of the second hidden layer to the Nth hidden layer in the diagram shown in FIG. 25 can be sequentially obtained based on the arithmetic expression shown in FIG.

  FIG. 29 is a diagram showing an arithmetic expression for obtaining the value y of the output layer in the diagram shown in FIG. Specifically, the output value y (estimated value of process bias for the evaluation point E: scalar value) is given by the matrix equation shown in the upper part of FIG. That is, the output value y is expressed as a matrix [W] and a matrix [h (N, 1) to h (N, M (N))] (Nth hidden layer neurons h (N, 1) to h (N, M). (N)) and the scalar value b (N + 1). Here, the contents of the matrix [W] are as shown in the lower part of FIG. 29, and the individual components (parameters W (u, v)) and the scalar value b (N + 1) of the matrix [W] are also described later. This is the learning information L obtained by the learning stage.

  As described above, the values of the first hidden layer in the diagram shown in FIG. 25 are the parameters W (1, v), b prepared in advance as learning information L for the feature amounts x1 to xn given as the input layers. (1, v) can be obtained by applying each parameter of the second hidden layer to each value of the first hidden layer using parameters W (2, v), can be obtained by acting b (2, v),..., each value of the Nth hidden layer is prepared in advance as learning information L for each value of the (N−1) th hidden layer. The values of the output layer y are prepared in advance as learning information L for each value of the Nth hidden layer. The parameter parameters W (N + 1, v) and b (N + 1) are applied. It can be obtained more. Specific arithmetic expressions are as shown in FIGS.

  Note that, as described in §2.4 (2) and (3), when adopting a modified example of creating a plurality of image pyramids, the feature value given as the input layer is an n-dimensional vector ( x1-xn), but a vector of V.n dimensions (V is the total number of image pyramids), but the number of input layers in the diagram shown in FIG. There is no change in the basic configuration and operation.

  As described above, the calculation for obtaining the estimated value y of the process bias for a certain evaluation point E has been described using the neural network shown in FIG. The same calculation is performed for a large number of defined evaluation points, and an estimated value y of the process bias is obtained for each evaluation point. In the figure pattern shape correction apparatus 100 shown in FIG. 1, the pattern correction unit 140 corrects the pattern shape based on the estimated value y of the process bias for each evaluation point thus obtained (step S5 in FIG. 4). Will be executed.

<3.2 Learning stage of neural network>
As described above, in the case of the embodiment shown in FIG. 24, the estimation calculation unit 132 is configured by a neural network, and uses the learning information L set in advance to calculate the signal value transmitted to each neuron. Will do. Here, the substance of the learning information L is the parameters W (u, v), b () described as the components of the matrices [W], [b] in the lower part of FIG. 26, the lower part of FIG. 28, and the lower part of FIG. u, v) and the like. Therefore, in order to construct such a neural network, it is necessary to obtain learning information L by a learning stage executed in advance.

  That is, the neural network included in the estimation calculation unit 132 includes dimension values obtained by actual dimension measurement of the actual figure pattern 20 actually formed on the actual substrate S by a lithography process using a large number of test pattern figures. Process bias estimation processing is performed using, as learning information L, parameters W (u, v), b (u, v), and the like obtained in the learning stage using the feature amounts obtained from each test pattern figure. become. Such a process in the learning stage of the neural network is a known technique, but here, an outline of a process suitable for the learning stage of the neural network used in the invention of the prior application will be briefly described.

  FIG. 30 is a flowchart showing a learning stage procedure for obtaining learning information L used by the neural network shown in FIG. First, in step S81, a test pattern graphic creation process is executed. Here, the test pattern graphic corresponds to, for example, the original graphic pattern 10 as shown in FIG. 2A, and a simple graphic such as a rectangle or an L-shaped graphic is usually used. Actually, thousands of test pattern figures having different sizes and shapes are created.

  Subsequently, in step S82, an evaluation point E is set on each test pattern graphic. Specifically, a process of defining a large number of evaluation points E at predetermined intervals on the contour lines of individual test pattern figures may be performed. In step S83, a feature amount is extracted for each evaluation point E. The feature quantity extraction process in step S83 is the same as the process described in §2, and is executed by a unit having a function equivalent to that of the feature quantity extraction unit 120. According to the procedure described in §2, the feature amounts x1 to xn are extracted for each evaluation point E, respectively.

  The estimation calculation unit learning process in step S84 is a process of determining learning information L (that is, parameters W (u, v), b (u, v), etc.) using the feature amount extracted in step S83. is there. In order to execute this learning process, actual dimensions obtained by an actual lithography process are required. Therefore, in step S85, the lithography process is actually executed based on the test pattern graphic created in step S81, and the actual substrate S is created. In step S86, the actual dimension of each figure is measured for the actual figure pattern formed on the actual substrate S. This measurement result is used for the learning process in step S84.

  As described above, the learning stage process shown in FIG. 30 includes a process (process executed by a computer program) executed on the computer consisting of steps S81 to S84 and a process executed on the actual board consisting of steps S85 and S86. And composed of In the estimation calculation unit learning process in step S84, the learning information L used for the neural network is determined based on the feature amounts x1 to xn obtained by the processing on the computer and the actual dimensions measured on the actual board. It will be processing.

  FIG. 31 is a flowchart showing a detailed procedure of the estimation calculation unit learning in step S84 in the flowchart shown in FIG. First, in step S841, the design position and feature amount of each evaluation point are input. Here, the design position of the evaluation point is the position on the test pattern figure of the evaluation point set in step S82, and the feature amount of the evaluation point is the feature amount x1 to xn extracted in step S83. Subsequently, in step S842, the actual position of each evaluation point is input. Here, the actual position of the evaluation point is determined based on the actual dimension of each figure on the actual substrate S actually measured in step S86. In step S843, the actual bias of each evaluation point is calculated. This actual bias corresponds to the amount of deviation between the design position of the evaluation point input in step S841 and the actual position of the evaluation point input in step S842.

  For example, when a rectangle such as the original graphic pattern 10 shown in FIG. 3A is created as a test pattern graphic in step S81, the evaluation points E11, E12, E13, etc. are formed on the rectangular outline in step S82. In step S83, feature amounts x1 to xn are extracted for each of these evaluation points E11, E12, and E13. The position and feature amount of each evaluation point E11, E12, E13 are input in step S841.

  On the other hand, the actual figure pattern 20 as shown in FIG. 3B, for example, is formed on the actual substrate S by the lithography process in step S85, and the actual figure pattern 20 is formed by measuring the actual dimension in step S86. The actual dimensions are measured for each side of the rectangle. By this measurement, the actual positions E21, E22, and E23 of the evaluation points are determined as the points where the evaluation points E11, E12, and E13 are moved in the normal direction of the contour line, respectively. The actual positions E21, E22, E23 of each evaluation point are input in step S842.

  Therefore, in step S843, as shown in FIG. 3B, the actual bias y11, y12, y13 is calculated as the difference between the design position of each evaluation point E11, E12, E13 and the actual position E21, E22, E23. The Actually, for example, the difference “b− between the horizontal width b of the rectangular pattern forming the actual graphic pattern 20 shown in FIG. 3B and the horizontal width a of the rectangular pattern forming the original graphic pattern 10 shown in FIG. The actual bias may be determined by obtaining a value y obtained by dividing “a” by 2. Of course, in actuality, test pattern figures having a scale of several thousand are created, and a large number of evaluation points are set on the contour lines of the individual figures. Therefore, the procedure of steps S841 to S843 is a huge number of evaluation points. Will be executed for each. Here, focusing on one evaluation point E, for the evaluation point E, a combination of the feature amounts x1 to xn and the actual bias y is prepared as a learning material.

  Subsequently, in step S844, the parameters W and b are set to initial values. Here, the parameters W and b are the parameters W (u, v) and b (u described as the components of the matrices [W] and [b] in the lower part of FIG. 26, the lower part of FIG. 28, and the lower part of FIG. , V) and the like, and becomes a value constituting the learning information L. As an initial value, a random value may be given by a random number. In other words, at the initial stage before learning, the parameters W and b that constitute the learning information L have frank values.

  Each of the subsequent steps S845 to S848 is an actual learning process, and by performing this learning process, the parameters W and b, which were initially set to frank values, are gradually updated. Eventually, the value is corrected to an accurate value that sufficiently functions as the learning information L. First, in step S845, an operation for estimating the process bias y from the feature amounts x1 to xn is executed.

  Specifically, a neural network as shown in FIG. 24 is prepared. Of course, at this stage, random numbers are given as initial values to the parameters W and b constituting the learning information L, and this neural network cannot perform a normal function as the estimation calculation unit 132. It is a thing. The feature quantities x1 to xn input in step S841 are given to the input layer of this incomplete neural network, the calculation using the learning information L consisting of incomplete values is performed, and the estimated value y of the process bias is used as the output layer. calculate. Of course, the estimated value y of the process bias obtained initially is far from the observed actual bias.

  Therefore, in step S846, a residual with respect to the actual bias at that time is calculated. That is, a difference between the estimated value y of the process bias obtained in step S845 and the calculated actual bias value obtained in step S843 is obtained, and this difference is set as a residual for the evaluation point E. If this residual is less than or equal to a predetermined tolerance, the learning information L at that time (that is, parameters W (u, v), b (u, v), etc.) is sufficiently practical learning information. Therefore, the learning stage can be completed.

  Step S847 is a procedure for determining whether or not the learning stage can be completed. Actually, since a residual is obtained for each of a large number of evaluation points, in practice, for example, if the amount of improvement in the residual sum of squares is below a specified value, a determination is made to end learning. A determination method may be adopted. If it is not determined that the learning has ended, the parameters W (u, v), b (u, v), etc. are updated in step S848. Specifically, updating is performed to increase or decrease the values of the parameters W (u, v), b (u, v), etc. by a predetermined amount so that the effect of reducing the residual occurs. As for the specific update method, methods based on various algorithms are known as learning methods in neural networks, so the explanation is omitted here, but the basic policy is to evaluate the evaluation points of many test pattern figures. An algorithm is employed that comprehensively considers the residuals and performs a total adjustment such that each residual is reduced overall.

  In this way, steps S845 to S848 are repeatedly executed until a positive determination is made in step S847. As a result, the values of the parameters W (u, v), b (u, v), etc. constituting the learning information L are gradually corrected in the direction of decreasing the residual, and finally in step S847. A positive determination is made and the learning phase ends. The learning information L (parameters W (u, v), b (u, v), etc.) obtained at the learning end stage is information suitable for obtaining an estimated value y of the process bias close to the actual bias in the output layer. It has become. Therefore, the neural network including the learning information L obtained at the learning end stage functions as the estimation calculation unit 132 in the prior invention.

<<< §4. Geometric pattern shape estimation method according to the prior invention >>>
The invention of the prior application has been described as the figure pattern shape estimation apparatus 100 ′ or the figure pattern shape correction apparatus 100 having the configuration shown in FIG. Here, a brief description will be given of the invention of the prior application as a method invention called a figure pattern shape estimation method.

  When the invention of the prior application is grasped as an invention of a figure pattern shape estimation method, the method estimates the shape of an actual figure pattern formed on an actual substrate by simulating a lithography process using the original figure pattern. It will be a way to do. Then, in this method, the computer inputs the original graphic pattern input stage in which the original graphic pattern 10 including the contour line information indicating the boundary between the inside and the outside of the graphic is input (the pattern created in step S1 in FIG. And an evaluation point setting step (step S2 in FIG. 4) in which the computer sets an evaluation point E at a predetermined position on the contour line of the input graphic, and each evaluation for the original graphic pattern 10 input by the computer. A feature amount extraction stage (step S3 in FIG. 4) for extracting feature amounts x1 to xn indicating features around the point E, and an original figure of each evaluation point E based on the extracted feature amounts x1 to xn A process bias estimation step (step S4 in FIG. 4) for estimating a process bias y indicating the amount of deviation between the position on the pattern 10 and the position on the actual graphic pattern 20; Constructed.

  Here, in the feature amount extraction stage (step S3 in FIG. 4), based on the original figure pattern 10, an original image creation stage (FIG. 7 and step S32) and image pyramid creation processing including reduction processing (step S35 in FIG. 7) for creating a reduced image Qk (preparation image) based on the original image Q1. The image pyramid creation stage (steps S33 to S35 in FIG. 7) for creating the image pyramid PP composed of the layer images P1 to Pn, and the evaluation points E for the respective layer images P1 to Pn constituting the created image pyramid PP. A feature amount calculating step (step S37 in FIG. 7) for calculating feature amounts x1 to xn based on pixel values of pixels in the vicinity of

  Here, in the process bias estimation stage (step S4 in FIG. 4), an estimated value corresponding to the feature amounts x1 to xn for the evaluation point E is calculated based on the learning information L obtained in the learning stage performed in advance. And an estimation calculation step of outputting the calculated estimated value as the estimated value y of the process bias for the evaluation point E.

  When the feature amount extraction unit 120 described in §2 is used, a filter processing stage that performs a filter process using a predetermined image processing filter on the original image Q1 or the reduced image Qk in the image pyramid creation stage. (Step S33 in FIG. 7) and the reduction processing stage (Step S35 in FIG. 7) for performing the reduction processing on the image Pk after the filter processing are alternately executed, whereby a plurality of hierarchical images P1 to Pn are executed. An image pyramid PP consisting of can be created.

  Specifically, in the procedure described in §2.2, images in which the filtered image (filtered image Pk obtained in step S33 in FIG. 7) is set as hierarchical images P1 to Pn at the image pyramid creation stage. A pyramid PP has been created. On the other hand, in the procedure of the modified example described in §2.4 (1), in the image pyramid creation stage, the image after filtering (filtered image Pk) and the image before filtering (prepared image Qk) The difference image Dk is created, and an image pyramid PD is created in which the created difference images are the hierarchical images D1 to Dn.

<<< §5. Basic Configuration of Shape Correction Device According to the Present Invention >>
So far, in §1 to §4, the shape correction apparatus for graphic patterns according to the prior invention has been described. As described above, the technique according to the present invention has been developed for application to the figure pattern shape correcting apparatus according to the prior invention. However, the present invention is not limited to application to the prior application invention. A feature of the present invention is that, when performing a simulation of a lithography process, an evaluation point is set by a unique method, and shape correction is performed on an original graphic pattern based on the result of simulation based on the evaluation point. Therefore, the present invention can be widely applied to conventionally known general graphic pattern shape correction apparatuses. However, in this section 5 and later, for convenience of explanation, a specific embodiment in which the present invention is applied to the figure pattern shape correcting apparatus according to the prior invention described in sections 1 to 4 will be described.

  The basic configuration of the figure pattern shape correcting apparatus according to the embodiment described here is the same as the apparatus according to the invention of the prior application described in §1 to §4. That is, the shape correction apparatus 100 described here includes an evaluation point setting unit 110, a feature amount extraction unit 120, a bias estimation unit 130, and a pattern correction unit 140 as shown in FIG. When the actual figure pattern 20 is formed on the actual substrate S by the process, the shape of the original figure pattern 10 is corrected so that the actual figure pattern 20 matches the original figure pattern 10, and correction actually used in the lithography process It has a function of creating a graphic pattern 15.

  Actually, the function of the graphic pattern shape correction apparatus 100 is realized by incorporating a dedicated program into a general-purpose computer. Therefore, the evaluation point setting unit 110, the feature amount extraction unit 120, the bias estimation unit 130, and the pattern correction unit 140 described above are each configured by incorporating a predetermined program into a computer.

  Here, as described in §1, the evaluation point setting unit 110 is for individual figures constituting the original figure pattern 10 (hereinafter referred to as unit figures and denoted by the same reference numeral 10 as the original figure pattern). The evaluation point E is set at a predetermined position on the contour line indicating the boundary between the inside and the outside. FIG. 3 (a) shows an example in which three evaluation points E11, E12, E13 are set on the rectangular unit graphic 10, but in actuality, it goes around the outline of the unit graphic 10 once. A number of evaluation points are set on the route to be performed. A feature of the present invention resides in this evaluation point setting method. A specific evaluation point setting method will be described in detail in §6.

  The feature amount extraction unit 120 plays a role of extracting feature amounts x1 to xn indicating features around each evaluation point E for the original graphic pattern 10. In §2, a procedure using image pyramids PP and PD as a feature amount extraction method unique to the invention of the prior application is shown. Of course, a method of extracting feature amounts using the image pyramids PP and PD can also be adopted in implementing the present invention. However, the feature quantity extraction unit 120 used in the present invention is not limited to one that extracts feature quantities by the method described in Section 2. In carrying out the present invention, as the feature quantity extraction unit 120, a unit that extracts feature quantities by an arbitrary method may be adopted. For example, instead of using the image pyramid PP composed of a plurality of n hierarchical images P1 to Pn, a process of calculating n feature values x1 to xn for each evaluation point E using a plurality of n calculation functions is performed. It is also possible. As each calculation function, for the evaluation point E (X, Y) located at the coordinate values X and Y, by assigning the coordinate value X and Y as a variable, the evaluation point E (X, Y) and the original graphic pattern A function (for example, a function used in the additional embodiment of the prior application) that can calculate a predetermined function value by quantifying the positional relationship with each figure included in the graph 10 may be used.

  The bias estimation unit 130 shifts the position of each evaluation point on the original graphic pattern 10 and the position on the actual graphic pattern 20 based on the feature values x1 to xn for each evaluation point extracted by the feature value extraction unit 120. It serves to estimate the process bias y that represents the quantity. In §3, the procedure for estimating the process bias y by the estimation calculation by the neural network is shown. Of course, the same procedure can be adopted in implementing the present invention. However, the bias estimation unit 130 used in the present invention is not limited to the one that estimates the process bias y by the method described in §3. In carrying out the present invention, a unit that estimates the process bias y by an arbitrary method may be adopted as the bias estimation unit 130.

  The pattern correction unit 140 plays the role of creating the corrected graphic pattern 15 by correcting the original graphic pattern 10 based on the estimated value y of the process bias output from the bias estimation unit 130. The correction processing by the pattern correction unit 140 is executed in consideration of the position of each evaluation point E set by the evaluation point setting unit 110 and the estimated value y of the process bias estimated for the evaluation point E. become. Therefore, specific correction processing according to the present invention will be described in detail in §7.

  In the end, the shape correction apparatus 100 according to the present invention is similar to the shape correction apparatus 100 according to the prior application invention shown in FIG. The basic functions of these components are the same as those of the device according to the prior application. However, a feature of the present invention is that the evaluation point setting unit 110 and the pattern correction unit 140 employ unique processing functions. Hereinafter, this point will be described in detail.

<<< §6. Details of evaluation point setting unit >>
Here, a detailed configuration and operation of the evaluation point setting unit 110 in the shape correction apparatus 100 according to the present invention will be described. FIG. 32 is a block diagram showing the configuration of the evaluation point setting unit 110 in the figure pattern shape correcting apparatus 100 (see FIG. 1) according to the basic embodiment of the present invention. The basic function of the evaluation point setting unit 110 is to set an evaluation point E at a predetermined position on the contour line indicating the boundary between the inside and the outside of each unit graphic constituting the original graphic pattern 10.

  In order to realize such a basic function, the evaluation point setting unit 110 shown in FIG. 32 includes a unit graphic input unit 111, a unit graphic dividing unit 112, a divided graphic vector defining unit 113, a unit graphic vector defining unit 114, and normal end points. A definition unit 115, an endpoint reconstruction unit 116, an evaluation score definition unit 117, and a supplemental endpoint definition unit 118 are provided. Each of these elements is actually configured by incorporating a predetermined program into a computer. Note that the endpoint reconstruction unit 116 is not an essential component for the present invention, and therefore, the endpoint reconstruction unit 116 may be omitted when implementing the present invention. However, in practice, it is possible to set the evaluation point more efficiently if the end point reconstruction unit 116 is provided. Therefore, a preferred embodiment provided with the end point reconstruction unit 116 will be described below.

  As shown in the figure, the evaluation point setting unit 110 shown here is given the original graphic pattern 10 and the maximum beam forming size Bmax as inputs. Here, as shown in FIG. 1, the original figure pattern 10 is a figure pattern that becomes the basis of the lithography process, and is usually constituted by an assembly of a large number of unit figures. On the other hand, the maximum beam forming size Bmax is the maximum beam forming size of the drawing apparatus used in the lithography process, and corresponds to the size of the maximum irradiation range by one shot of the light beam or electron beam irradiated by the drawing apparatus.

