JP4919266B2 - Apparatus and computer program for analyzing particle position on wafer - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To accurately calculate a coordinate data conversion/correction formula for a short time so as to effectively search particles on a wafer from their data that are measured by a particle counter, by a scanning electron microscope (SEM). <P>SOLUTION: A first coordinate data 20 measured by a general-purpose particle counter, and a second coordinate data 22 measured by an SEM or an equivalent high accurate measuring device concerning particles on the same wafer, are input (S11 and S12). Based on a difference between the first coordinate data 20 and the second coordinate data 22, an orthogonal conversion (translation and rotation) formula 38 to approximate the first coordinate data 20 to the second coordinate data 22 is calculated by a minimum square method (S18). The orthogonal conversion formula 38 is used to convert the first coordinate data 20 to a converted first coordinate data (S19). Based on a difference between the converted first coordinate data and the second coordinate data 22, an in-plane distribution formula 39 of displacement that can be removed by correction of translation and rotation is calculated by a least square method (S20). Then, the orthogonal conversion formula 38 and the in-plane distribution formula 39 are output. <P>COPYRIGHT: (C)2008,JPO&amp;INPIT

Description

  The present invention relates to an apparatus and a computer program for analyzing the positions of particles or defects (hereinafter collectively referred to as “particles”) present on a semiconductor wafer.

  In order to inspect and evaluate the size, structure, composition, and the like of particles present on a semiconductor wafer, the following method is generally performed. First, the coordinate value of the particles on the wafer is measured using an apparatus capable of detecting particles on the wafer at high speed, for example, a laser scattering type particle inspection apparatus (hereinafter referred to as “particle counter”). Subsequently, an apparatus capable of inspecting particles with a high-magnification image, such as a scanning electron microscope (SEM), an optical microscope, an ion beam micromachining apparatus, a micro-Auger electron microscope, or a confocal microscope (hereinafter referred to as “SEM etc.”) ), The particles are searched from the wafer based on the particle coordinate values measured by the particle counter, and the found particles are examined in detail.

  In the above method, in order to make the coordinate data from the particle counter usable in the SEM or the like, the coordinate data is converted from the coordinate system of the particle counter to the coordinate system such as the SEM (for example, orthogonal transformation or Affine transformation) is performed. Then, based on the coordinate value of each converted particle, the particle is searched for by SEM or the like. However, even when a position on the wafer corresponding to the converted coordinate value or its periphery is searched, a situation in which particles are not found often occurs. One of the reasons is that there is an error in the parameters used in the above coordinate transformation (for example, the orthogonal transformation parameter and the rotation parameter).

  In contrast, the inventor of the present invention has already disclosed a method for accurately determining parameters for coordinate transformation using a normal wafer product (a wafer whose particle position is not known in advance). (Patent Document 1). In this method, the position of a large number of particles on a wafer is measured with a particle counter, and then a small number, for example, two particles are selected from the particles, and the small number of particles are found by SEM or the like. Measure the coordinate value of the particle. Then, based on the coordinate value measured by the particle counter of the small number of particles and the coordinate value measured by SEM or the like, a parameter value for coordinate transformation (for example, orthogonal transformation) is calculated by the least square method. After that, another particle is selected, the particle is found by SEM or the like, and the parameter value of the already calculated coordinate transformation is corrected based on the coordinate value of the particle by the particle counter and the coordinate value by SEM or the like. Then, the accuracy of the parameter values for coordinate transformation is sequentially improved by sequentially repeating the same processing for other particles. However, this method assumes that the found particles are the correct pair. If you accidentally pair the wrong particles in proximity, the subsequent coordinate transformation will be wrong.

In order to eliminate particle pairing errors, a standard wafer on which an artificially arranged pattern of precisely arranged particles is preliminarily formed is used, and the coordinate value of the particle pattern of the standard wafer is measured with a particle counter. A method of calculating a parameter value for coordinate conversion to be applied to coordinate data from a particle counter based on a measurement result is known.
Japanese Patent Laid-Open No. 10-12686

  As described above, according to the method of Patent Document 1, it is necessary to correctly pair particles in order to obtain sufficiently accurate coordinate conversion parameters. For this reason, a large number of particles detected by a particle counter are required. There is a problem that it takes a considerably long working time because it is necessary to sequentially find out the particles corresponding to each of the particles by SEM or the like by trial and error.

  In addition, the method using a standard wafer on which a predetermined particle pattern is formed has a problem that the standard wafer is very expensive. In addition, standard wafers become increasingly contaminated during repeated use, but repeated use of standard wafers is difficult because contaminated standard wafers can no longer be used. For these reasons, the standard wafer method is not very practical.

  Accordingly, one object of the present invention is to effectively search for the particles with a second device such as SEM based on the coordinate data of the particles on the wafer measured by the first device such as a particle counter. An object of the present invention is to obtain a conversion formula or correction formula for coordinate data in a shorter time.

  Another object is to obtain a coordinate data conversion formula or correction formula with higher accuracy.

  Another object is to enable the above-mentioned object to be achieved by using a normal wafer product without using a standard wafer.

  According to a first aspect of the present invention, an apparatus for analyzing the position of particles on a wafer includes means for inputting first coordinate data having coordinate values according to a first coordinate system of a number of particles on the wafer, Means for inputting second coordinate data having coordinate values according to the second coordinate system of the plurality of particles, and each of the first coordinate data closest to each other from the input first coordinate data and second coordinate data. Means for searching and extracting a large number of coordinate pairs each composed of a coordinate value and each coordinate value in the second coordinate data, and using the extracted large number of coordinate pairs, the first coordinate system and the second coordinate system Means for determining a coordinate conversion formula for correcting at least translational and rotational misalignment between the coordinate system and means for outputting the determined coordinate conversion formula.

