Method, apparatus, and program for analyzing transient capacity changes

Abstract

High time constant resolution can be obtained even with a low signal-to-noise ratio (SNR) for signals related to transient capacitance changes. [Solution] A method for analyzing transient capacitance changes applied to a DLTS device includes a capacitance signal acquisition step (S1) for acquiring a capacitance signal relating to the time change of transient capacitance, and an estimation step (S7, S8, S9) for estimating the posterior distribution of the capacitance signal's time constant by performing Bayesian estimation based on the capacitance signal and a physical model including the magnitude and time constant of the transient capacitance change.

Description

[Technical Field]

[0001] This invention relates to a method, apparatus, and program for analyzing changes in transient capacitance. [Background technology]

[0002] Semiconductors contain various defects, including vacancies, substituted atoms, and interstitial atoms. When defects exist in a semiconductor, the potential in the vicinity changes, and defect levels are formed in the band gap. Among these, levels closer to the center of the band gap than donor and acceptor levels are called deep levels.

[0003] Deep energy levels present in semiconductors alter semiconductor properties and device characteristics through the capture and release of carriers (conduction electrons and holes). Therefore, accurately determining the density, capture cross-section, and energy levels of such deep levels is extremely important. The release of carriers from deep levels causes transient changes in junction capacitance, and it is known that the magnitude of this change depends on the density, while the time constant depends on the capture cross-section and energy levels.

[0004] Based on such transient phenomena of junction capacitance, Deep Level Transient Spectroscopy (DLTS) has been used to evaluate deep levels by measuring changes in transient capacitance that have been intentionally induced. For example, Patent Document 1 discloses a DLTS measuring apparatus.

[0005] DLTS is a type of capacitance transient spectroscopy, and several types of DLTS exist. Among them, Laplace DLTS (Laplace Deep Level Transient Spectroscopy), described in Non-Patent Document 1, can obtain a higher time constant resolution for the time constant of transient capacitance changes due to deep levels than the time constant resolution of DLTS, thereby enabling the separation and evaluation of multiple levels with similar time constants. [Prior art documents] Patent Literature

[0006] Patent Literature 1 Japanese Unexamined Patent Publication No. 2017-017135 Non-Patent Literature

[0007] Non-Patent Literature 1 L. Dobaczewski et al. “Laplace transform deep-level transient spectroscopic studies of defects in semiconductors.” J. Appl. Phys. 76, 194-198 (1994) Summary of the Invention Problem to be Solved by the Invention

[0008] In order to obtain high time constant resolution in Laplace DLTS, it is necessary that a signal obtained by measuring a change in transient capacitance has a high signal-to-noise ratio (hereinafter also simply referred to as SN ratio). For example, when the ratio of the time constants of two deep levels to be separately evaluated is 2, according to Laplace DLTS, a measurement signal having a relatively high SN ratio of about 1000 is required to separate the two deep levels.

[0009] However, it is not easy to achieve an SN ratio of about 1000 in the measurement of transient capacitance change. Although it is possible to improve the SN ratio by averaging multiple measurement data, an enormous number of measurements are required to achieve an SN ratio of about 1000. A new method is required to obtain high time constant resolution even when the SN ratio of a signal relating to a change in transient capacitance is low.

[0010] An object of the present invention is to obtain high time constant resolution even when the SN ratio of a signal relating to a change in transient capacitance is low. Means for Solving the Problem

