JP2009260185A - Characteristic distribution analysis method and apparatus, substrate classification method and apparatus, program for allowing computer to execute characteristic distribution analysis method or substrate classification method, computer-readable recording medium storing program, and classification criterion data - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a characteristic distribution analysis method for hierarchically setting classification criteria for classifying substrates. <P>SOLUTION: A characteristic distribution analysis method includes: a step (S101) of preparing a first-layer distinction distribution group composed of a set of distinction distributions which represent distinctions of the characteristic distributions of respective substrates; a step (S102) of quantitatively evaluating the degree of similarity between the characteristic distributions of the respective substrates and the respective distinction distributions; a step (S103) of quantitatively evaluating associations among some distinction distributions, which are included in the first-layer distinction distribution group and appear simultaneously on the identical substrate, on the basis of the degree of similarity; a step (S104) of integrating some distinction distributions included in the first-layer distinction distribution group on the basis of the associations while maintaining the positions of the respective distinction distributions on the substrates so as to prepare a new distinction distribution on an assumed substrate; and a step (S105) of setting a set of the new distinction distribution and the distinction distributions in the first-layer distinction distribution group except for those subjected to the integration as a second-layer distinction distribution group. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a characteristic distribution analysis method and apparatus, and more particularly to a characteristic distribution analysis method and apparatus for creating a classification standard for classifying a substrate according to the characteristic distribution on the substrate.

  The present invention also relates to a substrate classification method and apparatus for classifying a substrate according to a characteristic distribution on the substrate.

  The present invention also relates to a program for causing a computer to execute such a characteristic distribution analysis method or substrate classification method.

  The present invention also relates to a computer-readable recording medium recording such a program.

  The present invention also relates to classification reference data serving as a reference for classifying a substrate according to a characteristic distribution on the substrate.

  In a production line for thin film devices such as semiconductor wafers, display devices, and hard disk magnetic heads, various inspections are performed for the purpose of improving yield and stabilizing. These inspections include, for example, a pattern inspection for detecting a defect in a circuit pattern caused by a foreign substance attached on a substrate, an electrical characteristic inspection for inspecting an electrical characteristic of a formed circuit, and the like. The production line monitors these inspection results on a daily basis.For example, abnormalities have occurred in the manufacturing process based on the increase in the number of defects detected by pattern inspection and fluctuations in electrical characteristics measured by electrical characteristic inspection. Check whether there is any. If an abnormality occurs in a certain manufacturing process among a plurality of manufacturing processes that are sequentially performed on the board, the inspection results should be investigated and analyzed to quickly identify the cause and take countermeasures. Thus, damage due to yield reduction can be minimized. Therefore, a system for collecting inspection information and processing history of each manufacturing apparatus is provided in the manufacturing line.

  When an abnormality occurs in the manufacturing process, the inspection result often appears as a characteristic distribution on the substrate surface. These characteristic distributions differ depending on the state of the abnormality that has occurred and are closely related to the cause of the abnormality. For this reason, it is possible to indirectly confirm the presence / absence of an abnormality in the process, the cause of the abnormality, and the like by surveying the trend of the characteristic distribution occurring in the process. Therefore, it is very effective to detect the tendency of the characteristic distribution in the inspection process at an early stage. However, generally speaking, it is difficult to express the characteristic distribution with numerical values such as monitoring of temporal changes in characteristic values and statistical values obtained by normal statistical processing. For this reason, it is actually difficult to detect and monitor anomalies using characteristic distributions.

  In order to overcome these difficulties, the characteristic distribution is analyzed based on the shape of the characteristic distribution and the frequency of occurrence of similar characteristic distributions, etc. Several techniques have been proposed for automatically creating the.

  For example, Patent Document 1 (Japanese Patent Application Laid-Open No. 11-45919) describes a method of creating a density value image from information obtained by adding the defect positions of a plurality of substrates inspected by an inspection apparatus and grasping the state of occurrence of the defect. Has been. However, in this method, when an abnormality occurs in a plurality of manufacturing processes up to the inspection process, an image in which the characteristic distribution due to each abnormality cause is added is created. For this reason, this method cannot obtain a characteristic distribution representing the characteristics of each cause of abnormality and is not suitable for analyzing the cause of abnormality.

Another Patent Document 2 (Japanese Patent No. 3734008) describes a method of classifying substrates having a high positional correlation of defect distributions into the same category by paying attention to the similarity of defect distribution positions. Specifically, an area is set on each substrate to be classified. Next, for each substrate, the number of defects in each region arranged in order is considered as a waveform, and the similarity of waveforms is examined for all substrate combinations using a measure such as a correlation coefficient, and the similarity is high. Classify boards into the same category. Then, the distribution shape of the substrate having the highest correlation coefficient with the substrate included in each category is set as the distribution shape that represents the characteristics of the category, and similar distribution substrates are classified into the same group using the distribution shape as a reference for classification. Therefore, even if an abnormality occurs in a plurality of processes, the substrates are classified according to the distribution shape for each abnormality cause.
Japanese Patent Laid-Open No. 11-45919 Japanese Patent No. 3734008

  Here, in the method of Patent Document 2, the analysis result, that is, the characteristic distribution that is a reference for classification is determined by the equality based on the similarity of the waveform, and the classification result of the board is uniformly determined according to the characteristic distribution. End up. However, the analyst may, for example, want to roughly classify the board by broadly setting a standard for classifying the board based on his intention, or conversely, to narrowly classify the board by setting the standard narrowly. is there. Further, there are cases where it is desired to classify the boards hierarchically, for example, to classify the boards into an upper group and a lower group included in the upper group.

  SUMMARY OF THE INVENTION An object of the present invention is to provide a characteristic analysis analysis method and apparatus capable of hierarchically setting a classification standard for classifying a board according to a characteristic distribution on the board.

  Another object of the present invention is to provide a substrate classification method and apparatus for classifying substrates according to the characteristic distribution on the substrate.

  The present invention also relates to a program for causing a computer to execute such a characteristic distribution analysis method or substrate classification method.

  The present invention also relates to a computer-readable recording medium recording such a program.

  The present invention also relates to classification reference data serving as a reference for classifying a substrate according to a characteristic distribution on the substrate.