  This analyzing apparatus inputs first coordinate data according to the first coordinate system and second coordinate data according to the second coordinate system of a large number of particles on the wafer. In a preferred embodiment, coordinate data measured by a general-purpose particle counter is input as the first coordinate data, and coordinate accuracy is higher than that of the general-purpose particle counter to the extent equivalent to SEM or the like as the second coordinate data. Coordinate data measured by the reference machine is input. When the closest pair of the coordinate value in the first coordinate data and the coordinate value in the second coordinate data is extracted from the input coordinate data, a more correct pair (that is, the same particle) A large number of pairs with a high probability of corresponding to. A coordinate conversion formula between the first coordinate system and the second coordinate system is calculated using the extracted many coordinate pairs. In this way, by extracting a number of correct coordinate pairs as much as possible and processing them in a batch, as in the prior art, the particles corresponding to each of the particles detected by the particle counter are searched sequentially with SEM or the like. Therefore, it is possible to calculate a highly accurate coordinate conversion formula in a shorter time. Further, according to this analysis apparatus, the coordinate conversion formula can be calculated using a normal wafer product without using a standard wafer.

  In addition to the above-described configuration, this analysis apparatus reduces the number of coordinate values in the first coordinate data to be equal to or less than the first number before searching for the coordinate pair from the first coordinate data and the second coordinate data. In addition, there may be further provided means for reducing the number of coordinate values in the second coordinate data to the second number or less. In a preferred embodiment, the number of coordinate values of the first coordinate data and the number of coordinate values of the second coordinate data are limited to appropriate numbers set by the operator, for example, several hundreds or more. By reducing the number of coordinate values in this way, the problem that the number of coordinate values to be processed is too large and an erroneous pair is formed is increased, resulting in a long processing time. It becomes easy to calculate a coordinate conversion formula with high accuracy in a short time.

  The analyzing apparatus further includes means for removing outlier coordinate pairs whose coordinate pair distance is greater than or less than a predetermined distance threshold value from among the extracted many coordinate pairs before calculating the parameter value of the coordinate transformation. Further, it may be provided. When the coordinate value of the first coordinate system and the coordinate value of the second coordinate system constituting each coordinate pair correspond to the same particle, the distance between the coordinate values (coordinate pair distance) is within a certain distance range. It is a trap to enter. Therefore, if there is a coordinate pair whose coordinate pair distance is abnormally large or small compared to other coordinate pairs, the coordinate value of the first coordinate system and the coordinate value of the second coordinate system constituting the coordinate pair are There is a high possibility that it falls under different particles. Therefore, an erroneous pair can be eliminated by removing outlier coordinate pairs whose coordinate pair distance is greater than or less than a predetermined distance threshold from the extracted coordinate pairs. As a result, it is easy to calculate a coordinate conversion formula with high accuracy.

  Furthermore, the analyzing apparatus applies coordinate transformation according to the determined coordinate transformation formula to a large number of coordinate values according to the first coordinate system included in the extracted numerous coordinate pairs, and performs a large number according to the transformed first coordinate system. Based on a difference vector between a plurality of coordinate values according to the calculated first coordinate system and a plurality of coordinate values according to the second coordinate system included in the plurality of coordinate pairs. Means for determining an in-plane distribution formula for representing an in-plane distribution of positional deviation between the converted first coordinate system and the second coordinate system; and means for outputting the determined in-plane distribution formula; May be further provided. By the above coordinate conversion with respect to the coordinates of the first coordinate system, at least translational and rotational misalignment between the first coordinate system and the second coordinate system can be corrected. However, an in-plane positional shift that cannot be removed only by translation and rotation correction still remains in the coordinate values of the first coordinate system. This in-plane positional shift is another main cause of the problem that particles cannot be found by searching for a position corresponding to the converted coordinate value only by coordinate conversion according to the prior art. On the other hand, in the above analysis apparatus, after the coordinate conversion formula is determined, the coordinate value between the coordinate value of the converted first coordinate system and the coordinate value of the second coordinate system obtained by applying the coordinate conversion formula is used. Based on the difference vector, an in-plane distribution formula for representing an in-plane distribution of positional deviation between the converted first coordinate system and the second coordinate system is determined. As a result, the in-plane distribution formula can be applied to the coordinate values of the converted first coordinate system, and by this application, the positional deviation is removed from the coordinate values of the converted first coordinate system, and the second coordinates High-precision coordinate values suitable for the system can be obtained.

  In accordance with another aspect of the present invention, an apparatus for analyzing the position of particles on a wafer includes means for inputting first coordinate data having coordinate values according to a first coordinate system of a number of particles on the wafer, and a number on the wafer. Means for inputting second coordinate data having coordinate values according to the second coordinate system of the particle, and between the first coordinate system and the second coordinate system using the input first coordinate data and second coordinate data Means for determining a coordinate conversion formula for correcting at least translational and rotational misalignment, and applying a coordinate conversion according to the determined coordinate conversion formula to the first coordinate data, thereby converting the first conversion data according to the converted first coordinate system. Based on a difference vector between the means for calculating one coordinate data, the calculated converted first coordinate data, and the second coordinate data, between the converted first coordinate system and the second coordinate system. In-plane to represent in-plane distribution of misalignment And means for determining the fabric type, and means for outputting the determined coordinate conversion formula and the in-plane distribution formula.

