JPH04363044A - Recognition method of two-dimensional shape in semiconductor evaluation method - Google Patents

Abstract

PURPOSE:To recognize the positional relationship of strings and points at high speed and to shorten the evaluation time of a semiconductor element. CONSTITUTION:A line segment 901 before a point Pi is turned clockwise, and it is made to coincide with a line segment 902 behind the point pi. In this case, when the angle of rotation is designated as -xsii, the sum total SIGMADELTAi of angles at the point Pi is -2pi-xsii, and an angle SIGMADELTAi-1 at a point Pi-1 which is by one prior to the point Pi is -xsii-1. In the same manner, the SIGMADELTAj is -2pi-xsij and the SIGMADELTAj-1 is -xsij-1. Thereby, when the sum total of the angles is -2pi-xsi, a loop 903 is formed; when the sum total is -xsi, the loop is not formed. Based on this, it is judged whether a point of intersection 904 is generated or not. A point of intersection C1 exists on a line segment between thetai-1 and thetai where the sum total of the angles is changed. In the same manner, a point of intersection C2 exists on a line segment between thetaj and thetaj-1. Based on this, a point of intersection is computed.

Description

[Detailed description of the invention]

[Object of the invention]

0002

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a two-dimensional shape recognition method used in evaluating semiconductor devices.

0003

2. Description of the Related Art Conventionally, in a two-dimensional shape recognition method that handles a two-dimensional space, a string model representing the shape of a material region as shown in FIG. 3 is generally used. The string model is a two-dimensional shape 302 of a material by a series (string) 301 of line segments Si connecting points Pi and Pi+1.
represents. Therefore, the data to be stored are the coordinates of the points, the number of the starting point of the point sequence, and the order of the point sequence 303, and are easy to handle. Here, the starting point can be selected from any one point in the point sequence.

This two-dimensional shape recognition method is based on process simulation technology (for example, S.M. Sze, “VLSI TECHN
OLOGY'', McGraw-Hill, 1983).The numerical calculation program used in this process simulation is called a process simulator.

Using the conventional two-dimensional shape recognition method, FIG.
When a process simulation of a material deposition process is performed using a string model as shown in FIG. 1, strings 401 representing the surface shape may intersect with each other, resulting in loops 402 and hollow regions 403. This poses a problem in that the simulation cannot be performed correctly. This phenomenon is a serious problem because the loop 402 occurs more frequently when the number of line segments is increased in order to accurately represent the surface shape.

FIG. 5 is an enlarged view of the portion in FIG. 4 where a loop occurs. Conventionally, by moving a string 502 representing the surface shape of the base material 501 due to deposition (FIG. 5(a)), a newly deposited material region 503 is moved.
Loop 5 generated in string 504 representing the surface shape of
05 was erased by generating a new point 507 at the intersection 506 (FIG. 5(b)).

In that case, it is necessary to determine whether the strings 504 intersect, and if the number of line segments is N, it is necessary to determine whether one line segment intersects with another line segment. must be performed (N-1)/2 times, the calculation time increases parabolically as the number of line segments increases.

Furthermore, when performing a process simulation of the etching process, as shown in FIG. 6(a), a string 601 representing the shape of the surface material intersects with a string 602 representing the underlying material 606, resulting in a calculated overlapping region 60.
3 may occur, making it impossible to perform a correct simulation. Overlapping area 60 as shown in FIG. 6(b)
3, it is determined whether a point of a string 601 representing the shape of the surface material exists inside the base material region 606, and if it exists, it is erased by generating a new point 605 at the intersection 604. At this time, as shown in FIG. 7, whether or not the point R exists inside the region 701 can be determined by, for example,
Let the angle defined by and point R be δi, and the number of line segments be n, then

[0009]

[Math 1]

The integral value of the angle is 2π when the point R is inside the area, 0 when it is outside the area, and π when it is on the string. However, since the angle δi is integrated, there is a problem that the calculation time increases parabolically as the number of line segments increases.

[0011]

[Problems to be Solved by the Invention] As described above, in conventional two-dimensional shape recognition methods, the calculation time required to recognize the positional relationships of strings and points becomes parabolic as the number of line segments increases. There was a problem that the amount of water was increasing. For this reason,
Even in process simulation of the shape of a deposition process, an etching process, or a lithography process in a semiconductor device, the calculation time increases, and the simulation cannot be performed within a practical calculation time.