[0011] The present invention for solving the above problem includes, for example, the embodiments described below. (Item 1) a capacitance signal acquisition step of acquiring capacitance signals (C(t), ΔC(t)) relating to a time change of a transient capacitance (C); an estimation step of performing Bayesian estimation based on said capacitance signal and a physical model including the magnitude of a transient capacitance change and a time constant to estimate a posterior distribution of the time constant (τ) of said capacitance signal; a method for analyzing a transient capacitance change, comprising: (Item 2) The analysis method according to Item 1, wherein said capacitance signal is a capacitance signal (ΔC(t)) relating to a time change of said transient capacitance change. (Item 3) for said capacitance signal (C(t), ΔC(t)), a variance estimation step of estimating a variance of statistical noise (σ 2 ); an SN ratio calculation step of calculating a signal-to-noise ratio (snr) based on said capacitance signal and said variance of noise; further comprising: The analysis method according to Item 1 or 2, wherein said estimation step is performed on said capacitance signal among the plurality of said capacitance signals when said signal-to-noise ratio is equal to or higher than a predetermined threshold. (Item 4) said transient capacitance is a transient capacitance relating to deep levels formed in a semiconductor, said estimation step comprises: an optimal solution calculation step of performing data fitting on said capacitance signal to calculate an optimal solution set of the number of types of deep levels (n_est) that reproduce said capacitance signal and optimal values of parameters (sol); a Bayesian estimation step of generating an initial value based on said optimal solution set, performing said Bayesian estimation using the generated said initial value, and extracting a plurality of sample values (τ i ) of said time constant; a posterior distribution estimation step of performing kernel density estimation on said plurality of sample values of said time constant to estimate said posterior distribution of said time constant (τ); The analysis method described in item 3, including the method described in item 3. (Section 5) The capacitance signal is a signal measured at multiple measurement temperatures. The process further includes a temperature signal acquisition step to obtain a temperature signal (T) relating to the measured temperature, The aforementioned posterior distribution estimation step further, The plane plotting the measured temperature and the time constant (1 / T - lnτT) 2 The analysis method described in item 4, wherein two-dimensional kernel density estimation is performed on the multiple sample values ​​of the time constant in ), and the posterior distribution of the time constant is estimated. (Section 6) The capacitance signal is a signal measured at multiple measurement temperatures. The process further includes a temperature signal acquisition step to obtain a temperature signal (T) relating to the measured temperature, The Bayesian estimation step further involves multiple sample values ​​(ΔC) of the magnitude of the transient capacity change. i Extract ) The aforementioned posterior distribution estimation step further, The analysis method according to item 4 or 5, wherein two-dimensional kernel density estimation is performed on the plurality of sample values ​​of the capacitance signal in a plane (T-ΔC plane) plotting the measured temperature and the change in the transient capacitance (ΔC) of the capacitance signal, and the posterior distribution of the capacitance signal is estimated. (Section 7) The estimation step described above is: In the plot, a posterior distribution display step is performed, in which the posterior distribution of the time constant or the posterior distribution of the capacitance signal is displayed in heatmap format. The analysis method described in item 5 or 6, further including the method described in item 5 or 6. (Section 8) The time constant of the transient capacitance change included in the physical model has a temperature dependence. The analysis method according to any one of items 1 to 7, wherein the capacitance signal is a signal measured at multiple measurement temperatures. (Section 9) A capacitance signal acquisition unit acquires capacitance signals (C(t), ΔC(t)) relating to the time change of transient capacitance (C), An estimation unit that performs Bayesian estimation based on the capacitance signal and a physical model including the magnitude and time constant of the transient capacitance change, and estimates the posterior distribution of the time constant (τ) of the capacitance signal, A device for analyzing transient capacitance changes, including [specific component / feature]. (Section 10) On the computer, A capacitance signal acquisition function that acquires capacitance signals (C(t), ΔC(t)) relating to the time change of transient capacitance (C), An estimation function that performs Bayesian estimation based on the capacitance signal and a physical model including the magnitude and time constant of the transient capacitance change, and estimates the posterior distribution of the time constant (τ) of the capacitance signal, A program to achieve this. [Effects of the Invention]

[0012] According to the present invention, high time constant resolution can be obtained even if the signal-to-noise ratio of the signal with respect to transient capacitance changes is low. [Brief explanation of the drawing]

