Information processing device, information processing method, and computer program

Abstract

This information processing device comprises a reception unit that receives a plurality of first feature amounts, and a processing unit that estimates a plurality of second feature amounts from the plurality of first feature amounts on the basis of a multiple regression model. The multiple regression model is expressed using a coefficient matrix in which multiple regression coefficients of a plurality of multiple regression equations are collected. The processing unit executes substitution of the plurality of first feature amounts into the multiple regression model, and estimation of the plurality of second feature amounts from the multiple regression model using the inverse matrix of the coefficient matrix. The plurality of first feature amounts include functional feature amounts of a product. The plurality of second feature amounts include at least one of structural feature amounts of the product and measurement device feature amounts of a measurement device that has measured the functional feature amounts of the product.

Description

Information processing device, information processing method, and computer program Cross-reference of related applications

[0001] This application is related to Japanese Patent Application No. 2025-016748, filed on 4 February 2025, and Japanese Patent Application No. 2026-016154, filed on 3 February 2026, and claims priority based on these Japanese patent applications. All contents described in these Japanese patent applications are incorporated herein by reference as constituting this specification.

[0002] The technologies disclosed herein relate to information processing devices, information processing methods, and computer programs.

[0003] Japanese Patent Publication No. 2009-99960 discloses a quality control method using a multiple regression model in which characteristic quantities related to manufacturing conditions measured during the manufacturing process and structural characteristic quantities of intermediate products are used as explanatory variables, and the electrical characteristics of the final product are used as the dependent variable. This quality control method estimates the electrical characteristics of the final product from various characteristic quantities measured during the manufacturing process, and determines that a defective product has occurred when the estimated value deviates from a standard value.

[0004] Incidentally, the final product manufactured through several manufacturing processes will have structural variations due to factors such as manufacturing variability. Understanding the structure of the product is crucial for controlling its quality. However, in the case of products such as semiconductor devices, it can be difficult to measure the internal structure of the semiconductor substrate (e.g., impurity concentration distribution). Furthermore, even if it is possible to indirectly measure the internal structure of the semiconductor substrate using test patterns, the reduction in production capacity due to securing test patterns within the surface of the semiconductor substrate is also a problem. For this reason, there is a need for technology to identify specific features from directly measurable features during the manufacturing process of a product. It should be noted that such problems are not limited to products like semiconductor devices, but can occur in other types of products as well. This specification provides technology that enables the identification of specific features from directly measurable features during the manufacturing process of a product.

[0005] The information processing device disclosed herein may include a receiving unit that receives a plurality of first features, and an estimation unit that estimates a plurality of second features from the plurality of first features using a multiple regression model. The multiple regression model may be a model expressed using a coefficient matrix that aggregates the multiple regression coefficients of a plurality of multiple regression equations. The plurality of target variables included in the multiple regression model may be the plurality of first features. The plurality of explanatory variables included in the multiple regression model may be the plurality of second features. The processing unit may be configured to substitute the plurality of first features received by the receiving unit into the multiple regression model, and to estimate the plurality of second features from the multiple regression model using the inverse of the coefficient matrix. The plurality of first features may include functional features of a product. The plurality of second features may include at least one of the structural features of the product and the measurement device features of a measuring device that measured the functional features of the product. Here, the inverse of the coefficient matrix is ​​a broad concept that includes the pseudo-inverse matrix.

[0006] The above-described information processing device can estimate at least one of the following from the functional characteristics of the product: the structural characteristics of the product and the measuring device characteristics of the measuring device. Therefore, the above-described information processing device can, for example, grasp at least one of the structural characteristics of the product and the measuring device characteristics of the measuring device, which are difficult to measure.

[0007] This specification also discloses an information processing method performed by an information processing device. This information processing method may include a receiving step of receiving a plurality of first features and an estimation step of estimating a plurality of second features from the plurality of first features based on a multiple regression model. The multiple regression model may be a model represented using a coefficient matrix that aggregates the multiple regression coefficients of a plurality of multiple regression equations. The plurality of dependent variables included in the multiple regression model may be the plurality of first features. The plurality of independent variables included in the multiple regression model may be the plurality of second features. The estimation step may include substituting the plurality of first features received in the receiving step into the multiple regression model and estimating the plurality of second features using the inverse matrix of the coefficient matrix. The plurality of first features may include functional features of a product. The plurality of second features may include at least one of the structural features of the product and the measuring device features of a measuring device that measured the functional features of the product.