In order to solve the above problems, the characteristic analysis method of the present invention is:
A characteristic distribution analysis method for creating a classification standard for classifying the above-mentioned substrates for a group of substrates each having a characteristic distribution,
A feature distribution group creating step of creating a first layer feature distribution group composed of a set of feature distributions representing the characteristics of the characteristic distribution of each substrate;
A similarity evaluation step for quantitatively evaluating the similarity between the characteristic distribution of each of the substrates and the characteristic distribution;
A relevance evaluation step for quantitatively evaluating relevance in which several feature distributions included in the first layer feature distribution group appear simultaneously on the same substrate based on the similarity;
Based on the relationship, several feature distributions of the first layer feature distribution group are integrated while maintaining the position of each feature distribution on the substrate, and a new one on the assumed substrate is obtained. A feature distribution integration process for creating a unique feature distribution;
A set of the new feature distribution and the remaining feature distribution group obtained by removing the feature distribution targeted for integration from the first layer feature distribution group is defined as a second layer feature distribution group. A hierarchical structure creating step for sequentially and repeatedly executing the similarity evaluation step, the relevance evaluation step, and the feature distribution integration step for the group.

  Here, the “characteristic distribution” refers to the characteristics associated with an arbitrary inspection item inspected in the inspection process, such as the number of defects in pattern inspection and the measured value of some electrical characteristics in electrical characteristic inspection, along the substrate surface. Distribution.

  Further, the “feature distribution” means a distribution that shows a feature different from a normal (in other words, normal) characteristic distribution. For example, in the case of the above pattern inspection, it refers to a distribution of defects that occur densely at a specific position. A “feature” is grasped as a “feature” if it appears in at least a part of the characteristic distribution on the substrate.

  In addition, “similar” between a characteristic distribution of a certain substrate and a certain feature distribution means that the characteristic distribution and the feature distribution show similar changes as the substrate moves along the substrate surface. “Similarity” means the degree of “similarity” expressed quantitatively in terms of numerical values.

  In addition, “relevance” in which several feature distributions appear on the same substrate at the same time is, for example, when it is assumed that a characteristic distribution of a certain substrate has a feature represented by a certain feature distribution A. This means that there is a relationship such that the distribution has the characteristics represented by another feature distribution B at the same time. “Relevance” is high means that the frequency of occurrence is high at the same time.

  Also, “integrating” several feature distributions while maintaining the position of each feature distribution on the substrate means that the feature distributions are maintained while maintaining the position of each feature distribution on the substrate. Means to create a new feature distribution that is arranged on the assumed substrate and has both the features represented by those feature distributions.

  According to the characteristic distribution analysis method of the present invention, a multi-layer feature distribution group having a hierarchical structure is created as a classification standard for classifying substrates. Therefore, by using these multi-layer feature distribution groups as classification criteria for classifying the substrates, it is possible to perform classification that reflects the intention of the person in charge of analysis. For example, a board can be roughly (coarsely) classified using a wide classification standard composed of upper layer feature distribution groups, and conversely, a board can be classified finely using a narrow classification standard composed of lower layer feature distribution groups. It becomes possible. Further, the boards can be classified hierarchically, such as classifying the boards into a higher group and a lower group included in the upper group. As a result, it is possible to observe the characteristic distribution in the substrate group, in particular, the state of the feature distribution from a bird's-eye view.

  In one embodiment, the characteristic analysis analysis method repeatedly executes the similarity evaluation step, the relevance evaluation step, and the feature distribution integration step sequentially on the uppermost feature distribution group obtained by the hierarchical structure creation step. Features.

  In the characteristic analysis analysis method of this embodiment, a feature distribution group having a hierarchical structure of three or more layers is created as a classification standard for classifying substrates.

  The characteristic analysis analysis method according to an embodiment is characterized in that, in the feature distribution group creating step, distributions independent of each other are extracted as the feature distribution from the characteristic distribution of the substrate group.

  In the characteristic analysis method of this embodiment, the obtained characteristic distribution is a characteristic expression of the characteristic distribution of the substrate group to be analyzed with high accuracy.

  The characteristic analysis analysis method according to an embodiment is characterized in that, in the similarity evaluation step, the similarity is evaluated by projection from a vector representing the characteristic distribution of the substrate group to a vector representing each feature distribution.

  In the characteristic distribution analysis method of this embodiment, the similarity between the characteristic distribution and the feature distribution can be accurately and quantitatively evaluated in the similarity evaluation step.

  In the characteristic analysis method according to an embodiment, in the relevance evaluation step, a correlation coefficient between the similarities between the characteristic distribution of each of the substrates and the characteristic distribution is obtained, and the correlation coefficient is calculated. The relevance is evaluated based on the above.

  In the characteristic distribution analysis method of this embodiment, in the relevance evaluation step, the relevance in which several feature distributions included in the first layer feature distribution group appear simultaneously on the same substrate is quantitatively evaluated. can do.

  In the feature analysis analysis method according to an embodiment, in the feature distribution integration step, a feature distribution set having the greatest relevance of the feature distributions in the first layer feature distribution group is selected, and the features forming the set are selected. The distribution is integrated to create the new feature distribution.

  In the characteristic distribution analysis method of this embodiment, in the feature distribution integration step, a set of feature distributions to be integrated can be selected with high accuracy.

  In the characteristic analysis analysis method according to one embodiment, in the feature distribution integration step, for each of the several feature distributions to be integrated, an average value of similarity between the feature distribution and the characteristic distribution of each of the substrates And performing the integration by weighting and adding the characteristic values of the several characteristic distributions to be integrated with the average values of the similarities calculated for the respective characteristic distributions. To do.

  In the characteristic distribution analysis method of this embodiment, a new characteristic distribution reflecting the characteristic distribution state of the substrate group can be created in the characteristic distribution integration step.

  In the characteristic analysis analysis method according to an embodiment, when the relevance evaluation process is performed on the uppermost feature distribution group, the relevance between any feature distributions in the uppermost feature distribution group is determined in advance. The similarity evaluation step, the relevance evaluation step, and the feature distribution integration step are sequentially executed until the threshold value is equal to or less than the threshold value or the feature distribution group included in the uppermost feature distribution group becomes one. To do.

  In the characteristic distribution analysis method according to this embodiment, the relevance between any of the feature distributions within the uppermost feature distribution group is equal to or less than a predetermined threshold value, or the feature distribution included in the uppermost feature distribution group. When the number is one, the hierarchical structure creating process is terminated. Therefore, a hierarchical structure with an appropriate number of layers can be created.