[0013] [Figure 1] This is a diagram illustrating the usage of an analytical device according to one embodiment of the present invention. [Figure 2] This diagram illustrates the data processing performed by an analysis device according to one embodiment of the present invention. [Figure 3] This is a block diagram illustrating the functions of an analytical device according to one embodiment of the present invention. [Figure 4] This is a block diagram illustrating the functions of an analytical device according to one embodiment of the present invention. [Figure 5] This is a flowchart illustrating the data processing procedure performed by an analysis device according to one embodiment of the present invention. [Figure 6] This is a diagram illustrating the capacitive signal conversion step. [Figure 7] This is a diagram illustrating the variance estimation step. [Figure 8] This is a diagram illustrating the steps for calculating the optimal solution. [Figure 9]This is a diagram illustrating the steps for calculating the optimal solution. [Figure 10] This is a diagram illustrating the posterior distribution estimation step. [Figure 11] This is an example of a schematic diagram showing the posterior distribution of the time constant in heatmap format. [Figure 12] This is an example of a schematic diagram that displays the posterior distribution of the magnitude of volume change in a heatmap format. [Figure 13] This figure illustrates the characteristics of the physical model used in the analysis method according to another embodiment of the present invention and the advantages of dividing it into temperature regions. [Figure 14] This is a simulation result comparing the time constant resolution of the analysis method of the present invention and the Laplace DLTS method in Example 1. [Figure 15] This graph shows the minimum signal-to-noise ratio (SNR) required to separate the two time constants in Example 1. [Figure 16] This is a simulation result comparing the time constant resolution of the analysis method of the present invention and the Laplace DLTS method in Example 2. [Figure 17] This is the DLTS signal to be analyzed in Example 3. [Figure 18] This is an Arrhenius plot obtained by applying the analysis method of the present invention to the DLTS signal shown in Figure 17. [Modes for carrying out the invention]

[0014] Embodiments of the present invention will be described in detail below with reference to the accompanying drawings. In the following description and drawings, the same reference numerals indicate the same or similar components, and therefore, redundant explanations of the same or similar components will be omitted.

[0015] In this specification, the term "signal" can be interpreted not only as literally meaning a signal, but also as meaning data. Similarly, the term "data" can be interpreted not only as literally meaning data, but also as meaning a signal.

[0016] [Device Overview] <Usage> Figure 1 is a diagram illustrating the usage of an analytical device according to one embodiment of the present invention.

[0017] An analysis device 1 according to one embodiment of the present invention is a device that acquires a capacitance signal C(t) relating to the time change of transient capacitance (C) from a measuring device 90 and analyzes the change in transient capacitance of the acquired capacitance signal. If the transient capacitance measured by the measuring device 90 is, for example, a transient capacitance relating to a defect level formed in a semiconductor, a DLTS measuring device can be used as the measuring device 90. In one embodiment of the analysis device 1, the transient capacitance signal acquired from the measuring device 90 is analyzed.

[0018] The measuring device 90 includes a transient capacitance meter 91, a temperature controller 92, and a temperature-variable probe 93. The sample to be measured 99 (e.g., a semiconductor wafer) is placed inside the probe 93, and the temperature inside the probe 93 is controlled by the temperature controller 92. Electrodes 94 are placed on the surface of the sample 99. The transient capacitance meter 91 measures the transient change in the junction capacitance of the sample 99 at a certain temperature through the electrodes 94 and probe 95. Here, junction capacitance refers to the depletion layer capacitance at the metal-semiconductor interface or the depletion layer capacitance at the interface of semiconductors with different conductivity types. This measurement of transient capacitance change by the transient capacitance meter 91 is performed while sweeping the temperature of the sample 99 with the temperature controller 92. The analysis device 1 can acquire a capacitance signal C(t) relating to the time change of transient capacitance (C) and a temperature signal T relating to the measurement temperature from the measuring device 90.

[0019] The analysis device 1 acquires these capacitance signals and temperature signals measured by the measuring device 90, for example, through a network 9. The analysis device 1 can be a general-purpose computer, such as a personal computer.

[0020] <Overview of signal processing> Figure 2 is a diagram illustrating the data processing performed by an analysis device according to one embodiment of the present invention.

[0021] When there is only one type of deep energy level in a semiconductor, the transient capacitance change due to the deep energy level is expressed by Equation 1.

[0022]

number

[0023] In reality, semiconductors contain multiple types of deep energy levels. When there are multiple types of deep energy levels, the transient capacitance change is a superposition of these individual changes. The transient capacitance change due to multiple types of deep energy levels is expressed by Equation 2.

[0024]

number

[0025] Therefore, if we can separate the components of each exponential function from the superposition of exponential functions shown in Equation 2, it becomes possible to distinguish and evaluate multiple types of deep energy levels.