  According to this analysis apparatus, the coordinate conversion formula for correcting the translational and rotational misalignment between the first coordinate system and the second coordinate system, and the translation and rotation correction based on the coordinate conversion formula can be removed. An in-plane distribution formula representing the in-plane distribution of misalignment that cannot be obtained is obtained. Of the coordinate conversion formula and the in-plane distribution formula obtained in this way, first, the coordinate conversion formula is applied to the first coordinate data, whereby the positional deviation between translation and rotation can be corrected. After that, by applying an in-plane distribution formula to the first coordinate data corrected in this way, it is possible to remove a positional shift that cannot be removed only by translation and rotation. As a result, highly accurate coordinate values suitable for the second coordinate system can be obtained. Moreover, according to this analysis apparatus, the coordinate conversion formula and the in-plane distribution formula can be obtained using a normal wafer product without using a standard wafer.

  According to still another aspect of the present invention, an apparatus for analyzing the position of particles on a wafer includes means for inputting first coordinate data having coordinate values according to a first coordinate system of a number of particles on a wafer, Means for inputting a coordinate transformation equation for correcting at least translational and rotational errors between the system and the predetermined second coordinate system; and a transformation obtained by applying the coordinate transformation equation to the first coordinate system. Means for inputting an in-plane distribution expression for representing an in-plane distribution of a difference vector between one coordinate system and the predetermined second coordinate system; and coordinate conversion according to the coordinate conversion expression for the input first coordinate data , And applying the difference vector correction according to the in-plane distribution formula to the calculated converted first coordinate data, the corrected first coordinate data according to the converted first coordinate system is applied to the corrected first coordinate data. Means for calculating the coordinate data and the corrected second And means for outputting coordinate data.

  According to this analysis apparatus, the coordinate conversion formula for correcting the translational and rotational misalignment between the first coordinate system and the second coordinate system, and the translation and rotation correction based on the coordinate conversion formula can be removed. By inputting an in-plane distribution expression that represents an in-plane distribution of misalignment, and by first applying the coordinate conversion expression to the first coordinate data out of the input coordinate conversion expression and in-plane distribution expression, translation is performed. And correct the misalignment of rotation. After that, by applying an in-plane distribution formula to the first coordinate data corrected in this way, a positional shift that cannot be removed only by translation and rotation is removed. As a result, highly accurate coordinate values suitable for the second coordinate system can be obtained.

  The present invention further provides a computer program for analyzing the position of particles on a wafer according to the same principle as the apparatus according to the present invention described above.

  According to one aspect of the present invention, the second device such as SEM effectively searches for the particle based on the coordinate data of the particle on the wafer measured by the first device such as a particle counter. Thus, a coordinate data conversion / correction formula for performing the above can be obtained in a shorter time.

  According to another aspect of the present invention, a more accurate coordinate data conversion / correction formula can be obtained.

  Further, according to the present invention, the above conversion formula can be obtained using a normal wafer product without using a standard wafer.

  Hereinafter, an embodiment of the present invention will be described with reference to the drawings.

  FIG. 1 shows an overall configuration of an apparatus (hereinafter referred to as “analysis apparatus”) for analyzing the position of particles on a wafer according to an embodiment of the present invention.

  As shown in FIG. 1, the analysis apparatus includes a conversion / correction formula calculation unit 10 and a coordinate conversion / correction unit 12. Each of the conversion / correction formula calculation unit 10 and the coordinate conversion / correction unit 12 can be typically realized by a computer in which a computer program for instructing each control process is installed. The coordinate conversion / correction unit 12 may be realized by the same computer or by another computer.

  The conversion / correction formula calculation unit 10 includes first coordinate data 20 having coordinate values according to the first coordinate system of a large number of particles existing on a certain semiconductor wafer, and second values of a large number of particles on the same wafer. Second coordinate data 22 having coordinate values according to the coordinate system is input. Then, the conversion / correction formula calculation unit 10 uses the input first coordinate data 20 and second coordinate data 22 to convert a coordinate value according to the first coordinate system into a coordinate value according to the second coordinate system. A plurality of types of conversion / correction expressions (actually, a plurality of coefficient values, that is, parameter values that define these expressions) 24 are determined and output.

Here, for the “first coordinate data 20”, for example, coordinate data of a large number of particles on a certain wafer measured using a general-purpose particle counter is employed. On the other hand, the “second coordinate data 22” includes, for example, an inspection device (hereinafter referred to as “reference device” ) that can measure the coordinate value of the particles with higher accuracy comparable to a device that examines particles in detail ( such as the above SEM ). The coordinate data of a large number of particles on the same wafer, measured using “ Accordingly, the “first coordinate system” followed by the first coordinate data 20 corresponds to the coordinate system of the measurement values of the general-purpose particle counter, and the “second coordinate system” followed by the second coordinate data 22 is the measurement value of the reference machine. It corresponds to the coordinate system. As the “one wafer”, a normal wafer product (that is, a wafer whose particle coordinate values are not known in advance) can be used, and a standard wafer need not be used. The conversion / correction formula 24 output from the conversion / correction formula calculation unit 10 includes two types of formulas: an orthogonal transformation formula (parameter value of the formula) and an in-plane distribution formula (parameter value of the formula). The orthogonal transformation formula is a coordinate transformation formula for correcting a translational and rotational misalignment between the first coordinate system and the second coordinate system, and is expressed as follows.

  Here, the coordinate values (X, Y) expressed in capital letters are coordinate values measured by the reference machine, and the coordinate values (x, y) expressed in small letters are coordinate values measured by the particle counter. The coefficients θ, α, and β are parameters that define this orthogonal coordinate transformation formula, the parameter θ is a rotation parameter, and the parameters α and β are translation parameters.

  On the other hand, the in-plane distribution formula expresses the distribution (in-plane distribution) on the coordinate plane of the positional deviation between the first coordinate system and the second coordinate system that cannot be removed only by correcting the translation and rotation by the orthogonal transformation. An expression to express. The in-plane distribution and the in-plane distribution formula of the positional deviation that cannot be removed by this rotation and translation correction will be specifically described later.

