JP7310558B2 - Prediction device, prediction program, generation device and generation program - Google Patents

Description

The present invention relates to a prediction device, a prediction program, a generation device and a generation program.

With the advancement of electronic equipment, high quality is required for the semiconductors mounted in the equipment. In recent years, various types of semiconductors have been produced by high-mix low-volume production, and reliability tests for quality assurance have become more and more important. On the other hand, as the integration of semiconductors progresses, the man-hours for reliability tests also increase.

Conventionally, a method of predicting the quality of a semiconductor substrate from actual test data has been proposed as a method for improving the efficiency of a semiconductor reliability test. For example, in the conventional method, the quality of the board is predicted by obtaining the relational expression between the information related to the quality such as the number of life cycles of the solder joint and the hardness of the cross section of the joint from actual data.

JP 2013-32931 A Japanese Patent Application Laid-Open No. 2002-310888 JP-A-3-128431

However, the above method has a problem that the accuracy of predicting the quality of the substrate may be lowered. For example, in the conventional method, when the design values such as the size and material are changed, and the characteristics of the substrate are greatly changed, there is a possibility that the post-change quality prediction accuracy is lowered.

An object of one aspect is to suppress deterioration in accuracy of predicting the quality of a substrate.

In one aspect, a predictor comprises an extractor, a generator and a calculator. The extraction unit obtains the total value of integrated values of amplitudes in a predetermined frequency range corresponding to each of a plurality of degrees of progress of the test, when changes in the amount of deformation of the board in the test of deforming the board are expressed in the frequency domain. is extracted as the feature quantity of the substrate. The generator generates a model representing the relationship between the feature amount and the predetermined design value of the substrate. The calculator uses the model generated by the generator to calculate the predicted value of the feature amount from the design value of the board.

In one aspect, it is possible to prevent deterioration in accuracy of predicting the quality of the board.

FIG. 1 is a diagram illustrating a configuration example of a prediction device according to a first embodiment; FIG. 2 is a diagram for explaining the amount of deformation. FIG. 3 is a diagram showing an example of design information. FIG. 4 is a diagram for explaining a hysteresis curve. FIG. 5 is a diagram for explaining the slope of the deformation amount. FIG. 6 is a diagram for explaining a feature amount extraction method. FIG. 7 is a diagram for explaining a model generation method. FIG. 8 is a diagram for explaining a method of calculating predicted values. FIG. 9 is a diagram showing an example of predicted values. FIG. 10 is a flowchart showing the flow of prediction processing. FIG. 11 is a flow chart showing the flow of processing for extracting feature amounts. FIG. 12 is a diagram illustrating a hardware configuration example.

Exemplary embodiments of a prediction device, a prediction program, a generation device, and a generation program according to the present invention will be described below in detail with reference to the drawings. It should be noted that the present invention is not limited by these examples. Moreover, each embodiment can be appropriately combined within a range without contradiction.

[Function configuration]
The configuration of the prediction device according to the embodiment will be described with reference to FIG. FIG. 1 is a diagram illustrating a configuration example of a prediction device according to a first embodiment; As shown in FIG. 1 , the prediction device 10 has an interface section 11 , a storage section 12 and a control section 13 .

The interface unit 11 is an interface for data input/output and data communication with other devices. Further, for example, the interface unit 11 is a NIC (Network Interface Card), and may perform data communication via the Internet.

The storage unit 12 is an example of a storage device that stores data, programs executed by the control unit 13, and the like, such as a hard disk or memory. The storage unit 12 stores performance information 121 , design information 122 and model information 123 .

The performance information 121 is the result of a temperature cycle test (T/C test) of a semiconductor substrate. A T/C test is a test in which the temperature of the substrate under test is changed repeatedly. The performance information 121 includes information necessary for creating a hysteresis curve, which will be described later. For example, the performance information 121 includes the number of repetitions of the test, the amount of deformation for each temperature, and the like. Further, as shown in FIG. 2, the amount of deformation at each temperature is represented by the distance between a predetermined position of the substrate and a reference position. FIG. 2 is a diagram for explaining the amount of deformation.