The characteristic distribution analyzer of this invention is
A characteristic distribution analyzer for creating a classification standard for classifying the above-mentioned substrates for a group of substrates each having a characteristic distribution,
A feature distribution group creating unit that creates a first layer feature distribution group composed of a set of feature distributions representing the characteristics of the characteristic distribution of each substrate;
A similarity evaluation unit that quantitatively evaluates the similarity between the characteristic distribution of each of the substrates and the feature distribution;
A relevance evaluation unit that quantitatively evaluates relevance in which several feature distributions included in the first layer feature distribution group appear simultaneously on the same substrate based on the similarity;
Based on the relationship, several feature distributions of the first layer feature distribution group are integrated while maintaining the position of each feature distribution on the substrate, and a new one on the assumed substrate is obtained. A feature distribution integration unit for creating a simple feature distribution;
A hierarchical structure creation unit having a set of the new feature distribution and the remaining feature distribution group obtained by removing the feature distribution targeted for integration from the first layer feature distribution group as a second layer feature distribution group; Have.

  According to the characteristic distribution analyzer of the present invention, a feature distribution group of a plurality of layers having a hierarchical structure is created as a classification standard for classifying substrates. Therefore, by using these multi-layer feature distribution groups as classification criteria for classifying the substrates, it is possible to perform classification that reflects the intention of the person in charge of analysis. For example, a board can be roughly (coarsely) classified using a wide classification standard composed of upper layer feature distribution groups, and conversely, a board can be classified finely using a narrow classification standard composed of lower layer feature distribution groups. It becomes possible. Further, the boards can be classified hierarchically, such as classifying the boards into a higher group and a lower group included in the upper group. As a result, it is possible to observe the characteristic distribution in the substrate group, in particular, the state of the feature distribution from a bird's-eye view.

The substrate classification method of this invention is
A substrate classification method for classifying a substrate group using a classification criterion for a group of substrates each having a characteristic distribution,
A characteristic distribution analysis method according to claim 1, wherein a feature distribution group of a plurality of layers having a hierarchical structure is created as the classification standard,
The feature distribution included in the feature distribution group forming the classification criterion is compared with the characteristic distribution on each substrate included in the substrate group, and the substrate is classified for each feature distribution.

  According to the substrate classification method of the present invention, classification that reflects the intention of the person in charge of analysis is possible. For example, a board can be roughly (coarsely) classified using a wide classification standard composed of upper layer feature distribution groups, and conversely, a board can be classified finely using a narrow classification standard composed of lower layer feature distribution groups. It becomes possible. Further, the boards can be classified hierarchically, such as classifying the boards into a higher group and a lower group included in the upper group. As a result, it is possible to observe the characteristic distribution in the substrate group, in particular, the state of the feature distribution from a bird's-eye view.

The substrate classification apparatus of the present invention is
A board classification device that classifies the board using a classification standard for a board group consisting of a plurality of boards each having a characteristic distribution,
A characteristic distribution analysis device according to claim 8 is provided, and by this characteristic distribution analysis device, a feature distribution group of a plurality of layers having a hierarchical structure is created as the classification criterion,
A classification processing unit is provided that compares the feature distribution included in the feature distribution group that constitutes the classification criterion with the characteristic distribution on each substrate included in the substrate group, and classifies the substrate for each feature distribution. .

  According to the substrate classification apparatus of the present invention, classification that reflects the intention of the person in charge of analysis is possible. For example, a board can be roughly (coarsely) classified using a wide classification standard composed of upper layer feature distribution groups, and conversely, a board can be classified finely using a narrow classification standard composed of lower layer feature distribution groups. It becomes possible. Further, the boards can be classified hierarchically, such as classifying the boards into a higher group and a lower group included in the upper group. As a result, it is possible to observe the characteristic distribution in the substrate group, in particular, the state of the feature distribution from a bird's-eye view.

  The program of the present invention is a characteristic distribution analysis program for causing a computer to execute the characteristic distribution analysis method.

  Moreover, the program of this invention is a board | substrate classification program for making a computer perform the said board | substrate classification method.

  A computer-readable recording medium according to the present invention is a computer-readable recording medium in which the characteristic distribution analysis program is recorded.

  A computer-readable recording medium according to the present invention is a computer-readable recording medium in which the substrate distribution program is recorded.

Moreover, the classification standard data of this invention is
Classification group data serving as a reference for classifying a substrate according to the characteristic distribution on the substrate for a group of substrates each having a characteristic distribution,
It has a multi-layer feature distribution group with a hierarchical structure,
Of the multi-layer feature distribution group, the lowest-layer feature distribution group is composed of a set of feature distributions representing the characteristics of the characteristic distribution of each substrate,
The upper-layer feature distribution group other than the lowermost layer maintains several feature distributions included in the lower-layer feature distribution group immediately below the layer, and maintains the position of each feature distribution on the substrate. However, it consists of a set of a feature distribution obtained by integration and a remaining feature distribution group obtained by removing the feature distribution targeted for integration from the feature distribution group in the lower layer.

  Hereinafter, the present invention will be described in detail with reference to the illustrated embodiments.

  FIG. 1 shows a schematic flow schematically showing a characteristic distribution analysis method according to an embodiment of the present invention.

  The characteristic distribution analysis method of this embodiment is a method of creating a classification standard for classifying a substrate group consisting of a plurality of substrates each having a “characteristic distribution” through the manufacturing process. `` Characteristic distribution '' refers to the distribution along the substrate surface for characteristics related to any inspection item inspected in the inspection process, such as the number of defects in pattern inspection and measured values of some electrical characteristics in electrical characteristic inspection. Point to. In this example, a “characteristic distribution” obtained as a result of pattern inspection is an analysis target. As shown in FIG. 2, the pattern inspection refers to an inspection process for detecting a circuit pattern defect 202 generated on a substrate 201 due to adhesion of foreign matter or the like during the manufacturing process. In this pattern inspection, the coordinates of each defect 202 on the substrate 201 are obtained as the inspection result, and the distribution 203 of these defects 202 becomes the “characteristic distribution”. When an abnormality occurs in a certain manufacturing apparatus, circuit pattern defects often occur at a specific location on the substrate surface. Therefore, in this example, the characteristic distribution analysis method is applied to the result of the pattern inspection to aim at early detection of equipment abnormality occurring in the manufacturing process.

  In step S101 (feature distribution group creation step) in FIG. 1, a predetermined set of feature distributions of n different from the characteristic distribution of the substrate group to be analyzed is formed by a known method in the field of pattern recognition. A first layer feature distribution group is created.