[0008] This specification also discloses a computer program for an information processing device. The computer program may be configured to cause the information processing device to perform a receiving process for receiving a plurality of first features, and an estimation process for estimating a plurality of second features from the plurality of first features based on a multiple regression model. The multiple regression model may be a model represented using a coefficient matrix that aggregates the multiple regression coefficients of a plurality of multiple regression equations. The plurality of dependent variables included in the multiple regression model may be the plurality of first features. The plurality of independent variables included in the multiple regression model may be the plurality of second features. The estimation process may include substituting the plurality of first features received in the receiving process into the multiple regression model, and estimating the plurality of second features using the inverse matrix of the coefficient matrix. The plurality of first features may include functional features of a product. The plurality of second features may include at least one of the structural features of the product and the measurement device features of a measuring device that measured the functional features of the product.

[0009] This figure schematically shows the configuration of the information processing system of the first embodiment. This figure shows the flow of processing performed by the information processing device included in the information processing system of the first embodiment. This figure schematically shows the configuration of the information processing system of the second embodiment. This figure shows the position of semiconductor devices (i.e., chips) on the wafer surface where a first type of structural feature is measured using a QC device. This figure shows the position of semiconductor devices (i.e., chips) on the wafer surface where a second type of structural feature is measured using a QC device. This figure shows the position of semiconductor devices (i.e., chips) on the wafer surface where first and second types of structural feature are measured using a QC device. This figure shows the flow of processing performed by the information processing device included in the information processing system of the second embodiment. This figure schematically shows the configuration of the measuring device used in the information processing system of the third embodiment. This figure schematically shows the wafer distribution of the first electrical feature measured by the measuring device in Figure 6. This figure schematically shows the wafer distribution of the second electrical feature measured by the measuring device in Figure 6. This figure schematically shows the wafer distribution of the third electrical feature measured by the measuring device in Figure 6. This figure schematically shows the wafer distribution of the fourth electrical feature measured by the measuring device in Figure 6. This figure schematically shows the wafer distribution of the fifth electrical feature measured by the measuring device in Figure 6. This figure schematically shows the wafer distribution of the sixth electrical feature measured by the measuring device in Figure 6. This figure schematically shows the wafer distribution of the seventh electrical feature measured by the measuring device in Figure 6. This figure schematically shows the wafer distribution of the eighth electrical feature measured by the measuring device in Figure 6. This figure schematically shows the wafer distribution of the first structural feature estimated based on a multiple regression model that does not consider the variability of the measuring device in Figure 6. This figure schematically shows the wafer distribution of the second structural feature estimated based on a multiple regression model that does not consider the variability of the measuring device in Figure 6. This figure schematically shows the wafer distribution of the third structural feature estimated based on a multiple regression model that does not consider the variability of the measuring device in Figure 6. This figure schematically shows the wafer distribution of the fourth structural feature estimated based on a multiple regression model that does not consider the variability of the measuring device in Figure 6. This figure schematically shows the wafer distribution of the first structural feature estimated based on a multiple regression model that considers the variability of the measuring device in Figure 6.This figure schematically shows the wafer distribution of the second structural feature quantity estimated based on a multiple regression model that takes into account the variability of the measurement device in Figure 6. This figure schematically shows the wafer distribution of the third structural feature quantity estimated based on a multiple regression model that takes into account the variability of the measurement device in Figure 6. This figure schematically shows the wafer distribution of the fourth structural feature quantity estimated based on a multiple regression model that takes into account the variability of the measurement device in Figure 6. This figure schematically shows the wafer distribution of the first measurement device feature quantity estimated based on a multiple regression model that takes into account the variability of the measurement device in Figure 6. This figure schematically shows the configuration of the measurement device used in the information processing system of the fourth embodiment. This figure shows the time series distribution of the first electrical feature quantity on a lot basis, measured for each of the three testers included in the measurement device in Figure 10. This figure shows the time series distribution of the second electrical feature quantity on a lot basis, measured for each of the three testers included in the measurement device in Figure 10. This figure shows the time series distribution of the third electrical feature quantity on a lot basis, measured for each of the three testers included in the measurement device in Figure 10. This figure shows the time series distribution of the fourth electrical feature quantity on a lot basis, measured for each of the three testers included in the measurement device in Figure 10. This figure shows the time-series distribution of the fifth electrical feature per lot, measured for each of the three testers included in the measurement device in Figure 10. This figure shows the time-series distribution of the measured structural feature per lot. This figure shows the time-series distribution of the first structural feature estimated based on a multiple regression model that does not consider the variability of the measurement device in Figure 10. This figure shows the time-series distribution of the second structural feature estimated based on a multiple regression model that does not consider the variability of the measurement device in Figure 10. This figure shows the time-series distribution of the first structural feature estimated based on a multiple regression model that considers the variability of the measurement device in Figure 10. This figure shows the time-series distribution of the second structural feature estimated based on a multiple regression model that considers the variability of the measurement device in Figure 10. This figure shows the time-series distribution of the first measurement device feature estimated based on a multiple regression model that considers the variability of the measurement device in Figure 10. This figure shows the time-series distribution of the second measurement device feature estimated based on a multiple regression model that considers the variability of the measurement device in Figure 10.