Design information 122 is one or more design values and qualities for each board. FIG. 3 is a diagram showing an example of design information. As shown in FIG. 3, the design information 122 includes the thickness, number of layers, coefficient of linear expansion, and Young's modulus as design values of the substrate. The design information 122 also includes the number of T/C test repetitions until a failure occurs as the board quality. Hereinafter, the number of times the T/C test is repeated until a failure occurs may be referred to as the number of failure T/Cs.

Also, the quality may be represented by a continuous value such as the number of failure T/Cs, or may be represented by discrete value labels such as "High", "Medium", and "Low". Note that the label may be determined according to the number of failure T/Cs. For example, the label is "Low" if 0 < number of failure T/Cs < 400, "Medium" if 400 ≤ number of failure T/Cs < 600, and It may be determined as "High".

In the example of FIG. 3, the design value (i) (thickness) of the substrate α is 1 mm, the design value (ii) (number of layers) is 5 layers, and the design value (iii) (linear expansion coefficient) is 20 ppm. /°C, the design value (iv) (Young's modulus) is 20 GPa, and the number of failure T/C is 300 times. Also, the quality of the substrate α may be represented by the label “Low”.

The model information 123 is parameters and the like of the generated model. For example, the model information 123 is a model formula or the like for creating a response surface to be described later.

The control unit 13 executes a program stored in an internal storage device using, for example, a CPU (Central Processing Unit), MPU (Micro Processing Unit), GPU (Graphics Processing Unit), etc., as a work area. It is realized by Also, the control unit 13 may be implemented by an integrated circuit such as an ASIC (Application Specific Integrated Circuit) or an FPGA (Field Programmable Gate Array). The control unit 13 has an extraction unit 131 , a selection unit 132 , a generation unit 133 and a calculation unit 134 .

The extraction unit 131 obtains the sum of amplitude integrated values in a predetermined frequency range corresponding to each of a plurality of degrees of progress of the test, when the change in the amount of deformation of the board in the test for deforming the board is expressed in the frequency domain. A value is extracted as a feature quantity of the substrate.

In this embodiment, first, the extraction unit 131 calculates changes in the amount of deformation of the substrate with respect to temperature changes in the T/C test. The T/C test can be said to be a test in which the substrate is deformed by repeatedly increasing and decreasing the temperature within a predetermined range.

Specifically, the extraction unit 131 obtains the change in the amount of deformation by differentiating the hysteresis curve representing the amount of deformation when the temperature of the substrate is repeatedly changed between 40° C. and 140° C. at each point. Note that the extraction unit 131 acquires the hysteresis curve from the performance information 121 .

FIG. 4 is a diagram for explaining a hysteresis curve. The hysteresis curve is a curve obtained by combining a curve representing the amount of deformation during temperature increase and a curve representing the amount of deformation during temperature decrease for each T/C number. For example, the substrate temperature changes from 40° C. to 140° C. when the temperature rises, and changes from 140° C. to 40° C. when the temperature drops.

A curve 201c in FIG. 4 represents the amount of deformation of the substrate when the temperature is raised when the number of times of T/C is one. A curve 202c represents the deformation amount of the substrate when the temperature is lowered when the number of T/C is one. A curve 231c represents the deformation amount of the substrate when the temperature is raised when the T/C number is 600 times. A curve 232c represents the deformation amount of the substrate when the temperature is lowered when the number of times of T/C is 600 times.

In this embodiment, the feature amount is extracted based on the deformation amount of the portion corresponding to the plastic deformation of the substrate. Here, elastic deformation and plastic deformation will be described. Elastic deformation is deformation in which an object deformed by a load returns to its original shape when the load is removed. On the other hand, plastic deformation is deformation in which an object deformed by a load does not return to its original shape even after the load is removed. Note that the temperature change in the T/C test is an example of the load.

Here, the substrate is molded in hot conditions. In addition, cracks and breaks that lead to failure of the substrate occur during plastic deformation during cooling. This is because thermal stress begins to occur when the temperature is lowered, starting from a stress-free high temperature state.