  The coordinate transformation / correction unit 12 obtains the transformation / correction equation 24 determined by the transformation / correction equation computing unit 10, that is, an orthogonal transformation equation (orthogonal transformation parameter) and an in-plane distribution equation (in-plane distribution parameter). input. Further, the coordinate conversion / correction unit 12 inputs the coordinate data 26 of particles of an arbitrary wafer measured by the particle counter. Then, the coordinate transformation / correction unit 12 performs orthogonal transformation using the inputted orthogonal transformation formula and positional deviation correction using the inputted in-plane distribution formula on the coordinate data 26 by the inputted particle counter. . As a result, the positional deviation between the coordinate system (first coordinate system) of the particle counter and the coordinate system (second coordinate system) of the reference machine is removed with high accuracy from the coordinate data 26 by the particle counter, and the reference High-precision coordinate data 28 suitable for the machine coordinate system (second coordinate system) is obtained. The coordinate conversion / correction unit 12 outputs high-accuracy coordinate data 28 that is obtained in this manner and that is suitable for the coordinate system (second coordinate system) of the reference machine.

  Hereinafter, the operations of the conversion / correction formula calculation unit 10 and the coordinate conversion / correction unit 12 described above will be described in detail. First, the operation of the coordinate conversion / correction unit 12 will be described, and then the operation of the conversion / correction formula calculation unit 10 will be described.

  FIG. 2 shows an operation flow of the coordinate conversion / correction unit 12.

  As shown in FIG. 2, the coordinate transformation / correction unit 12 outputs an orthogonal transformation equation and an in-plane distribution equation for a particle counter (actually, those equations outputted in advance from the transformation / correction equation calculation unit 10). Parameter value) 24 is read (step S1). Further, the coordinate conversion / correction unit 12 reads coordinate data 26 representing the coordinate values of a large number of particles on an arbitrary semiconductor wafer measured using the same particle counter (S2).

  Thereafter, the coordinate transformation / correction unit 12 performs orthogonal transformation on the inputted coordinate data 26 using the inputted orthogonal transformation equation (parameter value of the equation) (S3). By applying this orthogonal transformation, translation and rotation corrections are applied to the coordinate data 26 measured by the particle counter, and the coordinate system of the particle counter (first coordinate system) and the coordinate system of the reference machine (second coordinate). Translational and rotational misalignment with the system) is eliminated. As a result, the coordinate data 26 conforming to the first coordinate system is converted into coordinate data conforming to the coordinate system that substantially coincides with the second coordinate system in the coordinate origin and the coordinate axis direction. Hereinafter, the coordinate data transformed from the input coordinate data 26 by this orthogonal transformation is referred to as “transformed coordinate data”, and the coordinate system followed by the transformed coordinate data is referred to as “transformed first coordinate system”.

  Thereafter, the coordinate conversion / correction unit 12 uses the input in-plane distribution formula to remove the positional deviation that could not be removed by the translation and rotation correction from the converted coordinate data (S4). The method can be easily understood from the explanation of the in-plane distribution formula described later, but the outline is as follows. That is, each of a large number of coordinate values constituting the converted coordinate data is substituted into the input in-plane distribution formula. Then, the displacement between the converted first coordinate system and the second coordinate system at the position of each assigned coordinate value (that is, the coordinate value of the converted first coordinate system corresponding to the same position and the second coordinate system). A difference vector between the coordinate values) is calculated. Next, the calculated difference vector is subtracted from each coordinate value. As a result, the positional deviation is removed from the respective coordinate values, and coordinate values that are accurately adapted to the second coordinate system are obtained. This process is performed for each of a large number of coordinate values constituting the converted coordinate data.

  In this way, in step S4, by applying the in-plane distribution formula, the converted coordinate data according to the above-described converted first coordinate system is corrected to coordinate data that is accurately adapted to the second coordinate system. The coordinate conversion / correction unit 12 outputs the coordinate data 28 that is accurately matched to the second coordinate system thus obtained (S5). Since the output coordinate data 28 is accurately adapted to the coordinate system (second coordinate system) of the reference machine, in other words, the coordinate system used in the SEM or the like, if the coordinate data 28 is used, the SEM or the like is used. Thus, particles on the wafer can be easily found.

  Next, the operation of determining the above-described orthogonal transformation formula and in-plane distribution formula by the transformation / correction formula computing unit 10 will be described. The meanings of the orthogonal transformation equation and the in-plane distribution equation will become clear from the following description, and the operation and advantages of the coordinate transformation / correction unit 12 described above should be understood more easily.

  FIG. 3 shows a flow of operations of the conversion / correction formula calculation unit 10.

  As shown in FIG. 3, the conversion / correction formula computing unit 10 is a coordinate value (according to the coordinate system of the particle counter, that is, the first coordinate system) of a large number of particles measured on a certain wafer. And second coordinate data 22 having coordinate values (according to the coordinate system of the reference machine, that is, the second coordinate system) of a large number of particles on the same wafer measured by the reference machine. Input (steps S11 and S12). The input first coordinate data 20 and second coordinate data 22 include not only measured coordinate values but also measured particle size values.