  On the other hand, from the evaluation point setting unit 110, information on the contour line segment O sandwiched between the first end point T1 and the second end point T2 is output together with information on the evaluation point E. Each of the end points T1 and T2 is a point defined on the contour line of each unit graphic constituting the original graphic pattern 10, and is a point for defining both ends of the contour line segment O. Moreover, in the case of the Example shown here, the evaluation point E is a point defined in the midpoint of the outline O. In FIG. 32, only one set of contour line segment O is drawn, but actually, a large number of contour line segments are set on the contour line of each unit graphic, and an evaluation point is set for each contour segment. Will be. Hereinafter, a specific procedure for obtaining such an output will be described.

<6.1 Division of unit graphic>
A unit graphic input unit 111 shown in FIG. 32 is a component for inputting individual unit graphics constituting the original graphic pattern 10. In the case of the embodiment described here, each unit graphic is constituted by a polygon, and FIG. 2A shows an example in which a rectangle is input as the original graphic pattern 10. An actual original figure pattern 10 used for manufacturing a semiconductor device or the like is constituted by a complex figure assembly in which a large number of fine unit figures having various shapes are collected. The unit figure is composed of polygons.

  The unit graphic dividing unit 112 shown in FIG. 32 executes a process of dividing each unit graphic input by the unit graphic input unit 111 with a linear dividing line to form a plurality of divided graphics. As described above, since each unit graphic is a polygon, each divided graphic obtained by dividing the unit graphic by a straight dividing line also becomes a polygon. FIG. 33 is a plan view showing an example of a specific division process performed by the unit graphic division unit 112. Here, for convenience of explanation, the case where the original figure pattern 10 composed of one unit figure is inputted is taken as an example, and the unit figure is also denoted by the reference numeral “10” similarly to the original figure pattern.

  FIG. 33 (a) is a plan view showing an example in which the unit figure dividing unit 112 performs division on the elongated strip-like unit figure 10 having the width of the dimension Wsplit. Specifically, the unit graphic input unit 111 inputs a long and narrow strip-shaped unit graphic 10 that extends along a predetermined longitudinal axis (X-axis in the illustrated example) and has linear upper and lower sides parallel to each other. Assuming that the unit figure dividing unit 112 divides the band-like unit figure 10 by a plurality of dividing lines (indicated by broken lines in the figure) arranged at predetermined intervals along the longitudinal axis (X axis). A plurality of divided figures 10a, 10b, 10c,..., 10j, 10k, 10l are formed in a one-dimensional manner along the longitudinal axis (X axis) (as will be described later, each divided figure). Are arranged in order from the left and right ends alternately toward the center).

  In the case of the illustrated example, dividing lines indicated by broken lines are arranged from the left end position and the right end position at intervals of the same dimension Wsplit as the width of the band-shaped unit graphic 10. Specifically, first, a dividing line is arranged at a position Wsplit from the left end position indicated by the alternate long and short dash line to define the divided figure 10a, and then the position of Wsplit from the right end position indicated by the alternate long and short dash line to the left A dividing line is arranged to define a divided figure 10b, and then a dividing line is arranged at a position Wsplit from the right dividing line to the right of the dividing figure 10a to define a divided figure 10c, and so on. The dividing lines are alternately arranged from the left and right ends toward the center. When the width Wrest of the remaining portion left in the central portion becomes Wrest ≦ 2 × Wsplit, dividing lines 10k and 10l are defined by arranging dividing lines for dividing the remaining portion into two. For this reason, the divided figures 10a to 10j are squares with Wsplit on one side, and the divided figures 10k and 10l at the center are rectangles with dimensions of the horizontal width.

  In a semiconductor device or the like, an elongated strip-shaped unit graphic 10 as shown in FIG. 33A is frequently used as a pattern constituting a wiring layer or the like. Of course, the arrangement interval of the dividing lines does not necessarily have to coincide with the vertical width Wsplit of the band-shaped unit graphic 10, and may be set to an arbitrary dimension. In this case, each divided figure becomes a rectangle. As in the example shown in FIG. 33 (a), division is performed alternately from the left and right ends at a predetermined interval Wsplit, and finally, divided figures 10k and 10l having a width of Wrest / 2 are arranged at the center. The reason for doing so is to avoid placing dividing lines in the immediate vicinity of the left and right ends of the unit graphic 10. As will be described later, since the evaluation point is set at the midpoint position of the side of each divided figure, when the horizontal width of the divided figures 10a and 10b at both ends is reduced, the evaluation point is closest to the vertex of the band-like unit figure 10. This is not preferable. If divided by the method shown in FIG. 33 (a), the horizontal width of the divided figures 10a and 10b at both ends can be set to Wsplit, and the position separated by a distance Wsplit / 2 from the vertex (not a distance from the vertex but a certain distance). An evaluation point can be set at (position).

  FIG. 33B is a plan view showing an example in which the unit graphic dividing unit 112 performs division on the rectangular unit graphic 10 having a wider vertical width. Thus, when the unit graphic input unit 111 inputs the unit graphic 10 that spreads on the XY plane, the unit graphic dividing unit 112 first sets a horizontal dividing line parallel to the X axis at a predetermined interval in the Y axis direction. A plurality of strip-like figures extending in the X-axis direction are formed by dividing the unit figure 10 by the plurality of horizontal dividing lines.

  In the example shown in FIG. 33 (b), horizontal dividing lines indicated by broken lines are arranged from the upper end position and the lower end position at intervals based on a predetermined dimension Wsplit. Specifically, first, a horizontal dividing line is arranged at the Wsplit position below the upper end position indicated by the alternate long and short dash line to define the divided graphic 10a, and then the lower end position indicated by the alternate long and short dashed line is moved upward to the Wsplit position. A horizontal dividing line is arranged to define a divided figure 10b, and then a horizontal dividing line is arranged at a position Wsplit downward from a horizontal dividing line below the divided figure 10a to define a divided figure 10c. In this way, horizontal dividing lines are alternately arranged from the upper and lower ends toward the center. Then, when the vertical width Wrest of the remaining portion left in the center portion becomes Wrest ≦ 2 × Wsplit, a horizontal dividing line for dividing the remaining portion into two is arranged to define the divided figures 10d and 10e. For this reason, elongated strip-shaped figures 10a, 10b, 10c having a vertical width Wsplit and elongated strip-shaped figures 10d, 10e having a vertical width with a fractional dimension are formed. As described above, it is also evaluated that the divided figures 10d and 10e having the width of Wrest / 2 are arranged at the center by alternately dividing from the upper and lower ends with the width of the predetermined interval Wsplit. This is to avoid the point being set immediately near the vertex of the unit graphic 10.

  Thus, when the original rectangular unit figure 10 is divided into a plurality of band-like figures 10a, 10b, 10c, 10d, and 10e, each of the plurality of band-like figures 10a, 10b, 10c, 10d, and 10e By dividing by a plurality of vertical dividing lines arranged at predetermined intervals along the X axis and parallel to the Y axis, a plurality of divided figures (not shown) arranged two-dimensionally can be formed. That is, since each of the strip-like figures 10a, 10b, 10c, 10d, and 10e is an elongated figure extending in the X-axis direction as shown in FIG. 33 (a), as in the example shown in FIG. 33 (a), If each is divided horizontally, a plurality of divided figures arranged two-dimensionally can be obtained. For example, if divided by vertical dividing lines arranged at intervals of Wsplit along the X axis, a divided figure group including a large number of squares each having Wsplit can be obtained.

  FIG. 33 (c) is a plan view showing an example in which the unit graphic dividing unit 112 performs division on the unit graphic 10 formed of an L-shaped band having a width Wsplit. Also in this example, if the same method as in FIG. 33 (b) is applied, first, horizontal division lines parallel to the X axis are arranged at intervals of Wsplit along the Y axis, and division by these horizontal division lines is performed. . FIG. 33 (c) shows a state in which such division is performed, and four sets of squares 10a, 10b, 10c, and 10d and a set of elongated strip-like figures 10e are formed. Therefore, if the elongated band-shaped figure 10e is further divided by a plurality of vertical dividing lines arranged at a predetermined interval (for example, Wsplit) along the X axis and parallel to the Y axis, the band shape is obtained as in FIG. The figure 10e can be divided into a plurality of divided figures (not shown). For example, if the band-like figure 10e is divided by vertical dividing lines arranged at intervals of Wsplit along the X axis, a divided figure group in which squares whose sides are Wsplit are arranged in the X axis direction can be obtained.

  In the above, an example of division for a unit graphic having a shape made of a rectangle or a combination of rectangles has been shown. However, the original graphic pattern may include a unit graphic having an oblique side. FIG. 34 is a plan view showing an example of a specific division process performed on the parallelogram type unit graphic 10 by the unit graphic dividing unit 112 shown in FIG.

  Assume that the unit graphic input unit 111 inputs a parallelogram unit graphic 10 as shown in FIG. The unit graphic 10 is a parallelogram having a height of Wsplit and is elongated in the horizontal direction. The above-described dividing method shown in FIG. 33A can also be applied to such a parallelogram unit graphic 10. That is, as shown in FIG. 34 (b), the unit graphic dividing unit 112 arranges dividing lines indicated by broken lines, for example, at intervals of the dimension Wsplit from the left end position indicated by the alternate long and short dash line. Can be divided into four. As a result, the unit figure 10 is divided into four divided figures 10a, 10b, 10c, and 10d as shown in FIG. 34 (c).

  Here, the divided figures 10b and 10c located in the middle are squares with one side being Wsplit, but the divided figures 10a and 10d located at both ends are trapezoids whose height is Wsplit. If the dividing method shown in FIG. 33 (b) is applied, the unit figure 10 having an arbitrary shape is divided by a plurality of horizontal dividing lines, thereby forming a plurality of strip-like figures extending in the X-axis direction. This can be further divided by a vertical dividing line to finally form a divided figure composed of a plurality of trapezoids. In practice, the unit graphic input unit 111 inputs the unit graphic 10 formed of a polygon, and the unit graphic dividing unit 112 divides the unit graphic 10 to form a divided graphic formed of a trapezoid. Is preferred.

  Here, the “trapezoid” is generally defined as “a set of quadrilaterals whose opposite sides are parallel (Kojien 6th edition)”. FIG. 35 (a) is a typical “trapezoid” meeting such a definition, and in this example, the height and the bottom base are set to the dimension Wsplit. FIG. 35B is a square with one side being Wsplit, and the upper base, the lower base, and the height are all set to the dimension Wsplit, and two sets of opposite sides are parallelograms. If the upper and lower bases are not of dimension Wsplit, they are rectangular. On the other hand, FIG. 35C shows a special trapezoid whose bottom is smaller than the dimension Wsplit and whose height is Wsplit but whose upper base is zero. Therefore, the term “trapezoid” in the present application widely includes not only a figure corresponding to a general trapezoid definition but also a figure corresponding to an expanded definition including a square, a rectangle, and a triangle.

  As described above, by applying the dividing method shown in FIG. 33 (b), the unit figure 10 made of an arbitrary polygon can be divided into divided figures made of “trapezoids” as shown in FIG. In addition, if the interval between the dividing lines is set to the predetermined interval Wsplit, as shown in FIGS. 35 (a), (b), and (c), the trapezoidal shape is such that the width is Wsplit or less and the width Wsplit or less. It can be divided into figures. In practicing the present invention, it is preferable to set a predetermined dimension Wsplit in the unit graphic dividing unit 112 to form a trapezoidal divided graphic having a vertical width Wsplit or less and a horizontal width Wsplit or less. The reason will be described below.

  The corrected graphic pattern created by the graphic pattern shape correcting apparatus 100 shown in FIG. 1 is used in an actual lithography process. Here, the actual lithography process includes an exposure step of irradiating the actual substrate S with a light beam or an electron beam using an optical drawing apparatus or an electron beam drawing apparatus. In this exposure step, the maximum irradiable area that can be exposed by one-shot beam irradiation on the actual substrate S is determined by the maximum beam forming size Bmax of each drawing apparatus.

  For example, in a drawing apparatus capable of irradiating a trapezoidal shaped beam, if the maximum beam forming size Bmax is 20 nm, the one-shot beam irradiation by the drawing apparatus irradiates in a square shape having a maximum side of 20 nm. Only regions can be formed. Therefore, for example, when it is desired to perform exposure on a square region having a side of 30 nm, it is necessary to irradiate a total of four shots while shifting the irradiation position in the vertical and horizontal directions. Considering these points, in order to perform the exposure process as efficiently as possible, individual unit figures constituting the correction figure pattern 15 used in the actual lithography process are also the values of the maximum beam forming size Bmax of the drawing apparatus. It is preferable to make the shape into consideration.

  Here, let us consider a case where shape correction is performed on the parallelogram unit graphic 10 as shown in FIG. According to the dividing method described above, the unit graphic 10 is divided into four sets of divided graphics 10a, 10b, 10c, and 10d as shown in FIG. At this time, if the unit graphic dividing unit 112 has a function of setting the maximum beam forming size Bmax of the drawing apparatus used in the lithography process, the arrangement interval Wsplit of the dividing lines used for dividing the unit graphic is set to the maximum beam forming. The division process set to the size Bmax or less can be performed.

  If the dividing method described above is employed, as shown in FIG. 35, each divided figure obtained by the dividing process becomes a trapezoid having a vertical width Wsplit or less and a horizontal width Wsplit or less. Therefore, if the unit figure dividing unit 112 sets the arrangement interval Wsplit of the dividing lines to be equal to or less than the maximum beam forming size Bmax, each of the divided figures obtained by the dividing process is less than the vertical width Bmax and less than the horizontal width Bmax. It becomes a trapezoid. This is advantageous in improving the efficiency of the exposure process (reducing the total number of shots) when an actual lithography process is performed using the corrected figure pattern 15 finally obtained.

  As will be described later, some of the sides of the individual divided graphics obtained by the division processing by the unit graphic dividing unit 112 are adopted as contour segments to be moved when the pattern correction unit 140 creates the corrected graphic pattern, The contour of the corrected graphic pattern is formed by the contour line segment after the movement.

  FIG. 36 is a plan view showing an example of the corrected unit graphic 15 obtained by performing shape correction on each of the divided graphics 10a, 10b, 10c, and 10d constituting the unit graphic 10 shown in FIG. 34 (c). is there. As shown in the figure, the divided figures 10a, 10b, 10c, and 10d are corrected to the divided figures 15a, 15b, 15c, and 15d, respectively. After the correction, the divided figures 15a, 15b, 15c, and 15d are corrected. A unit graphic 15 is configured. Specifically, in the case of this example, by moving the upper and lower sides of the divided figures 10b and 10d shown in FIG. 34 (c) as outline segments, the divided figures 15b and 15d having a slightly reduced vertical width are obtained. ing.

  In the case of this example, the shape correcting apparatus 100 shown in FIG. 1 corrects the unit graphic 10 shown in FIG. 34 (c) included in the original graphic pattern 10 to thereby correct the unit graphic after correction shown in FIG. Thus, a shape correction process for creating a corrected graphic pattern 15 including 15 is performed, and this corrected graphic pattern 15 is used in an actual lithography process. Here, let us consider what exposure process is performed based on the corrected unit graphic 15 shown in FIG. 36 in this actual lithography process.

  FIG. 37 is a plan view showing an example of an exposure process based on the corrected unit graphic 15 shown in FIG. Here, a thick square represents an irradiation area with one side having the maximum beam forming size Bmax. In other words, an exposure apparatus used in an actual lithography process has a function of irradiating a light beam or an electron beam onto a region within the thick square by one shot irradiation. Of course, the actual irradiation area is only the portion corresponding to the inner area of the unit graphic 15.

  Therefore, in the example shown in FIG. 37, the exposure process based on the unit graphic 15 is completed by a total of four shots. That is, in the first shot, irradiation exposure is performed on the hatched divided figure 15a in the thick square in FIG. 37 (a), and in the second shot, in FIG. 37 (b). Irradiation exposure is performed on the inner area of the hatched divided figure 15b in the thick square, and in the third shot, the hatched divided figure 15c in the thick square in FIG. Irradiation exposure is performed on the inner area, and in the fourth shot, irradiation exposure is performed on the inner area of the hatched divided figure 15d in the thick square in FIG.

  In this way, the exposure process based on the corrected unit graphic 15 has been completed for a total of four shots. The unit graphic dividing unit 112 is caused to form a trapezoidal divided graphic having a vertical width Bmax or less and a horizontal width Bmax or less. This is because the unit graphic 15 after correction is created by performing correction for moving the sides of the divided graphic as individual contour lines in the pattern correction unit 140.

  Of course, even if such division processing or correction processing is adopted, the effect of reducing the number of shots during the exposure process is not always obtained. For example, in the example of FIG. 36, the divided figures 15b and 15d are figures obtained by slightly reducing the vertical width of the divided figures 10b and 10d. 37 (b) and 37 (d) cannot be performed in one shot. However, if the above-described division processing and correction processing are employed, it is possible to obtain a corrected graphic pattern 15 that can improve the efficiency of the exposure process when viewed as a whole graphic pattern including a large number of unit graphics.

  In the block diagram of the evaluation point setting unit 110 shown in FIG. 32, the maximum beam forming size Bmax is given to the unit graphic dividing unit 112. This is a drawing apparatus used by the unit graphic dividing unit 112 in the actual lithography process. The maximum beam forming size Bmax is set, and the arrangement interval of the dividing lines used for dividing the unit graphic is set to be equal to or less than the maximum beam forming size Bmax. Of course, such a function is not an indispensable function for carrying out the present invention. However, in practice, if such a function is provided, it is preferable for improving the efficiency of the exposure process as described above. .

<6.2 Definition of vector and normal end point>
Next, processing functions of the divided graphic vector defining unit 113, the unit graphic vector defining unit 114, and the normal endpoint defining unit 115 in the evaluation point setting unit 110 shown in FIG. 32 will be described. As described in §6.1, the unit graphic 10 is divided into a plurality of divided graphics by the division processing by the unit graphic dividing unit 112. Then, some of the sides of the divided figure are employed as outline segments to be moved during correction.

  For example, in the example shown in FIG. 34 (c), the unit graphic 10 is divided into four sets of divided graphics 10a, 10b, 10c, and 10d. Since each of these divided figures is a trapezoid having four sides, the total number of sides of the divided figure is 16. However, the total number of sides constituting the contour line of the original unit graphic 10 is ten. Therefore, it is necessary to perform processing for extracting 10 sets of sides constituting the contour line from a total of 16 sets of sides. The role of the divided graphic vector defining unit 113 and the unit graphic vector defining unit 114 is to extract a specific side constituting the outline of the unit graphic 10 in this way, and the role of the normal end point defining unit 115 is thus It is to define normal end points at both ends of each extracted side.

  FIG. 38 shows a divided figure vector definition unit 113, a unit figure vector definition unit 114, and a normal end point definition unit 115 shown in FIG. 32 for the quadrilateral unit graphic 10 after the four divisions shown in FIG. FIG. Hereinafter, the processing performed by the definition units 113, 114, and 115 will be described in detail, taking the parallelogram unit graphic 10 as an example.

  First, the divided graphic vector defining unit 113 makes a round around a predetermined forward direction along the outline of the polygon that forms the divided graphic for each divided graphic formed by the division processing by the unit graphic dividing unit 112. Then, a process for defining divided graphic vectors on each side of the polygon is performed. For example, in the example shown in FIG. 34 (c), four sets of divided figures 10a, 10b, 10c, and 10d are formed. Therefore, for each divided figure, for example, if the clockwise direction is defined as the forward direction, as shown in FIG. 38 (a), a clockwise forward arrow A1 in each divided figure 10a, 10b, 10c, 10d. ~ A4 can be defined, and a divided figure vector can be defined on the side of each trapezoid so that the outline of the trapezoid constituting each divided figure goes around in the directions indicated by the forward arrows A1 to A4. it can.

  FIG. 38 (b) is a plan view showing the divided vectors defined in this way. For example, the trapezoid constituting the divided figure 10a has four vertices ξ1 to ξ4 as shown in FIG. 38 (a), and the first side ξ1-ξ2 and the second side ξ2-ξ3 , A third side ξ3-ξ4 and a fourth side ξ4-ξ1. Therefore, the divided graphic vector defining unit 113 performs a process of defining four sets of divided graphic vectors Va1, Va2, Va3, V4a for the divided graphic 10a as shown in FIG.

  In other words, the divided graphic vector Va1 is a vector along the first side ξ1-ξ2 with the vertex ξ1 as the start point and the vertex ξ2 as the end point. The divided graphic vector Va2 has the vertex ξ2 as the start point and the vertex ξ3 as the start point. The divided figure vector Va3 is a vector along the third side ξ3-ξ4 with the vertex ξ3 as the start point and the vertex ξ4 as the end point as the end point. The vector Va4 is a vector along the fourth side ξ4-ξ1 with the vertex ξ4 as the start point and the vertex ξ1 as the end point.