The present invention has been made in view of the above circumstances, and its purpose is to reduce the number of angle calculations and to judge string intersections from angle calculations, thereby reducing the number of times required for recognizing the positional relationships between strings and points. An object of the present invention is to provide a two-dimensional shape recognition method in a semiconductor device evaluation method that can shorten calculation time.

[Configuration of the invention]

[0014]

[Means for Solving the Problems] In order to achieve the above object, the first invention provides a two-dimensional coordinate system in which an arbitrary point R for determining whether it is inside or outside a region exists on a coordinate axis. is set, and angle calculation is performed only when the sign of the coordinates of the point sequence representing the area with respect to the two-dimensional coordinate system changes, and angle calculation is performed to recognize the positional relationship between the point R and the area. configured. FIG. 8 shows a specific example of the first invention, in which a coordinate axis 802 passing through a point R for determining the positional relationship with respect to an area 801 represented by a string is used, and a point Q1 that is different from the sign of the y coordinate of the starting point P1 is used. After searching in the direction of the point sequence, calculate the angle Δ1 defined by point P1, point R, and point Q1, and then calculate the angle Δ2 again at point Q2 with a different sign on the y-axis,
Finally, calculate the angle Δ3 defined by the previously discovered point Q2, starting point P1, and point R, and calculate the sum ΣΔi of the angle Δi.
Calculate. This ΣΔi is 0, π, or 2
The location of point R is recognized based on π.

[0015] The second invention calculates an angle defined by a point on a series of points representing an area and the line segments before and after it, and calculates the intersection point from the sum of the angles calculated from the first invention at the point. It is configured to extract existing line segments and determine their combination. FIG. 9 shows a specific example of the second invention. When a line segment 901 in front of point Pi is rotated clockwise to match a line segment 902 after point Pi, the rotation angle is -ξi. Then, the sum of angles ΣΔi at point Pi becomes -2π-ξi, and the angle ΣΔi-1 at point Pi-1 immediately before point Pi is -ξi-1
(Figure 9(a)). Similarly, ΣΔj is −2π−ξ
j, ΣΔj+1 is −ξj+1 (Fig. 9(b)
). According to the above, if the sum of angles is -2π-ξ, a loop 903 is formed, and if it is -ξ, no loop is formed. Based on this, it is determined whether or not the intersection 904 has occurred. There is an intersection C1 on the line segment between θi-1 and θi where the sum of angles changes, and similarly θ
Since the intersection point C2 exists on the line segment between j and θj+1, the intersection point calculation can be performed.

The two-dimensional shape recognition method in the semiconductor device evaluation methods of the first and second inventions described above is used to calculate, for example, a change in shape of a semiconductor device during a deposition process or an etching process.

[0017]

[Operation] In the first invention, as described above, a two-dimensional coordinate system with an arbitrary straight line as the coordinate axis is used, and angle calculation is performed only when the sign of a coordinate different from the coordinate axis of the point sequence changes. By calculating the angle to recognize the positional relationship between a point and the area, if the number of times the string intersects the coordinate axis is I times (2 times in Figure 8), the number of angle calculations will be I + 1 times, so the calculation Time is reduced. especially,
The number of times I that the string intersects with the coordinates is determined by the shape represented by the string model and is therefore independent of the number N of line segments, and generally I<N, so the calculation time is also shortened from this point of view.

In the second invention, it is confirmed that a loop exists from the angle defined by the point representing the area and the front and back line segments, and the angle calculated from the first invention at the point. However, by finding the intersection points of the strings, the sum of angles can be calculated at high speed according to the first invention, so that the position of the intersection point can also be recognized at high speed. Here, when there is only one intersection point in one line segment, the two angle calculations (the angle calculation defined by the point representing the area and the front and rear line segments, and the angle calculation according to the first invention) are The intersection calculation, which was conventionally performed N(N-1)/2 times, only needs to be calculated for the number of loops that occur, so the calculation time increases linearly as the number of line segments increases. and is fast. On the other hand, when there are multiple intersections within one line segment, it is known that the intersection exists within the line segment, but it is not possible to specify the other line segment that intersects, so conventional intersection point calculation methods are used. Use this to search for intersecting line segments. In this case, the calculation time will be longer than when there is only one intersection in one line segment, but since the line segment where the intersection exists is already known, the number of calculations is N at most. The calculation time increases linearly with the increase in the number of line segments, and is faster than conventional methods.