[0010] The following describes an example of how the technology disclosed herein is applied to the manufacturing process of semiconductor devices. The technology disclosed herein can estimate structural features relating to the structure of a semiconductor device from electrical features relating to the electrical properties of the manufactured semiconductor device. It should be noted that the technology disclosed herein is not limited to this example but is applicable to other examples as well.

[0011] (First Embodiment) As shown in Figure 1, the information processing system 1 used in the manufacturing process of a semiconductor device comprises an information processing device 10, a data server 20, and a chip test device 30.

[0012] The information processing device 10 is composed of a computer and includes a receiving unit 12, a storage unit 14, a processing unit 16, and a display unit 18.

[0013] The receiving unit 12 of the information processing device 10 includes a network interface and is connected to a network NW. The information processing device 10 is configured to communicate with the data server 20 and the chip test device 30 via the network NW.

[0014] The storage unit 14 of the information processing device 10 includes ROM (Read Only Memory) and RAM (Random Access Memory). The storage unit 14 stores various computer programs 15. The storage unit 14 also functions as a work area for executing various computer programs 15.

[0015] The processing unit 16 of the information processing device 10 includes a microprocessor composed of a CPU (Central Processing Unit) and the like. The processing unit 16 is connected to other elements constituting the information processing device 10 via a communication bus, and is capable of data communication with these elements. The processing unit 16 executes the following processes based on various computer programs 15 stored in the storage unit 14.

[0016] The display unit 18 includes, for example, a display screen. The display unit 18 displays an operation screen for receiving instructions from the operator. The display unit 18 also displays the results obtained when the processing unit 16 performs a process described later.

[0017] The data server 20 stores various data measured by the chip test device 30. The various data stored in the data server 20 are provided to the information processing device 10 in response to a request from the information processing device 10. Note that the information processing device 10 may be configured to directly receive the various data measured by the chip test device 30 and store them in the storage unit 14 without using such an external data server 20.

[0018] The chip test device 30 is a device that measures electrical characteristic quantities related to the electrical characteristics of manufactured semiconductor devices (i.e., chips), and includes a transmission unit 32 and a measurement unit 34. The electrical characteristic quantities are not particularly limited, and for example, may include at least one of collector-emitter breakdown voltage, collector leakage current, threshold voltage, on-voltage, body diode forward voltage, gate capacitance, gate-collector capacitance, switching losses during turn-on and turn-off processes, switching time, delay time, surge voltage, reverse recovery time during reverse recovery process, reverse recovery current, and surge voltage. These electrical characteristic quantities may be measured under temperature conditions such as room temperature and high temperature, and conditions such as voltage values and current values. A plurality of electrical characteristic quantities of the semiconductor device measured by the measurement unit 34 are transmitted to the data server 20 via the transmission unit 32. A plurality of electrical characteristic quantities are stored in the data server 20 in association with the ID information of the semiconductor device.

[0019] Here, before explaining the processing flow executed by the information processing device 10, a procedure for creating a multiple regression model used in the processing flow will be explained.

[0020] A multiple regression equation for predicting an arbitrary scalar value y' ｍ = (x １ , ···, x Ｎ ) of a plurality of electrical characteristic quantities Y' Ｔ = (y' １ , ···, y' Ｍ ) using a plurality of structural characteristic quantities X is represented by Equation 1 below. Here, M is the number of electrical characteristic quantities, N is the number of structural characteristic quantities, a ｍ,ｎ is a multiple regression coefficient, and b​​ｍ is an offset value.

[0021] This multiple regression equation is not particularly limited. For example, it may be created by machine learning data on a plurality of electrical characteristic amounts and a plurality of structural characteristic amounts obtained when mass-producing a semiconductor device, or it may be created by machine learning data on a plurality of electrical characteristic amounts and a plurality of structural characteristic amounts obtained using device simulation of a semiconductor device. The structural characteristic amounts are not particularly limited. For example, they may include at least one of semiconductor substrate thickness, trench depth of a trench gate, trench width of a trench gate, gate insulating film thickness of a trench gate, impurity concentration of each part, contact resistance of an electrode, and Schottky barrier.

[0022] For each of the plurality of electrical characteristic amounts, the plurality of multiple regression equations created are expressed as Y′ = AX + B by using a coefficient matrix (A) that summarizes the multiple regression coefficients.

[0023] Here, in Equation 2, by moving the offset term group B = (b １ , ···, b Ｍ ) to the left side, Y′ - B = Y = (y １ , ···, y Ｍ ), provided that y ｍ = y′ ｍ - b ｍ , it is expressed as Y = AX.