  Moreover, these four sets of vectors Va1, Va2, Va3, and Va4 are defined in a direction that goes around the trapezoidal outline forming the divided figure 10a along the forward arrow A1, and the end point of one vector is The relationship is the starting point of the next vector. Therefore, an assembly of the four sets of vectors Va1, Va2, Va3, and Va4 constitutes a vector group that goes around the trapezoidal outline forming the divided figure 10a clockwise.

  Of course, the divided figure vector defining unit 113 may define the counterclockwise direction as the forward direction and perform the same processing. In that case, an assembly of four sets of vectors Va1, Va2, Va3, and Va4 constitutes a vector group that goes around the trapezoidal outline forming the divided figure 10a counterclockwise. As described above, whether the forward direction is clockwise or counterclockwise can be arbitrarily set, but one of the settings needs to be commonly applied to all the divided figures. For example, in the example shown in FIG. 38 (a), the forward arrows A1 to A4 are all clockwise, but they may be all counterclockwise. However, the setting cannot be changed for each divided figure such that the forward arrow A1 is clockwise and the forward arrow A2 is counterclockwise (to eliminate duplicate vector pairs as will be described later).

  FIG. 38 shows an example in which the divided figure is a quadrangle, but in general terms, the divided figure vector definition unit 113 extends along the contour line to each vertex of the divided figure formed of a K-gon. Numbers are assigned to the first vertex to the Kth vertex in the order of clockwise or counterclockwise, and the kth vertex is the starting point, and the (k + 1) th vertex (provided that k = K, the first vertex) The process of defining the divided figure vector for the divided figure is performed by repeatedly performing the process of defining the k-th divided figure vector with) as the end point from k = 1 to K.

  Thus, the divided figure vector defining unit 113 defines a total of 16 sets of divided figure vectors Va1 to Vd4 on each of the four sides of each divided figure 10a, 10b, 10c, and 10d, as shown in FIG. Will be. In FIG. 38 (b), for convenience of illustration, two vectors defined on the same side are depicted with a slight shift from the position of the side, but actually these two vectors are drawn. Are vectors defined redundantly on the same side. For example, the vectors Va2 and Vb4 shown in FIG. 38B are both vectors defined on the sides ξ2-ξ3.

  The unit graphic vector defining unit 114 searches for overlapping vector pairs that are arranged on overlapping sides of a pair of adjacent polygons adjacent to each other from the set of divided graphic vectors defined in this way, and whose directions are opposite to each other. The overlapping section portion of the searched overlapping vector pair is removed, and processing for defining a plurality of unit graphic vectors arranged along the contour line of the unit graphic 10 is performed with the remaining vectors.

  For example, in the example shown in FIG. 38 (b), since a total of 16 sets of divided graphic vectors Va1 to Vd4 are defined, an overlapping vector pair is searched from these 16 sets of divided graphic vectors Va1 to Vd4. Then, the process of removing the overlapping section portion of the searched overlapping vector pair is performed. Here, the overlapping vector pair is, as described above, “a pair of vectors that are arranged on overlapping sides of a pair of adjacent polygons adjacent to each other and whose directions are opposite to each other”. In the example shown in b), the vectors Va2 and Vb4 are searched as the first overlapping vector pair, the vectors Vb2 and Vc4 are searched as the second overlapping vector pair, and the vectors Vc2 and Vd4 are searched as the third overlapping vector pair. Explored.

  Since each of these overlapping vector pairs overlaps in all the sections, a process of removing them as they are is performed. FIG. 38 (c) is a plan view showing a state after such removal processing is performed, and the overlapping vector pairs (Va2, Vb4), (Vb2, Vc4), (Vc2) shown in FIG. 38 (b). , Vd4) are all removed. Here, the 16 sets of vectors Va1 to Vd4 shown in FIG. 38 (b) are referred to as “divided graphic vectors”, so the 10 sets of vectors shown in FIG. 38 (c) are the 16 sets shown in FIG. 38 (b). In order to distinguish from a set of vectors, they will be referred to as “unit graphic vectors”, and the reference numerals will be reassigned to V1 to V10. Therefore, the unit graphic vectors V1 to V10 shown in FIG. 38 (c) are actually the same as the divided graphic vectors Va1, Vb1,..., Va3, Va4 shown in FIG.

  The unit graphic vectors V1 to V10 obtained in this way are vectors arranged on the contour line of the unit graphic 10, and are defined in a direction that goes around the contour line in the forward direction (clockwise direction in the illustrated example). And the end point of one vector is the start point of the next vector. Therefore, an aggregate of ten unit graphic vectors V1 to V10 constitutes a vector group that goes around the outline of the unit graphic 10 clockwise.

  The normal end point definition unit 115 performs a process of defining normal end points at the start point positions (the same applies to the end point positions) of the individual unit graphic vectors thus defined. FIG. 38 (d) is a plan view showing a state in which normal end points A to J (indicated by x in the figure) are defined at the start positions of the 10 sets of unit graphic vectors V1 to V10 shown in FIG. 38 (c). is there. Each of the normal end points A to J defined in this way is a vertex located on the outline of the unit graphic 10 among the vertices of the divided graphics 10a, 10b, 10c, and 10d shown in FIG. . In other words, each of the normal end points A to J is an end point that defines both ends of the side located on the outline of the unit graphic 10 among the sides of each divided graphic. Note that the endpoint defined in this way is referred to as a “normal endpoint” for the purpose of distinguishing it from a “replenishment endpoint” additionally defined by a supplemental endpoint definition unit 118 described later.

  39, the L-shaped unit graphic 10 is processed by the unit graphic dividing unit 112, the divided graphic vector defining unit 113, the unit graphic vector defining unit 114, and the normal end point defining unit 115 shown in FIG. It is a top view which shows a broken example. When the L-shaped unit graphic 10 as shown in FIG. 39 (a) is input by the unit graphic input unit 111, the unit graphic dividing unit 112 performs a dividing process as shown in FIG. 39 (b). Three sets of divided figures 10a, 10b, and 10c are formed.

  Then, for these divided figures 10a, 10b, and 10c, forward arrows A1 to A3 are set in the clockwise direction as shown in the figure, and the divided figure vector definition unit 113 calculates the total as shown in FIG. 39 (c). Twelve sets of divided graphic vectors Va1 to Vc4 are defined. Subsequently, the unit graphic vector definition unit 114 searches for overlapping vector pairs, and performs a process of removing the overlapping section portion of the searched overlapping vector pairs. In the case of the example shown in FIG. 38 (b) described above, since the entire section of the searched overlapping vector pair is the overlapping section portion, the overlapping vector pair is completely removed, but FIG. 39 (c) In the example shown in FIG. 2, there are overlapping vector pairs that are partially duplicated.

  Specifically, in the example shown in FIG. 39 (c), the vectors Va3 and Vb1 are searched as the first overlapping vector pair, and the vectors Vb2 and Vc4 are searched as the second overlapping vector pair. Here, since the second overlapping vector pair Vb2 and Vc4 are all overlapping section parts, a process for removing them completely is performed. However, the first overlapping vector pair Va3 and Vb1 is shown in FIG. As shown in the upper part of (d), since only a part is an overlapping section part (part indicated by a bold line), processing for removing only the overlapping section part is performed. As a result, as shown in the lower part of FIG. 39 (d), only the non-overlapping section part remains as the unit graphic vector V3.

  FIG. 39 (e) is a plan view showing a state after the above-described removal processing is performed by the unit graphic vector definition unit 114, and shows a state in which nine sets of unit graphic vectors V1 to V9 remain. Has been. The unit graphic vectors V1 to V9 thus obtained are vectors arranged on the contour line of the L-shaped unit graphic 10 shown in FIG. 39 (a), and are forward (in the illustrated example, the clockwise direction). ) In a direction that goes around the contour line, and the end point of one vector is the start point of the next vector. Therefore, an aggregate of these nine sets of unit graphic vectors V1 to V9 constitutes a vector group that goes around the outline of the unit graphic 10 clockwise.

  The normal end point definition unit 115 performs a process of defining normal end points at the start point positions of the individual unit graphic vectors thus defined. FIG. 39 (f) is a plan view showing a state in which normal end points A to I (indicated by x in the figure) are defined at the start positions of the nine unit graphic vectors V1 to V9 shown in FIG. 39 (e). is there.

  Next, an example of processing for a so-called perforated unit graphic in which a region outside the graphic exists inside will be described. In FIG. 40, processing by the unit graphic dividing unit 112, the divided graphic vector defining unit 113, the unit graphic vector defining unit 114, and the normal endpoint defining unit 115 shown in FIG. It is a top view which shows the example. In this example, the unit graphic input unit 111 inputs a square-shaped unit graphic 10 as shown in FIG. In the case of the illustrated square-shaped unit graphic 10, the graphic main body 10 </ b> X is a hatched area, but a rectangular hole 10 </ b> Y exists inside. That is, such a perforated unit graphic 10 has an outer contour line Oout and an inner contour line Oin. Even when such a perforated unit graphic 10 is input, basically, the same processing as described above may be executed.

  First, the unit graphic dividing unit 112 performs a dividing process as shown in FIG. 40B to form eight sets of divided figures 10a to 10h. For these divided figures 10a to 10h, as shown in FIG. 40 (c), forward arrows A1 to A8 are set in the clockwise direction, and the divided figure vector defining unit 113 shows them in FIG. 40 (d). Thus, a total of 32 sets of divided graphic vectors Va1 to Vh4 are defined. Subsequently, the unit graphic vector definition unit 114 searches for overlapping vector pairs, and performs a process of removing the overlapping section portion of the searched overlapping vector pairs.

  FIG. 40 (e) is a plan view showing a state after the above-described removal processing is performed by the unit graphic vector definition unit 114, and shows a state in which 20 sets of unit graphic vectors V1 to V20 remain. Yes. It should be noted that the unit graphic vectors V1 to V12 are vectors arranged on the outer outline Oout of the square-shaped unit graphic 10 shown in FIG. In the case of the example shown in FIG. 40, the unit graphic vectors V13 to V20 are defined in the direction that goes around the contour line in the clockwise direction). It is a vector arranged on the inner contour line Oin, and is defined in a direction that makes a round of the contour line in the reverse direction (in the example shown, the counterclockwise direction).

  In the present application, for such a unit graphic of perforation, a figure constituting the outer contour line Oout is called a “normal figure”, and a figure constituting the inner outline Oin is called an “anti-figure”. In the case of the illustrated example, the unit graphic vectors V1 to V12 are a vector group that goes around the normal graphic in the forward direction, and the unit graphic vectors V13 to V20 are a vector group that goes around the anti-graphic in the reverse direction. Therefore, in the case of a perforated unit graphic, when the vector group makes a round in the forward direction along the contour line, it can be determined that the contour line is a regular graphic that constitutes the outer contour line Oout of the unit graphic. When making a round in the opposite direction along the contour line, it can be determined that the contour line is an anti-graphic that constitutes the inner contour line Oin of the unit graphic. Such a difference between a regular figure and an opposite figure can be used for the endpoint reconstruction process described in §6.3.

  The normal end point definition unit 115 performs a process of defining normal end points at the start point positions of the individual unit graphic vectors thus defined. FIG. 40 (f) is a plan view showing a state in which normal end points A to T (indicated by x in the figure) are defined at the start positions of the 20 sets of unit graphic vectors V1 to V20 shown in FIG. 40 (e). is there. As illustrated, normal end points are defined for both the outer contour line Oout and the inner contour line Oin of the unit graphic 10 with a hole.

<6.3 Reconstruction of endpoints>
Next, the function of the end point reconstruction unit 116 in the evaluation point setting unit 110 shown in FIG. 32 will be described. The end point reconstruction unit 116 is a component that performs reconstruction for correcting the number or position of the normal end points defined on the outline of the unit graphic by the normal end point definition unit 115. As described in §6.2, the normal end point definition unit 115 defines the normal end points based on the vertex positions of the individual divided figures, so that the division processing by the unit figure division unit 112 is appropriately performed. If so, the number and location of defined normal endpoints should be appropriate. In practice, however, more efficient evaluation point setting is possible by adjusting the number and position of the normal end points defined in this way.

  Therefore, in the case of the embodiment described here, the end point restructuring unit 116 performs reconstruction on the normal end point defined by the normal end point defining unit 115. Of course, such a reconstruction process is not an essential process for the present invention. Therefore, the end point reconstruction unit 116 may be omitted when implementing the present invention. However, in practice, it is possible to set the evaluation point more efficiently if the end point reconstruction unit 116 is provided. The end point reconstruction unit 116 reconstructs the normal end points defined by the normal end point definition unit 115 by reducing the number or correcting the positions. Hereinafter, several methods for concrete reconstruction will be described.

(1) Reconstruction by three-point end point removal processing FIG. 41 is a schematic diagram showing a procedure when a three-point end point removal processing is adopted as the end point reconstruction processing by the end point reconstruction unit 116 shown in FIG. (FIG. 41 (a)) and a flow chart (FIG. 41 (b)). In the end point removal processing, a part or all of the normal end points (actual end points that do not actually constitute the vertices of the polygons constituting the unit figure) are defined for some or all of the unit figures defined by the normal end point definition unit 115. It can be said that the reconstruction is performed by reducing the number of end points.

  As described in §6.2, the normal end points defined by the normal end point definition unit 115 are defined on the contour line of the unit graphic 10 in a predetermined order. For example, in the example shown in FIG. 38 (d), the normal end points are defined in the order of A to J on the outline of the unit graphic 10, and in the example shown in FIG. 39 (f), the contour of the unit graphic 10 is defined. In the example shown in FIG. 40 (f), A to L are defined on the line in the order of A to I, and A to L on the outer contour line Oout of the unit graphic 10 and M to T on the inner contour line Oin. The end points are usually defined in this order. The three-point end point removal processing described here determines whether or not to remove a normal end point to be determined with reference to the distance between the previous normal end point and the next normal end point. The method is adopted.

  Now, a total of N normal end points T (1) to T (N) are defined on one contour line of the unit graphic, and the normal end point is set with the n-th normal end point T (n) as a determination target. Consider a case where it is determined whether or not T (n) should be removed. In this case, as shown in FIG. 41 (a), the distance between the nth normal end point T (n) to be removed and the previous (n-1) th normal end point T (n-1). L1 and a distance L2 between the nth normal end point T (n) to be removed and the next (n + 1) th normal end point T (n + 1) are obtained.

  However, there are some points to be noted about the distance L1. For example, in FIG. 41 (a), when the normal end point T (n-1) has already been removed, the distance between the previous normal end point T (n-2) and T (n). Is L1. When the normal end point T (n-2) is also a removal target, the distance between the previous normal end point T (n-3) and T (n) is further set to L1. After all, the distance L1 here is, in general terms, the n-th normal end point T (n) to be removed and the normal end point T (n−m) that is not immediately to be removed. (However, m is a natural number, and when nm <1, it is defined as a distance to T (n−m + N)). Thus, after the distances L1 and L2 are defined, the n-th normal end point T (n) is determined as a removal target when both of the following two determination conditions are satisfied.

  The first determination condition is a condition that “at least one of L1 and L2 is equal to or less than a predetermined reference value Wmerge”. Here, Wmerge is a predetermined reference value set in advance, and in general, it is preferable to set a value smaller than Wsplit used by the unit graphic dividing unit 112 for the dividing process. The reference value Wmerge removes the normal end point T (n) when the normal end point T (n) to be removed is close to the adjacent normal end point T (n−m) or T (n + 1) to some extent. Thus, it is a value that defines a critical approach distance when it is determined that the normal end point T (n−m) or T (n + 1) should be fused.

  If the reference value Wmerge is set large, the possibility that it is determined that the normal end point T (n) should be removed increases, and if the reference value Wmerge is set small, the possibility decreases. Of course, if the possibility that it should be removed increases, the calculation burden will be reduced accordingly, but the simulation accuracy will decrease, and if the possibility decreases, the simulation accuracy will increase, but the calculation load will increase. Become. Therefore, in practice, the reference value Wmerge may be set to an appropriate value in consideration of the balance between maintaining the accuracy of the simulation and reducing the calculation burden.

  The second determination condition is a condition that “the three normal end points T (n−1), T (n), and T (n + 1) are on a straight line”. FIG. 41 (a) shows a state where such a condition is satisfied. For example, when the normal end point T (n) is the vertex of the unit graphic, the normal end point T (n−1) is Since T (n + 1) is an end point on a separate side, the condition is not satisfied. Therefore, the second determination condition is a condition that “the three points are on the same side”. In other words, if the normal end point that does not constitute the vertex of the polygon that forms the unit graphic is called an intermediate normal end point, the second determination condition is “the normal end point T (n) that is the removal determination target is“ The condition is “intermediate normal end point”.

  FIG. 41 (b) is a flowchart showing a procedure of endpoint reconstruction based on such a three-point endpoint removal process. First, in step SS1, a parameter n indicating the number of the normal end point to be removed is set to n = 1, and in step SS2, it is determined whether L1 ≦ Wmerge. If a negative determination is made here, it is determined in step SS3 whether L2 ≦ Wmerge. If a positive determination is made in either step SS2 or SS3, then in step SS3, whether or not the three points T (n-1), T (n), and T (n + 1) are on a straight line. Is determined and a positive determination is made, in step SS5, a process for removing the normal end point T (n) is performed. On the other hand, if a negative determination is made in step SS3 or SS4, in step SS6, a process is performed in which the normal end point T (n) is not a removal target.

  Such a process is repeatedly executed through steps SS7 and SS8 until n = N is reached while increasing the parameter n by 1. When n = N is reached, the process proceeds from step SS7 to SS9, and the normal end points to be removed are collectively removed.

  In the above processing procedure, when n = 1, the removal determination target is the first normal end point T (1). Therefore, the normal end point T (n−1) in each determination condition is Nth. Needs to be read as the normal end point T (N). Similarly, when n = N, the removal determination target is the Nth normal end point T (N). Therefore, the normal end point T (n + 1) in each determination condition is the first normal end point T (1 ).

  Eventually, if the reconstruction using the three-point end point removal processing described here is adopted as a general theory, the end point reconstruction unit 116 is defined as a total N defined for one outline of one unit graphic. The normal end points are referred to as the first normal end point T (1) to the Nth normal end point T (N) in order along the contour line, and attention is paid to the nth normal end point T (n). The (n-1) th normal end point T (n-1) (where n = 1, the Nth normal end point T (N): the same applies hereinafter) and the nth normal end point T (n) The distance between them is L1, and the nth normal end point T (n) and the (n + 1) th normal end point T (n + 1) (however, when n = N, the first normal end point T (1): the same applies hereinafter). And L2 is at least one of L1 and L2 is equal to or less than a predetermined reference value Wmerge, and the normal end point T ( -1), T (n), and T (n + 1), when the three points are on a straight line, the determination process for removing the nth normal end point T (n) is repeatedly executed from n = 1 to N. Then, the end point removal process for removing the normal end point that is the removal target is performed.

  42 applies the three-point end point removal processing shown in FIG. 41 to the normal end points A to J on the parallelogram unit graphic 10 shown in FIG. It is a top view which shows the example done. Here, FIG. 42A shows a state in which the normal end points D and I (indicated by white triangles) are determined to be removed before reconstruction, and FIG. The state after the reconstruction in which the normal end points D and I determined to be removed are removed is shown.

  In the example shown in FIG. 42, the reason why the normal end point D is determined to be removed is that the first determination condition “Lde ≦ Wmerge” is satisfied for the distance Lde between the end points D and E, and “three end points This is because the second determination condition that “C, D, and E are on a straight line” is satisfied. Similarly, the reason that the normal end point I is determined to be removed is that the first determination condition “Lij ≦ Wmerge” is satisfied for the distance Lij between the end points I and J, and “three end points H, I, This is because the second determination condition that “J is on a straight line” is satisfied. Eventually, by the end point reconstruction process, the end point D is merged with the end point E, the end point I is merged with the end point J, and the ten normal end points are reduced to eight.

  By removing the end points D and I, the accuracy of the simulation performed later will be slightly reduced. However, since the distances Lde and Lij are both equal to or less than the reference value Wmerge, there is no practical problem. On the other hand, by removing the end points D and I, the calculation load of the simulation is reduced.