[0019]

Embodiments Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. Here, the devices applied to this embodiment include a CPU, an input device connected to this CPU, and a ROM.
A conventional computer with memory such as , RAM, etc. and an output device is used. Arithmetic processing and the like in each step are performed by a calculation unit of the CPU, and data storage such as the sum of angles generated in each step is performed in a memory such as a RAM.

As an embodiment of the first invention, a processing procedure for calculating the sum of angles will be explained using the flowchart of FIG. First, in step 101, the number P1 of the starting point of the point sequence of the string model is stored in the storage memory PS, and the point P
The code S1 of the y coordinate obtained by converting the coordinate of 1 is stored in the storage memory SS, and the total angle θT and point number i are initialized to 0 and 1, respectively. Next, in step 102, the point number is advanced by one, and in step 103, the point number is
It is determined whether or not is equal to point P1. Point Pi
is not equal to point P1, in step 104, the y-coordinate of point Pi is converted into a two-dimensional coordinate system whose x-coordinate axis is a straight line passing through point R, and after extracting the sign Si of the y-coordinate, in step 105, It is determined whether the sign Si of the y coordinate has changed or whether the point Pi is on the x coordinate axis. If the above conditions are satisfied, in step 105, the angle θ formed by the two straight lines defined by the points PS and R, and the points Pi and R is calculated, and the sum of the angles θT, PS, and SS is updated, and then step 105 is performed. Return to 102. Further, if the above conditions are not satisfied, the process directly returns to step 102.

On the other hand, if point Pi is equal to point P1 in step 103, point Pi has returned to its original point, so the angle θ formed by two straight lines defined by point PS and point R, and point P1 and point R is calculated. Then, calculate the final sum of angles θT. FIG. 10 shows an example of calculating the sum of angles in order to determine whether an arbitrary point P in a semiconductor process simulation exists in an air region according to each step described above. . Note that the shaded area in the figure indicates the air area. The sum of angles θT is θT
=θ1 +θ2 −θ3 +θ4+θ5 =2π, and it can be determined that point P is within the air region. Furthermore, since the number of angle calculations can be reduced, high-speed processing is possible. Note that although the x-axis was used in this example,
The y-axis may also be used.

Next, as an embodiment of the second invention, a processing procedure for calculating an intersection point will be explained using the flowchart shown in FIG. First, in step 201, the starting point P1 of the string
, and initialize the point number i to 1. Next, in step 202, the point number is advanced by one, and in step 203
In, point Pi+1 and point Pi, point Pi and point Pi−
1 Calculate the angle θi between the two line segments defined by
Remember. Next, in step 204, the sum total of angles θTi at point Pi is calculated and stored using the processing procedure for calculating the sum of angles shown in FIG.

Thereafter, in step 205, it is determined whether the point Pi is equal to the point P1, and if they are not equal, the process returns to step 202 to continue calculation. If the point Pi is equal to the point P1, the angle θi and the angle θT are determined in step 206.
Extract the line segment where the intersection exists from the comparison of i, and perform Step 2
In step 07, a combination of line segments found to have intersections in step 206 is determined. Here, if there are multiple intersection points within a line segment, it can be recognized from the process in step 207 that there are intersection points within one line segment, but it is not possible to extract the intersecting other line segment. I can't. Therefore, in step 208, it is determined whether all combinations of line segments having intersections have been determined. If all combinations have been determined, the process ends immediately.

On the other hand, if all the combinations have not been determined, in step 209, a line segment that intersects is searched for by the conventional calculation of the intersection of two line segments, and a combination is determined. In this case, the other line segment that intersects is searched using the conventional intersection point calculation of two line segments, but since one line segment with an intersection point is already known, the intersection point calculation is performed at most. It is sufficient to perform the process the number of times equal to the number.