[0024] In this specification, the multiple regression model expressed as Y = AX is referred to as a forward model. The multiple regression model created by the above procedure is stored in the storage unit 14 of the information processing apparatus 10. Note that standardization processing may be performed on each of the explanatory variable and the objective variable so that the average becomes zero. In this case, the offset term group B becomes a zero vector, and the procedure of moving the above offset term group is omitted.

[0025] Next, referring to FIG. 2, the processing flow executed by the processing unit 16 of the information processing apparatus 10 will be described.

[0026] First, the processing unit 16 accesses the data server 20 via the receiving unit 12 and receives multiple electrical characteristic quantities of the semiconductor device stored in the data server 20 (step S1).

[0027] Next, the processing unit 16 substitutes the received electrical features into the multiple regression model (step S2).

[0028] Next, the processing unit 16 calculates the inverse matrix (A) of the coefficient matrix (A) of the multiple regression model. － ) is used to estimate multiple structural features from the multiple regression model (step S3). Specifically, the processing unit 16 converts the forward model shown in equation 3 above to the reverse model, i.e., X = A － By calculating Y, multiple structural features of the semiconductor device are estimated.

[0029] In this way, the information processing device 10 can estimate multiple structural features from multiple electrical features of a semiconductor device. Therefore, the information processing device 10 can estimate structural features of a semiconductor device that are difficult to measure, for example. Furthermore, the information processing device 10 can estimate multiple structural features of a semiconductor device while reducing the area of ​​the test pattern that is reserved to indirectly measure the structural features of the semiconductor device. Therefore, the information processing device 10 can estimate the structural features of a semiconductor device while suppressing a decrease in production capacity.

[0030] Note that the above processing flow applies when the coefficient matrix (A) is invertible. If the coefficient matrix (A) is not invertible, in step S3, the inverse matrix (A － ) instead of the pseudo-inverse matrix (A Ｔ A) －１ A Ｔ By using the least squares method, multiple structural features can be estimated from the multiple regression model.

[0031] Note that the pseudo-inverse matrix (A Ｔ A) －１ A Ｔ In order to use this, we need the pseudo-inverse matrix (A) as shown in equation 4 below. Ｔ A) －１ A ＴThere is a constraint that the rank of the algorithm must be equal to or greater than the number of structural features (N).

[0032] For example, the multiple regression coefficient a ｍ,ｎ If the matrix is ​​sparse with many zeros, it may not satisfy equation 4 above. Such a sparse matrix with many zeros can occur when it contains many terms of structural features that do not significantly contribute to changes in electrical features. For example, changes in gate insulating film thickness have almost no contribution to changes in the breakdown voltage of a semiconductor device. The multiple regression coefficient a of such structural feature terms ｍ,ｎ This can be zero as a result of statistical testing. Also, if the number of structural features (N) > the number of electrical features (M) exists, it may not satisfy equation 4 above. For example, the relationship N > M may occur when the structure of the semiconductor device is complex. The second embodiment described below is an example that can handle cases where equation 4 above is not satisfied.

[0033] (Second Embodiment) As shown in Figure 3, the information processing system 2 is characterized by further comprising a QC (Quality Control) device 40 compared to the information processing system 1 of the first embodiment.

[0034] The QC device 40 is a device for measuring structural features related to the structure of a semiconductor device, and comprises a transmission unit 42 and a measurement unit 44. The structural features measured by the QC device 40 are not particularly limited, but examples include trench depth and gate insulating film thickness. The structural features of the semiconductor device measured by the measurement unit 44 are transmitted to the data server 20 via the transmission unit 42. The data server 20 stores multiple structural features linked to the ID information of the semiconductor device.

[0035] The QC device 40 measures the structural features of a semiconductor device (i.e., a chip) on a specific wafer within a single lot. The selection of wafers to be measured varies. For example, different wafers may be selected for each process included in the manufacturing process, and the structural features may be measured on a specific chip on the selected wafer surface. The location of the chip on which the structural features are measured also varies within the selected wafer surface. As an example, the following measurement locations are illustrated. For example, as shown in Figure 4A, a specific structural feature among multiple structural features may be measured at nine points distributed above, below, left, and right of the center of the wafer 50. Also, as shown in Figure 4B, a specific structural feature among multiple structural features may be measured at 17 points distributed radially from the center of the wafer 50. Therefore, as shown in Figure 4C, one type of structural feature is measured for the chip shown in white, and two types of structural features are measured for the chip shown in black. Thus, the number and types of structural features measured by the QC device 40 vary from chip to chip. Furthermore, the number and types of structural features measured on a particular chip may differ from those pre-set due to various causes that occur during the manufacturing process (such as rework or wafer outages).

[0036] Next, with reference to Figure 5, the processing flow executed by the processing unit 16 of the information processing device 10 will be described.