Elastic deformation is linear with respect to temperature change, but plastic deformation decreases with respect to temperature change. Utilizing this fact, as shown in FIG. 5, the extracting unit 131 extracts a feature amount based on the differential value of the hysteresis curve when the temperature is lowered, that is, the amount of deformation in the range where the slope is equal to or less than the threshold. FIG. 5 is a diagram for explaining the slope of the deformation amount.

Next, the extraction unit 131 converts the deformation amount data in the range of plastic deformation into amplitude with respect to frequency by a conversion method such as FFT (Fast Fourier Transform). In other words, the extraction unit 131 transforms the data expressed in the temperature domain into a spectrum in the frequency domain.

When the T/C test is repeated, the plastic deformation mode changes due to the change in the size of the defects appearing in the substrate due to thermal stress. The scale of the defective portion is represented by a sense of scale as shown in FIG. FIG. 6 is a diagram for explaining a feature amount extraction method.

As shown in FIG. 6, here, when the number of times of T/C is 200, it is assumed that a defect of a sense of scale occurs with a range of about 1/100 or less of the four corner sides of the substrate as a guideline. Also, when the number of T/Cs is 400, it is assumed that a defect of a scale occurs with a side that is in the range of about 1/100 or less of the surface of the substrate as a guideline. Also, when the number of times of T/C is 600, it is assumed that a defective scale occurs in a range of 1/100 or more of the substrate area as a guideline.

In this way, by repeating the T/C test, the number of discretely generated small-scale cracks in the form of dots increases, connects continuously in a linear pattern, and further expands in size in a plane. At this time, the deformation amount data of plastic deformation is subjected to high-frequency fluctuations corresponding to point-like defects, medium-frequency fluctuations corresponding to side-like defects, and low-frequency fluctuations corresponding to surface-like defects. change is added.

As shown in FIG. 6, the plastic deformation mode changes from high frequency, intermediate frequency, and low frequency, corresponding to the frequency of the applied fluctuation. Furthermore, when the deformation amount data is represented in the frequency domain, an amplitude peak appears in the domain corresponding to the frequency applied as the variation.

It is conceivable that the scale of defects appearing on the board may differ depending on differences in design and individual differences. Therefore, the sense of scale explained using FIG. 6 is only a guideline, and the number of T/Cs for each of high, intermediate, and low frequencies is fixedly determined for all substrates regardless of sense of scale. good too.

The extraction unit 131 extracts the total value of the amplitude integrated values in the frequency range corresponding to each of the plurality of repetition times of the test as the feature amount of the board. In this embodiment, the extraction unit 131 calculates the first integrated value of the amplitude in the frequency range of 1 to 3 [10 ^-2 Hz] corresponding to 200 T/C times. Also, the extraction unit 131 calculates a second integrated value of the amplitude in the frequency range of 4 to 8 [10 ⁻³ Hz] corresponding to 400 T/C times. Also, the extraction unit 131 calculates the third integrated value of the amplitude in the frequency range of 4 to 8 [10 ⁻⁴ Hz] corresponding to 600 T/C times. Then, the extraction unit 131 calculates the total value of the first integrated value, the second integrated value, and the third integrated value, and extracts the calculated total value as a feature amount.

The extraction unit 131 can obtain a value obtained by integrating the amplitude of the frequency with respect to the frequency as an integrated value. As shown in FIG. 6, a new amplitude peak appears in the frequency domain and the integral value of the amplitude increases as the scale of the defective portion changes. Therefore, the extracting unit 131 can calculate the feature amount representing the accumulation of thermal fatigue of the substrate based on the integrated value of the amplitude.

Note that the T/C test is an example of a test in which the substrate is deformed and a test in which the substrate is deformed by repeatedly increasing and decreasing the temperature within a predetermined range. The test here is not limited to the T/C test, and may be, for example, a test in which an object is deformed by applying pressure, voltage, or the like.

The selection unit 132 selects, from among the design values, the contribution to the number of test repetitions until the board fails, based on a model representing the relationship between the board design value and the number of test repetitions until the board fails. A predetermined number of design values are selected in descending order of rate.