  Here, the “feature distribution” means a distribution showing characteristics different from the normal (in other words, normal) characteristic distribution among the characteristic distributions of the substrate group to be analyzed. A “feature” is recognized as a “feature” if it appears in at least a part of the characteristic distribution on the substrate. For example, in the example of the pattern inspection result shown in FIG. 2, the defects 202 (defect distribution 203) dense in the lower right region of the substrate are considered to have different characteristics from the normal characteristic distribution. Feature distribution ". The defects 202 scattered in the region not included in the defect distribution 203 are not included in the “feature distribution” because they are considered to be normal characteristic distributions. When a plurality of substrates have the same feature distribution, they are created as an aggregated feature distribution. Therefore, the obtained n feature distributions can list abnormal characteristic distributions occurring in the characteristic distribution of the analysis target substrate.

  FIGS. 3A to 3E show examples of feature distributions 301, 302,..., 305 when n = 5. A feature distribution 301 in FIG. 3A represents a feature that defects are concentrated in an elliptical region at the lower right of the substrate. A feature distribution 302 in FIG. 3B represents a feature that defects are concentrated in a circular region in the center of the substrate. A feature distribution 303 in FIG. 3C represents a feature that defects are concentrated in a ¼ arc-shaped region along the upper right edge of the substrate. A feature distribution 304 in FIG. 3D represents a feature that defects are densely packed in an elliptical region in the lower left portion of the substrate. A feature distribution 305 in FIG. 3E represents a feature that defects are concentrated in a ¼ arc-shaped region along the upper left edge of the substrate.

  Next, in step S102 (similarity evaluation step) in FIG. 1, the characteristic distribution of each substrate included in the substrate group to be analyzed and the characteristic distribution obtained in step S101 are obtained by a known method in the field of pattern recognition. The similarity between n feature distributions included in the first layer feature distribution group is obtained.

  Here, “similar” between a characteristic distribution of a certain substrate and a certain feature distribution means that the characteristic distribution and the feature distribution show similar changes as they move along the substrate surface. “Similarity” is a quantitative representation of the degree of “similarity” in terms of numerical values. If the degree of similarity between a characteristic distribution of a certain substrate and a certain feature distribution is high, the characteristic distribution of the substrate has substantially the same distribution as the feature distribution. For example, the characteristic distribution of the substrate 201 in FIG. 2 has a high degree of similarity with the feature distribution 301 in FIG. 3A, and the degree of similarity is low with respect to the feature distributions 302 to 305. A specific method for calculating the similarity will be described later.

  Next, in step S103 (relevance evaluation step) in FIG. 1, based on the similarity obtained in step S102, several feature distributions included in the first layer feature distribution group are simultaneously formed on the same substrate. Quantitatively evaluate the relevance that appears.

  Here, “relevance” in which several feature distributions appear simultaneously on the same substrate is, for example, when it is assumed that the characteristic distribution of a certain substrate has the characteristics represented by the certain feature distribution A. This means that there is a relationship such that the characteristic distribution has characteristics represented by another characteristic distribution B at the same time. “Relevance” is high means that the frequency of occurrence is high at the same time.

  For example, the defect distribution 404 of the substrate 401 shown in FIG. 4A is similar to the feature distribution 304 shown in FIG. In the case where such a substrate 401 exists, for example, a substrate 402 shown in FIG. 4B has a defect distribution 405 similar to the feature distribution 304 shown in FIG. 3D, and FIG. The occurrence frequency of the substrate having the defect distribution 406 similar to the feature distribution 301 shown in FIG. In such a case, the feature distribution 301 and the feature distribution 304 are considered highly related. The relationship between such feature distributions is quantitatively evaluated for all combinations.

  Next, in step S104 (feature distribution integration step) in FIG. 1, a set of feature distributions that maximizes the relevance obtained in step S103 is selected. Then, the two feature distributions forming the set are integrated while maintaining the position of each feature distribution on the substrate, and a new feature distribution on the assumed substrate is created. Here, “integrating” several (in this example, two) feature distributions while maintaining the positions of the respective feature distributions on the substrate means that the feature distributions are placed on the respective feature distribution substrates. This means that a new feature distribution is created that is arranged on the assumed substrate while maintaining the position at, and has both the features represented by those feature distributions. Therefore, the “new feature distribution” includes both the “features” of the feature distributions targeted for integration. As a result, the “new feature distribution” becomes a “rougher” feature distribution than the feature distribution targeted for integration. In this way, a new feature distribution reflecting the state of the characteristic distribution of the substrate group is created.

  For example, as shown in FIG. 5, the first layer feature distribution group G1 is made up of a set of feature distributions 301, 302,..., 305 shown in FIGS. Also, it is assumed that among the feature distributions 301 to 305, the set of feature distributions having the maximum relevance is the set of the feature distribution 301 and the feature distribution 304. At this time, the feature distribution 301 and the feature distribution 304 are arranged on the assumed substrate while maintaining the positions of the feature distributions 301 and 304 on the substrate, and the feature distributions 301 and 304 are arranged. A new feature distribution 502 having both the features represented by is created.

  Note that, since the feature distribution set that maximizes the relevance is selected as the set of feature distributions to be integrated, the set of feature distributions to be integrated can be selected with high accuracy.

  Next, in step S105 (hierarchical structure creating step) in FIG. 1, the new feature distribution created in step S104 and the remaining feature distribution obtained by removing the feature distribution targeted for integration from the first layer feature distribution group. A set with the feature distribution group is created as a second layer feature distribution group. For example, as shown in FIG. 5, a new feature distribution 502 and the remaining feature distribution groups 303, 302, and 305 obtained by removing the feature distributions 301 and 304 that are targets of integration from the first layer feature distribution group G1 Is a second layer feature distribution group G2. As a result, a hierarchical structure is created in which the first layer feature distribution group G1 is the lowest layer and the second layer feature distribution group G2 is the upper layer immediately above it.

  Next, in step S106 in FIG. 1, it is determined whether there is a set of feature distributions to be integrated in the second layer feature distribution group G2 created in step S104. If there is a set of feature distributions to be integrated in the second layer feature distribution group G2 (YES in S106), the process returns to step S102, and the processes from step S102 to step S105 are sequentially repeated.