[0037] First, the processing unit 16 accesses the data server 20 via the receiving unit 12 and receives multiple electrical feature quantities and at least one measured structural feature quantity of the semiconductor device stored in the data server 20 (step S11).

[0038] Next, the processing unit 16 creates a modified multiple regression model using known structural features (step S12). The known structural features include at least one measured structural feature. The known structural features may be the average value of at least one structural feature measured for each of the multiple chips. The modified multiple regression model is created by modifying the initial multiple regression model, which is the trained multiple regression model shown in Equation 3 above. For example, structural feature x １ Assuming that is known, the initial multiple regression model is modified as follows:

[0039] Here, in this modified multiple regression model, let A' be the coefficient matrix and N' be the number of structural features (= N - number of known structural features). In this case, the constraint on the pseudoinverse of the modified multiple regression model is expressed as follows.

[0040] Next, the processing unit 16 determines whether or not the above number 6 is satisfied (step S13). The number of multiple structural features (N') included in the modified multiple regression model is less than the number of multiple structural features (N) included in the initial multiple regression model. Therefore, even if the constraint of the above number 4 is not satisfied in the initial multiple regression model, the constraint of the above number 6 can be satisfied in the modified multiple regression model. If the constraint of the above number 6 is satisfied, the process proceeds to step S14. If the constraint of the above number 6 is not satisfied, the process ends.

[0041] Next, the processing unit 16 substitutes the received multiple electrical features into a modified multiple regression model (step S14).

[0042] Next, the processing unit 16 calculates the pseudo-inverse matrix (A') of the modified multiple regression model. Ｔ A') －１ A' Ｔ Multiple structural features are estimated from the modified multiple regression model (Step S15).

[0043] Thus, the information processing device 10 of the second embodiment can estimate multiple structural features from multiple electrical features of a semiconductor device based on a modified multiple regression model using known structural features, even when the initial multiple regression model cannot perform inverse calculations due to the constraints of the pseudo-inverse matrix. In other words, by using known structural features, the number of structural features in the initial multiple regression model can be increased. For this reason, the information processing device 10 of the second embodiment can estimate a variety of structural features of semiconductor devices with more complex structures.

[0044] Furthermore, according to the information processing device 10 of the second embodiment, the estimation accuracy of other structural features can be improved by utilizing known structural features.

[0045] Furthermore, as explained with reference to Figure 4, the number and types of structural features measured by the QC device 40 vary from chip to chip. Also, the number and types of structural features measured on a particular chip may differ from those set in advance due to various causes that occur in the manufacturing process (such as rework or wafer out). According to the information processing device 10 of the second embodiment, a modified multiple regression model can be created by dynamically changing known structural features according to the number and types of structural features measured by the QC device 40. For this reason, the information processing device 10 of the second embodiment can estimate multiple structural features of a semiconductor device even if the number and types of structural features measured by the QC device 40 fluctuate due to various causes that occur in the manufacturing process (such as rework or wafer out).

[0046] In the above embodiment, the measured values ​​of structural features measured by the QC device 40 were used as known structural features. Alternatively, design values ​​of structural features with very little variation may be used as known structural features. Or, a combination of the measured values ​​of structural features measured by the QC device 40 and design values ​​of structural features with very little variation may be used as known structural features. For example, for the sake of simplicity, it was assumed that the process would end if the constraints were not met in step S13. Alternatively, in step S13, if the constraints were not met, the process would return to step S12 and perform further processing, such as adding more known structural features.

[0047] The structural characteristics of a semiconductor device estimated based on the techniques of the first and second embodiments described above may be affected by variations in the measuring devices used to measure the electrical characteristics of the semiconductor device. These variations in measuring devices include variations that occur during each measurement process of each device, as well as variations in measurement processes between devices. The following describes techniques for suppressing such variations in measuring devices.

[0048] (Third Embodiment) Figure 6 shows a schematic configuration of a measuring device 60 for measuring the electrical characteristics of a semiconductor device (i.e., a chip 68). Note that the measuring device 60 is an example of the chip test device 30 shown in Figure 1. The measuring device 60 includes a probe 62, a first stage 64, and a second stage 66. The first stage 64 and the second stage 66 are configured to move alternately between a measurement position and a standby position, for example, using a rotary table. In this example, the first stage 64 is positioned at the measurement position, and the second stage 66 is positioned at the standby position. The chips 68 are placed on the stage in the standby position in the order in which they were cut from the wafer. Therefore, the chips 68 are placed alternately on the first stage 64 and the second stage 66 in the order in which they were cut from the wafer.

[0049] Figures 7A to 7H schematically show the wafer distribution of eight types of electrical features measured using the measuring device 60. The color scheme of the chips indicates the relative magnitude of the measured values ​​of the corresponding electrical features. Black indicates a case where the measured value of the electrical feature is relatively high.