  FIG. 43 shows the reconstruction of the end points by applying the three-point end point removal processing shown in FIG. 41 to the normal end points A to I on the L-shaped unit graphic 10 shown in FIG. 39 (f). It is a top view which shows the example. Here, FIG. 43 (a) shows a state where the normal end point D (indicated by a white triangle) is determined to be removed before reconstruction, and FIG. 43 (b) shows this state. The state after the reconstruction in which the normal end point D determined as the removal target is removed is shown.

  In the example shown in FIG. 43, the reason why the normal end point D is determined to be removed is that the first determination condition “Lcd ≦ Wmerge” is satisfied for the distance Lcd between the end points C and D, and “three end points” This is because the second determination condition that “C, D, and E are on a straight line” is satisfied. Eventually, by the end point reconstruction process, the end point D is merged with the end point C, and the nine normal end points are reduced to eight. Again, this reconstruction will slightly reduce the accuracy of the simulation performed later. However, since the distance Lcd is equal to or less than the reference value Wmerge, there is no practical problem. On the other hand, by removing the end point D, the calculation burden of simulation is reduced.

(2) Reconstruction by 4-point type endpoint removal processing FIG. 44 is a schematic diagram showing a procedure in a case where 4-point type endpoint removal processing is adopted as the endpoint reconstruction processing by the endpoint reconstruction unit 116 shown in FIG. (FIG. 44 (a)) and flowchart (FIG. 44 (b)). The end point removal processing described here removes some or all of the intermediate normal end points for some or all of the unit graphics defined by the normal end point definition unit 115, as in the above-described three-point end point removal processing. This is a process for performing reconstruction by reducing the number of normal end points. However, the four-point end point removal processing described here uses two adjacent normal endpoints as a removal determination target, and the two normal end points that are the determination target are the previous normal end points. And a distance from the next normal end point, and a method of determining which to remove as well as judging whether to remove is adopted.

  Now, a total of N normal end points T (1) to T (N) are defined on one contour line of the unit graphic, of which the nth normal end point T (n) and the (n + 1) th normal end point are defined. Consider a case where two points of T (n + 1) are set as determination targets, and it is determined whether or not the determination target is to be removed and which of the two points is to be removed. In this case, as shown in FIG. 44 (a), a distance L2 between two points of the nth normal end point T (n) and the (n + 1) th normal end point T (n + 1) to be removed is obtained. When both of these determination conditions are satisfied, one of them is determined as a removal target.

  The first determination condition is a condition that “L2 is a predetermined reference value Wmerge or less”. Here, Wmerge is a predetermined reference value set in advance as in the above-described three-point end point removal processing, and is generally smaller than Wsplit used by the unit graphic division unit 112 for the division processing. It is preferable to set a value. The reference value Wmerge is determined that, when two sets of normal end points T (n) and T (n + 1) to be removed are close to each other, by removing one of them, both should be merged It is a value that determines the critical approach distance when doing. Therefore, similarly to the three-point end point removal processing, the reference value Wmerge may be set to an appropriate value in consideration of the balance between maintaining the accuracy of the simulation and reducing the calculation burden.

  The second determination condition is that the (n-1) th normal end point T (n-1) immediately before the nth normal end point T (n) and the (n + 1) th normal end point T (n + 1). Considering the next (n + 2) th normal end point T (n + 2), “the four normal end points T (n−1), T (n), T (n + 1), T (n + 2) are straight It is on the line. FIG. 44 (a) shows a state where such a condition is satisfied. For example, when the normal end point T (n) is the vertex of the unit graphic, the normal end point T (n−1) is Since T (n + 1) is an end point on a separate side, the condition is not satisfied. Therefore, the second determination condition is a condition that “the four points are on the same side”. In other words, if the normal end point that does not constitute the vertex of the polygon that forms the unit graphic is called an intermediate normal end point, the second determination condition is “the normal end point T (n) that is a removal determination target and T (n + 1) is an intermediate normal end point ”.

  When both of the above two determination conditions are satisfied, one of the normal end points T (n) and T (n + 1) is determined as a removal target. Here, which is to be removed is determined by setting the distance between the normal end points T (n) and T (n−1) to L1, and the distance between the normal end points T (n + 1) and T (n + 2) to L3. Sometimes, it may be determined based on the magnitude relationship between the distances L1 and L3. That is, when L1 <L3, the normal end point T (n) is the removal target, and when L1> L3, the normal end point T (n + 1) is the removal target. By doing so, the distance between the two end points (L1 + L2 in the former case and L2 + L3 in the latter case) sandwiching the end point to be removed can be made as small as possible. Can be small. When L1 = L3, either normal end point T (n) or T (n + 1) may be the removal target. If the four points are not on a straight line but the three points are on a straight line, a method according to the above-described three-point end point removal processing may be executed.

  Here, there are some points to be noted about the distance L1. For example, in FIG. 44 (a), when the normal end point T (n-1) has already been removed, the distance between the previous normal end point T (n-2) and T (n). Is L1. When the normal end point T (n-2) is also a removal target, the distance between the previous normal end point T (n-3) and T (n) is further set to L1. After all, the distance L1 here is, in general terms, the n-th normal end point T (n) to be removed and the normal end point T (n−m) that is not immediately to be removed. (However, m is a natural number, and when nm <1, it is defined as a distance to T (n−m + N)).

  FIG. 44 (b) is a flowchart showing a procedure of endpoint reconstruction based on such a four-point endpoint removal process. First, in step SS11, a parameter n indicating the number of the normal end point to be removed is set to n = 1, and in step SS12, it is determined whether L2 ≦ Wmerge. If a positive determination is made here, whether or not the four points T (n−1), T (n), T (n + 1), and T (n + 2) are on a straight line in step SS13. Determined. Here, if a positive determination is made, one of T (n) and T (n + 1) is to be removed, but in order to determine which should be removed, in step SS14, A condition determination that satisfies L1 ≦ L3 is performed (instead, a condition determination that satisfies L1 <L3 may be performed). If an affirmative determination is made here, the end point T (n) is a removal target in step SS15, and if a negative determination is made, the end point T (n + 1) is a removal target in step SS16. .

  On the other hand, if a negative determination is made in step SS13, it is determined in step SS17 whether or not three points T (n-1), T (n), and T (n + 1) are on a straight line. If an affirmative determination is made here, the process proceeds to step SS15, where the end point T (n) is to be removed, and if a negative determination is made, the process proceeds to step SS18, where T (n), T (n + 1), It is determined whether or not three points T (n + 2) are on a straight line. If a positive determination is made in step SS18, the process proceeds to step SS16, and the end point T (n + 1) is set as a removal target. This is the same processing as the above-described three-point end point removal processing. If a negative determination is made in step SS12 or a negative determination is made in step SS18, the process proceeds to step SS19, where T (n) and T (n + 1) are not targeted for removal. Is done.

  Such processing is repeatedly executed through steps SS20 and SS21 while increasing parameter n by 1 until n ≧ N is satisfied. If the normal end point T (n) has already been removed, the processing procedure for the parameter n can be skipped. When n ≧ N is satisfied, the process proceeds from step SS20 to SS22, and the normal end points to be removed are collectively removed.

  In the above processing procedure, when n = 1, the removal determination target on the left side in FIG. 44 is the first normal end point T (1). Therefore, the normal end point T (n−1) in each determination condition described above. ) Needs to be read as the Nth normal end point T (N). Similarly, when n = N−1, the left removal determination target is the (N−1) th normal end point T (N−1), and the right removal determination target is the Nth normal end point T (N). Therefore, the normal end point T (n + 2) in the above determination conditions needs to be read as the first normal end point T (1). In addition, when n = N, the removal determination target on the left side is the Nth normal end point T (N). Therefore, the normal end point T (n + 1) in each determination condition is the first normal end point T ( It is necessary to replace the normal end point T (n + 2) with the second normal end point T (2).

Eventually, if the reconstruction using the four-point end point removal processing described here is adopted as a general theory, the end point reconstruction unit 116 has a total N defined for one contour line of one unit graphic. The normal end points are referred to as the first normal end point T (1) to the Nth normal end point T (N) in order along the contour line, respectively, and the nth normal end point T (n ) And the normal end point T (n−m) that is not to be removed immediately before that (where m is a natural number, and when n−m <1, T (n−m + N)) The distance is L1, and the nth normal end point T (n) and the (n + 1) th normal end point T (n + 1) (however, when n = N, the first normal end point T (1): the same applies hereinafter) The distance between them is L2, and the (n + 1) th normal end point T (n + 1) and the (n + 2) th normal end point T (n + 2) However, when n = N−1, the distance between the first normal end point T (1) and n = N when the distance between the second normal end point T (2) (the same applies hereinafter) is L3. ,
L2 is equal to or less than a predetermined reference value Wmerge, and normal end point T (n-1) (where n = 1, Nth normal end point T (N): the same applies hereinafter), T (n), T When the four points (n + 1) and T (n + 2) are on a straight line, if L1 <L3, the normal end point T (n) is to be removed, and if L1> L3, the normal end point T (n + 1) is selected. If it is a removal target, and L1 = L3, either the normal end point T (n) or the normal end point T (n + 1) is the removal target,
L2 is equal to or less than a predetermined reference value Wmerge, and the three normal end points T (n−1), T (n), and T (n + 1) are on a straight line, but the normal end point T (n + 2) is the straight line. If it is not on the line, the normal endpoint T (n) is the removal target,
L2 is equal to or less than a predetermined reference value Wmerge, and the three normal end points T (n), T (n + 1), and T (n + 2) are on a straight line, but the normal end point T (n-1) is the straight line. If it is not on the line, the normal end point T (n + 1) is to be removed,
This process is repeatedly executed while increasing n by 1 until n ≧ N is satisfied, and end point removal processing is performed to remove the normal end point that is the removal target.

  As the end point reconstruction process executed by the end point reconstructing unit 116, even when such a four-point end point removal process is adopted, the result is almost the same as when the above-described three-point end point removal process is adopted. can get. However, as described above, the four-point end point removal process can select a more preferable end point as a removal target than the three-point end point removal process. Can be made smaller.

(3) Reconstruction by end point rearrangement processing In the three-point or four-point end point removal processing described so far, the end point reconstruction unit 116 reconstructs end points by removing existing normal end points. However, the end point rearrangement process described here removes the intermediate normal end points from a part of the contour lines, and places new intermediate normal end points on each side of the part of the contour lines. The end point is normally reconstructed by the placement process.

  FIG. 45 is a schematic diagram illustrating a procedure when the end point rearrangement process is adopted as the end point reconstruction process by the end point reconstruction unit 116 illustrated in FIG. 32. Assume that normal end points A to H are defined on one side constituting a specific outline of a specific unit graphic as shown in FIG. 45 (a) (these normal end points are defined as normal end point definitions). Part 115). Here, for convenience of explanation, among these normal end points A to H, the normal end points A and H constituting the vertexes of the polygon as the unit graphic are called corner normal end points, and the normal end points B to G not forming the vertices are called. It will be called an intermediate normal end point.

  When reconstruction is performed by the endpoint rearrangement process described here, the endpoint reconstruction unit 116 first performs a process of temporarily removing intermediate normal endpoints defined on the contour line. FIG. 45 (b) shows a state in which intermediate normal end points B to G are removed from normal end points A to H shown in FIG. 45 (a). In FIG. 45, only the upper side of the polygon constituting one contour line is shown, but actually, one contour line constitutes a loop along each side of the polygon. Thus, a process of once removing the intermediate normal end point is performed for each side of the contour line. FIG. 45 (b) shows a state in which only the corner normal end points A and H are left by removing the intermediate normal end point for the upper side of the contour line.

  Subsequently, the end point reconstruction unit 116 performs end point rearrangement processing by rearranging the intermediate normal end points at predetermined intervals on each side of the contour line from which the intermediate normal end points have been removed. 45 (c), (d), and (e) show examples in which intermediate normal end points are rearranged on the upper side of the contour line. More specifically, FIG. 45 (c) is an example in which a predetermined reference interval Lreg is set, and the intermediate normal end points are rearranged every reference interval Lreg starting from the position of the left corner normal end point A. . For the normal end points A to E, the interval between the adjacent end points becomes the reference interval Lreg, but the normal end point E-H becomes the fraction interval Lodd. For example, when the length of the side AH is 45 nm and the reference interval Lreg is set to 10 nm, the fraction interval Lodd = 5 nm.

  On the other hand, in FIG. 45 (d), the interval between the normal end points C and D in the central portion is the fraction interval Lodd, and the normal end points A to B, B to C, D to E, and E to H are used as references. In this example, the interval Lreg is used. In general, in the case of a fine graphic pattern such as a semiconductor device, an error at the time of exposure near the vertex of a polygon tends to be large, and the originally rounded shape tends to be rounded. For this reason, the calculation load of the simulation can be reduced if the interval between the corner normal end point and the intermediate normal end point adjacent thereto is as far as possible. From this point of view, the fractional interval Lodd is set at the center of the side AH as shown in FIG. 45 (d), rather than being arranged at a position adjacent to the corner normal end point H as shown in FIG. 45 (c). It is preferable to arrange in the vicinity. When the length of the side AH is 45 nm, the interval between the end points is 10, 10, 5, 10, 10 nm in order from the left.

  FIG. 45 (e) shows an example in which all the end point intervals are set to the equal interval Leven. If an optimal value is determined in advance as the value of Leven, the intermediate normal end points can be rearranged at positions where the side AH is equally divided so that the equal interval Leven closest to the optimal value is obtained. For example, when the optimum value of Leven is set to 10 nm, if the length of the side AH is 45 nm, Leven = 11.25 nm when dividing this into four, and Leven = 9 nm when dividing into five, 6 In the case of division, Leven = 7.5 nm, so that Leven = 9 nm is obtained as the value closest to the optimum value of 10 nm. Therefore, as shown in the figure, the side AH may be divided into five, and intermediate normal end points may be rearranged at equal intervals of Leven = 9 nm.

  FIG. 46 is a flowchart showing a basic procedure for reconstructing endpoints when the endpoint rearrangement process shown in FIG. 45 is adopted. First, in step SS31, a process of temporarily removing intermediate normal end points (normal end points not constituting a vertex) on a specific contour to be processed is performed. Subsequently, in step SS32, a process of arranging a new intermediate normal end point on each side of the polygon constituting the contour line is performed. A specific method is as shown in FIGS. 45 (c) to (e).

(4) Different Use of End Point Removal Processing and End Point Rearrangement Processing So far, the three-point or four-point end point removal processing (FIGS. 41 to 44) and the end point rearrangement processing (FIGS. 45 to 46) have been described. Here, the end point removal processing can be applied to any contour line of any unit graphic, and may be applied to all contour lines of all unit graphics included in the original graphic pattern 10. On the other hand, there are cases where the end point rearrangement process is inappropriate when applied depending on the contour line.

  In the first place, the present invention is characterized in that the unit figure is divided into a plurality of divided figures and the normal end points are defined based on the vertex positions of the divided figures. Therefore, the unit figure is defined based on the vertex positions of the divided figures. However, even if a process that removes some normal endpoints (a process that reduces the number of normal endpoints) is performed, the feature of “normal endpoints defined based on the vertex positions of the split figure” will not be lost. This is because when the process of rearranging the normal end points (the process of correcting the position) is performed, the above characteristics are lost for the rearranged intermediate normal end points.

  For example, in the example shown in FIG. 42, the normal end points D and I indicated by white triangles are removed, but each of the other normal end points is “four sets of divided figures 10a shown in FIG. 34 (c)”. It has a feature of “normal end points defined based on vertex positions of ˜10d”. Here, if each normal end point is defined at a position based on the vertex positions of the divided figures 10a to 10d, the exposure beam shot is performed in the exposure process based on the corrected figure pattern 15 as described with reference to FIGS. The advantage is that the number can be reduced. This is because the horizontal position of the intermediate normal end points B, C, D defined on the upper side of the unit graphic 10 shown in FIG. 38 (d) and the horizontal direction position of the intermediate normal end points I, H, G defined on the lower side. This is because they are aligned.

  However, when the end point rearrangement process is performed on the example of the unit graphic 10 shown in FIG. 38 (d), the positions of the corner normal end points A, E, F, J are not changed, but the intermediate normal end points B, C, The positions of D, G, H, and I are corrected and rearranged at positions that are unrelated to the vertex positions of the four sets of divided figures 10a to 10d. Then, there is a possibility that the horizontal position of the intermediate normal end point defined on the upper side of the unit graphic 10 and the horizontal position of the intermediate normal end point defined on the lower side are not aligned, and there is an advantage that the number of exposure beam shots can be reduced. There is a risk of being lost.

  Therefore, for the unit graphic shown in FIG. 42 and the unit graphic shown in FIG. 43, it is preferable to rearrange the end points based on the end point removal processing (FIGS. 41 to 44). On the other hand, with respect to the square-shaped unit graphic (so-called perforated unit graphic) as shown in FIG. It is preferable to perform rearrangement of the end points based on the above, and rearrange the end points based on the end point rearrangement processing (FIGS. 45 to 46) for the inner contour line Oin.

  47 applies the end point rearrangement process based on the procedure of FIG. 46 to the normal end points M to T on the inner outline Oin of the square-shaped unit graphic 10 shown in FIG. 40 (f). It is a top view which shows the example which performed reconstruction. Specifically, intermediate normal end points O and P on the lower side NQ of the rectangle constituting the inner contour line Oin and intermediate normal end points S and T on the upper side MR are temporarily removed, and a new intermediate normal point is set on the lower side NQ. An end point U is arranged, and a new intermediate normal end point V is arranged on the upper side MR.

  By performing such end point rearrangement processing, the intermediate normal end points U and V on the inner contour line Oin are in positions that are not related to the vertex positions of the eight divided figures 10a to 10h shown in FIG. Will be placed. However, since the inside of the figure surrounded by the outer contour line Oout becomes an exposure area, the inside of the figure surrounded by the inner contour line Oin becomes a non-exposure area. Therefore, the intermediate normal end point U on the inner contour line Oin. , V are set at arbitrary positions, the merit of reducing the number of exposure beam shots is not affected.

  On the other hand, as can be seen from the arrangement of the intermediate normal end points shown in FIG. 47 (a), the intermediate normal end points B, C, E, F, H, I, K, and L on the outer contour line Oout are always In contrast to the corner normal end points A, D, G, J, which are defined to a certain extent (basically, a position separated by Wsplit), the intermediate normal end points O, P, S and T may be defined very close to the corner normal end points M, N, Q, and R. Moreover, as described above, the error at the time of exposure near the vertex of the polygon increases, and the originally rounded shape tends to be rounded. For this reason, it is possible to reduce the computational burden of the simulation if the interval between the corner normal end point and the intermediate normal end point adjacent thereto is as far as possible.

  In consideration of such circumstances, the intermediate normal end points defined on the outer contour line Oout are rearranged based on the end point removal processing (FIGS. 41 to 44), and are determined according to the vertex positions of the respective divided figures. It is preferable that the arrangement is maintained as it is, so that the advantage of reducing the number of exposure beam shots can be enjoyed. On the other hand, for the intermediate normal end points defined on the inner contour line Oin, the end points are rearranged based on the end point rearrangement processing (FIGS. 45 to 46), and are located as far as possible from the corner normal end points. It is preferable to arrange a new intermediate normal end point so that the merit of reducing the calculation load of simulation can be enjoyed.

  As described in §6.2, regarding the perforated unit figure 10, the figure constituting the outer outline Oout is referred to as a “regular figure” and the figure constituting the inner outline Oin is referred to as an “anti-figure”. Then, when the unit graphic vector group makes a round in the forward direction along the contour line (clockwise direction in the embodiment described here), the contour line is a normal graphic that forms the outer contour line Oout of the unit graphic 10. If the unit graphic vector group makes a round in the opposite direction along the contour line (counterclockwise direction in the embodiment described here), the contour line is the inner contour line Oin of the unit graphic 10. It can be determined that it is an anti-figure that constitutes.

  Therefore, when there is a possibility of handling a unit graphic of a hole, the end point reconstruction unit 116 performs end point removal processing (FIGS. 41 to 44) and end point rearrangement processing (FIGS. 45 to 46). A normal execution point on the regular figure surrounded by the unit figure vector around the forward direction (in the case of the example shown in FIG. 47 (a), the outer outline Oout is provided). For the upper normal end point, the end point is reconstructed by the end point removal process, and the normal end point on the opposite figure surrounded by the unit figure vector around the opposite direction to the forward direction (see Fig. 47 (a)) In the case of the example shown, the end point reconstruction may be performed by the end point rearrangement process for the normal end point on the inner outline Oin.