  For example, when the processes of steps S102 and S103 are executed for the second layer feature distribution group G2, as shown in FIG. 6, the feature distribution 303 and the feature distribution 305 to be integrated in the second layer feature distribution group G2. It is assumed that there was a pair. At this time, the feature distribution 303 and the feature distribution 305 are arranged on the assumed substrate while maintaining the positions of the feature distributions 303 and 305 on the substrate, and the feature distributions 303 and 305 are arranged. A new feature distribution 602 having both the features represented by is created (S104). In this example, the new feature distribution 602 represents a feature that defects are concentrated in a semicircular arc-shaped region along the upper edge of the substrate. Then, a set of the new feature distribution 602 and the remaining feature distribution group 302 obtained by removing the feature distributions 303 and 305 that are the integration targets from the second layer feature distribution group G2 is referred to as a third layer feature distribution group G3. To do. In this way, in addition to the first layer feature distribution group G1 and the second layer feature distribution group G2, the third layer feature distribution group G3 having the second layer feature distribution group G2 as a lower layer immediately below is created (S105). ).

  Next, in step S106 again, it is determined whether or not there is a set of feature distributions to be further integrated in the current uppermost feature distribution group (third layer feature distribution group G3 in the above example). If there is no longer any set of feature distributions to be integrated in the currently uppermost feature distribution group (NO in S106), the series of processes is terminated. Thereby, a hierarchical structure having an appropriate number of layers can be created.

  If the relevance of any feature distribution within the current uppermost feature distribution group falls below a predetermined threshold or if the current uppermost feature distribution group has one feature distribution, integration is performed. It is determined that there is no longer a set of feature distributions to be performed. In the example of FIG. 6, it is assumed that the relevance between any of the feature distributions 502, 602, and 302 within the third layer feature distribution group G3 is equal to or less than a predetermined threshold value.

  In this way, according to the characteristic analysis method, as the classification reference data, a plurality of layer feature distribution groups (in the above example, the first layer feature distribution group G1, the second layer feature distribution group G2, A third layer feature distribution group G3) is created. Therefore, by using these multi-layer feature distribution groups as classification criteria for classifying the substrates, it is possible to perform classification that reflects the intention of the person in charge of analysis. For example, a board can be roughly (coarsely) classified using a wide classification standard composed of upper layer feature distribution groups, and conversely, a board can be classified finely using a narrow classification standard composed of lower layer feature distribution groups. It becomes possible. Further, the boards can be classified hierarchically, such as classifying the boards into a higher group and a lower group included in the upper group. As a result, it is possible to observe the characteristic distribution in the substrate group, in particular, the state of the feature distribution from a bird's-eye view.

  Note that several methods have already been proposed for the above-described feature distribution group creation step (step S101) and similarity evaluation step (step S102) in the field of pattern recognition, and either method may be used.

  In the above example, the “characteristic distribution” obtained as a result of the pattern inspection is an analysis target. However, the present invention is not limited to this. The characteristic analysis and analysis method of the present invention is not limited to pattern inspection results, and can be widely applied to general characteristics such as defects and electrical characteristics distributed in a plane along the substrate surface.

  FIG. 7 shows a configuration of a characteristic distribution analysis apparatus 700 according to an embodiment of the present invention suitable for implementing the above characteristic distribution analysis method (see FIG. 1).

  The characteristic distribution analysis apparatus 700 includes a characteristic distribution information collection unit 702, a characteristic distribution group storage unit 705, a feature distribution group creation unit 706, a feature distribution group storage unit 707, a similarity evaluation unit 708, and a relevance evaluation. A unit 709, a feature distribution integration unit 710, a hierarchical structure creation unit 711, and a data output unit 712. An input device 701, an inspection device 703, and an inspection information collection system 704 are connected to the characteristic distribution information collection unit 702 of the characteristic distribution analysis device 700, respectively. Further, an output device 713 is connected to the data output unit 712.

  The inspection device 703 is arranged in a factory production line, and actually inspects various characteristics of the substrate. The inspection data obtained by the inspection apparatus 703 is transmitted from the inspection apparatus 703 to the inspection information collection system 704 and the characteristic distribution information collection unit 702 of the characteristic distribution analysis apparatus 700 as necessary.

  The inspection information collection system 704 collects inspection information from the inspection device 703. In this example, the inspection information collection system 704 stores inspection data such as defect data, inspection date and time, and substrate identification number (ID) of the substrate processed by the inspection apparatus 703. Further, the inspection information collection system 704 transmits necessary inspection data to the characteristic distribution information collection unit 702 of the characteristic distribution analyzer 700.

  The input device 701 is composed of, for example, a keyboard and a mouse. In this example, the input device 701 is used to input a condition designation of a group of substrates to be analyzed to the characteristic distribution analyzer 700.

  The characteristic distribution information collection unit 702 collects board inspection data that matches the conditions of the board to be analyzed transmitted from the input device 701 to the characteristic distribution analysis apparatus 700 from the inspection apparatus 703 and the inspection information collection system 704, and Characteristic distribution information representing the characteristic distribution on the substrate is created, and the created characteristic distribution information is transmitted to the characteristic distribution group storage unit 705. At this time, if necessary, the characteristic distribution information collection unit 702 obtains inspection information such as a substrate identification number (ID) and inspection date and time from the inspection apparatus 703 and the inspection information collection system 704 and associates them with the characteristic distribution information. May be passed to the characteristic distribution group storage unit 705.

  The characteristic distribution group storage unit 705 receives the characteristic distribution information about the analysis target substrate group from the characteristic distribution information collection unit 702 and stores it inside.

  The feature distribution group creation unit 706 receives the characteristic distribution information about the analysis target substrate group stored in the characteristic distribution group storage unit 705, and performs the processing (feature distribution group) in step S101 in FIG. A creation step) is performed to create a first layer feature distribution group consisting of a predetermined set of n independent feature distributions. The created first layer feature distribution group is sent from the feature distribution group creation unit 706 to the feature distribution group storage unit 707 and stored as a feature distribution group forming the lowest layer of the hierarchical structure.

  The feature distribution group storage unit 707 stores the information of the feature distribution groups created by the feature distribution group creation unit 706 and the hierarchical structure creation unit 711 together with the hierarchical structure information.

  The similarity evaluation unit 708 receives the characteristic distribution information about the analysis target substrate group stored in the characteristic distribution group storage unit 705, and performs the processing of step S102 (similarity evaluation step) in FIG. The degree of similarity between the characteristic distribution and each feature distribution is quantitatively evaluated. The evaluation result on the similarity is transmitted from the similarity evaluation unit 708 to the relevance evaluation unit 709 together with information on each feature distribution. Further, the similarity evaluation unit 708 receives information (feature distribution information) about the feature distribution included in the feature distribution group forming the uppermost layer of the hierarchical structure described later from the feature distribution group storage unit 707, and performs step S102 in FIG. The process (similarity evaluation step) is performed to quantitatively evaluate the similarity between the characteristic distribution of each substrate and each characteristic distribution.