  Thereafter, the conversion / correction formula calculation unit 10 reduces the number of coordinate values included in the input first coordinate data 20 and second coordinate data 22 to an appropriate number or less, in steps S14 and S15. Perform processing. That is, the operator inputs the first coordinate value number 32 and the second coordinate value number 34 to the conversion / correction formula calculation unit 10. Then, only the number of coordinate values corresponding to the first coordinate value number 32 is selected from the large number of coordinate values included in the first coordinate data 20 in the descending order of the particle size. The coordinate value of is removed. Similarly, from the large number of coordinate values included in the second coordinate data 22, only the number of coordinate values corresponding to the second coordinate value number 34 is selected and left in the descending order of the particle size, so that the particle size is smaller. Other coordinate values are removed. Thus, by limiting the coordinate values of the first coordinate data 20 and the second coordinate data 22 to a predetermined number of coordinate values having a relatively large particle size, both the first coordinate data 20 and the second coordinate data 22 can be obtained. The probability of including coordinate values corresponding to the same particle is improved, thereby improving the accuracy of the calculated orthogonal transformation formula and in-plane distribution formula. In addition, the burden of processing a lot of useless coordinate values that are not useful for improving the accuracy of the orthogonal transformation formula and the in-plane distribution formula is avoided.

  Here, the first coordinate value number 32 and the second coordinate value number 34 may be the same number, or may be different numbers. This is desirable for the purpose of obtaining a high orthogonal transformation formula and in-plane distribution formula. Incidentally, from this point of view, the wafer serving as the source of the first coordinate data 20 and the second coordinate data 22 has several hundred particles or more on the surface, and these particles are as much as possible on the wafer surface. A wafer that is dispersed over the entire area and has as little particle concentration as possible, such as scratches and clusters, is preferred.

  When the process of reducing the number of coordinates in steps S14 and S15 described above is completed, the process of step S16, that is, searching for the closest coordinate pair from the first coordinate data 20 and the second coordinate data 22 is performed. Processing to extract is performed. That is, first, one coordinate value is selected from a large number of coordinate values included in the first coordinate data 20. Thereafter, one coordinate value that is closest to the selected coordinate value (that is, the distance from the selected coordinate value is the smallest) is selected from a large number of coordinate values included in the second coordinate data 22. Is done. In this way, two coordinate values respectively selected from the first coordinate data 20 and the second coordinate data 22 are extracted as one coordinate pair. As a result, a large number of coordinate pairs each extracted from one coordinate value in the first coordinate data 20 and one coordinate value in the second coordinate data 22 that are closest to each other are extracted. There is a high probability that the coordinate value in the first coordinate data 20 and the coordinate value in the second coordinate data 22 constituting each coordinate pair extracted in this way correspond to the same particle. .

  When the coordinate pair search and extraction process in step S16 is completed, the process in step S17, that is, the process of removing a coordinate pair having an abnormally large coordinate pair distance as an outlier is performed. Here, the coordinate pair distance means a distance between two coordinate values constituting each coordinate pair. FIG. 4 specifically explains this coordinate pair distance. In FIG. 4, coordinate values (x, y) indicated by lowercase letters indicate one coordinate value in the first coordinate data 20, and coordinate values (X, Y) indicated by uppercase letters are 1 in the second coordinate data 22. One coordinate value is indicated, and both coordinate values (x, y) and (X, Y) constitute one coordinate pair. The coordinate pair distance in this coordinate pair is the length of the difference vector dr between the coordinate value (x, y) and the coordinate value (X, Y), that is, the absolute value | dr |. In FIG. 4, the angle θ is an angle with respect to a predetermined reference direction (for example, x axis or X axis) 44 of the start point (x, y) of the difference vector dr.

In the outlier removal processing in step S17, first, the coordinate pair distance | dr | is calculated for all the coordinate pairs extracted in step S16. Then, on the display screen of this analysis device (for example, a computer), a distribution diagram is shown in which the distance between the coordinate pairs | dr | of all the coordinate pairs as a function of the angle θ in FIG. Is done. The operator inputs a coordinate pair distance threshold dr ₀ (reference number 36 in FIG. 3) as illustrated in FIG. 5 on the displayed distribution map. As shown in the example of FIG. 5, the coordinate pair distance threshold dr ₀ is usually set so that the majority of coordinate pairs 50 are densely packed in the range below and the small number of coordinate pairs 52 are dispersed in the range above it. Is set to the value of | dr |.

When the coordinate pair distance threshold dr ₀ is set, a coordinate pair 52 having a large coordinate pair distance | dr | exceeding the coordinate pair distance threshold dr ₀ out of the coordinate pairs extracted in step S16 is used as an outlier. Only the coordinate pair 50 that is removed and has a small coordinate pair distance | dr | that is less than or equal to the coordinate pair distance threshold dr ₀ is left as a valid coordinate pair. Here, a case has been described in which a coordinate pair having a coordinate pair distance | dr | equal to or greater than the coordinate pair distance threshold dr ₀ is removed as an outlier, but this is merely an example. Depending on the distribution of the inter-coordinate pair distance | dr |, a coordinate pair having a inter-coordinate-pair distance | dr | that is equal to or smaller than a certain threshold value may be removed as an outlier.

  It is highly probable that the coordinate pairs 52 removed as outliers include coordinate pairs composed of coordinate values corresponding to different particles. This is because a coordinate pair consisting of coordinate values corresponding to the same particle is unlikely to have a significantly different distance between the coordinate pairs | dr | as compared to other coordinate pairs. Accordingly, by removing the outlier, the probability that only the coordinate pair composed of coordinate values corresponding to the same particle is left as an effective coordinate pair is further increased.

  Referring to FIG. 3 again, after the outlier removal process in step S17 described above is completed, the process in step S18, that is, the process of determining the orthogonal transform equation (parameter value of the equation) is performed. That is, by using the difference vector dr of many effective coordinate pairs left in step S17 described above, the coordinate value according to the coordinate system (first coordinate system) of the particle counter is obtained by the least square method, and the coordinate system of the reference machine. A parameter value (optimum value) for orthogonal transformation is calculated to approximate the coordinate value according to (second coordinate system). As shown in the orthogonal transformation equation described above, the parameter value of the orthogonal transformation is obtained from the translation parameter values α and β for translating the first coordinate system and the rotation parameter value θ for rotating the first coordinate system. Composed.