<6.4 Definition of evaluation points>
Here, the function of the evaluation score definition unit 117 in the evaluation score setting unit 110 shown in FIG. 32 will be described. This evaluation point definition unit 117 is based on the normal end points defined on the contour line of the unit graphic by the normal end point definition unit 115 or in the case of the embodiment in which the end point reconstruction unit 116 described in §6.3 is provided. The component defining the evaluation point E based on the normal end point obtained by the reconstruction by the end point reconstructing unit 116. That is, the evaluation point definition unit 117 performs a process of defining an evaluation point between two normal end points arranged adjacent to each other on the contour line of each unit graphic.

  The position for defining each evaluation point E may be any position in principle as long as it is between a pair of adjacent normal end points, but in practice, it is the midpoint position of a pair of normal end points. Is preferably defined as follows. This is because a more appropriate simulation result is obtained when the evaluation point is set at the center point of the contour line segment when determining the deviation amount (process bias) about the contour line segment sandwiched between the pair of normal end points by simulation. This is because it is considered to be obtained.

  Therefore, in the embodiment described here, the evaluation point definition unit 117 performs a process of defining evaluation points at the midpoint positions of two normal end points arranged adjacent to each other on the outline of the unit graphic. FIG. 48 (a) shows normal end points (marked by x) on the parallelogram unit graphic 10 after the end point reconstruction shown in FIG. 42 (b). 48 (b) shows an example in which evaluation points 1 to 8 (black circles) are defined based on these normal end points A to H. Specifically, the evaluation point 1 is defined at the center position on the contour line segment AB sandwiched between the pair of normal end points AB, and the contour line segment BC sandwiched between the pair of normal end points BC. Above, an evaluation point 2 is defined at the center position, and..., An evaluation point 8 is defined at the center position on the contour line segment HA sandwiched between the pair of normal end points HA. .

  Similarly, FIG. 49 (a) shows normal end points (marked by x) on the L-shaped unit graphic 10 after the end point reconstruction shown in FIG. 43 (b). 49 (b) shows an example in which evaluation points 1 to 8 (black circles) are defined based on these normal end points A to H. Each evaluation point is defined at the midpoint position of each contour line segment. FIG. 50 (a) shows normal end points (marked with x) on the square-shaped unit graphic 10 after the end point reconstruction shown in FIG. FIG. 50 (b) shows an example in which evaluation points 1 to 18 (black circles) are defined based on these normal end points A to R. Again, any evaluation point is defined at the midpoint position of each contour line segment.

  Each evaluation point defined in this way corresponds to the evaluation points E11, E12, and E13 shown in FIG. 3, and the feature quantity extraction unit 120 shown in FIG. The bias estimation unit 130 extracts the process bias estimate y for each of these evaluation points. The pattern correction unit 140 corrects the position of the contour line segment including the evaluation point based on the estimated value y of the process bias obtained for each evaluation point.

<6.5 Definition of replenishment endpoints>
Next, the function of the replenishment endpoint definition unit 118 in the evaluation point setting unit 110 shown in FIG. 32 will be described. This supplementary endpoint defining unit 118 has a function of searching for an intermediate normal endpoint that is a normal endpoint that does not constitute a polygon vertex for each unit graphic, and additionally defining a supplementary endpoint at the same position as the searched intermediate regular endpoint. Fulfill. As described above, the normal end points defined by the normal end point definition unit 115 and the normal end points obtained by the reconstruction by the end point reconstructing unit 116 are the corner normal end points and the polygon vertices constituting the vertex of the polygon. It is divided into intermediate normal end points that are not configured. Of these, the supplementary endpoint definition unit 118 additionally defines supplementary endpoints at the same position for the intermediate normal endpoint.

  Here, first, the necessity of additionally defining the supplemental end point in addition to the normal end point will be described. As described above, when the evaluation point definition process by the evaluation point definition unit 117 is completed, an evaluation point is determined at the midpoint position for each of the outline segments sandwiched between a pair of adjacent normal end points. For example, in the example shown in FIG. 48 (b), the evaluation point 1 is defined on the contour line segment AB sandwiched between the pair of normal end points AB, and the contour line sandwiched between the pair of normal end points BC. Evaluation point 2 is defined on the minute BC. Then, a feature amount is extracted for each evaluation point, an estimated value y of the process bias is obtained, and the position of the contour line segment including the evaluated point is corrected based on the estimated value y of the process bias.

  For example, in the example shown in FIG. 48 (b), as a result of the simulation, an estimated value y (1) = − 1 nm is obtained for the evaluation point 1, and an estimated value y (2) for the evaluation point 2 ) =-2 nm. In this case, when the lithography process is executed using the parallelogram original figure pattern 10 shown in FIG. 48B as it is, the point corresponding to the evaluation point 1 on the actual figure pattern 20 obtained on the actual substrate S is It is estimated by simulation that the position is shifted to the inner side by 1 nm, and the point corresponding to the evaluation point 2 is shifted to the inner side by 2 nm. Therefore, for example, the pattern correction unit 140 performs a process of moving the contour line segment AB having the evaluation point 1 by 1 nm to the outside and moving the contour line segment BC having the evaluation point 2 by 2 nm to the outside, thereby correcting the corrected graphic pattern 15. The correction process for creating the image is performed.

  At this time, it can be easily understood as a geometric concept that the contour line segment AB and the contour line segment BC are moved separately and independently. However, in terms of data processing on the computer, inconvenience occurs if the intermediate normal end point B remains a single end point. In the present invention, as shown in the example of FIG. 3B, correction is performed to move each evaluation point in a direction orthogonal to the contour line. Therefore, in order to move the contour line segment AB and the contour line segment BC according to different correction amounts, the normal end point B serving as the right end of the contour line segment AB and the left end of the contour line segment BC are used. The normal end point B that plays the role of needs to be handled as a separate end point in data processing. In view of such computer processing, in the present invention, the supplementary end point B ′ is additionally defined at exactly the same position with respect to the intermediate normal end point B. The supplementary end point B ′ additionally defined in this way can be handled as an end point of only one contour line segment, and the existing intermediate normal end point B can be handled as an end point of only the other contour line segment.

  For example, in the case of the parallelogram unit graphic shown in FIG. 48 (b), supplementary end points B ', C', F ', G' are additionally defined at the same positions for the intermediate normal end points B, C, F, G. In this case, as shown in FIG. 51 (a), in addition to the eight normal end points A to H (marked by x), four further supplementary end points B ′, C ′, F ′, G ′ (square marks). Will be added and a total of 12 endpoints will be defined. Then, for example, the left end of the contour line segment AB is the normal end point A, the right end is the replenishment end point B ', the left end of the contour line segment BC is the normal end point B, the right end is the replenishment end point C', and the left end of the contour line segment CD Is the normal end point C, the right end is the normal end point D, the upper end of the contour line segment DE is the normal end point D, the lower end is the normal end point E, the right end of the contour line segment EF is the normal end point E, and the left end is the replenishment end point F '. The right end of the line segment FG is the normal end point F, the left end is the supplement end point G ', the right end of the contour line segment GH is the normal end point G, the left end is the normal end point H, the lower end of the contour line segment HA is the normal end point H, and the upper end is normal It can be the end point A.

  If the two ends of the eight contour segments are defined in this way, for example, the contour segment AB and the contour segment BC can be moved separately and independently (in terms of computer processing, the normal endpoint B and the supplemental endpoint) B ′ can be moved to another coordinate position). Note that the reason why additional supplementary endpoints are defined only for intermediate normal endpoints is that one intermediate normal endpoint may be separated into two endpoints that occupy two different positions after correction, as described above. On the other hand, one corner normal end point remains as one corner normal end point after correction. Such a situation will be described in detail in Section 7 with specific examples.

  Similarly, in the case of the L-shaped unit graphic shown in FIG. 49 (b), if supplementary end points F ′ and H ′ are additionally defined at the same positions for the intermediate normal end points F and H, respectively, FIG. As shown in the figure, in addition to the eight normal end points A to H (marked by x), two additional end points F ′ and H ′ (square marks) are added to define a total of ten end points. Become. Then, for example, the right end of the contour line segment EF can be the normal end point E, the left end can be the supplemental end point F ′, the right end of the contour line segment FG can be the normal end point F, and the left end can be the normal end point G. The lower end of the line segment GH can be the normal end point G, the upper end can be the replenishment end point H ', the lower end of the contour line segment HA can be the normal end point H, and the upper end can be the normal end point A. Can be processed.

  In addition, in the case of the square-shaped unit graphic shown in FIG. 50 (b), the supplementary end points B are placed at the same positions for the intermediate normal end points B, C, E, F, H, I, K, L, O, and R, respectively. If ', C', E ', F', H ', I', K ', L', O ', R' are additionally defined, 18 normal end points A are obtained as shown in FIG. In addition to .about.R (mark x), there are 10 additional end points B ', C', E ', F', H ', I', K ', L', O ', R' (square marks). A total of 28 endpoints will be defined. Then, for example, the left end of the contour line segment AB is the normal end point A, the right end is the replenishment end point B ′, the left end of the contour line segment BC is the normal end point B, the right end is the replenishment end point C ′, and the left end of the contour line segment CD Is the normal end point C, the right end is the normal end point D, and so on, and each contour line segment can be moved independently.

  FIG. 52 is a schematic diagram (FIGS. (A) and (b)) and a flowchart (FIG. (C)) showing a specific procedure of the supplementary endpoint definition process performed by the supplementary endpoint definition unit 118 shown in FIG. As described above, the supplementary endpoint defining unit 118 searches for an intermediate normal endpoint for each unit graphic, and performs a process of additionally defining a supplementary endpoint at the same position as the searched intermediate regular endpoint. Here, the process for searching for the intermediate normal end point can be performed specifically by the following procedure.

  Assume that a total of N normal end points are defined on a specific contour line of a specific unit graphic to be processed. Among these N normal end points, a part is a corner normal end point constituting a polygon vertex, and the remaining part is a middle normal end point not constituting a polygon vertex. The search process performed here is a process for finding an intermediate normal end point from among N normal end points.

  Therefore, all the N normal end points are designated as the first normal end point T (1) to the Nth normal end point T (N) in the order along the contour line, as shown in FIG. With the nth normal end point T (n) as a determination target, it is determined whether or not it is an intermediate normal end point. In this determination, as shown in the figure, three points of the (n-1) th normal end point T (n-1), the nth normal end point T (n), and the (n + 1) th normal end point T (n + 1) are obtained. Use. Oa in the figure is a contour segment connecting two end points T (n-1) and T (n), and Ob in the diagram is a contour segment connecting two end points T (n) and T (n + 1). is there. When the nth normal end point T (n) is determined to be the intermediate normal end point, as shown in FIG. 52 (b), the replenishment end point T is located at the same position as the nth normal end point T (n). (N) ′ is additionally defined. In the figure, the normal end point T (n) is indicated by x and the replenishment end point T (n) ′ is indicated by a square mark.

  If the supplementary end point T (n) ′ is additionally defined at the same position when the nth normal end point T (n) is the intermediate normal end point, the left end of the contour line segment Oa is set as the normal end point T (n−1). And the right end can be the replenishment end point T (n) ′. Further, the left end of the contour line segment Ob can be a normal end point T (n), and the right end can be a normal end point T (n + 1). Since the end points T (n) and T (n) ′ can be moved separately and independently, the contour segments Oa and Ob can be moved independently and independently by the pattern correction unit 140. There is no problem in performing the correction process.

  FIG. 52 (c) is a flowchart showing a specific procedure of the replenishment endpoint definition process performed by the replenishment endpoint definition unit 118. First, in step SS41, a parameter n indicating the number of the normal end point to be determined whether or not it is an intermediate normal end point is set to n = 1, and in step SS42, the (n-1) th normal end point T ( It is determined whether or not three points of (n-1), the nth normal end point T (n), and the (n + 1) th normal end point T (n + 1) are on a straight line. Here, if an affirmative determination is made, the end point T (n) to be determined is an intermediate normal end point (an end point that does not constitute a polygonal vertex). Therefore, in step SS43, this intermediate normal end point T A supplementary end point T (n) ′ is additionally defined at the same position as (n). If a negative determination is made in step SS42, the end point T (n) to be determined is the normal corner end point (the end point constituting the vertex of the polygon), so that the replenishment end point T (n) ′ No additional definitions are made.

  Such processing is repeatedly executed through steps SS44 and SS45 while increasing the parameter n by 1 until n = N is reached. When n = N is reached, the replenishment endpoint definition process is complete. By performing such processing, the replenishment endpoints indicated by the square marks in FIGS. 51 (a), (b), and (c) are defined.

  In general terms, the supplementary endpoint defining unit 118 sets a total of N normal endpoints defined for one contour line in the order along the contour, respectively, from the first normal endpoint T (1) to the first regular endpoint T (1) to Tth. When called the N normal end point T (N), paying attention to the nth normal end point T (n), the (n-1) th normal end point T (n-1) (where n = 1 Nth normal end point T (N)), nth normal end point T (n), (n + 1) th normal end point T (n + 1) (provided that n = N, the first normal end point T ( When the three points 1)) are on a straight line, the n-th normal end point T (n) is determined as an intermediate normal end point, and a process of additionally defining a supplementary end point at the same position as the intermediate normal end point is performed by n = 1 to N may be repeatedly executed.

<<< §7. Details of pattern correction unit >>
Subsequently, the pattern correction unit 140 will be described in detail. FIG. 53 is a block diagram showing the pattern correction unit 140 and related components in the shape correction apparatus 100 for graphic patterns according to the basic embodiment of the present invention shown in FIG. The basic function of the pattern correction unit 140 is to modify the position of each evaluation point E set by the evaluation point setting unit 110 on the basis of the estimated value y of the process bias output from the bias estimation unit 130. 10 is performed to create a corrected figure pattern 15.

  Here, the function of the evaluation point setting unit 110 is as described in detail in §6, and processing for defining the normal end point T, the supplemental end point T ′, and the evaluation point E for each unit graphic constituting the original graphic pattern 10. Is done. The information on each point can be referred to as information on the contour line segment O. That is, the position information of each normal end point T and each supplement end point T ′ is information indicating the positions of both ends of the specific contour line segment O, and the position information of the evaluation point E is on the contour line segment O. This is information indicating the position of the defined evaluation point. The pattern correction unit 140 creates the corrected graphic pattern 15 by performing a moving process and an expansion / contraction process on the contour line segment O and a new contour line adding process based on the information on the contour line segment O.

  As shown in FIG. 53, the pattern correction unit 140 includes a contour segment movement processing unit 141, a contour segment addition processing unit 142, and a contour segment expansion / contraction processing unit 143. Hereinafter, the function of each of these components will be described in detail by taking an L-shaped unit graphic shown in FIG. 51 (b) as an example. As described above, the figure pattern shape correction apparatus 100 according to the present invention is actually configured by incorporating a dedicated program into a computer. Accordingly, each of the above-described components 141, 142, and 143 included in the pattern correction unit 140 is actually configured by incorporating a dedicated program into the computer.

<7.1 Outline segment movement processing>
Here, first, the function of the contour segment movement processing unit 141 shown in FIG. 53 will be described. As shown in the figure, the contour segment movement processing unit 141 includes information on the contour line segment O defined by the evaluation point setting unit 110 (normal end point T, supplemental end point T ′, evaluation point E) along with information on the original graphic pattern 10. Position coordinates and information indicating their mutual relationship). In addition, the bias estimation unit 130 provides an estimated value y of process bias for each evaluation point E.

  FIG. 54 is an enlarged plan view showing each end point and each evaluation point defined on the L-shaped unit graphic shown in FIG. 51 (b). In this figure, the normal end points A to H are indicated by x, the replenishment end points F ′ and H ′ are indicated by square marks, the evaluation points 1 to 8 are indicated by circles, and the reference numerals 1 to 8 of the evaluation points are indicated. Is described in the circle. Contour lines sandwiched between adjacent end points are denoted by reference numerals O1 to O8. For example, the portion sandwiched between the normal end points AB is the contour line segment O1, and the portion sandwiched between the normal end points BC is the contour line segment O2. Of the eight normal end points A to H, six normal end points A, B, C, D, E, and G are corner normal end points constituting the vertex of the polygon, and the remaining two normal end points F and H are intermediate normal end points that do not constitute a vertex of the polygon. As for the two intermediate normal end points F and H, the replenishment end points F ′ and H ′ are defined at the same position as described above.

  FIG. 55 is a diagram showing an example of a data format representing the interrelationship between each end point and each evaluation point shown in FIG. As described above, information on the contour line segment O is given from the evaluation point setting unit 110 to the contour line segment movement processing unit 141. Specifically, the information on the contour line segment O is shown in FIG. Will be given in the data format shown. In this data format, one end point and one evaluation point are associated with each other (in the figure, enclosed in parentheses), and these data pairs are along the outline of the unit graphic. They are arranged in the order of clockwise.

  For example, the first data pair (A, 1) is a data pair in which the end point A and the evaluation point 1 are associated with each other. It shows that point 1 is defined. Similarly, the second data pair (B, 2) is a data pair in which the end point B and the evaluation point 2 are associated with each other on the contour line segment O2 starting from the end point B and ending at the end point C. It shows that evaluation point 2 is defined.

  The sixth data pair (F ′, Φ) is a data pair in which the supplementary end point F ′ and the evaluation point Φ are associated with each other. Here, the evaluation point Φ is an evaluation point that does not actually exist, and the data “Φ” is empty data provided for the convenience of expressing the supplementary end point F ′ in the form of a data pair. Similarly, the ninth data pair (H ′, Φ) is also a data pair in which the supplementary end point H ′ is associated with the evaluation point Φ, and the data “Φ” is empty data.

  If the data format shown in FIG. 55 is adopted, all the end points including the normal end point and the replenishment end point can be expressed as data pairs, respectively. Of course, since the data constituting each data pair includes the position coordinate values of each end point and each evaluation point, the position of each end point or each evaluation point on the two-dimensional plane can be specified. Moreover, since each data pair is listed in the clockwise order along the contour line of the unit graphic, the contour line segment sandwiched between adjacent end points can be recognized and defined on the contour line segment. The evaluation point can be recognized. For example, the position of the contour line segment O1 sandwiched between the adjacent end points A-B can be specified by two sets of data pairs (A, 1) and (B, 2), and on the contour line segment O1 The position of the evaluation point 1 can be specified.

  In the case of a perforated unit figure as shown in FIG. 51 (c), a regular figure constituting the outer outline Oout and an inverse figure constituting the inner outline Oin are formed. As in the example, it is preferable to enumerate each data pair in the clockwise order along the contour line, and for counter-graphics, it is preferable to enumerate each data pair in the counterclockwise order along the contour line. . By doing so, it becomes possible to identify whether each contour is the outer contour line Oout or the inner contour line Oin based on the enumeration order of each data pair. In addition, the inside and outside of the unit graphic can be recognized.

  In the embodiment shown in FIG. 53, the original graphic pattern 10 is given to the contour line segment movement processing unit 141. However, in performing the contour segment segment movement processing, the contour segment segment is received from the evaluation point setting unit 110. It is sufficient that the data shown in FIG. 55 is given to the movement processing unit 141 and the estimated value y of the process bias for each evaluation point is given from the bias estimation unit 130 to the contour segment movement processing unit 141. That is, the original graphic pattern 10 is not essential information for the contour segment movement processing unit 141. However, since the original graphic pattern 10 is information that directly indicates the shape of the unit graphic, in practice, this is given to the contour line segment movement processing unit 141 for reference in performing the contour segment segment movement process. It is preferable to provide.

  FIG. 56 is a plan view showing a state in which the contour line segment moving process is performed on the L-shaped unit graphic 10 shown in FIG. 54 by the contour segment segment moving processing unit 141. A contour line segment indicated by a broken line in the figure indicates a state before the movement process, and a contour line segment indicated by a solid line in the figure indicates a state after the movement process. In the movement processing of the contour line segment, for each evaluation point, the normal end point or the supplemental end point adjacent to one side of the evaluation point along the contour line of the unit graphic is used as the first end point and adjacent to the other side. A contour line segment having the normal end point or the supplemental end point as the second end point is defined, and the contour line segment for each evaluation point is converted into the contour line segment by a correction amount corresponding to the estimated value of the process bias of the evaluation point. This is done by moving in the orthogonal direction. At this time, either a normal end point or a supplemental end point is selected for each contour line segment so that each end point of one contour line segment is not used redundantly as each end point of another contour line segment.