  The relevance evaluation unit 709 receives the similarity between the characteristic distribution of each substrate and each feature distribution from the similarity evaluation unit 708, performs the process of step S103 (relevance evaluation step) in FIG. The relationship in which several feature distributions included in the group appear simultaneously on the same substrate is quantitatively evaluated. The evaluation result on the relevance is transmitted from the relevance evaluation unit 709 to the feature distribution integration unit 710 together with information on each feature distribution.

  The feature distribution integration unit 710 receives the evaluation result regarding the above-mentioned relationship from the relevance evaluation unit 709, performs the process of step S104 in FIG. 1 (feature distribution integration step), and sets a set of feature distributions to be integrated. select. Then, the two feature distributions forming the set are integrated while maintaining the position of each feature distribution on the substrate, and a new feature distribution on the assumed substrate is created. This integration result is sent from the feature distribution integration unit 710 to the hierarchical structure creation unit 711 together with information on each feature distribution. If there is no longer a set of feature distributions to be integrated in the received feature distribution group, the integration process is not performed.

  The hierarchical structure creation unit 711 receives the integration result and information of each feature distribution from the feature distribution integration unit 710, performs the process of step S105 in FIG. 1 (hierarchical structure creation process), and obtains a new feature obtained by the integration. A set of the distribution and the remaining feature distribution group obtained by removing the feature distribution targeted for integration from the original feature distribution group is created as a new feature distribution group (for example, the second layer feature distribution group). The information of the created new feature distribution group is transmitted from the hierarchical structure creation unit 711 to the feature distribution storage unit 707 together with the hierarchical structure information.

  The data output unit 712 receives the analysis result stored in the feature distribution group storage unit 707 after the series of characteristic distribution analysis processing, that is, information on a multi-layer feature distribution group having a hierarchical structure, and outputs the information. The data format used in the device 713 is processed and sent to the output device 713. At this time, if necessary, the data output unit 712 evaluates the inspection information such as the substrate identification number and the inspection date and time from the respective components in the characteristic distribution analysis apparatus 700, or the similarity and relevance used in the analysis processing. A value or the like may be received and processed into a format used by the output device 713.

  The output device 713 outputs the result of characteristic distribution analysis by the characteristic distribution analyzer 700 through a monitor, paper output, a magnetic disk, a portable semiconductor memory, or the like.

  When the characteristic distribution analyzer 700 can acquire all the information necessary for the characteristic distribution analysis process from either the inspection device 703 or the inspection information collection system 704, only the one that can be acquired is connected to the characteristic distribution analyzer 700. May be.

  In addition, the characteristic distribution analysis apparatus 700 periodically collects inspection information from the inspection apparatus 703 and the inspection information collection system 704 regardless of an instruction from the input apparatus 701, and automatically executes the characteristic distribution analysis processing and outputs the result. You may output to the apparatus 713.

  Further, the input device 701 and the output device 713 may be the same device, for example, a device in which a display unit serving as an output device is provided with a keyboard serving as an input device and configured integrally. Further, the input device 701 and the output device 713 may be included in the characteristic distribution analysis device 700.

  The output device 713 may receive and output information other than information necessary for the characteristic distribution analysis processing from the input device 701, the inspection device 703, or the inspection information collection system 704 through the characteristic distribution analysis device 700.

  With the characteristic distribution analysis apparatus 700 having this configuration, the above-described characteristic distribution analysis method can be realized.

  Note that the above-described characteristic distribution analysis method may be constructed as a program for causing a computer to execute.

  Further, such a program may be recorded on a computer-readable recording medium such as a CD-ROM and distributed. By installing the program in a general-purpose computer, the characteristic distribution analysis method can be executed by the general-purpose computer.

  The present invention is not limited to the characteristic distribution analysis apparatus 700 for pattern inspection, but can be applied to any information in which defects and electrical characteristics are distributed in a plane. In that case, the characteristic distribution information collection unit 702 is connected to an inspection apparatus or an information collection system in which target data is stored.

  Next, as a first embodiment, a method for realizing steps S101 to S104 in FIG. 1 will be described with a specific example.

  FIG. 8 shows a specific procedure for realizing step S101 (feature distribution group creation step) in FIG. 1 using a certain independent component analysis as one of the multivariate analysis methods.

  First, in step S1011 in FIG. 8, a lattice map is created based on information representing defect coordinates of a substrate to be analyzed. As shown in FIG. 9 (a), the lattice map divides the surface of the substrate 201 into a lattice shape extending vertically and horizontally, and each lattice region (in this example, a square region) 902 has a lattice region 902. This is the number of defects present. For example, if the defect distribution shown in FIG. 2 exists on the surface of the substrate 201, a lattice map as shown in FIG. 9B is created. The shade of the lattice in the figure represents the number of defects.

  Next, in step S1012 in FIG. 8, n independent components are extracted from the lattice map of the substrate group to be analyzed using an independent component analysis technique. Independent component analysis is a multivariate analysis technique that represents a plurality of variables as a linear combination of statistically independent variables. In this example, the number of defects in each lattice region 902 (see FIG. 9A) in the lattice map is arranged in the horizontal direction, and the characteristic distribution of the substrate is represented by a numeric string having the same number of elements as the number of lattice regions 902. Furthermore, by arranging the numeric strings created from the lattice map of each substrate in the vertical direction, the characteristic distribution of the substrate group to be analyzed can be represented by a matrix of (number of substrates × number of lattices). Independent component analysis is applied to this matrix to extract n independent components.

  Finally, in step S1013 in FIG. 8, a lattice map is created from each of the n independent components extracted in step S1012 to obtain a feature distribution. Each independent component extracted by independent component analysis is represented by the same number of values as the original variable. That is, the independent components extracted in step S1012 are represented by the same number of values as the number of grid regions 902. By using the values of these independent components as the values of the grids at the corresponding positions of the character string of the characteristic distribution created in step S1012, feature distributions independent of each other can be obtained. Note that the magnitude of the independent component obtained by the independent component analysis is a normalized value, and the value of the grid is meaningless. Therefore, the feature distribution obtained by the above method is meaningful only in the tendency of the value on the lattice map.