  Through the above processing, a highly accurate orthogonal transform equation (orthogonal transform parameter) can be obtained in a short time.

  When the above-described orthogonal transformation equation determination processing in step S18 is completed, the orthogonal transformation processing in step S19 is performed thereafter. That is, the coordinate values (coordinate values (x, x, x in FIG. 4) according to the first coordinate system on the first coordinate data 20 side that constitutes a large number of effective coordinate pairs (coordinate pairs 50 in FIG. 5) left in step S17 described above. y)) is subjected to orthogonal transformation using the orthogonal transformation equation (orthogonal transformation parameter) calculated in step S18 described above. As a result, the coordinate values according to the first coordinate system are subjected to translational and rotational correction by orthogonal transformation, and as a result, the coordinate system (hereinafter referred to as “transformation number”) substantially coincides with the second coordinate system in the coordinate origin and coordinate axis directions. Is converted into coordinate values (hereinafter referred to as “converted coordinate values”).

  However, the transformed coordinate value according to the transformed first coordinate system obtained by this orthogonal transformation and the coordinate value according to the second coordinate system on the second coordinate data 22 side constituting the valid coordinate pair (the coordinate value (X in FIG. 4) , Y)), there is still a misregistration between them. This misalignment is a misalignment inherent in the first coordinate system that cannot be removed only by correcting translation and rotation. The distribution (in-plane distribution) of this misalignment in the surface area of the wafer is non-uniform or complex, and therefore this misalignment cannot be removed by translational and rotational correction. Incidentally, this misalignment is effective not only by translation and rotation but also by other coordinate transformations according to the prior art including other correction components, such as affine transformations, because of its non-uniform or complex in-plane distribution. Often cannot be removed.

  FIG. 6 shows an example of a positional shift having this complicated in-plane distribution. That is, FIG. 6 shows the distribution of the difference vector between the converted coordinate value according to the converted first coordinate system and the coordinate value according to the second coordinate system constituting the effective coordinate pair. In FIG. 6, a circle 60 points to the wafer, and a large number of line segments 62 arranged so as to draw the vortex shown in the wafer 60 represent the difference vector. In FIG. 6, the length (absolute value) of the difference vector 62 is enlarged at a very large magnification as compared with the dimension of the wafer 60. That is, in FIG. 6, the length of the horizontal line shown on the lower left outside of the wafer 60 corresponds to the length of 35 μm of the difference vector 62.

  FIG. 7 illustrates the difference vector. In FIG. 7, coordinate values (x *, y *) are converted coordinate values according to the converted first coordinate system obtained by orthogonal transformation, and coordinate values (X, Y) are coordinate values according to the second coordinate system. Yes, both constitute a valid coordinate pair. The vector dr * is a difference vector between the coordinate pair (X, Y) and (x *, y *).

  If the example shown in FIG. 6 is seen, the in-plane distribution of the difference vector (position shift | offset | difference) between the coordinate value according to the conversion 1st coordinate system and the coordinate value according to the 2nd coordinate system will be complicated, and direct conversion and It should be easily understood that it cannot be removed only by coordinate transformation according to the prior art such as affine transformation. Incidentally, the average value of the lengths of the difference vectors illustrated in FIG. 6 (that is, the size of the positional deviation) was about 20 μm.

Refer to FIG. 3 again. When the orthogonal transformation process in step S19 is completed, the process in step S20, that is, the process for determining the in-plane distribution expression representing the in-plane distribution of the positional deviation remaining after the orthogonal transformation described above is performed. . That is, the difference vector dr * as shown in FIG. 7 is calculated for each of the many effective coordinate pairs described above. Here, in the present embodiment, the difference vector dr * is a directional component of the radius r and the angle ψ when coordinate values (x *, y *) according to the first coordinate system are displayed in polar coordinates, that is, the radial component dr * r and angular direction component dr * ψ are decomposed to calculate respective direction components dr * r and dr * ψ. Then, by using the values dr * r and dr * ψ of the difference vector dr * of the coordinate pair at a number of positions (r, ψ), the in-plane distribution formula, that is, the value of the difference vector dr * r by the least square method And dr * ψ are determined as functions of polar coordinate values (r, ψ) of coordinate values (x *, y *) according to the first coordinate system. This in-plane distribution formula is expressed as follows.

Where f (r,
ψ) and g (r, ψ) are both the polynomial up to the third order of the radius r, the polynomial up to the third order of the trigonometric functions sinψ and cosψ of the angle ψ, and the product of these terms. It can be expressed as a predetermined polynomial that is appropriately combined and the coefficient of each term is an unknown number determined by the least square method.

In step S20, the function f (r,
The coefficient values (in-plane distribution parameter values) of a number of terms constituting ψ) and g (r, ψ) are determined by the least square method. If an arbitrary coordinate value (r, ψ) according to the first transformation coordinate system is substituted into this in-plane distribution formula, the coordinate value (r, ψ) and the second coordinate that coincides with the actual position on the wafer. A difference vector between coordinate values according to the system will be obtained.

  FIG. 8 shows the distribution of the optimized difference vector obtained by using the coefficient defined by the least square method with respect to the actual difference vector shown in FIG. It is shown. Comparing FIG. 8 with FIG. 6, it is understood that the distribution of the difference vector based on the in-plane distribution equation shown in FIG. 8 is a good reproduction of the distribution of the actual difference vector shown in FIG. It should be done.