[0050] In the wafer distributions shown in Figures 7A to 7G, chips with relatively high electrical feature measurements are concentrated in specific parts of the wafer. On the other hand, in the wafer distribution shown in Figure 7H, the magnitudes of the electrical feature measurements appear alternately. This type of wafer distribution is thought to be influenced by the difference between the first stage 64 and the second stage 66. For example, it is thought that the electrical feature measurements of chips placed on the first stage 64 are measured to be relatively high, while the electrical feature measurements of chips placed on the second stage 66 are measured to be relatively low.

[0051] Figures 8A to 8D show the wafer distribution of four types of structural features estimated based on the multiple regression model described in Equation 3 above. The color scheme of the chips indicates the relative magnitudes of the estimated values ​​of the corresponding structural features. Black indicates cases where the estimated value of the structural feature is relatively high.

[0052] In the wafer distributions of Figures 8A and 8C, the estimated values ​​of structural features alternate in magnitude. Thus, the estimated values ​​of structural features, which are estimated based on electrical features that include the effect of the difference between the first stage 64 and the second stage 66, also reflect the effect of the difference between the first stage 64 and the second stage 66.

[0053] In order to suppress the differences between the first stage 64 and the second stage 66, that is, the variability between stages, the multiple regression model shown in equation 3 above is modified as follows.

[0054] The above multiple regression model of number 7 uses multiple electrical features Y' Ｔ = (y' １ ,・・・, y' Ｍ The variables that explain ) include multiple structural features X Ｔ = (x １ ,・・・, x Ｎ In addition to the above, multiple measurement device features W Ｔ= (w １ ,・・・, w P ) has been added. As a result, the number of rows in the coefficient matrix has increased by P columns. The measurement device features are not particularly limited, but may include at least one of the following, for example, measurement temperature, resistance, inductance, and capacitance in the measurement circuit. There may be multiple resistances, inductances, and capacitances in the measurement circuit. For example, the wafer distribution of electrical features in Figure 7H may be due to the difference in stage temperatures between the first stage 64 and the second stage 66, i.e., the measurement temperature.

[0055] Figures 9A to 9E show the wafer distribution of four types of structural features and one measurement device feature estimated based on the multiple regression model of equation 7 described above. As shown in Figure 9E, the variability between the first stage 64 and the second stage 66 is well reflected in the measurement device feature. Therefore, in the multiple regression model of equation 7 described above, the influence based on variability between stages is statistically separated. As a result, as can be seen by comparing Figures 8A and 8C with Figures 9A and 9C described above, the influence of variability between stages is suppressed in the four types of structural features estimated based on the multiple regression model of equation 7 described above, and pure structural variability is extracted.

[0056] (Fourth Embodiment) Figure 10 shows a schematic of a measuring device 70 for measuring the electrical characteristics of a semiconductor device (i.e., a chip 74). Note that the measuring device 70 is an example of the chip test device 30 shown in Figure 1. The measuring device 70 is equipped with a plurality of testers 72. The plurality of testers 72 are testers of the same product and have the specification to output the same measured value for the same electrical characteristics. A plurality of chips 74 are assigned to each of the plurality of testers 72 in lot units.

[0057] Figures 11A to 11E show the time-series distributions of five types of electrical characteristics measured by each of the three testers 72, and one type of structural characteristic measured by the QC device. The QC device corresponds to the QC device 40 shown in Figure 3.

[0058] In Figures 11A to 11C, no significant difference is observed in the time-series distribution of electrical features among the three testers 72. On the other hand, in Figure 11D, only the electrical features measured by the second tester 72 show a significant increase midway through the process. Furthermore, in Figure 11E, the electrical features measured by the third tester 72 consistently show outlier values. These time-series distributions of electrical features suggest that there is variability among testers 72 with the same specifications.

[0059] Figures 12A and 12B show the time-series distributions of two types of structural features estimated based on the multiple regression model of number 5 described above, i.e., the multiple regression model modified by one type of structural feature measured. In Figure 12A, only the structural feature estimated based on the electrical feature measured by the second tester 72 shows a significant increase from a certain point. In Figure 12B, the structural feature estimated based on the electrical feature measured by the third tester 72 consistently shows an outlier value. Thus, the estimated values ​​of structural features estimated based on electrical features that include variability among the testers 72 also reflect the influence of variability among the testers 72.

[0060] To suppress such variability among the testers 72, the multiple regression model shown in equation 7 above is used. The measurement device features introduced into the multiple regression model are not particularly limited, but may include, for example, at least one of the measurement environment conditions at the time of measurement and the serial number information of the measurement device.