  In the above example, independent component analysis was used to create the feature distribution. However, a few similar methods have already been proposed in the field of pattern recognition, and either method may be used. For example, in step S1012 in FIG. 8, the feature distribution can also be obtained by using a technique called principal component analysis which is one of multivariate analysis techniques instead of using independent component analysis. In that case, the feature distributions are extracted so as to be uncorrelated with each other. In order to create the feature distribution, a method that can obtain the best result may be selected depending on the tendency of the characteristic distribution of the substrate to be analyzed.

  Next, the calculation method of similarity in step S102 (similarity evaluation step) in FIG. 1 will be specifically described with reference to FIG. In the above method, if the number of lattice regions 902 is g, the created feature distribution can be described as a vector in a g-dimensional space (coordinate space), and therefore n feature distributions have n as axes. A dimensional subspace (coordinate space) is formed. A lattice map of the characteristic distribution of each substrate can be described as points in this n-dimensional subspace. For example, when the number of feature distributions is 2, as shown in FIG. 10, the two feature distributions form a two-dimensional subspace composed of two feature distribution vectors 1001 and 1002. A substrate characteristic distribution 1003 can be described as points in this two-dimensional subspace. In this two-dimensional subspace, the value 1004 obtained by projecting the substrate characteristic distribution 1003 onto the axis of the feature distribution 1001 can be considered as a ratio including the tendency of the distribution represented by the feature distribution 1001. Similarly, a value 1005 obtained by projecting the substrate characteristic distribution 1003 onto the axis of the feature distribution 1002 can be considered as a ratio including the tendency of the distribution in which the substrate characteristic distribution 1003 is represented by the feature distribution 1002. Therefore, in this example, when a characteristic distribution of a substrate is described in an n-dimensional subspace with n feature distributions as axes, the value of the characteristic distribution is projected onto each feature distribution axis in the coordinate space. The obtained value is set as the similarity to each feature distribution.

  In the above example, the projection from the characteristic distribution of the substrate to each feature distribution is used as the similarity. However, several methods for calculating similarity are already proposed in the field of pattern recognition, and any method may be used. For example, instead of using projection on each feature distribution, a correlation coefficient between the characteristic distribution of the substrate and each feature distribution may be used as the similarity. In short, it is only necessary to select a method that provides the best results depending on the tendency of the characteristic distribution of the substrate to be analyzed.

  Next, a method for evaluating the relevance of the feature distribution in step S103 (relevance evaluation step) in FIG. 1 will be specifically described with reference to FIG. When the relationship between the two feature distributions is high, the frequency of the two feature distributions appearing simultaneously on the substrate included in the analysis target substrate group is high. Therefore, when the similarity of each substrate is plotted on a two-dimensional space (coordinate space) with the similarity of the substrate with respect to each feature distribution as axes 2001 and 2002, both feature distributions 2001 are obtained as shown in FIG. , 2002, the distributions 1003a, 1003b,. On the other hand, when the relationship between the two feature distributions is low, the frequency of the two feature distributions appearing simultaneously on the substrates included in the analysis target substrate group is low. Therefore, when the similarity of each substrate is plotted on a two-dimensional space with the similarity of the substrate for each feature distribution as axes 2001 and 2002, the correlation is similar to the similarity for both feature distributions as shown in FIG. The distributions 1003c, 1003d,. From this, the relationship between the two feature distributions can be calculated by the correlation coefficient of the similarity of the analysis target substrate group with respect to each feature distribution. The relevance of the feature distribution set having a larger correlation coefficient is higher.

  FIG. 12 shows a specific procedure for realizing step S104 (feature distribution integration step) in FIG.

  First, in step S1041, a combination of feature distributions having the maximum relevance calculated in step S103 is selected from all combinations of n feature distributions included in the first layer feature distribution group G1.

  Next, in step S1042, for each feature distribution selected in step S1041, an average value of the similarity between the feature distribution and the characteristic distribution of each substrate is calculated.

  Finally, in step S1043, the value of each feature distribution is weighted with the average value of the similarity calculated in step S1042 and added. In this way, the two feature distributions that form a pair having the maximum relevance are integrated. Thereby, a new feature distribution reflecting the state of the characteristic distribution of the substrate group can be created.

  Next, as Example 2, a method for classifying a substrate based on the analysis result of the characteristic distribution obtained by the characteristic distribution analysis method, that is, the classification reference data will be described.

  In this example, similar to the processing in step S102 of FIG. 1, the degree of similarity between the characteristic distribution of each substrate to be classified and each feature distribution included in the classification reference data is evaluated. At this time, it is determined that a substrate having a similarity equal to or higher than a certain threshold value falls under the feature distribution group. Thereby, each board | substrate of analysis object can be classified into the group for every feature distribution contained in the said classification reference | standard data. The classification result by this classification method is expressed by a plurality of classification results having a hierarchical structure, similar to the analysis result by the characteristic distribution analysis method.

  A characteristic distribution analysis apparatus according to an embodiment of the present invention suitable for carrying out the substrate classification method can be realized with the same configuration as that of FIG. After the similarity evaluation unit 708 in FIG. 7 evaluates the similarity, a substrate having a similarity higher than a certain threshold may be classified into the feature distribution. Data 780 representing the classification result is stored in the feature distribution group storage unit 707 in association with the feature distribution. Data 780 representing the classification result is output by the output device 713 via the data output unit 712. Thereby, the person in charge of analysis can know the classification result of the board.

  In addition, you may construct | assemble as a program for making a computer perform the above-mentioned board | substrate classification method.

  Further, such a program may be recorded and distributed on a computer-readable recording medium such as a CD-ROM. The board classification method can be executed by a general-purpose computer by installing the program on the general-purpose computer.

It is a figure which shows the general | schematic flow of the characteristic distribution analysis method of one Embodiment of this invention. It is a figure which shows the example of the test result of the pattern test | inspection on a board | substrate. (A)-(e) is a figure which illustrates the type of feature distribution. (A), (b) is a figure explaining the concept of the relationship of feature distribution. It is a figure which illustrates the method of integration of feature distribution. It is a figure explaining the hierarchical structure of classification reference data while illustrating the method of integration of feature distribution. It is a figure which shows the structure of the characteristic distribution analyzer of one Embodiment of this invention. It is a figure which shows the example of the specific process flow of step S101 in FIG. It is a figure which shows the concept of a lattice map typically. It is a figure explaining the similarity calculation method of the characteristic distribution of a board | substrate with respect to feature distribution. It is a figure explaining the evaluation method of the mutual relationship of feature distribution. It is a figure which shows the example of the specific process flow of step S104 in FIG.