[0026] To distinguish between multiple types of deep energy levels, the analysis device 1 according to one embodiment performs Bayesian estimation based on the capacitance signal C(t) acquired from the measurement device 90 and a physical model including the magnitude of the transient capacitance change and its time constant, and estimates the posterior distribution of the time constant τ of the capacitance signal C(t) acquired from the measurement device 90. As will be compared and examined in the embodiments described later, the posterior distribution of the time constant τ estimated by the analysis device 1 makes it possible to obtain a high time constant resolution that can distinguish between multiple types of deep energy levels, even when the signal-to-noise ratio of the capacitance signal is relatively low.

[0027] In this embodiment, a model assuming additive white Gaussian noise as the physical model is used to perform Bayesian estimation of the capacitance signal C(t) relating to the time evolution of transient capacitance. The physical model used in this embodiment is represented by Equation 3. In Equation 3, N(μ,σ 2 ) has a mean of μ and a variance of σ 2 This refers to a Gaussian distribution.

[0028]

number

[0029] In this embodiment, as illustrated in Equation 3, Bayesian estimation of the capacitance signal is performed assuming that the capacitance signal C(t) acquired from the measuring device 90 follows a one-dimensional Gaussian distribution. The assumed physical model includes the variability of the measured values. By performing Bayesian estimation using such a physical model that includes the variability of the measured values, it becomes possible to obtain a statistically valid estimate (posterior distribution) regardless of the noise level, and analysis that takes uncertainty into account becomes possible.

[0030] In other embodiments, the time constant of the transient capacitance change included in the physical model is temperature-dependent, and the capacitance signal C(t) relating to the time change of transient capacitance is a signal measured at multiple measurement temperatures. To distinguish between multiple types of deep levels, the analysis apparatus in other embodiments performs Bayesian estimation based on the capacitance signal C(t) obtained from the measurement device 90, measured at multiple measurement temperatures, and a physical model that includes the magnitude and time constant of the transient capacitance change, and whose time constant is temperature-dependent, to estimate the posterior distribution of the time constant τ of the capacitance signal C(t) obtained from the measurement device 90. Details of the physical model in other embodiments will be described later.

[0031] [Device Configuration] Figures 3 and 4 are block diagrams illustrating the functions of an analysis device according to one embodiment of the present invention. Figure 4 is a detailed block diagram of the estimation unit shown in Figure 3.

[0032] An analysis device 1 according to one embodiment comprises a data processing unit 10, an auxiliary storage device 20, an input device 31, a display screen 32, and a communication interface unit (communication I / F unit) 33. The analysis device 1 can be configured using, for example, a general-purpose computer such as a personal computer, a laptop PC, or a tablet terminal.

[0033] In this embodiment, the analysis device 1 comprises, as hardware components, an auxiliary storage device 20, an input device 31, a display screen 32, and a communication I / F unit 33. Although not shown, the analysis device 1 further comprises, as hardware components, a processor such as a CPU for data processing and memory used by the processor as a work area for data processing.

[0034] The auxiliary storage device 20 is a non-volatile storage device that stores the operating system (OS), various control programs, and data generated by the programs, and is composed of, for example, flash memory, eMMC (embedded Multi Media Card), SSD (Solid State Drive), etc. In this embodiment, the auxiliary storage device 20 stores the capacity signal 21, temperature signal 22, converted capacity signal 23, noise variance 24, signal-to-noise ratio 25, optimal solution set data 26, sample of the magnitude of capacity change 27a, sample of the time constant 27b, posterior distribution of the magnitude of capacity change 28a, posterior distribution of the time constant 28b, and analysis program P. Of the data stored in the auxiliary storage device 20, the capacity signal 21 and temperature signal 22 are data acquired from the measuring device 90.

[0035] The analysis program P is a computer program for implementing the various parts 11-17 and 171-174 within the data processing unit 10, which is a software-based functional block described later. These functional blocks are implemented by installing the analysis program P into the auxiliary storage device 20 or memory of the analysis device 1, and then having the processor execute the analysis program P. The analysis program P may also be installed into the analysis device 1 via a network 9 such as the Internet, connected by the communication I / F unit 33. Alternatively, the analysis program P may be installed into the analysis device 1 by having the analysis device 1 read a computer-readable, non-temporary, tangible recording medium, such as a memory card, on which the analysis program P is recorded. The analysis program P can also be an application for, for example, a tablet terminal.