  The example shown in FIG. 56 is an example in which the estimated value y of the process bias for each of the evaluation points 1 to 8 has a negative value (the outline of the original unit graphic 10 is shifted inward by simulation of the lithography process). The correction processing is shown for an example in which a result is obtained. That is, when the lithography process is executed using the original unit graphic 10 as it is, a real graphic 20 that is smaller than the original unit graphic 10 is obtained. Correction processing for obtaining the unit graphic 15 is performed.

  The thick line arrows shown in FIG. 56 indicate the moving direction of each evaluation point. In the example shown here, since the estimated value y of the process bias for the evaluation points 1 to 8 is a negative value, the evaluation points 1 to 8 are all moved in the outward direction of the unit graphic. For example, when the estimated value of the process bias at the evaluation point 1 is y (1) = − 1 nm, a process of moving the evaluation point 1 outward by 1 nm as indicated by a bold arrow in the figure is performed. As described above, in the present invention, the evaluation point is moved in a direction perpendicular to the contour line segment including the evaluation point. In addition, the evaluation point is moved for each outline segment including the evaluation point. Therefore, in the case of the illustrated example, the evaluation point 1 is moved outward by 1 nm as indicated by the thick arrow, and the contour line segment O1 including the evaluation point 1 is also translated in the same manner.

  In the example shown in FIG. 56, the outline segments O2 to O8 are similarly translated outward. The point to be noted here is the behavior of the intermediate normal end points F and H and the supplementary end points F ′ and H ′ additionally defined at the same positions. In the example shown in the figure, the estimated value y of the process bias for the evaluation point 5 and the estimated value y of the process bias for the evaluation point 6 are different from each other. The amount of movement of O6 also has a different value. For this reason, the contour segments O5 and O6 have different movement amounts even if the movement direction is the same, and therefore, as shown in the figure, after the movement processing, both are separated. However, since both ends of the contour line segment O5 are end points E and F ′ and both ends of the contour line segment O6 are end points F and G, even if the positions of the end points F and F ′ are different, There is no problem.

  The same applies to the outline segments O7 and O8. As shown in the figure, the contour line segment O7 and the contour line segment O8 have different amounts of movement, so that both are separated after the movement process. However, since both ends of the contour line segment 7 are end points G and H ′ and both ends of the contour line segment 8 are end points H and A, even if the positions of the end points H and H ′ are different, There is no problem. That is, the substantial processing on the computer in this movement processing is correction of the data shown in FIG. 55, but it is not necessary to make any correction to the structure of the data format shown in FIG. It is only necessary to correct the coordinate value of each evaluation point. The reason why the supplementary endpoints F ′ and H ′ are additionally defined for the intermediate normal endpoints F and H by the supplementary endpoint definition unit 118 is for the sake of convenience.

  On the other hand, for the corner normal end points A, B, C, D, E, and G, the supplementary end points are not additionally defined. Therefore, as shown in the drawing, these normal corner end points are separated into two different positions after the movement process. For example, the corner normal end point B is separated into a right end position of the contour line segment O1 and an upper end position of the contour line segment O2 after the movement process. In this way, the corner normal end points separated into two after the movement process are handled by the contour line segment expansion / contraction processing unit 143 described later.

<7.2 Outline segment addition processing>
Next, the function of the contour line segment addition processing unit 142 shown in FIG. 53 will be described. When the intermediate normal end point and the replenishment end point that were in the same position before the movement process are separated into two different positions after the movement process, the contour line addition processing unit 142 connects the positions after the movement process. It has a function of performing an additional process of adding a new contour line segment.

  In the example shown in FIG. 56, the intermediate normal end points F and H and the replenishment end points F ′ and H ′ are arranged at different positions by the movement processing of the contour line segment. Therefore, a gap is generated between the intermediate normal end point F and the replenishment end point F ′, and a gap is also generated between the intermediate normal end point H and the replenishment end point H ′. The contour segment addition processing unit 142 performs a process of adding a new contour segment in order to fill this gap.

  FIG. 57 is a plan view showing a state in which the contour line addition processing is performed on the unit graphic after the movement processing shown in FIG. 56 by the contour line addition processing unit 142. A portion indicated by a bold line in the figure is a newly added contour line segment. Specifically, for the intermediate normal end point F and the replenishment end point F ′ that were in the same position before the movement process, a new contour line segment O5 ′ that connects the position after the movement process is added. For the intermediate normal end point H and the replenishment end point H ′ that are at the same position, a new contour line segment O7 ′ that connects the positions after the movement process is added.

  However, in the case of the embodiment described here, as described above, the information of each end point and each evaluation point constituting the unit graphic is expressed in the data format illustrated in FIG. By performing the process of correcting the coordinate values of the end points and the evaluation points in each data pair indicated in a simple data format (the above-described contour line segment movement process), the contour line segment addition process is also automatically performed.

  For example, the sixth data pair (F ′, Φ) in FIG. 55 is data corresponding to the newly added contour line segment O5 ′ in FIG. Specifically, the data “F ′” in the data pair (F ′, Φ) is information indicating the coordinate value of the end point F ′ that is the starting end of the contour segment O5 ′, and the data “Φ” is the contour segment O5. This is information indicating the position of the evaluation point for ′. Actually, since the data “Φ” is empty data, the contour segment O5 ′ is a contour segment having no evaluation point. The coordinate value of the end point F that is the end of the contour line segment O5 ′ is indicated by the data “F” in the seventh data pair (F, 6).

  Similarly, the ninth data pair (H ′, Φ) in FIG. 55 is data corresponding to the newly added contour line segment O7 ′ in FIG. Specifically, the data “H ′” in the data pair (H ′, Φ) is information indicating the coordinate value of the end point H ′ that is the starting end of the contour segment O7 ′, and the data “Φ” is the contour segment O7. This is information indicating the position of the evaluation point for ′. Actually, since the data “Φ” is empty data, the contour line segment O7 ′ is a contour line segment having no evaluation point. The coordinate value of the end point H that is the end of the contour line segment O7 ′ is indicated by the data “H” in the tenth data pair (H, 8).

  In the end, if the data format illustrated in FIG. 55 is used, the addition processing by the contour line addition processing unit 142 is automatically performed by performing the movement processing by the contour segment movement processing unit 141. That is, the end points F and F ′ and the end points H and H ′ defined at the same position before the movement process move to different positions, and in each data pair shown in FIG. 55, these end points F, F ′, H and H When the coordinate value of 'is rewritten with a new coordinate value after the movement process, a new contour segment O5' connecting the end points F and F 'is automatically added, and the end points H and H' are connected. A new contour line segment O7 'is automatically added. Therefore, when the data format illustrated in FIG. 55 is used, the addition processing by the contour segment addition processing unit 142 is realized by the movement processing by the contour segment movement processing unit 141. There is no need to perform a significant data processing operation.

<7.3 Outline Segment Expansion Processing>
Next, the function of the contour line segment expansion / contraction processing unit 143 shown in FIG. 53 will be described. As described in §7.1, when the moving process is performed, the corner normal end point is separated into two positions. For example, in the example shown in FIG. 57, corner normal end points A (shown as A0, A1, and A2 in the figure), B, C, D, E, and G are two positions after the movement process. Are separated. The contour line segment expansion / contraction processing described here is intended to create a new corner normal end point by fusing the two corner normal end points thus separated.

  For this reason, the contour line segment expansion / contraction processing unit 143 determines that the normal end point that is a normal end point of the polygon before the moving process is separated into two different positions after the moving process. Expansion and contraction processing is performed to expand and contract each contour line segment including the corner normal end points after separation so that the two corner normal end points are merged to become a new corner normal end point.

  Specifically, in the case of the embodiment described here, the contour line segment expansion / contraction processing unit 143 is used when a certain corner normal end point is separated into a first moving end point and a second moving end point by the moving process. An intersection of a straight line including the first post-movement contour line with the first moving end point as one end point and a straight line including the second post-movement contour line with the second moving end point as one end point The intersection processing is determined to be a new corner normal end point, and an extension process is performed such that one end point becomes a new corner normal end point with respect to the first post-movement contour line segment and the second post-movement contour line segment. Do.

  Here, focusing on the corner normal end point A in the example shown in FIG. 57, a specific procedure of the expansion / contraction process will be described. Here, as shown in FIG. 57, the corner normal end point A before the movement process is indicated by a symbol A0, and the corner normal end point A0 is the first movement end point A1 and the second movement end point A2 after the movement process. Consider the case of separation. In this case, a second line having the first moving end point A1 as one end point and the first moving end point A2 as a straight line including the first post-moving contour line segment O8 and the second moving end point A2 as one end point. The intersection point J with the straight line (indicated by the alternate long and short dash line in the figure) including the post-movement outline O1 is obtained. Then, the intersection J is set as a new corner normal end point A, and one end point is a new corner normal end point A with respect to the first post-movement contour segment O8 and the second post-movement contour segment O1. The expansion / contraction process is performed.

  FIG. 58 is a plan view showing a state in which the contour line segment expansion / contraction processing has been performed on the unit graphic shown in FIG. The first post-movement contour line segment O8 is stretched so that its upper end becomes a new corner normal end point A, and the second post-movement contour line segment O1 has a new corner normal end point A at its left end. It is stretched to become. Thus, the two moving end points A1 and A2 shown in FIG. 57 are merged with the new corner normal end point A. If similar expansion / contraction processing is performed on the remaining corner normal end points B, C, D, E, and G, a corrected unit graphic (corrected graphic pattern 15) as shown by a solid line in FIG. 58 is obtained.

  As shown in the figure, the corrected unit graphic (corrected graphic pattern 15 indicated by a solid line) is a figure that is slightly larger than the unit graphic before correction (original graphic pattern 10 indicated by a broken line). Here, if the simulation result based on the original graphic pattern 10 is correct and appropriate correction is performed based on the simulation result, the actual substrate S can be obtained by performing an actual lithography process using the corrected graphic pattern 15. On the top, the same actual graphic pattern 20 as the original graphic pattern 10 indicated by a broken line is formed.

  This corrected figure pattern 15 (solid line) is eventually processed with respect to the original figure pattern 10 (broken line) by the outline line movement process described in §7.1 and the outline line addition process described in §7.2. This is a pattern constituted by unit graphics having the outline of the outline after the expansion / contraction processing described in §7.3 is performed. However, when the data of the data format shown in FIG. 55 is used to express the unit graphic constituting the original graphic pattern 10, the unit graphic constituting the corrected graphic pattern 15 is also data of the data format shown in FIG. Will be expressed. The difference between the data indicating the original graphic pattern 10 and the data indicating the corrected graphic pattern 15 is only the position information (coordinate values) of the end points and the evaluation points included in each data pair shown in FIG.

<7.4 Repeat Correction Process>
In §7.3, the example in which the corrected graphic pattern 15 indicated by the solid line in FIG. 58 is obtained by performing correction by the pattern correction unit 140 based on the original graphic pattern 10 indicated by the broken line in FIG. If an appropriate correction is performed based on the correct simulation result, the actual graphic pattern 20 on the actual substrate S is the same as the original graphic pattern 10 by performing an actual lithography process using the corrected graphic pattern 15. The explanation to the effect of forming was performed.

  However, in practice, it is not always possible to perform appropriate correction once. For example, in the “contour line segment movement process” in §7.1, when the estimated value of the process bias at a certain evaluation point is y of −1 nm, the correction process of moving the evaluation point by +1 nm is exemplified. Such a correction process is not necessarily an appropriate correction process. In fact, a correction process for moving the evaluation point by +1.1 nm may be an optimal correction process.

  FIG. 1 shows an example in which a corrected graphic pattern 15 is obtained by applying the original graphic pattern 10 to the shape correction apparatus 100. Usually, a lithography process is performed using the corrected graphic pattern 15 thus obtained. Even if the actual graphic pattern is formed on the actual substrate S, the actual graphic pattern 20 obtained does not exactly match the original graphic pattern 10 at the initial design. This is because the graphic included in the original graphic pattern 10 and the graphic included in the corrected graphic pattern 15 are different in size and shape, so that there is a difference in the influence of the proximity effect when the lithography process is executed. .

  Therefore, in practice, as shown in FIG. 1, it is necessary to repeatedly perform the process of giving the corrected figure pattern 15 output from the pattern correction unit 140 to the figure pattern shape correcting apparatus 100 again. That is, the corrected graphic pattern 15 is given to the shape correcting apparatus 100 instead of the original graphic pattern, and the correction graphic pattern 15 is subjected to correction processing again to obtain a new corrected graphic pattern, and this new corrected graphic pattern is obtained. Is again applied to the shape correction apparatus 100, and a process of obtaining a new corrected figure pattern is repeated.

  Such repetition of the correction process is also shown in the flowchart of FIG. That is, the correction processing in steps S2 to S5 is initially performed on the original graphic pattern created in step S1, but is performed on the corrected graphic pattern obtained in step S5 after the second time. Thus, the correction process of steps S2 to S5 is repeatedly executed until it is determined that the correction is completed in step S6. The actual steps of exposure, development, and etching constituting the lithography process in step S7 are executed based on the last corrected figure pattern finally obtained by such repeated processing.

  In order to repeat such correction processing, in the figure pattern shape correction apparatus 100 shown in FIG. 1, the correction figure pattern 15 created by the pattern correction unit 140 is added to the feature quantity extraction unit 120. The function of extracting the feature amount indicating the feature around the evaluation point on the pattern 15 is provided, and the bias estimation unit 130 causes the position of the evaluation point on the corrected graphic pattern 15 and the actual graphic pattern 20 on the basis of the feature amount. A function for estimating the process bias indicating the amount of deviation from the position of the position is provided, and the pattern correction unit 140 further corrects the corrected graphic pattern 15 based on the estimated value of the process bias output from the bias estimation unit 130. If you have a function to create a new corrected figure pattern There.

  By doing so, it is possible to repeatedly execute correction on the corrected graphic pattern 15 and to create a more appropriate corrected graphic pattern. When the correction graphic pattern 15 is corrected again, the definition of the endpoints and evaluation points has already been completed, so that the processing by the evaluation point setting unit 110 can be omitted. That is, when the corrected graphic pattern 15 drawn at the lower end of the block diagram shown in FIG. 1 is returned to the shape correcting apparatus 100 again according to the upward arrow, it is not the evaluation point setting unit 110 but the feature amount extracting unit 120. Return it. The feature amount extraction unit 120 performs a feature amount extraction process for the existing evaluation points on the returned corrected graphic pattern 15, and the bias estimation unit 130 performs a process bias for the existing evaluation points on the returned corrected graphic pattern 15. What is necessary is just to obtain the estimated value y.

  When repeating such correction processing, the contour line segment expansion / contraction processing unit 143 in the pattern correction unit 140 is subjected to processing for expanding / contracting the contour line segment, and then the contour line segment after expansion / contraction processing is performed. It is preferable to provide a function of performing processing for correcting the position of the evaluation point.

  For example, the correction graphic pattern 15 shown in FIG. 58 is created in the expansion / contraction processing of the contour line segment described in §7.3. When returning the corrected graphic pattern 15 shown in FIG. 58 to the shape correcting apparatus 100 again, as described above, the processing by the evaluation point setting unit 110 can be omitted. This is because the end points A to H, F ′, and H ′ and the evaluation points 1 to 8 are already defined in the corrected graphic pattern 15 shown in FIG. However, the positions of the evaluation points 1 to 8 on the corrected graphic pattern 15 are not necessarily appropriate positions as shown in the figure. As described in §6.4, in order to obtain a more appropriate simulation result, it is preferable to define each evaluation point at the midpoint position of the contour line segment. However, when the expansion / contraction processing by the contour line segment expansion / contraction processing unit 143 is performed, the original evaluation point position deviates from the midpoint position of the contour line segment.

  Therefore, when the correction process is repeated, it is preferable that the contour line segment expansion / contraction processing unit 143 performs a process of correcting the position of the evaluation point after performing the process of expanding and contracting the contour line segment. Specifically, the position of each evaluation point may be corrected to the midpoint position of the new contour line segment. 59, the contour line segment expansion / contraction processing unit 143 shown in FIG. 53 performs processing for correcting the positions of the evaluation points 1 to 8 for the respective contour line segments O1 to O8 of the unit graphic after the expansion and contraction processing shown in FIG. It is a top view which shows the state. With this correction, the positions of the evaluation points 1 to 8 are the midpoint positions of the contour line segments O1 to O8, so that more appropriate simulation can be performed thereafter.

<<< §8. Features and merits of the present invention >>>
Finally, the features and merits of the present invention will be described.

<8.1 Features of Shape Correction Method According to the Present Invention>
So far, the present invention has been described as an apparatus invention called a figure pattern shape correction apparatus, but the present invention can also be understood as a method invention called a figure pattern shape correction method. In this way, when grasping as a method invention, the present invention relates to an original graphic so that the real graphic pattern matches the original graphic pattern when the real graphic pattern is formed on the real substrate by the lithography process based on the original graphic pattern. This is a figure pattern shape correction method for correcting a pattern shape and creating a corrected figure pattern that is actually used in the lithography process.

  In this shape correction method, an evaluation point setting stage in which the computer sets an evaluation point at a predetermined position on the contour line indicating the boundary between the inside and the outside of each unit figure constituting the original figure pattern (the above-described evaluation point setting) A stage executed by the unit 110), and a feature quantity extraction stage (a stage executed by the feature quantity extraction unit 120 described above) in which the computer extracts a feature quantity indicating features around the evaluation point for the original graphic pattern; A bias estimation stage in which the computer estimates a process bias indicating the amount of deviation between the position of the evaluation point on the original graphic pattern and the position on the actual graphic pattern based on the feature amount (executed by the bias estimation unit 130 described above) And the computer is based on the process bias estimate obtained by this bias estimation step. There, by performing correction to the original figure pattern, and a pattern correction step of generating a correction figure pattern (steps performed by the above-mentioned pattern correction unit 140), the.

  Here, in the evaluation point setting stage, a unit graphic input step (step executed by the unit graphic input unit 111 described above) for inputting individual unit graphic consisting of polygons, and the unit graphic is divided by a linear dividing line A unit graphic dividing step (step executed by the unit graphic dividing unit 112 described above) for forming a divided graphic composed of a plurality of polygons, and for each divided graphic, a polygon outline constituting the divided graphic is used. A divided graphic vector defining step (a step executed by the divided graphic vector defining unit 113 described above) for defining a divided graphic vector on each side of the polygon so as to make a round around a predetermined forward direction A set of divided figure vectors is placed on overlapping sides of a pair of adjacent polygons that are adjacent to each other, and overlapping directions whose directions are opposite to each other. A unit graphic vector definition that searches for a pair of tokens, removes overlapping sections of the searched overlapping vector pair, and defines a plurality of unit graphic vectors arranged along the outline of the unit graphic with the remaining vectors A step (a step executed by the unit graphic vector definition unit 114 described above) and a normal end point definition step (executed by the normal end point definition unit 115 described above) for defining a normal end point at the start position of each unit graphic vector. Step), and an evaluation point definition step for defining an evaluation point between two normal end points arranged adjacent to each other on the contour line of the unit graphic (step executed by the evaluation point definition unit 117 described above), For each unit graphic, the middle normal end point, which is a normal end point that does not constitute the vertex of the polygon, is searched and searched. And it has a middle normal replenishment endpoint definition step of defining additional supplemental endpoint in the same position as the end point (step executed by replenishing endpoint definition part 118 described above), the.

  In practice, in the evaluation point setting stage, in addition to the above steps, an endpoint reconstruction step (described above) that performs reconstruction to correct the number or position of the regular endpoints defined by the regular endpoint definition step. It is preferable to perform the step executed by the end point reconstruction unit 116, and to define the evaluation point based on the normal end point obtained by the above reconstruction in the evaluation point definition step.

  On the other hand, in the pattern correction stage, for each evaluation point, the normal end point or supplemental end point adjacent to one side of the evaluation point along the contour line of the unit graphic is the first end point, and the normal end adjacent to the other side is used. Define a contour line segment with the end point or supplemental end point as the second end point, and orthogonally intersect the contour line segment for each evaluation point by the correction amount according to the estimated value of the process bias of the evaluation point A contour segment moving step (step executed by the above-described contour segment movement processing unit 141) for performing a moving process of moving in a moving direction, and an intermediate normal end point and a supplementary end point that were in the same position before the moving process, In the case of separation into two different positions after the movement process, an outline line adding step for adding a new outline segment connecting the positions after the respective movement processes is performed (the above-described contour line segment) The step executed by the processing unit 142) and the corner normal end point which is a normal end point constituting the vertex of the polygon before the moving process is separated into two different positions after the moving process, Contour line segment expansion / contraction step for performing expansion / contraction processing to expand / contract each contour line segment including the corner normal end point after separation so that the two corner normal end points are merged to become a new corner normal end point (described above) Steps executed by the contour line segment expansion / contraction processing unit 143).