Explanation of symbols

200, 401, 402 Substrate 202 Defect 203, 404, 405, 406 Defect distribution 301, 302, ..., 305, 502, 602 Feature distribution 700 Property distribution analyzer 902 Lattice region G1 First layer feature distribution group G2 Second layer feature Distribution group G3 Third layer feature distribution group S101 Feature distribution group creation processing S102 Similarity evaluation processing S103 Relevance evaluation processing S104 Feature distribution integration processing S105 Hierarchical structure creation processing

Claims (16)

A characteristic distribution analysis method for creating a classification standard for classifying the above-mentioned substrates for a group of substrates each having a characteristic distribution,
A feature distribution group creating step of creating a first layer feature distribution group composed of a set of feature distributions representing the characteristics of the characteristic distribution of each substrate;
A similarity evaluation step for quantitatively evaluating the similarity between the characteristic distribution of each of the substrates and the characteristic distribution;
A relevance evaluation step for quantitatively evaluating relevance in which several feature distributions included in the first layer feature distribution group appear simultaneously on the same substrate based on the similarity;
Based on the relationship, several feature distributions of the first layer feature distribution group are integrated while maintaining the position of each feature distribution on the substrate, and a new one on the assumed substrate is obtained. A feature distribution integration process for creating a unique feature distribution;
A hierarchical structure creating step in which a set of the new feature distribution and the remaining feature distribution group obtained by removing the feature distribution targeted for integration from the first layer feature distribution group is a second layer feature distribution group. Having characteristic distribution analysis method. In the characteristic distribution analysis method according to claim 1,
A characteristic distribution analysis method, wherein the similarity evaluation step, the relevance evaluation step, and the feature distribution integration step are sequentially and repeatedly executed on the uppermost layer feature distribution group obtained by the hierarchical structure creation step. In the characteristic distribution analysis method according to claim 1 or 2,
In the feature distribution group creating step, a distribution independent of each other is extracted as the feature distribution from the characteristic distribution of the substrate group. In the characteristic distribution analysis method as described in any one of Claim 1 to 3,
A characteristic distribution analysis method characterized in that, in the similarity evaluation step, the similarity is evaluated by projection from a vector representing the characteristic distribution of the substrate group to a vector representing the characteristic distribution. In the characteristic distribution analysis method according to any one of claims 1 to 4,
In the relevance evaluation step, a correlation coefficient between the similarities between the characteristic distribution of each of the substrates and the characteristic distribution is obtained, and the relevance is evaluated based on the correlation coefficient. Characteristic distribution analysis method characterized by In the characteristic distribution analysis method according to any one of claims 1 to 5,
In the feature distribution integration step, a set of feature distributions having the greatest relevance among the feature distributions in the first layer feature distribution group is selected, and the feature distributions forming the set are integrated to create the new feature. A characteristic distribution analysis method characterized by creating a distribution. In the characteristic distribution analysis method according to any one of claims 1 to 6,
In the feature distribution integration step, for each of the several feature distributions to be integrated, an average value of similarity between the feature distribution and the characteristic distribution of each substrate is calculated, A characteristic distribution analysis method characterized in that the integration is performed by weighting and adding the characteristic values of the characteristic distribution with the average value of the similarity calculated for each characteristic distribution. In the characteristic distribution analysis method according to claim 2,
When the relevance evaluation step is performed on the uppermost layer feature distribution group, whether the relevance between feature distributions in the uppermost layer feature distribution group is equal to or lower than a predetermined threshold, or the uppermost layer The characteristic distribution analysis method is characterized in that the similarity evaluation step, the relevance evaluation step, and the feature distribution integration step are sequentially executed until one feature distribution is included in the feature distribution group. A characteristic distribution analyzer for creating a classification standard for classifying the above-mentioned substrates for a group of substrates each having a characteristic distribution,
A feature distribution group creating unit that creates a first layer feature distribution group composed of a set of feature distributions representing the characteristics of the characteristic distribution of each substrate;
A similarity evaluation unit that quantitatively evaluates the similarity between the characteristic distribution of each of the substrates and the feature distribution;
A relevance evaluation unit that quantitatively evaluates relevance in which several feature distributions included in the first layer feature distribution group appear simultaneously on the same substrate based on the similarity;
Based on the relationship, several feature distributions of the first layer feature distribution group are integrated while maintaining the position of each feature distribution on the substrate, and a new one on the assumed substrate is obtained. A feature distribution integration unit for creating a simple feature distribution;
A hierarchical structure creation unit having a set of the new feature distribution and the remaining feature distribution group obtained by removing the feature distribution targeted for integration from the first layer feature distribution group as a second layer feature distribution group; A characteristic distribution analyzer. A substrate classification method for classifying a substrate group using a classification criterion for a group of substrates each having a characteristic distribution,
A characteristic distribution analysis method according to claim 1, wherein a feature distribution group of a plurality of layers having a hierarchical structure is created as the classification standard,
A substrate classification method for classifying the substrate for each feature distribution by comparing the feature distribution included in the feature distribution group forming the classification criterion with the characteristic distribution on each substrate included in the substrate group. A board classification device that classifies the board using a classification standard for a board group consisting of a plurality of boards each having a characteristic distribution,
A characteristic distribution analysis device according to claim 9 is provided, and by this characteristic distribution analysis device, a feature distribution group of a plurality of layers having a hierarchical structure is created as the classification standard,
A classification processing unit for comparing the feature distribution included in the feature distribution group forming the classification criterion with the characteristic distribution on each substrate included in the substrate group, and classifying the substrate for each feature distribution; Substrate sorting device.   A characteristic distribution analysis program for causing a computer to execute the characteristic distribution analysis method according to claim 1.   A board classification program for causing a computer to execute the board classification method according to claim 10.   A computer-readable recording medium on which the characteristic distribution analysis program according to claim 12 is recorded.   A computer-readable recording medium on which the substrate distribution program according to claim 13 is recorded. Classification group data serving as a reference for classifying a substrate according to the characteristic distribution on the substrate for a group of substrates each having a characteristic distribution,
It has a multi-layer feature distribution group with a hierarchical structure,
Of the multi-layer feature distribution group, the lowest-layer feature distribution group is composed of a set of feature distributions representing the characteristics of the characteristic distribution of each substrate,
The upper-layer feature distribution group other than the lowermost layer maintains several feature distributions included in the lower-layer feature distribution group immediately below the layer, and maintains the position of each feature distribution on the substrate. Classification reference data consisting of a set of feature distributions integrated while the remaining feature distribution groups obtained by removing the feature distributions targeted for integration from the lower-layer feature distribution groups.