In this embodiment, the selection unit 132 selects two design values in descending order of contribution rate in a supervised learning model with each design value shown in FIG. 3 as an explanatory variable and quality as an objective variable. Also, the learning model may be a random forest, which is a model-based feature selection technique. For example, the selection unit 132 evaluates the prediction accuracy while replacing the design values used for quality prediction, and increases the contribution rate of the replaced design value when the prediction accuracy has changed significantly, and otherwise decreases the contribution rate. By doing so, the contribution rate of each design value is calculated.

The generation unit 133 generates a model representing the relationship between the feature amount and the predetermined design value of the board. Specifically, the generation unit 133 generates a model representing the relationship between the feature amount extracted by the extraction unit 131 and the design value selected by the selection unit 132 . In this embodiment, the generation unit 133 generates a model representing a response surface having a design value as an input and a feature amount as a response for each of a plurality of iterations.

A model generation method by the generation unit 133 will be described with reference to FIG. FIG. 7 is a diagram for explaining a model generation method. Here, it is assumed that the selection unit 132 selects the design value (i) and the design value (iii). First, the generation unit 133 plots the feature amount for each T/C number with respect to the design value of each board in the space of the model. Here, it is assumed that the model space is three-dimensional, with the x-axis corresponding to the design value (i), the y-axis corresponding to the design value (iii), and the z-axis corresponding to the feature amount.

In the example of FIG. 7, x _α1 is the feature quantity when the number of times of T/C is 200 times with respect to the design value of the substrate α. Also, x _α2 is a feature amount when the number of times of T/C is 400 times with respect to the design value of the substrate α. Also, x _α3 is a feature amount when the number of times of T/C is 600 times with respect to the design value of the substrate α. Also, x _β1 is a feature amount when the number of T/Cs is 200 times with respect to the design value of the substrate β. Also, x _β2 is a feature amount when the T/C count is 400 times with respect to the design value of the substrate β. Also, x _β3 is a feature amount when the T/C count is 600 times with respect to the design value of the substrate β.

Furthermore, the generation unit 133 plots the feature amount when the number of T/Cs of each substrate is the number of failure T/Cs. The number of failure T/Cs is not limited to the number of T/Cs when the substrate is completely damaged, but the number of T/Cs when the electrical characteristics are lost to the extent that it cannot be used for semiconductors. may be In addition, if the substrate is completely damaged, it becomes difficult to obtain effective feature values. good too.

Then, the generator 133 generates response surfaces 210S, 220S, 230S and 290S from the plotted results. The generation unit 133 can generate a response surface by a Gaussian process that superimposes a Gaussian distribution on the plotted data to create a surface. Henceforth, these response surfaces may be called a fatigue accumulation model.

The response surface 210S corresponds to the feature amount when the T/C count is 200 times. Also, the response surface 220S corresponds to the feature amount when the T/C count is 400 times. Also, the response surface 230S corresponds to the feature amount when the T/C count is 600 times. Also, the response curved surface 290S corresponds to the feature amount when the number of T/Cs is the number of failure T/Cs.

The calculation unit 134 uses the fatigue accumulation model generated by the generation unit 133 to calculate the predicted value of the feature amount from the board design values. Based on the response curve model, the calculation unit 134 obtains a regression equation representing the relationship between the number of times of T/C and the feature value of the target substrate whose design value is known and whose feature value is unknown, and uses the regression equation. to calculate the predicted value.

A method of calculating the predicted value will be described with reference to FIG. FIG. 8 is a diagram for explaining a method of calculating predicted values. The calculator 134 first inputs the design values of the target substrate into the fatigue accumulation model to obtain the fatigue accumulation formula. Here, the fatigue accumulation formula is a formula representing a feature amount with respect to the number of times of T/C.