[0061] Figures 13A to 13D show the time-series distributions of two types of structural features and two measurement device features estimated based on the multiple regression model of equation 7 described above. As shown in Figures 13C and 13D, the variability among the testers 72 is well reflected in the measurement device features. Therefore, in the multiple regression model of equation 7 described above, the influence based on the variability among the testers 72 is statistically separated. As a result, as can be seen by comparing Figures 12A and 12B with Figures 13A and 13B described above, the influence of the variability among the testers 72 is suppressed in the two types of structural features estimated based on the multiple regression model of equation 7 described above, and pure structural variability is extracted.

[0062] The third and fourth embodiments described above were examples of accurately estimating the structural features of a semiconductor device by suppressing variations in the measuring device. Instead of this example, only the measuring device features of the measuring device may be estimated. Specifically, in the multiple regression model of Equation 7 described above, multiple electrical features Y' Ｔ = (y' １ ,・・・, y' Ｍ From the variables that explain ), multiple structural features X Ｔ = (x １ ,・・・, x Ｎ ) may be deleted. Alternatively, instead of deleting it, all of the multiple structural features may be treated as known structural features, and the same formula derivation as in Equation 5 described in the second embodiment above may be performed. In these examples, multiple measurement device features can be estimated from multiple electrical features of the semiconductor device. This makes it possible to detect malfunctions such as failures of the measurement device at an early stage.

[0063] The following summarizes the features of the technology disclosed in this specification. Note that each of the technical elements described below is an independent technical element, and exhibits technical usefulness either individually or in various combinations.

[0064] (Aspect 1) An information processing device comprising: a receiving unit that receives a plurality of first features; and a processing unit that estimates a plurality of second features from the plurality of first features based on a multiple regression model, wherein the multiple regression model is a model expressed using a coefficient matrix that aggregates the multiple regression coefficients of a plurality of multiple regression equations, the plurality of target variables included in the multiple regression model are the plurality of first features, and the plurality of explanatory variables included in the multiple regression model are the plurality of second features, the processing unit is configured to perform the following: substituting the plurality of first features received by the receiving unit into the multiple regression model, and estimating the plurality of second features from the multiple regression model using the inverse matrix of the coefficient matrix, wherein the plurality of first features include functional features of a product, and the plurality of second features include at least one of the structural features of the product and the measuring device features of a measuring device that measured the functional features of the product.

[0065] (Aspect 2) The processing unit, when the coefficient matrix (A) is invertible, calculates the inverse matrix (A －１ The information processing apparatus according to embodiment 1, configured to estimate the plurality of second features from the multiple regression model using ).

[0066] (Aspect 3) When the coefficient matrix (A) is not invertible, the processing unit generates the pseudo-inverse matrix (A Ｔ A) －１ A Ｔ The information processing apparatus according to embodiment 1, configured to estimate the plurality of second features from the multiple regression model using the least squares method.

[0067] (Aspect 4) The processing unit is further configured to modify the initial multiple regression model to create the multiple regression model when the rank of the pseudo-inverse matrix of the learned initial multiple regression model is smaller than the number of the plurality of second features included in the initial multiple regression model, wherein the rank of the pseudo-inverse matrix of the modified multiple regression model is greater than or equal to the number of second features remaining after excluding some of the second features from the plurality of second features included in the initial multiple regression model, as described in Aspect 3.

[0068] (Aspect 5) The processing unit is configured to create the multiple regression model by modifying the initial multiple regression model by substituting some of the second features into the initial multiple regression model, wherein some of the second features include at least one of the design value and the measured value of the product, as described in Aspect 4.

[0069] (Aspect 6) An information processing apparatus according to any one of aspects 1 to 5, wherein the product is a semiconductor device, and the plurality of first feature quantities are a plurality of electrical feature quantities.

[0070] (Aspect 7) An information processing apparatus according to any one of aspects 1 to 6, wherein the plurality of second features include both the structural features and the measuring device features.

[0071] (Aspect 8) An information processing method executed by an information processing device, comprising: a receiving step of receiving a plurality of first features; and an estimation step of estimating a plurality of second features from the plurality of first features based on a multiple regression model, wherein the multiple regression model is a model represented using a coefficient matrix that aggregates the multiple regression coefficients of a plurality of multiple regression equations, the plurality of target variables included in the multiple regression model are the plurality of first features, the plurality of explanatory variables included in the multiple regression model are the plurality of second features, the estimation step comprises: substituting the plurality of first features received in the receiving step into the multiple regression model, and estimating the plurality of second features using the inverse matrix of the coefficient matrix, wherein the plurality of first features include functional features of a product, and the plurality of second features include at least one of the structural features of the product and the measuring device features of a measuring device that measured the functional features of the product.