[0036] The input device 31 can consist of, for example, a mouse or keyboard. The display screen 32 can consist of, for example, an LCD display or an OLED display. The input device 31 and the display screen 32 can also be integrated as a touch panel.

[0037] The communication interface unit 33 transmits and receives data to and from external devices such as the measuring device 90 via a wired or wireless network 9. The communication interface unit 33 may be various wired or wireless connections such as Ethernet®, Bluetooth®, and Wi-Fi®.

[0038] In this embodiment, the analysis device 1 includes a data processing unit 10 as part of its software configuration. The data processing unit 10 is a functional block realized by the processor executing the analysis program P.

[0039] The capacitance signal acquisition unit 11 acquires a capacitance signal 21(C(t)) relating to the time change of transient capacitance (C).

[0040] The temperature signal acquisition unit 12 acquires a temperature signal 22(T) related to the measured temperature.

[0041] The capacitance signal conversion unit 13 converts the capacitance signal 21 into a capacitance signal 23 (ΔC(t)) relating to the time change of transient capacitance.

[0042] The variance estimation unit 14 calculates the statistical noise variance 24(σ) for the capacitance signal 23. 2 We estimate ).

[0043] The signal-to-noise ratio calculation unit 15 (SNR calculation unit 15) calculates the signal-to-noise ratio 25 (SNR) based on the capacitance signal 23 and the noise dispersion 24.

[0044] The capacitance signal selection unit 16 selects from among a plurality of capacitance signals 23 those whose signal-to-noise ratio 25 is equal to or greater than a predetermined threshold. Based on this selection, the estimation unit 17 performs estimation for the capacitance signals 23 whose signal-to-noise ratio 25 is equal to or greater than the predetermined threshold.

[0045] The estimation unit 17 performs Bayesian estimation based on the capacitance signal 23 and a physical model including the magnitude of the transient capacitance change and the time constant, and estimates the posterior distribution 28b of the time constant (τ) of the capacitance signal 23. As shown in FIG. 4, in the present embodiment, the estimation unit 17 includes an optimal solution calculation unit 171, a Bayesian estimation unit 172, a posterior distribution estimation unit 173, and a posterior distribution display unit 174.

[0046] The optimal solution calculation unit 171 performs data fitting on the capacitance signal 23, and calculates an optimal solution set 26 including the number of types of deep levels (n_est) that reproduce the capacitance signal 23, and the optimal values (sol) of the time constant and the magnitude of the capacitance change.

[0047] The Bayesian estimation unit 172 generates an initial value based on the optimal solution set 26, and performs Bayesian estimation by, for example, the Markov-Chain Monte Carlo method (MCMC) using the generated initial value, to obtain a plurality of sample values 27b of the time constant (τ i ) to be extracted.

[0048] In another embodiment, the Bayesian estimation unit 172 further performs Bayesian estimation in the same manner as extracting the plurality of sample values 27b of the time constant (τ i ), and can extract a plurality of sample values 27a of the magnitude of the capacitance change (ΔC i ).

[0049] The posterior distribution estimation unit 173 performs kernel density estimation on the plurality of sample values 27b of the time constant, to estimate the posterior distribution 28b of the time constant (τ i ). Preferably, the posterior distribution estimation unit 173 further performs two-dimensional kernel density estimation on the plurality of sample values 27b of the time constant on a plane (1 / T-lnτT 2 ) obtained by plotting measurement temperatures and time constants, thereby estimating the posterior distribution 28b of the time constant.

[0050] In another embodiment, the posterior distribution estimation unit 173 further includes the measurement temperature and the magnitude of the transient capacitance change of the capacitance signal 23 (ΔCi By performing two-dimensional kernel density estimation on multiple sample values ​​27a of the magnitude of the volume change in a plane plotted between (T-ΔC plane) and (T-ΔC plane), the posterior distribution 28a of the magnitude of the volume change can be estimated.