From the fatigue accumulation formula, we can only obtain feature values for specific T/C times such as 200 times and 400 times. Therefore, the calculation unit 134 obtains a regression formula by regression analysis using the least squares method based on the fatigue accumulation formula. The regression formula may be a quadratic formula such as y=ax ² +bx+c (where y is a feature amount, x is the number of T/Cs, and a, b, and c are coefficients). Then, the calculation unit 134 can obtain the feature quantity and the predicted value of the number of failure T/Cs at an arbitrary number of T/Cs from the regression equation. Note that _x1 in FIG. 8 is the feature amount when the T/C count is 200 times. Also, x ₂ is the feature amount when the T/C count is 400 times. Also, x ₃ is a feature amount when the T/C count is 600 times. Also, _x9 is a feature quantity when the number of T/Cs is the number of failure T/Cs.

Further, the calculation unit 134 calculates the feature amount for a number of times greater than a predetermined number of times using a model, based on the design value of the board and the feature amount obtained by performing the test a predetermined number of times on the board. be able to. For example, the calculation unit 134 may use the feature amount obtained by performing the test on the target substrate for the number of times of 1/10 of the predicted number of failure T/Cs.

In the example of FIG. 8, the predicted number of T/C failures is 750, so the calculation unit 134 plots the feature values obtained from the 75 T/C tests as actual measurements on the same plane as the regression equation. . As a result, the calculation unit 134 can confirm the validity of the regression and finely adjust the regression equation. For example, if the error between the plotted feature quantity and the value of the corresponding regression formula is equal to or less than a threshold, the calculation unit 134 adopts the regression formula, You can ask for it. Further, the calculation unit 134 may further optimize the regression equation for the plotted feature amount using the method of least squares or the like.

Also, the feature amount may increase rapidly with the number of T/Cs. Therefore, as shown in FIG. 9, the regression equation may be represented by a predetermined scale such as logarithm. In that case, similarly, the calculation unit 134 can calculate the predicted value of the number of times of T/C for a specific feature amount.

[Process flow]
The flow of prediction processing by the prediction device 10 will be described with reference to FIG. FIG. 10 is a flowchart showing the flow of prediction processing. As shown in FIG. 10, first, the prediction device 10 extracts a feature quantity representing fatigue from the T/C test performance information 121 (step S11).

Next, the prediction device 10 selects a design value with a high contribution rate to quality from the design values of the board (step S12). Then, the prediction device 10 generates a response surface of the feature quantity for the selected design value (step S13). The processing from steps S11 to S13 is the processing of the learning process. After the learning process is completed, the operation process is processed.

In the operation process, the prediction device 10 first extracts the fatigue accumulation formula of the prediction target board from the response surface based on the design values of the prediction target board (step S21). Then, the prediction device 10 uses the fatigue accumulation formula to calculate the predicted value of the number of failure T/Cs (step S22). Also, the prediction device 10 may calculate a predicted value of the number of times of T/C leading to a specific feature amount.

The details of the process of extracting the feature quantity representing fatigue (step S11 in FIG. 10) will be described with reference to FIG. FIG. 11 is a flow chart showing the flow of processing for extracting feature amounts. As shown in FIG. 11, first, the prediction device 10 differentiates the hysteresis curve based on the performance information 121 at each point to calculate the slope (step S111). Next, the prediction device 10 extracts a range in which the slope of the hysteresis curve is equal to or less than the threshold as plastic deformation data (step S112).

Here, the prediction device 10 transforms the plastic deformation data into frequency domain data by FFT (step S113). Then, the prediction device 10 calculates integrated values of the amplitudes in the high, intermediate, and low frequency regions from the frequency domain data (step S114). Furthermore, the prediction device 10 calculates the total value of the integrated values of the amplitudes in the high, intermediate, and low frequency regions as a feature amount (step S115).

[effect]
As described above, the extraction unit 131 extracts amplitudes in a predetermined frequency range corresponding to each of a plurality of degrees of progress of the test when the change in the amount of deformation of the board in the test for deforming the board is expressed in the frequency domain. is extracted as the feature amount of the substrate. The generation unit 133 also generates a model representing the relationship between the feature amount and the predetermined design value of the board. The calculation unit 134 also uses the model generated by the generation unit 133 to calculate the predicted value of the feature amount from the design value of the board.