  In the figure pattern shape correcting method according to the present invention, a corrected figure pattern constituted by unit figures whose outlines are aggregates of outline segments after the movement process, the addition process, and the expansion / contraction process are performed. Is created. If such a shape correction method is adopted, when performing a simulation necessary for correcting the original figure pattern, an efficient evaluation point setting capable of reducing the calculation burden as much as possible while maintaining a practically sufficient simulation accuracy is performed. It becomes possible.

<8.2 Merits of defining endpoints using divided figures>
Here, the merit in the exposure process obtained by adopting the present invention will be described. An important feature of the present invention is that the unit figure constituting the original figure pattern is divided into divided figures composed of polygons, the end points are defined with reference to the vertex positions of the polygons, and the two arranged adjacently. An evaluation point is defined for each contour segment connecting two end points, and the position is corrected for each contour segment. By defining evaluation points in this way, it is possible to define an appropriate number of evaluation points at appropriate positions, so that when performing corrections to the original figure pattern, practically sufficient simulation accuracy is maintained. However, it is possible to set an efficient evaluation point that can reduce the calculation burden as much as possible.

  In addition, if the end points are defined based on the positions of the vertexes of the polygons forming the divided figure, the merit that the total number of shots can be reduced in the exposure process can be obtained. That is, in the conventional general method, a method of defining end points at predetermined intervals for each side of the unit graphic is adopted. However, such a conventional method has a demerit that the total number of shots increases. . In the present invention, such disadvantages can be eliminated. Hereinafter, this point will be described with specific examples.

  FIG. 60 is a plan view showing a procedure of a conventional method for defining end points at predetermined intervals for each side of a unit graphic. Now, when an original graphic pattern including a unit graphic 10 as shown in FIG. 60 (a) is given, a plurality of end points are defined on the contour line of the unit graphic 10 and two adjacent end points are connected. Consider making a correction by defining an evaluation score every minute. In this case, first, the vertices of the polygon forming the unit graphic 10 are defined as end points, and the end points are further defined at predetermined intervals on each side of the polygon. Here, for convenience of explanation, the vertical dimension of the unit graphic 10 is Wsplit, and the end points are defined on each side of the unit graphic 10 at predetermined intervals equal to or less than Wsplit.

  FIG. 60B is an example in which the end points A to N are defined on the contour line on the unit graphic 10 with such a policy. Here, the end points A, E, F, G, H, L, M, and N are the vertices of the polygon that forms the unit graphic 10, but the remaining end points B, C, D, I, J, and K are , Are endpoints defined on the sides of the polygon. As described above, since the end points are defined so that the interval between the adjacent end points is equal to or less than Wsplit, the interval between the end points is equal to or less than Wsplit, and the contour line sandwiched between the two adjacent end points The total length of the minutes is less than Wsplit.

  However, since the end points are defined independently for each side of the unit graphic 10, the end points B, C, D defined on the upper side of the polygon, and the end points I, C defined on the lower side of the polygon. There is no positional consistency between J and K. In other words, the lateral positions of the end points B, C, D are not aligned with the lateral positions of the end points I, J, K (see the broken line in FIG. 60 (b)).

  Since the shape correction for the unit graphic 10 is performed by moving individual contour segments, the corrected unit graphic 15 has a shape as shown in FIG. 60 (c), for example. That is, the corrected unit graphic 15 shown in FIG. 60 (c) moves the contour lines BC, CD, DE in the unit graphic 10 before correction shown in FIG. Is slightly moved outward, and the contour line segment JK is slightly moved inward.

  A general drawing apparatus used in the lithography process employs an operation of exposing a trapezoidal region with one shot, and the corrected unit graphic 15 shown in FIG. 60 (c) is used in such a drawing apparatus. In order to perform the exposure process based on the above, it is necessary to divide into a large number of rectangular areas as indicated by broken lines in the figure and to perform exposure by individual shots. That is, in the actual exposure process, it is necessary to perform individual shots for each of the nine independent rectangles shown by hatching in FIG. 60 (d), and the total number of shots is nine. As described above, in the conventional method, since the positions of the end points defined on the opposite sides of the polygon forming the contour line are not aligned, there is a demerit that the total number of shots increases when the contour line is a regular figure ( When the contour line is an anti-figure, such a disadvantage does not occur so much).

  On the other hand, FIG. 61 is a plan view showing the procedure in the case where the endpoints are defined based on the vertex positions of the polygons constituting the divided figure by the method according to the present invention. The unit graphic 10 shown in FIG. 61 (a) is exactly the same as the unit graphic 10 shown in FIG. 60 (a). Here, a plurality of end points are formed on the outline of the unit graphic 10 by the method according to the present invention. Let us consider defining and performing correction by defining an evaluation point for each contour segment connecting two adjacent end points.

  In this case, first, the unit figure 10 is divided into a plurality of divided figures. FIG. 61 (b) shows a state in which the unit graphic 10 is divided into five divided graphics. As described above, the division processing in the present invention is performed so that the size of each divided figure is equal to or less than the predetermined division interval Wsplit. Therefore, the vertical and horizontal dimensions of the five divided figures shown in FIG. Are both below Wsplit. A normal end point is defined at each vertex position of these five divided figures. FIG. 61 (b) shows a state in which normal end points A to N are defined on the contour line on the unit graphic 10 in such a manner. Here, the end points A, E, F, G, H, L, M, and N are corner normal end points that are the vertices of the polygon that forms the unit graphic 10, and the remaining end points B, C, D, and I , J, K are intermediate normal end points.

  When FIG. 60 (b) is compared with FIG. 61 (b), the points where 14 end points A to N are defined are the same, but in the former, the end points B, C, Whereas the position of D and the lateral positions of the end points I, J, and K defined on the lower side are not aligned and there is no consistency, in the latter, the lateral positions of the upper and lower end points are aligned and the consistency is ensured. Has been.

  FIG. 61 (c) shows a corrected unit graphic 15 obtained by correcting the unit graphic 10 shown in FIG. 61 (b). The unit graphic 15 after correction is obtained by moving the contour line segments BC, CD, DE in the unit graphic 10 before correction shown in FIG. 61 (b) slightly inward and moving the contour line segment IJ slightly outward. The line segment JK is slightly moved inward. FIG. 61 (d) is a diagram showing individual rectangular areas divided for performing the exposure process based on the unit graphic 15 after correction.

  When performing the splitting process shown in FIG. 61 (b), if the splitting interval Wsplit is set to be equal to or smaller than the maximum beam forming size Bmax of the drawing apparatus (setting Wsplit ≦ Bmax), the individual processing shown in FIG. 61 (d) is performed. The size of the rectangular area is likely to be equal to or less than the maximum beam forming size Bmax. The exposure process is performed by performing individual shots for each of the individual rectangular areas, and a rectangular area having a size of Bmax or less can be exposed with one shot by the drawing apparatus. In the case of the example shown in FIG. 61 (d), the size of any rectangular area shown by hatching is equal to or less than Bmax. Therefore, in the actual exposure process, each of the five independent rectangular areas has a separate 1 All you need is a shot.

  As a result, in the case of the above-described embodiment, a total of 9 shots (see FIG. 60 (d)) are required in the exposure method in the conventional method, whereas in the method of the present invention, a total of 5 shots are required. It will be over. As described above, in the present invention, since the end point definition using the divided figure is performed, there is an advantage that the efficiency of the exposure process (reduction of the total number of shots) can be achieved. Of course, depending on the moving direction and moving amount of each contour line when creating the corrected unit graphic 15 shown in FIG. 61 (c), the size of each rectangular area obtained after correction is the maximum beam forming size Bmax. In this case, the rectangular area cannot be exposed in one shot. However, if the method according to the present invention is employed, a total shot of the entire figure pattern including a large number of unit figures is obtained. The number will always decrease statistically.

<8.3 Benefits of defining supplemental endpoints>
In the present invention, as described above, normal end points are defined using divided graphics, and supplementary end points are additionally defined at the same positions for intermediate normal end points that are normal end points that do not constitute polygon vertices. Here, the merit of defining the supplementary end point for the intermediate normal end point will be described.

  The reason why the replenishment endpoints are defined in the present invention is that, as described in §6.5, two sets of contour segments located on both sides of one intermediate normal endpoint are separately and independently moved. For example, in the embodiment shown in FIG. 56, the supplemental end point F ′ is additionally defined at the position of the intermediate normal end point F so that the contour line segment O5 and the contour line segment O6 can be moved independently. Thus, by additionally defining the supplementary end point H ′ at the position of the intermediate normal end point H, the contour line segment O 7 and the contour line segment O 8 can be moved separately and independently.

  Moreover, in the present invention, the movement processing by the contour line segment movement processing unit 141 moves each evaluation point in a direction orthogonal to the contour line where the evaluation point is located (normal direction: the direction of the thick arrow in FIG. 56). Therefore, the moving direction of the contour line to be translated along with the evaluation point is also the normal direction. When such movement processing is performed, the intermediate normal end point after the movement and the supplementary end point thereof both exist on the normal line with respect to the position before the movement. For example, in the example shown in FIG. 56, the lateral positions of the end points F and F ′ after the movement are not different from those before the movement, and the vertical positions of the end points H and H ′ after the movement are the same as before the movement. Such a feature contributes to improving the efficiency of the exposure process (reducing the total number of shots).

  FIG. 62 is a plan view showing the merit of defining the supplement end point. Now, consider a case in which a rectangular unit graphic 10 as shown in FIG. 62A is given, and shape correction is performed on the rectangular unit graphic 10 by the method according to the present invention. Here, it is assumed that the unit graphic 10 is a rectangle having dimensions of a vertical width Wsplit and a horizontal width 4 × Wsplit. Here, Wsplit is a division interval of the division processing performed by the unit graphic division unit 112, and for convenience of explanation, consider a case where the maximum beam forming size of the drawing apparatus is set to Bmax and Wsplit = Bmax is set.

  FIG. 62B is a plan view showing a state in which the unit graphic 10 shown in FIG. 62A is divided by the unit graphic dividing unit 112. As shown in the figure, the unit graphic 10 is divided into four square-shaped divided figures shown by hatching, and the vertex position of each divided figure is set to 10 pieces as shown in FIG. Usually, end points A to J (x marks) are defined. Further, the replenishment end point defining unit 118 places the replenishment end points B ′, C ′, D ′, G ′, H ′, I ′ (square marks) at the same positions for the intermediate normal end points B, C, D, G, H, and I. Is additionally defined.

  Here, as a result of the correction processing performed by the pattern correction unit 140 on the unit graphic 10 shown in FIG. 62 (b), the corrected unit graphic 15 as shown in FIG. 62 (c) is obtained. Let's take it. Specifically, the contour line segments BC ′, CD ′, GH ′, HI ′ are slightly moved inward by the contour line segment movement processing unit 141, and the end points C ′ are between the end points B′-B. -C, end point D'-D, end point G'-G, end point H'-H, and end point I'-I are newly updated by the contour line segment addition processing unit 142. A new outline is added.

  However, since each contour line segment is moved in the normal direction, the end points B ′, B, C ′, C, D ′, D, G ′, G, H ′, H, I ′ after the movement process are used. , I in the horizontal direction is the same as the position before the movement process. Therefore, when the actual exposure process is performed based on the corrected unit graphic 15, if the setting of Wsplit = Bmax is made as described above, a thick square (one side is a drawing device) is shown in FIG. The exposure is completed by performing a total of four shots, as shown by the square having the maximum beam forming size Bmax. Of course, in the correction process shown in FIG. 62 (c), when a movement process for moving each contour segment to the outside of the figure is performed, a part having a vertical width exceeding Bmax occurs, and a total of four shots cannot be completed. However, the total number of shots for the entire graphic pattern including a large number of unit graphics is necessarily reduced statistically.

  Such a merit is also effective when the correction process described in §7.4 is repeated. For example, after the unit graphic 15 shown in FIG. 62 (c) is obtained by the first correction for the unit graphic 10 shown in FIG. 62 (a), the corrected unit graphic 15 is further corrected. Consider the case where the corrected unit graphic 16 shown in FIG. 63A is obtained by performing the second correction. The unit graphic 16 shown in FIG. 63 (a) is obtained by moving the contour segments BC ′, CD ′, GH ′, HI ′ of the unit graphic 15 shown in FIG. 62 (c) further inward. The lateral positions of the rear end points B ′, B, C ′, C, D ′, D, G ′, G, H ′, H, I ′, and I are not changed from the positions before the movement process.

  As shown in the data format example of FIG. 55, for the normal end points A, B, C, D, E, F, G, and H, the corresponding evaluation points 1 to 8 are recorded, whereas the supplementary end points F are recorded. For ′ and H ′, empty data of an evaluation point “Φ” that does not exist is recorded. This means that the evaluation point is not defined on the contour line segment added by the contour segment addition processing unit 142. Therefore, in the case of the example shown in FIG. 63 (a), the contour line segments B′B, C′C, D′ D, G′G, H′H, I′I added by the contour line segment addition processing unit 142 are used. There is no evaluation point above, and the movement processing based on the movement of the evaluation point position is not performed on these contour line segments. In other words, the position in the horizontal direction of these contour line segments remains unchanged even if the correction process is repeated many times.

  In the present invention, the significance of defining the supplementary end point at the same position as the intermediate normal end point is that when the correction process is performed, the positions of the intermediate normal end point and the supplemental end point change only in the normal direction of the contour line. Therefore, it is possible to perform an operation that does not change in the direction along the line, and such an operation provides a merit of improving the efficiency of the exposure process (reducing the total number of shots).

  FIG. 64 is a plan view showing disadvantages when the intermediate normal end point and the supplementary end point are moved in an arbitrary direction. Here, FIG. 64 (a) shows a corrected unit obtained by correcting the unit graphic 10 shown in FIG. 62 (b) by moving the positions of the intermediate normal end point and the supplemental end point in an arbitrary direction. A figure 17 is shown. In the corrected unit graphic 15 shown in FIG. 62 (c), the lateral positions of the end points B ′, B, C ′, C, D ′, D, G ′, G, H ′, H, I ′, and I are In contrast, in the unit graphic 17 after correction shown in FIG. 64A, the lateral positions of these end points are changed.

  Therefore, when an actual exposure process is performed based on the corrected unit graphic 17 shown in FIG. 64 (a), one shot of a drawing apparatus having a thick-line rectangle (maximum beam forming size Bmax) is shown in FIG. 64 (b). A total of seven shots are required, as shown by the rectangle of the size that can be exposed in (1). As described above, in the present invention, since the replenishment end points are defined and the movement direction of the intermediate normal end point and the replenishment end points is limited to the normal direction of the contour line, there is a merit of improving the efficiency of the exposure process. Will be obtained.

<8.4 Benefits of Reconstructing Endpoints>
In the embodiment of the present invention described above, the endpoints are reconstructed as described in §6.3. This reconstruction of the end points is not an essential requirement for carrying out the present invention. However, in practice, since the number and positions of the end points are corrected, the more efficient evaluation is performed. Point setting can be performed. Hereinafter, the merit by this end point reconstruction will be described based on a specific example.

  The L-shaped unit graphic 10 shown in FIG. 54 has the end point definition and the evaluation point definition as shown in FIG. 49 (b), and is indicated by a triangle mark by the end point reconstruction shown in FIG. The process which removes the end point D was performed. When correction processing is performed on the unit graphic 10 before correction shown in FIG. 54, the unit graphic 15 after correction shown in FIG. 58 is obtained as described above. The unit graphic 15 after correction has a shape that is a size larger than the unit graphic 10 before correction and is a graphic that retains the original L-shaped face shadow.

  On the other hand, the corrected unit graphic 18 shown in FIG. 65 is a graphic obtained when the end point reconstruction shown in FIG. 43 is not performed. That is, the end point Z (triangular mark) shown in FIG. 65 corresponds to the end point D shown in FIG. 43, and the corrected unit graphic 18 is obtained when it is assumed that the end point Z remains without being removed. It will be a corrected figure. Since the end point Z is an intermediate normal end point, if it remains without being removed by the end point reconstruction, the replenishment end point Z ′ is additionally defined by the process of defining the replenishment end point. The illustrated example is an example in which the intermediate normal end point Z is moved upward in the figure and the replenishment end point Z ′ is moved downward in the figure. A contour line segment Z′Z is newly added by the contour line segment adding process performed after the moving process.

  Here, when the corrected unit graphic 15 shown in FIG. 58 is compared with the corrected unit graphic 18 shown in FIG. 65, it can be seen that the contour line in the vicinity of the vertex C fluctuates significantly in the latter case. In general, in the case where the corner rounding effect (the effect of rounding the rounded portion near the vertex of the polygon) is large when the lithography process is performed, if the evaluation point exists near the vertex, the evaluation point As shown in the example shown in FIG. 65, the contour line in the vicinity of the vertex varies significantly. If the contour line in the vicinity of the vertex remarkably fluctuates, the basic shape of the figure before correction is distorted, which is not preferable for practical use.

  By reconstructing the end points described in §6.3, the end points near the vertexes of the unit graphic can be removed, and as a result, the evaluation points can be moved away from the vertices. For this reason, it can suppress that the outline of the vertex vicinity changes remarkably, and the merit that it becomes possible to perform more efficient evaluation point setting is acquired.

Lastly, the table of contents for the “Mode for Carrying Out the Invention” part is listed. The number [XXXX] after each heading is a paragraph number.
§1. Basic configuration of shape correction apparatus according to invention of prior application [0034]
1.1 Graphic pattern shape estimation device [0035]
1.2 Shape correction device for figure pattern [0056]
1.3 Basic concept of feature quantity extraction in the invention of the prior application [0071]
§2. Details of feature extraction unit [0086]
2.1 Processing Procedure by Original Image Creation Unit 121 [0087]
2.2 Processing procedure by image pyramid creation unit 122 [0103]
2.3 Processing Procedure by Feature Quantity Calculation Unit 123 [0128]
2.4 Modification of Feature Extraction Process [0144]
§3. Details of the bias estimation unit [0167]
3.1 Estimate calculation by neural network [0168]
3.2 Learning stage of neural network [0183]
§4. Geometric pattern shape estimation method according to the prior invention [0199]
§5. Basic configuration of shape correction apparatus according to the present invention [0205]
§6. Details of Evaluation Point Setting Unit [0213]
6.1 Division of unit graphic [0217]
6.2 Definition of vectors and normal endpoints [0243]
6.3 End point reconstruction [0268]
6.4 Definition of Evaluation Points [0316]
6.5 Definition of replenishment endpoints [0321]
§7. Details of pattern correction unit [0336]
7.1 Contour Line Movement Processing [0339]
7.2 Outline segment addition processing [0353]
7.3 Contour Line Stretching Process [0360]
7.4 Repeating the correction process [0367]
§8. Features and merits of the present invention [0377]
8.1 Features of the shape correction method according to the present invention [0378]
8.2 Merits of defining endpoints using divided figures [0384]
8.3 Benefits of defining supplemental endpoints [0397]
8.4 Merits of endpoint reconstruction [0409]

  The shape correction apparatus and shape correction method for a graphic pattern according to the present invention is based on a lithography process based on an original graphic pattern in a field where a specific material layer needs to be finely patterned, such as a semiconductor device manufacturing process. When forming a real figure pattern on a real substrate, it can be widely used as a technique for forming a real figure pattern having an accurate dimension.