[0051] The post-event distribution display unit 174 plots the measured temperature and the time constant on a plane (1 / T - lnτT). 2 In the plot of ), the posterior distribution 28b of the time constant is displayed in heatmap format.

[0052] In other embodiments, the post-distribution display unit 174 displays the measured temperature and the magnitude of the capacity change (ΔC). i In the plot of the plane (T-ΔC plane) where the two points are plotted, the posterior distribution 28a of the magnitude of the volume change is displayed in heatmap format.

[0053] [Processing Procedure] Figure 5 is a flowchart illustrating the data processing procedure performed by an analysis device according to one embodiment of the present invention.

[0054] In step S1 (capacitance signal acquisition step), a capacitance signal 21(C(t)) relating to the time change of transient capacitance (C) is acquired.

[0055] In step S2 (temperature signal acquisition step), a temperature signal 22(T) relating to the measured temperature is acquired.

[0056] In step S3 (capacitance signal conversion step), the capacitance signal 21 is converted into a capacitance signal 23 (ΔC(t)) relating to the time variation of the transient capacitance change.

[0057] Figure 6 is a diagram illustrating the capacitive signal conversion step. Of the six graphs shown in Figure 6, the top three graphs are graphs of the capacitive signal 21, and the bottom three graphs are graphs of the converted capacitive signal 23.

[0058] In the capacitance signal conversion step, the capacitance signal 23 (ΔC(t)) is obtained by subtracting the mean value of capacitance signal 21 (Avg(C(t))) from the capacitance signal 21 (C(t)). As shown in the three graphs in the lower part of Figure 6, by preprocessing the capacitance signal so that the mean value is zero, the analysis focuses only on the change in the capacitance signal (change from the mean value). This eliminates the steady-state capacitance parameter in the data fitting and Bayesian estimation performed in subsequent steps.

[0059] When attempting to data-fit the capacitance itself of a capacitance signal, the physical model will have a stationary capacitance C. ∞ The term is required. In contrast, according to the processing of the capacitance signal conversion step, the steady-state capacitance C ∞ By eliminating this term, data processing can be made faster and more accurate.

[0060] In step S4 (variance estimation step), the variance of the statistical noise 24(σ) is calculated for the capacitance signal 23. 2 We estimate ).

[0061] Figure 7 illustrates the variance estimation step. In the variance estimation step, the component representing the variability of the measured values ​​of the capacitance signal is separated from the component representing the steady-state change, and noise is estimated using only the component representing the variability of the measured values. This allows for even higher accuracy in data processing.

[0062] In a steady state, the capacitance data of capacitance signals 21 and 23 should ideally have a constant capacitance. However, in reality, the capacitance data of capacitance signals 21 and 23 exhibit long linear changes due to deep energy levels, etc. In the variance estimation step, in order to remove such linear changes, the capacitance data of capacitance signal 23 shown in (A) is fitted with a linear function, separating it into a steady (linear) change component shown in (B) and a variability component shown in (C). Then, the unbiased variance s is calculated for the variability component of capacitance signal 23 shown in (C) (the residual of capacitance signal 23). 2The following is calculated. In this embodiment, it is assumed that the residual of the capacitance signal 23 follows a Gaussian distribution, and the variance σ in the Gaussian distribution is calculated. 2 The unbiased variance s was calculated as follows: 2 Use this.

[0063] In step S5 (SNR calculation step), the signal-to-noise ratio 25 (SNR) is calculated based on the capacitance signal 23 and the noise variance 24.

[0064] In this embodiment, the signal-to-noise ratio is simply calculated by determining the ratio of the magnitude of change in the capacitance signal to the magnitude of the noise during a certain measurement time. Preferably, in order to reduce the influence of noise when estimating the magnitude of the signal, the difference between the average value taken over a predetermined section near the start of measurement and the average value taken over a predetermined section near the end of measurement is used as the signal.

[0065] In step S6 (capacitance signal selection step), capacitive signals 23 with a signal-to-noise ratio 25 equal to or greater than a predetermined threshold are selected from among the multiple capacitive signals 23. Based on this selection, the estimation processing shown in steps S7 to S9 is performed on the capacitive signals 23 whose signal-to-noise ratio 25 is equal to or greater than the predetermined threshold (Yes in S6). In this embodiment, capacitive signals 23 whose signal-to-noise ratio 25 is less than the predetermined threshold (No in S6) are not used in the estimation processing.