In this manner, the prediction device 10 can predict the number of tests until failure, etc., using not only the design value of the board but also the characteristic quantity representing fatigue. Therefore, according to the present embodiment, even when the design values are changed, it is possible to prevent deterioration of the prediction accuracy of the board quality.

Furthermore, according to this embodiment, the quality can be predicted with high accuracy, so that the man-hour required for the quality test can be reduced. In addition, by accumulating T/C test performance information, the accuracy of the response surface improves, and as a result, the accuracy of quality prediction improves.

In addition, the extraction unit 131 converts the change in the amount of deformation of the substrate with respect to temperature change in a test in which the substrate is deformed by repeatedly increasing and decreasing the temperature within a predetermined range, into amplitude with respect to frequency. Furthermore, the extracting unit 131 extracts, from the converted data, the total value of integrated values of the amplitudes in the frequency range corresponding to each of the plurality of repetitions of the test, as the characteristic amount of the board.

Thus, this embodiment can be applied to the T/C test. In addition, in this embodiment, a one-dimensional feature amount is obtained by summing the accumulated amplitude values in each frequency range, so it is possible to reduce the amount of calculation while securing sufficient information for model generation. Become.

Further, the selection unit 132 selects the number of test repetitions until failure of the board from among the design values based on the model representing the relationship between the design value of the board and the number of repetitions of the test until failure of the board. A predetermined number of design values are selected in descending order of the contribution rate to . The generation unit 133 also generates a model representing the relationship between the feature quantity and the design value selected by the selection unit 132 . In this way, by selecting a design value with a high contribution rate, it is possible to reduce the amount of calculation while improving the accuracy of the model.

In addition, the generation unit 133 generates a model representing a response surface having design values as inputs and characteristic amounts as responses for each of a plurality of iterations. As a result, if the design value is known, it becomes possible to easily obtain the calculation formula for calculating the predicted value.

Further, the calculation unit 134 uses a model to calculate the feature amount for the number of times greater than the predetermined number of times, based on the design value of the board and the feature amount obtained by performing the test a predetermined number of times on the board. . This makes it possible to further improve the calculation accuracy of the predicted value with a small number of tests.

In addition, in the present embodiment, the prediction device 10 has been described as performing both the learning process and the operation process. On the other hand, the learning process and the operational process may be performed by different devices. In that case, for example, the generation device executes the processing of the learning process, and the prediction device executes the processing of the operation process.

Also, the model generated by the prediction device 10 is not limited to a response surface. For example, the prediction device 10 may generate a multi-variable regression model with one or more design values and the number of T/Cs as explanatory variables, and a feature amount or the number of failure T/Cs as an objective variable.

[system]
Information including processing procedures, control procedures, specific names, and various data and parameters shown in the above documents and drawings can be arbitrarily changed unless otherwise specified. Further, the specific examples, distributions, numerical values, etc. described in the examples are only examples, and can be arbitrarily changed.

Also, each component of each device illustrated is functionally conceptual, and does not necessarily need to be physically configured as illustrated. That is, the specific forms of distribution and integration of each device are not limited to those shown in the drawings. That is, all or part of them can be functionally or physically distributed and integrated in arbitrary units according to various loads and usage conditions. Furthermore, all or any part of each processing function performed by each device can be implemented by a CPU and a program analyzed and executed by the CPU, or implemented as hardware based on wired logic.

[hardware]
FIG. 12 is a diagram illustrating a hardware configuration example. As shown in FIG. 12, the prediction device 10 has a communication interface 10a, a HDD (Hard Disk Drive) 10b, a memory 10c, and a processor 10d. 12 are interconnected by a bus or the like.

The communication interface 10a is a network interface card or the like, and communicates with other servers. The HDD 10b stores programs and DBs that operate the functions shown in FIG.

The processor 10d reads from the HDD 10b or the like a program that executes the same processing as each processing unit shown in FIG. It is a wear circuit. That is, this process performs the same function as each processing unit of the prediction device 10 . Specifically, the processor 10d reads a program having functions similar to those of the extraction unit 131, the selection unit 132, the generation unit 133, and the calculation unit 134 from the HDD 10b or the like. Then, the processor 10d executes processes for executing the same processes as those of the extraction unit 131, the selection unit 132, the generation unit 133, the calculation unit 134, and the like.