FIG. 11 shows, as an example, the step 20 described above.
1 to step 208, the material region 11
01 shows a case in which intersection point calculation is performed for a shape in which a hollow region 1102 occurs inside. The sums θi and θj of angles from point Pi to point Pj are −2π−ξi and −2π−ξj−1, respectively, and −ξ at other points, so the intersections C1, C2, and C
3, C4 is between point Pi-1 and point Pi, point Pj
and Pj+1, between Pi and Pi+1, and between Pj-1 and Pj, and the combinations of line segments are S1 and S2, S3 and S4. Furthermore, since the number of times of intersection calculation can be reduced, high-speed processing is possible.

FIG. 12 shows an example of the case where the process in step 209 described above is required.
, C2 1202 is located between points Pi-1 and Pi, and between points Pi and Pi+1, but it is not possible to determine the combination of line segments. In this case, the line segment S that intersects the line segments S1 and S2 is determined by step 209 described above.
3 using conventional intersection point calculation and calculate the intersection point.

[0027]

[Effects of the Invention] As explained above, according to the two-dimensional shape recognition method in the semiconductor device evaluation method of the present invention,
The number of angle calculations and intersection calculations is reduced. This makes it possible to reduce the calculation time required to recognize the positional relationships between strings and points, and to perform process simulations of deposition and etching processes at high speed when evaluating semiconductor devices.

[Brief explanation of drawings]

FIG. 1 is a flowchart showing a processing procedure for calculating the sum of angles according to the present invention.

FIG. 2 is a flowchart showing a processing procedure for calculating the intersection of strings according to the present invention.

FIG. 3 is a diagram showing a method of expressing a two-dimensional shape using a string model.

FIG. 4 is a diagram showing an example of a loop that occurs when a substance deposition process simulation is performed.

FIG. 5 is a diagram showing processing of a loop that has occurred.

FIG. 6 is a diagram illustrating an example of surface strings penetrating into other materials that occur when a material etching process is simulated.

FIG. 7 is a diagram showing a conventional method for calculating the sum of angles.

FIG. 8 is a diagram showing a method of calculating the sum of angles according to the present invention.

FIG. 9 is a diagram showing a method of calculating intersection points according to the present invention.

FIG. 10 is a diagram showing an example of shape recognition using the angle sum calculation method according to the present invention.

FIG. 11 is a diagram showing an example of intersection processing using the intersection calculation method according to the present invention.

FIG. 12 is a diagram illustrating an exception handling method for the intersection point calculation method according to the present invention.

[Explanation of symbols]

401, 502, 504, 601, 602 A string representing a material boundary 301, 702, 901, 902 A line segment of a string representing a material boundary 302, 501, 503, 606, 701, 801
Material region 303, 1101, 1201 Direction of string series 402, 505 String loop 403, 110
2 Hollow regions 506, 604, 1103, 1202 Intersections of strings 507, 605 Newly inserted points 603 Overlapping region 802 Coordinate axes 1001 Air region 1002 Polysilicon region 1003 Oxide film region 1004 Semiconductor region

Claims (2)

[Claims] [Claim 1] A two-dimensional closed area is expressed by a series of line segments connecting points, and the angle formed by the two straight lines is determined,
By finding the angle formed by two straight lines defined by both endpoints of one line segment of the series of line segments and any one point, and calculating for the number of line segments, the angle between any one point and the two-dimensional closed area When recognizing the positional relationship, the coordinates of the point sequence representing the two-dimensional closed area are transformed into a two-dimensional coordinate system with one coordinate axis passing through the arbitrary one point, and the coordinates of the starting point of the point sequence are After storing the code in advance, search for a point or a point on the coordinates where the code has a different sign from the code of the point where the previous code was stored, and find a point that is defined by the point where the previous code was stored and the arbitrary point. By calculating the angle formed by the straight line defined by the straight line, the point found from the search, and the straight line defined by the arbitrary point, and continuing the process of storing the sign of the coordinate of the searched point until returning to the starting point. A two-dimensional shape recognition method in a semiconductor device evaluation method, characterized in that the positional relationship of the arbitrary point with respect to the two-dimensional closed area is recognized. 2. An angle calculated by assuming that a point whose positional relationship with respect to the two-dimensional closed area is to be recognized is an arbitrary point in a sequence of points representing the area, and an angle formed by line segments before and after this arbitrary point. 2. A two-dimensional shape recognition method in a semiconductor device evaluation method according to claim 1, wherein intersection points of line segments representing said two-dimensional closed region are recognized by comparison.