1 to 18: Evaluation point 10: Original graphic pattern (unit graphic before correction)
10a to 10l: divided figure 10X: figure main body part 10Y: perforated part 15: corrected figure pattern (unit figure after correction)
15a to 10d: corrected divided figures 16, 17, 18: corrected unit figure 20: actual figure pattern 100: figure pattern shape correcting device 100 ': figure pattern shape estimating device 110: evaluation point setting unit 111: Unit graphic input unit 112: Unit graphic dividing unit 113: Divided graphic vector defining unit 114: Unit graphic vector defining unit 115: Normal endpoint defining unit 116: Endpoint reconstruction unit 117: Evaluation point defining unit 118: Supplementing endpoint defining unit 120: Feature amount extraction unit 121: original image creation unit 122: image pyramid creation unit 123: feature amount calculation unit 130: bias estimation unit 131: feature amount input unit 132: estimation calculation unit 140: pattern correction unit 141 1: contour line segment movement processing Unit 142: contour line segment addition processing unit 143: contour line segment expansion / contraction processing units A to D: individual pixels / individual pixels Pixel values A to Z: End points a to d: Horizontal distances or vertical distances A1 to A4 between the evaluation point E and the center point of each pixel A1 to A4: Forward arrows A0: Corner normal end points A1, A2 before moving processing: Normal corner end point Bmax after movement processing: Maximum beam forming size b, b (1, 1) to b (i + 1, M (i + 1)), b (N + 1): Neural network parameters C1, C2: Reference circle D1 Dn: difference images E, E11 to E23: evaluation points F1 to F5: figures (rectangles) constituting the original figure pattern 10
f (ξ): function used for calculation of neural network G: apportioned value GF33, GF55: Gaussian filter H: apportioned value h (1,1) to h (N, M (N)): neurons in hidden layer of neural network / The calculated value i: Parameter indicating the number of hidden layers of the neural network J: Intersection of two straight lines k: Parameter indicating the image number L: Learning information LF33, LF55: Laplacian filters L1, L2, L3: Distance Lcd between the end points , Lde, Lij: Distance between end points Leven: Distance between adjacent end points (equal interval)
Lod: Distance between adjacent end points (fractional interval)
Lreg: spacing between adjacent end points (reference spacing)
M1: Area density map M2: Edge length density map M3: Dose density maps M (1) to M (N): Dimensions of each hidden layer of the neural network N: Number of hidden layers of the neural network / total number of end points n: Image Number of pyramid layers / endpoint numbers O, O1 to O8, O5 ', O7': contour segment Oa, Ob: contour segment Oin: inner contour line (anti-graphic)
Oout: Outer outline (regular figure)
P1 to Pn: hierarchical image Pk: k-th hierarchical image PC: corrected image PD: image pyramid (sub-image pyramid)
PP: Image pyramid (main image pyramid)
Q1: First preparation image (original image)
Qk: k-th preparation image S: actual substrates S1 to S848: steps SS1 to SS44 of the flowchart: steps T1, T2, T (n-1), T (n), T (n + 1), T of the flowchart (N + 2): normal end points T ′, T (n) ′, B ′ to Z ′ ,: supplementary end points U: pixels u: pixel dimensions V1 to V20: unit graphic vectors Va1 to Vh4: divided graphic vectors W, W (1 11) to W (N + 1,1M (N)): Neural network parameters Wmerge: Fusion reference value Wrest: Residual portion width Wsplit: Split interval X: Coordinate axes x, x1 to xn on two-dimensional XY plane Y: coordinate axes y, y11 to y13 on the two-dimensional XY plane: process bias Z: deleted endpoints ξ: arguments ξ1 to ξ4 of function f: vertex of divided figure Φ: empty data of evaluation points that do not exist

Claims (21)

When the real graphic pattern (20) is formed on the real substrate (S) by the lithography process based on the original graphic pattern (10), the real graphic pattern (20) matches the original graphic pattern (10). A figure pattern shape correction apparatus (100) for correcting the shape of the original figure pattern (10) to create a corrected figure pattern (15) actually used in the lithography process,
An evaluation point setting unit (110) for setting an evaluation point (E) at a predetermined position on the contour line indicating the boundary between the inside and the outside of each unit figure (10) constituting the original figure pattern (10);
A feature amount extraction unit (120) for extracting feature amounts (x1 to xn) indicating features around the evaluation point (E) for the original figure pattern (10);
Based on the feature quantities (x1 to xn), a process bias (y indicating a deviation amount between the position of the evaluation point (E) on the original figure pattern (10) and the position on the real figure pattern (20) ) A bias estimation unit (130) for estimating
A pattern correction unit (15) for generating a corrected graphic pattern (15) by correcting the original graphic pattern (10) based on the estimated value (y) of the process bias output from the bias estimation unit (130). 140)
With
The evaluation point setting unit (110)
A unit graphic input unit (111) for inputting individual unit graphic (10) composed of polygons;
A unit graphic dividing unit (112) for dividing the unit graphic (10) with a linear dividing line to form a divided graphic (10a to 10l) composed of a plurality of polygons;
For each of the divided figures (10a to 10l), a divided figure vector (Va1) is placed on each side of the polygon so as to make a round around a predetermined forward direction along the outline of the polygon constituting the divided figure. To Vh4), a divided graphic vector defining unit (113);
From the set of divided graphic vectors (Va1 to Vh4), a search is made for overlapping vector pairs that are arranged on overlapping sides of a pair of adjacent polygons adjacent to each other and whose directions are opposite to each other. A unit graphic vector defining unit (114) that defines a plurality of unit graphic vectors (V1 to V20) arranged along the outline of the unit graphic (10) by removing the overlapping section portion of the unit graphic (10). )When,
A normal end point definition unit (115) for defining a normal end point (T) at the start point position of each unit graphic vector (V1 to V20);
An evaluation point defining unit (117) for defining an evaluation point (E) between two normal end points (T) arranged adjacent to each other on the contour line of each unit graphic (10);
For each unit graphic (10), an intermediate normal end point that is a normal end point (T) that does not constitute a vertex of the polygon is searched, and a supplementary end point (T ′) is additionally defined at the same position as the searched intermediate normal end point. A replenishment endpoint definition section (118);
Have
The pattern correction unit (140) is
For each evaluation point (E), the normal end point (T) or the supplemental end point (T ′) adjacent to one side of the evaluation point (E) along the outline of the unit graphic (10) is the first end point. And defining a contour line segment having the second end point as the normal end point (T) or the supplemental end point (T ′) adjacent to the other side, and the contour line segment for each evaluation point (E) An outline segment movement processing unit (141) for performing a movement process for moving in the direction orthogonal to the outline segment by a correction amount corresponding to the estimated value (y) of the process bias at the point (E);
When the intermediate normal end point and the replenishment end point (T ′) that were in the same position before the moving process are separated into two different positions after the moving process, new contour line segments that connect the positions after the moving process are displayed. A contour line segment addition processing unit (142) for performing additional processing;
When the corner normal end point, which is the normal end point (T) constituting the vertex of the polygon before the movement process, is separated into two different positions after the movement process, the two corner normal end points after separation are merged. A contour line segment expansion / contraction processing unit (143) for performing expansion / contraction processing to expand and contract each contour line segment including the corner normal end point after separation so as to become a new corner normal end point,
And creating a corrected graphic pattern (15) composed of unit graphics (10) whose contour line is an aggregate of contour line segments after performing the moving process, the adding process, and the expansion / contraction process. A figure pattern shape correction apparatus (100) characterized by In the graphic pattern shape correction apparatus (100) according to claim 1,
A figure pattern shape correction apparatus (100), wherein the unit figure dividing unit (112) divides the unit figure (10) to form a divided figure consisting of trapezoids. In the shape correction apparatus (100) for a graphic pattern according to claim 1 or 2,
When the unit graphic input unit (111) inputs an elongated strip-shaped unit graphic (10) having a linear upper side and a lower side that extend along a predetermined longitudinal axis and are parallel to each other,
The unit graphic dividing unit (112) divides the band-shaped unit graphic (10) by a plurality of dividing lines arranged at predetermined intervals along the longitudinal axis, thereby one-dimensionally along the longitudinal axis. A figure pattern shape correction apparatus (100) characterized by forming a plurality of divided figures arranged side by side. In the shape correction apparatus (100) for a graphic pattern according to claim 1 or 2,
When the unit graphic input unit (111) inputs the unit graphic (10) defined on the XY plane,
The unit figure dividing unit (112) arranges a plurality of horizontal dividing lines parallel to the X axis at predetermined intervals in the Y axis direction, and divides the unit figure (10) by the plurality of horizontal dividing lines, By forming a plurality of elongated strips extending in the X-axis direction, and dividing each of the plurality of strips by a plurality of vertical dividing lines arranged at predetermined intervals along the X-axis and parallel to the Y-axis A figure pattern shape correcting apparatus (100), wherein a plurality of divided figures arranged two-dimensionally are formed. In the shape correction apparatus (100) for a graphic pattern according to any one of claims 1 to 4,
The unit graphic dividing unit (112) has a function of setting the maximum beam forming size of the drawing apparatus used in the lithography process, and the arrangement interval of the dividing lines used for dividing the unit graphic (10) is less than the maximum beam forming size. A shape correction apparatus (100) for a graphic pattern characterized by setting. In the shape correction apparatus (100) for a graphic pattern according to any one of claims 1 to 5,
The divided graphic vector defining unit (113) assigns numbers to the vertices of the K-shaped divided graphic in the order of the first vertex to the Kth vertex in the clockwise or counterclockwise order along the contour line. The process of defining the kth divided figure vector (Va1 to Vh4) starting from the vertex of k and ending at the (k + 1) th vertex (where k = K, the first vertex) is k = A figure pattern shape correction apparatus (100) characterized by defining a divided figure vector for the divided figure by repeatedly performing steps 1 to K. In the shape correction apparatus (100) for a graphic pattern according to any one of claims 1 to 6,
The figure pattern shape correction apparatus, wherein the evaluation point definition unit (117) defines an evaluation point at the midpoint position of two normal end points arranged adjacent to each other on the contour line of the unit graphic (10) (100). In the shape correction apparatus (100) for a graphic pattern according to any one of claims 1 to 7,
The replenishment end point definition unit (118) defines a total of N normal end points defined for one contour line in the order along the contour line, respectively, from the first normal end point T (1) to the Nth normal end point. When calling T (N), paying attention to the nth normal end point T (n), the (n-1) th normal end point T (n-1) (however, if n = 1, the Nth Normal end point T (N)), nth normal end point T (n), and (n + 1) th normal end point T (n + 1) (where n = N, the first normal end point T (1)) When the three points are on a straight line, the n-th normal end point T (n) is determined as an intermediate normal end point, and n = 1 to N The figure pattern shape correction apparatus (100), which is repeatedly executed. In the shape correction apparatus (100) for a graphic pattern according to any one of claims 1 to 8,
When the contour line segment expansion / contraction processing unit (143) separates one corner normal end point into the first moving end point and the second moving end point by the moving process, the first moving end point is set as one end point. An intersection of a straight line including the first post-movement contour line segment and a straight line including the second post-movement contour line segment having the second movement end point as one end point is obtained, and the intersection point is determined as a new corner. A normal end point is used, and an expansion / contraction process is performed on the first post-movement contour segment and the second post-movement contour segment so that one end point becomes the new corner normal end point. Shape correction apparatus for graphic pattern (100). In the shape correction apparatus (100) for a graphic pattern according to any one of claims 1 to 9,
The evaluation point setting unit (110) performs an end point restructuring unit (rebuild for correcting the number or position of the normal end points defined on the outline of the unit graphic (10) by the normal end point definition unit (115) ( 116),
The figure pattern shape correction device (100), wherein the evaluation point definition unit (117) defines evaluation points based on the normal end points obtained by the reconstruction. In the shape correction apparatus (100) of the graphic pattern according to claim 10,
The end point reconstruction unit (116) reconstructs the normal end point (T) by the end point removal processing for removing a part or all of the intermediate normal end point for a part or all of the unit graphic (10). A figure pattern shape correction apparatus (100). In the shape correction apparatus (100) of the graphic pattern according to claim 11,
The end point reconstruction unit (116) sets a total of N normal end points defined for one contour line of one unit graphic (10) in the order along the contour line, respectively, as the first normal end point T. (1) to Nth normal end point T (N). Focusing on the nth normal end point T (n), the nth normal end point T (n) and the removal target located immediately before it. Normal end point T (n−m) (where m is a natural number, and when n−m <1, T (n−m + N)) is L1, and the nth normal end point T ( n) and the (n + 1) th normal end point T (n + 1) (however, when n = N, the first normal end point T (1): the same applies hereinafter) when the distance is L2.
At least one of L1 and L2 is equal to or less than a predetermined reference value Wmerge, and normal end point T (n-1) (where N = 1, Nth normal end point T (N)), T (n) , T (n + 1) are on the straight line, the determination process for removing the nth normal end point T (n) is repeatedly executed from n = 1 to N, and the removal target is obtained. A shape correction apparatus (100) for a graphic pattern, which performs an end point removal process for removing normal end points. In the shape correction apparatus (100) of the graphic pattern according to claim 11,
The end point reconstruction unit (116) sets a total of N normal end points defined for one contour line of one unit graphic (10) in the order along the contour line, respectively, as the first normal end point T. (1) to the Nth normal end point T (N), the nth normal end point T (n), and the normal end point T (n−m) (m) Is a natural number, and when n−m <1, the distance from T (n−m + N)) is L1, and the nth normal end point T (n) and the (n + 1) th normal end point T (n + 1) (However, when n = N, the distance between the first normal end point T (1): the same applies hereinafter) is L2, and the (n + 1) th normal end point T (n + 1) and the (n + 2) th normal end point T (n + 2) (however, when n = N−1, the first normal end point T (1), when n = N, the second normal end point T (2): the same applies hereinafter. ) The distance between the when the L3,
L2 is equal to or less than a predetermined reference value Wmerge, and normal end point T (n-1) (where n = 1, Nth normal end point T (N): the same applies hereinafter), T (n), T When the four points (n + 1) and T (n + 2) are on a straight line, if L1 <L3, the normal end point T (n) is to be removed, and if L1> L3, the normal end point T (n + 1) is selected. If it is a removal target, and L1 = L3, either the normal end point T (n) or the normal end point T (n + 1) is the removal target,
L2 is equal to or less than a predetermined reference value Wmerge, and the three normal end points T (n−1), T (n), and T (n + 1) are on a straight line, but the normal end point T (n + 2) is the straight line. If it is not on the line, the normal endpoint T (n) is the removal target,
L2 is equal to or less than a predetermined reference value Wmerge, and the three normal end points T (n), T (n + 1), and T (n + 2) are on a straight line, but the normal end point T (n-1) is the straight line. If it is not on the line, the normal end point T (n + 1) is to be removed,
The graphic pattern shape correction device (10) is executed by repeatedly performing the above process while increasing n by 1 until n ≧ N is satisfied, and performing the end point removal processing for removing the normal end point to be removed ( 100). In the shape correction apparatus (100) of the graphic pattern according to claim 10,
The end point reconstruction unit (116) temporarily removes the intermediate normal end points for a part of the contour lines, and arranges new intermediate normal end points on each side of the part of the contour lines, thereby performing normal end points. The figure pattern shape correction apparatus (100) characterized by reconstructing In the shape correction apparatus (100) of the graphic pattern according to claim 14,
After the end point restructuring unit (116) removes the intermediate normal end point for the specific contour line, the end point rearrangement process is performed by rearranging the intermediate normal end point at predetermined intervals on each side of the specific contour line. A figure pattern shape correcting apparatus (100) characterized by In the shape correction apparatus (100) of the graphic pattern according to claim 10,
The end point reconstruction unit (116) performs the end point removal processing according to any one of claims 11 to 13 and the end point rearrangement processing according to claim 14 or 15 for each contour line of the unit graphic (10). It has a function to execute selectively,
For normal end points on a regular figure surrounded by unit figure vectors (V1 to V20) around the forward direction, the end points are reconstructed by the end point removal processing, and the unit around the reverse direction opposite to the forward direction is used. A figure pattern shape correction apparatus (100), characterized in that, for normal end points on an anti-figure surrounded by figure vectors (V1 to V20), end point reconstruction is performed by the end point rearrangement process. In the shape correction apparatus (100) of the graphic pattern according to any one of claims 1 to 16,
The feature quantity extraction unit (120) indicates the feature quantity (E) on the corrected figure pattern (15) around the evaluation point (E) on the corrected figure pattern (15) created by the pattern correction unit (140). x1 to xn) has a function of extracting
The bias estimation unit (130) shifts the position of the evaluation point (E) between the position on the corrected graphic pattern (15) and the position on the actual graphic pattern (20) based on the feature values (x1 to xn). A function to estimate a process bias (y) indicating a quantity;
The pattern correction unit (140) performs a further correction on the corrected graphic pattern (15) based on the estimated value of the process bias (y) output from the bias estimation unit (130), so that a new correction is performed. It has a function to create a graphic pattern (15),
A graphic pattern shape correction apparatus (100), wherein correction for a corrected graphic pattern (15) is repeatedly executed. In the shape correction apparatus (100) of the graphic pattern according to claim 17,
The contour line segment expansion / contraction processing unit (143) performs a process of correcting the position of the evaluation point (E) for the contour line segment after the expansion / contraction process after performing the process of expanding / contracting the contour line segment. Shape correction apparatus for graphic pattern (100).   Computer as the graphic pattern shape correction device (100) according to any one of claims 1 to 18, or the evaluation point setting unit (110) or pattern correction unit (140) included in the graphic pattern shape correction device (100) A program that makes it work. When the real graphic pattern (20) is formed on the real substrate (S) by the lithography process based on the original graphic pattern (10), the real graphic pattern (20) matches the original graphic pattern (10). The figure pattern shape correcting method for correcting the shape of the original figure pattern (10) to create a corrected figure pattern (15) actually used in the lithography process,
An evaluation point setting step (S2) in which the computer sets an evaluation point (E) at a predetermined position on the contour line indicating the boundary between the inside and the outside of each unit figure (10) constituting the original figure pattern (10). )When,
A feature amount extraction step (S3) in which the computer extracts feature amounts (x1 to xn) indicating features around the evaluation point (E) for the original figure pattern (10);
A process in which the computer indicates a deviation amount between the position of the evaluation point (E) on the original graphic pattern (10) and the position of the actual graphic pattern (20) based on the feature values (x1 to xn). A bias estimation step (S4) for estimating the bias (y);
Pattern correction for creating a corrected graphic pattern (15) by the computer correcting the original graphic pattern (10) based on the estimated value (y) of the process bias obtained in the bias estimation step (S4) Stage (S5);
Have
The evaluation point setting step (S2)
A unit graphic input step (111) for inputting individual unit graphic (10) composed of polygons;
A unit graphic dividing step (112) for dividing the unit graphic (10) with a linear dividing line to form a divided graphic consisting of a plurality of polygons;
For each of the divided figures, a divided figure vector (Va1 to Vh4) is defined on each side of the polygon so as to go around the predetermined forward direction along the outline of the polygon that forms the divided figure. A divided figure vector defining step (113) to perform,
From the set of divided graphic vectors (Va1 to Vh4), a search is made for overlapping vector pairs that are arranged on overlapping sides of a pair of adjacent polygons adjacent to each other and whose directions are opposite to each other. A unit graphic vector defining step (114) of removing a plurality of overlapping section portions and defining a plurality of unit graphic vectors (V1 to V20) arranged along the outline of the unit graphic (10) by the remaining vectors. )When,
A normal end point defining step (115) for defining normal end points (T) at the start point positions of the individual unit graphic vectors (V1 to V20);
An evaluation point defining step (117) for defining an evaluation point (E) between two normal end points (T) arranged adjacent to each other on the contour line of the unit graphic (10);
For each unit graphic (10), an intermediate normal end point that is a normal end point that does not constitute a vertex of the polygon is searched, and a replenishment end point defining step (118) for additionally defining a replenishment end point at the same position as the searched intermediate normal end point When,
Have
The pattern correction step (S5)
For each evaluation point (E), the normal end point (T) or the supplemental end point (T ′) adjacent to one side of the evaluation point (E) along the outline of the unit graphic (10) is the first end point. And defining a contour line segment having the second end point as the normal end point (T) or the supplemental end point (T ′) adjacent to the other side, and the contour line segment for each evaluation point (E) A contour segment moving step (141) for performing a movement process for moving the point (E) in a direction orthogonal to the contour segment by a correction amount corresponding to the estimated value (y) of the process bias;
When the intermediate normal end point and the replenishment end point (T ′) that were in the same position before the moving process are separated into two different positions after the moving process, new contour line segments that connect the positions after the moving process are displayed. A contour segment adding step (142) for performing additional processing;
If the corner normal end point, which is the normal end point that formed the vertex of the polygon before the movement process, is separated into two different positions after the movement process, the two corner normal end points after the separation are merged to form a new one. A contour line segment expansion / contraction step (143) for performing expansion / contraction processing to expand / contract each contour line segment including the corner normal end point after separation so as to be a corner normal end point;
And creating a corrected graphic pattern (15) composed of unit graphics (10) whose contour line is an aggregate of contour line segments after performing the moving process, the adding process, and the expansion / contraction process. A shape correction method for a graphic pattern characterized by the above. The shape correction method for a graphic pattern according to claim 20,
The evaluation point setting stage (S2) further includes an end point restructuring step (116) for performing restructuring to correct the number or position of the normal end point (T) defined by the normal end point defining step (115). ,
In the evaluation point definition step (117), the evaluation point (E) is defined on the basis of the normal end point (T) obtained by the reconstruction, and a shape correction method for a graphic pattern.

Images