  In order to verify how accurate the calculated in-plane distribution formula is, the inventor has obtained the surface shown in FIG. 8 from the actual difference vector shown in FIG. I subtracted the difference vector based on the internal distribution formula. Incidentally, the subtraction processing performed in this verification is the correction of the in-plane distribution in step S4 in the process performed by the coordinate transformation / correction unit 12 shown in FIG. 2 with the difference vector shown in FIG. This corresponds to the application to the coordinate values of the converted first coordinate system.

  FIG. 9 shows the surface of the difference vector (that is, the residual difference vector that could not be removed by the in-plane distribution correction) between the difference vector of FIG. 6 and the optimized difference vector of FIG. 8 obtained as a result of this verification. The internal distribution is shown.

  In FIG. 9, the length of the lower left outer line segment of the wafer 60 corresponds to the length (absolute value) of the residual difference vector 66 of 8.3 μm. As can be seen from FIG. 9, the residual difference vector 66 is very small, and in fact, the average absolute value of the residual difference vector 66 was about 4 μm. If this is contrasted with the average value of the absolute value of the difference vector 62 immediately after the orthogonal transformation shown in FIG. 6 being about 20 μm, the particle counter can be corrected by adding a correction by the in-plane distribution equation. It can be seen that the measured first coordinate data 20 is corrected so as to accurately match the second coordinate data 22 measured by the reference machine.

  Refer to FIG. 3 again. When the calculation of the in-plane distribution formula in step S20 is completed, then in step S21, the calculated orthogonal transformation formula and in-plane distribution formula (actually, the orthogonal transformation parameters and the in-plane distribution that define these formulas are used. Parameter) 24 is output. The orthogonal transformation equation and in-plane distribution equation (orthogonal transformation parameter value and in-plane distribution parameter value) 24 output in this way are input to the coordinate transformation / correction unit 12 as already described with reference to FIG. become. As can be seen from what has already been described with reference to FIG. 9, the coordinate conversion / correction unit 12 performs coordinate conversion on the coordinate data 26 from the particle counter based on the input orthogonal conversion formula, and further receives the input. By correcting based on the in-plane distribution formula, coordinate data that is accurately matched to the coordinate system of the reference machine, in other words, the coordinate system such as SEM, can be obtained. Using the coordinate data makes it easier to find particles with SEM or the like.

  As mentioned above, although embodiment of this invention was described, this embodiment is only the illustration for description of this invention, and is not the meaning which limits the scope of the present invention only to this embodiment. The present invention can be implemented in various other modes without departing from the gist thereof.

  In addition, the coordinate conversion and correction formulas (for example, the orthogonal transformation formula and the in-plane distribution formula) calculated by the conversion / correction formula calculation unit 10 of the analysis apparatus according to the above embodiment are used for wafer particle inspection such as a particle counter. It represents the unique individuality of each device. Therefore, the conversion / correction formula calculation unit 10 of this analysis apparatus not only aims at inspecting and evaluating particles on the wafer, but also quantitatively reveals and evaluates and classifies the individuality of the wafer particle inspection apparatus. It can also be used for purposes.

1 is a block diagram showing the overall configuration of an apparatus for analyzing the position of particles on a wafer according to an embodiment of the present invention. 7 is a flowchart showing the operation of the coordinate conversion / correction unit 12. 7 is a flowchart showing the operation of the conversion / correction formula calculation unit 10. Explanatory drawing of coordinate pair distance. Distribution diagram of the distance | dr | between the coordinate pairs of all coordinate pairs displayed on the display screen to remove the outlier coordinate pairs and the angle θ. The figure which shows the actual example of in-plane distribution of the position shift (difference vector) which was not removed by orthogonal transformation. The figure explaining the meaning of the difference vector illustrated in FIG. The figure which shows in-plane distribution of position shift (difference vector) which the calculated in-plane distribution formula represents. The figure which shows the result of subtracting the optimization difference vector based on the in-plane distribution formula shown in FIG. 8 from the actual difference vector shown in FIG.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Conversion / correction type | formula calculation part 12 Coordinate conversion / correction part 20 The 1st coordinate data 22 of the particle | grains on a certain wafer measured with the particle counter The 2nd coordinate data 24 of the particle | grains on a certain wafer measured with the reference | standard machine Conversion / correction formula (orthogonal transformation formula and in-plane correction formula (orthogonal transformation parameters and in-plane correction parameters))
26 Coordinate data of particles on an arbitrary wafer measured by a particle counter 28 Coordinate data corrected and corrected 50 Valid coordinate pair 52 Coordinate pair 60 removed as an outlier Wafer 62 Difference vector (position) remaining immediately after orthogonal transformation Slip)
64 Difference vector (positional deviation) obtained from in-plane distribution formula
66 Difference vector (positional deviation) that is lost after in-plane distribution correction
dr The difference vector between the coordinate value (x, y) of the first coordinate system and the coordinate value (X, Y) of the second coordinate system in a certain coordinate pair
dr * Difference vector between the coordinate value (x *, y *) of the transformed first coordinate system and the coordinate value (X, Y) of the second coordinate system in a certain coordinate pair

Claims (8)