In this manner, the prediction device 10 operates as an information processing device that executes a learning method by reading and executing a program. Also, the prediction device 10 can read the program from the recording medium by the medium reading device, and execute the read program to realize the same function as the embodiment described above. It should be noted that the programs referred to in other embodiments are not limited to being executed by the prediction device 10 . For example, the present invention can be applied in the same way when another computer or server executes the program, or when they cooperate to execute the program.

This program can be distributed via a network such as the Internet. In addition, this program is recorded on a computer-readable recording medium such as a hard disk, flexible disk (FD), CD-ROM, MO (Magneto-Optical disk), DVD (Digital Versatile Disc), etc., and can be downloaded from the recording medium by a computer. It can be executed by being read.

10 prediction device 11 interface unit 12 storage unit 13 control unit 121 performance information 122 design information 123 model information 131 extraction unit 132 selection unit 133 generation unit 134 calculation unit 201c, 202c, 231c, 232c curves 210S, 220S, 230S, 290S response surface

Claims (8)

When the change in the amount of deformation of the substrate in the test for deforming the substrate is expressed in the frequency domain, the total value of the integrated values of the amplitudes in a predetermined frequency range corresponding to each of the plurality of degrees of progress of the test, an extraction unit that extracts as a feature amount of the substrate;
a generation unit that generates a model representing a relationship between the feature amount and a predetermined design value of the substrate;
a calculation unit that calculates a predicted value of the feature amount from the design value of the board using the model generated by the generation unit;
A prediction device characterized by comprising: The extraction unit extracts a change in the amount of deformation of the substrate with respect to temperature change in a test in which the substrate is deformed by repeatedly increasing and decreasing the temperature within a predetermined range, from data converted into amplitude with respect to frequency, a plurality of repetitions of the test. 2. The prediction apparatus according to claim 1, wherein a total value of integrated values of amplitudes in a frequency range corresponding to each number of times is extracted as the feature amount of the substrate. Based on the model representing the relationship between the design value of the board and the number of repetitions of the test until the board fails, the number of repetitions of the test until the board fails is selected from the design values further comprising a selection unit that selects a predetermined number of design values in descending order of contribution rate;
3. The prediction device according to claim 2, wherein the generation unit generates a model representing a relationship between the feature amount and the design value selected by the selection unit. 3. The prediction apparatus according to claim 2, wherein the generation unit receives the design value as an input and generates a model representing a response surface having the feature value as a response for each of the plurality of iterations. The calculation unit uses the model based on the design value of the board and the feature amount obtained by performing the test a predetermined number of times on the board. 2. The prediction device according to claim 1, which calculates When the change in the amount of deformation of the substrate in the test for deforming the substrate is expressed in the frequency domain, the total value of the integrated values of the amplitudes in a predetermined frequency range corresponding to each of the plurality of degrees of progress of the test, extracted as a feature quantity of the substrate,
generating a model representing a relationship between the feature amount and a predetermined design value of the substrate;
A prediction program for causing a computer to execute a process of calculating a predicted value of a feature amount from a design value of a substrate using the model generated by the generating process. When the change in the amount of deformation of the substrate in the test for deforming the substrate is expressed in the frequency domain, the total value of the integrated values of the amplitudes in a predetermined frequency range corresponding to each of the plurality of degrees of progress of the test, an extraction unit that extracts as a feature amount of the substrate;
a generation unit that generates a model representing a relationship between the feature amount and a predetermined design value of the substrate;
A generating device comprising: When the change in the amount of deformation of the substrate in the test for deforming the substrate is expressed in the frequency domain, the total value of the integrated values of the amplitudes in a predetermined frequency range corresponding to each of the plurality of degrees of progress of the test, extracted as a feature quantity of the substrate,
A generating program that causes a computer to execute a process of generating a model representing a relationship between the feature amount and a predetermined design value of the substrate.

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