[0072] (Aspect 9) A computer program for an information processing device, wherein the computer program is configured to cause the information processing device to perform a receiving process for receiving a plurality of first features, and an estimation process for estimating a plurality of second features from the plurality of first features based on a multiple regression model, wherein the multiple regression model is a model represented using a coefficient matrix that aggregates the multiple regression coefficients of a plurality of multiple regression equations, the plurality of target variables included in the multiple regression model are the plurality of first features, the plurality of explanatory variables included in the multiple regression model are the plurality of second features, the estimation process comprises substituting the plurality of first features received in the receiving process into the multiple regression model, and estimating the plurality of second features using the inverse matrix of the coefficient matrix, wherein the plurality of first features include functional features of a product, and the plurality of second features include at least one of the structural features of the product and the measurement device features of a measuring device that measured the functional features of the product.

[0073] Although embodiments have been described in detail above, these are merely illustrative and do not limit the scope of the claims. The technologies described in the claims include various modifications and changes to the specific examples illustrated above. The technical elements described in this specification or drawings exhibit technical usefulness individually or in various combinations, and are not limited to the combinations described in the claims at the time of filing. Furthermore, the technologies illustrated in this specification or drawings achieve multiple objectives simultaneously, and achieving even one of these objectives constitutes technical usefulness.

Claims

1. An information processing device comprising: a receiving unit that receives a plurality of first features; and a processing unit that estimates a plurality of second features from the plurality of first features based on a multiple regression model, wherein the multiple regression model is a model represented using a coefficient matrix that aggregates the multiple regression coefficients of a plurality of multiple regression equations, the plurality of target variables included in the multiple regression model are the plurality of first features, and the plurality of explanatory variables included in the multiple regression model are the plurality of second features, wherein the processing unit is configured to perform the following: substituting the plurality of first features received by the receiving unit into the multiple regression model, and estimating the plurality of second features from the multiple regression model using the inverse matrix of the coefficient matrix, wherein the plurality of first features include functional features of a product, and the plurality of second features include at least one of the structural features of the product and the measuring device features of a measuring device that measured the functional features of the product.

2. The processing unit, when the coefficient matrix (A) is invertible, calculates the inverse matrix (A －１ The information processing apparatus according to claim 1, configured to estimate the plurality of second features from the multiple regression model using ).

3. When the coefficient matrix (A) is not invertible, the processing unit calculates the pseudo-inverse matrix (A Ｔ A) －１ A Ｔ The information processing apparatus according to claim 1, configured to estimate the plurality of second features from the multiple regression model by least squares method using the method described above.

4. The processing unit is further configured to modify the initial multiple regression model to create the multiple regression model when the rank of the pseudo-inverse matrix of the learned initial multiple regression model is smaller than the number of the plurality of second features included in the initial multiple regression model, wherein the rank of the pseudo-inverse matrix of the modified multiple regression model is greater than or equal to the number of second features remaining after excluding some of the second features from the plurality of second features included in the initial multiple regression model, as described in claim 3.

5. The processing unit is configured to create a multiple regression model by modifying the initial multiple regression model by substituting some of the second features into the initial multiple regression model, wherein some of the second features include at least one of the design value and the measured value of the product, as described in claim 4.

6. The information processing apparatus according to any one of claims 1 to 5, wherein the product is a semiconductor device, and the plurality of first feature quantities are a plurality of electrical feature quantities.

7. The information processing apparatus according to any one of claims 1 to 5, wherein the plurality of second features include both the structural features and the measuring device features.

8. An information processing method executed by an information processing device, comprising: a receiving step of receiving a plurality of first features; and an estimation step of estimating a plurality of second features from the plurality of first features based on a multiple regression model, wherein the multiple regression model is a model represented using a coefficient matrix that aggregates the multiple regression coefficients of a plurality of multiple regression equations, the plurality of target variables included in the multiple regression model are the plurality of first features, and the plurality of explanatory variables included in the multiple regression model are the plurality of second features, and the estimation step comprises: substituting the plurality of first features received in the receiving step into the multiple regression model, and estimating the plurality of second features using the inverse matrix of the coefficient matrix, wherein the plurality of first features include functional features of a product, and the plurality of second features include at least one of the structural features of the product and the measuring device features of a measuring device that measured the functional features of the product.

9. A computer program for an information processing device, wherein the computer program is configured to cause the information processing device to perform a receiving process for receiving a plurality of first features, and an estimation process for estimating a plurality of second features from the plurality of first features based on a multiple regression model, wherein the multiple regression model is a model represented using a coefficient matrix that aggregates the multiple regression coefficients of a plurality of multiple regression equations, the plurality of target variables included in the multiple regression model are the plurality of first features, the plurality of explanatory variables included in the multiple regression model are the plurality of second features, the estimation process comprises substituting the plurality of first features received in the receiving process into the multiple regression model, and estimating the plurality of second features using the inverse matrix of the coefficient matrix, wherein the plurality of first features include functional features of a product, and the plurality of second features include at least one of the structural features of the product and the measurement device features of a measuring device that measured the functional features of the product.

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