Means for inputting first coordinate data having coordinate values according to a first coordinate system of a number of particles on the wafer;
Means for inputting second coordinate data having coordinate values according to a second coordinate system of the multiple particles on the wafer;
A plurality of coordinates each composed of the coordinate values in the first coordinate data and the coordinate values in the second coordinate data that are closest to each other from the input first coordinate data and second coordinate data Means for searching and extracting pairs;
Means for determining a coordinate conversion equation for correcting at least translational and rotational misalignment between the first coordinate system and the second coordinate system using the extracted multiple coordinate pairs;
Means for outputting the determined coordinate transformation formula;
An apparatus for analyzing the position of particles on a wafer , comprising:
Means for applying a coordinate transformation according to the determined coordinate transformation formula to a number of coordinate values according to the first coordinate system included in the number of coordinate pairs to calculate a number of coordinate values according to the transformed first coordinate system; ,
Based on the calculated multiple coordinate values according to the converted first coordinate system and the multiple coordinate values according to the second coordinate system included in the multiple coordinate pairs, the converted first coordinate system and the second coordinate Means for determining an in-plane distribution formula for representing an in-plane distribution of differences between the system;
An apparatus for analyzing the position of particles on a wafer, further comprising means for outputting the determined in-plane distribution formula. Means for inputting first coordinate data having coordinate values according to a first coordinate system of a number of particles on the wafer;
Means for inputting second coordinate data having coordinate values according to a second coordinate system of a number of particles on the wafer;
Using the input first coordinate data and second coordinate data, a coordinate conversion formula for correcting at least translational and rotational misalignment between the first coordinate system and the second coordinate system is determined. Means,
Means for applying a coordinate transformation according to the determined coordinate transformation formula to the first coordinate data to calculate transformed first coordinate data according to a transformed first coordinate system;
Based on a difference vector between the calculated converted first coordinate data and the second coordinate data, an in-plane distribution of positional deviation between the converted first coordinate system and the second coordinate system is represented. An apparatus for analyzing the position of a particle on a wafer, comprising: means for determining an in-plane distribution formula for the output; and means for outputting the determined coordinate conversion formula and in-plane distribution formula. Means for inputting first coordinate data having coordinate values according to a first coordinate system of a number of particles on the wafer;
Means for inputting a coordinate conversion formula for correcting at least translational and rotational errors between the first coordinate system and the predetermined second coordinate system;
In-plane distribution for representing an in-plane distribution of positional deviation between the converted first coordinate system and the predetermined second coordinate system obtained by applying the input coordinate conversion formula to the first coordinate system. Means for entering an expression;
Means for applying the coordinate transformation according to the inputted coordinate transformation formula to the inputted first coordinate data, and calculating transformed first coordinate data according to the transformed first coordinate system;
Means for calculating a corrected first coordinate data by applying a displacement correction according to the input in-plane distribution formula to the converted first coordinate data;
An apparatus for analyzing the position of particles on a wafer, comprising means for outputting the corrected first coordinate data.   In the in-plane distribution formula, each of the radial component and the angular component includes a polynomial up to a predetermined degree of radius r, a polynomial up to a predetermined degree of trigonometric functions sinψ and cosψ of angle ψ, and a product thereof as appropriate. The apparatus according to claim 1, wherein the apparatus is a predetermined polynomial combined. Inputting first coordinate data having coordinate values according to a first coordinate system of a number of particles on the wafer;
Inputting second coordinate data having coordinate values according to a second coordinate system of the multiple particles on the wafer;
A plurality of coordinates each composed of the coordinate values in the first coordinate data and the coordinate values in the second coordinate data that are closest to each other from the input first coordinate data and second coordinate data Searching for and extracting pairs;
Determining a coordinate transformation equation for correcting at least translational and rotational misalignment between the first coordinate system and the second coordinate system using the extracted multiple coordinate pairs;
Outputting the determined coordinate transformation formula;
Applying a coordinate transformation according to the determined coordinate transformation formula to a number of coordinate values according to the first coordinate system included in the number of coordinate pairs to calculate a number of coordinate values according to the transformed first coordinate system; ,
Based on the calculated multiple coordinate values according to the converted first coordinate system and the multiple coordinate values according to the second coordinate system included in the multiple coordinate pairs, the converted first coordinate system and the second coordinate Determining an in-plane distribution equation to represent the in-plane distribution of differences between the systems;
A computer program for causing a computer to execute the step of outputting the determined in-plane distribution formula . Inputting first coordinate data having coordinate values according to a first coordinate system of a number of particles on the wafer;
Inputting second coordinate data having coordinate values according to a second coordinate system of the multiple particles on the wafer;
Using the input first coordinate data and second coordinate data, a coordinate conversion formula for correcting at least translational and rotational misalignment between the first coordinate system and the second coordinate system is determined. Steps,
Applying a coordinate transformation according to the determined coordinate transformation formula to the first coordinate data to calculate transformed first coordinate data according to the transformed first coordinate;
Based on a difference vector between the calculated converted first coordinate data and the second coordinate data, an in-plane distribution of positional deviation between the converted first coordinate system and the second coordinate system is represented. A computer program for causing a computer to execute a step of determining an in-plane distribution formula for outputting and a step of outputting the determined coordinate conversion formula and the in-plane distribution formula. Inputting first coordinate data having coordinate values according to a first coordinate system of a number of particles on the wafer;
Inputting a coordinate conversion formula for correcting at least translational and rotational misalignment between the first coordinate system and a predetermined second coordinate system;
In-plane distribution for representing an in-plane distribution of positional deviation between the converted first coordinate system and the predetermined second coordinate system obtained by applying the input coordinate conversion formula to the first coordinate system. Entering an expression;
Applying the coordinate transformation according to the inputted coordinate transformation formula to the inputted first coordinate data to calculate transformed first coordinate data;
A computer program for causing a computer to execute a step of calculating corrected first coordinate data by applying positional deviation correction according to the input in-plane distribution formula to the calculated converted first coordinate data.   In the in-plane distribution formula, each of the radial component and the angular component includes a polynomial up to a predetermined degree of radius r, a polynomial up to a predetermined degree of trigonometric functions sinψ and cosψ of angle ψ, and a product thereof as appropriate. The computer program according to claim 5, wherein the computer program is a predetermined polynomial.

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