[0066] In steps S7-S9 (estimation steps), Bayesian estimation is performed based on the capacitance signal 23 and a physical model that includes the magnitude and time constant of the transient capacitance change, and the time constant (τ) of the capacitance signal 23 is calculated. i We estimate the posterior distribution 28b of ).

[0067] In step S7 (optimal solution calculation step), data fitting is performed on the capacitance signal 23 to calculate the optimal solution set 26, which is the number of deep levels (n_est) that reproduce the capacitance signal 23 and the optimal values ​​(sol) of the parameters (time constant and magnitude of capacitance change).

[0068] In the optimal solution calculation step, the combination of the number of types n in the deep energy levels and the optimal solution when the number of types n is that value is calculated for multiple numbers of types n. From these combinations, the best result is adopted as a set of the estimated true number of types and the optimal solution (sol). The optimal solution (sol) is the result of data fitting (optimal value of parameters) when the number of types n in the deep energy levels is the number of types n_est obtained by estimation.

[0069] In this embodiment, data fitting is performed on the model shown in Equation 4. For example, the Trust Region Reflective method is used for data fitting.

[0070]

number

[0071] Figures 8 and 9 illustrate the steps for calculating the optimal solution. In this embodiment, two improvements are made to how the residuals are calculated. The first is to evaluate only the low-frequency components, and the second is to introduce an acceptable range for the residuals.

[0072] Let me explain the first improvement. In this embodiment, by applying the Fast Fourier Transform (FFT) to the residuals, the residuals are converted to the frequency domain, and only the low-frequency components of the residuals are used as an indicator for model selection. This reduces the influence of noise and further improves the accuracy of data processing. As indicated by the arrow labeled 81 in the graph of Figure 8, when focusing on the frequency components, the signal mainly consists of low-frequency components. In contrast, the noise is flat across the entire frequency domain (it is white noise). Therefore, by using only the low-frequency components of the residuals for evaluation of the optimal solution calculation, the accuracy of data processing can be further improved.

[0073] Let me explain the second improvement. When adopting the number of deep levels n that minimizes the fitting residual as the true n, if we adopt the n that minimizes the residual as the true n, the number of deep levels (n_est) that reproduce the capacitance signal 23 may become too large. In this embodiment, by introducing a tolerance range for the residual, we can estimate the value of n (n=3) indicated by the arrow labeled 82 (instead of the value of n that minimizes the residual in the graph of Figure 9 (n=4)) as the number of deep levels (n_est) that reproduces the capacitance signal 23.

[0074] In step S8 (Bayesian estimation step), sample values ​​are extracted by performing Bayesian estimation. In this embodiment, initial values ​​are generated based on 26 sets of optimal solutions, and Bayesian estimation is performed using the Markov-Chain Monte Carlo method (MCMC) with the generated initial values ​​to obtain multiple sample values ​​27b(τ) of the time constant. i ) are extracted. More preferably, Bayesian estimation can be performed using the Hamiltonian Monte Carlo method, which is a type of MCMC method.

[0075] In other embodiments, in step S8, multiple sample values ​​of the time constant 27b(τ i Similarly to extracting ), perform Bayesian estimation and obtain multiple sample values ​​27a(ΔC) of the magnitude of the volume change. i ) can be extracted.

[0076] In this embodiment, the initial values ​​for Bayesian estimation are randomly generated according to Equation 5. In the equation, sol is the optimal solution (sol) of the capacitance signal 23, and is included in the calculated set of optimal solutions 26. In the equation, α is a parameter that determines the variability of the initial values.

[0077]

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[0078] The physical model used in Bayesian estimation is shown in Equation 6. In the equation, σ 2 This is the variance estimated by the variance estimation unit. The value obtained by Bayesian estimation is the time constant τ. i and the magnitude of the transient capacitance change ΔC i That is the case.

[0079]

number

[0080] In this embodiment, the prior distribution used for Bayesian estimation is shown in Equation 7. In the equation, U is a uniform distribution. Note that the prior distribution used for Bayesian estimation is not limited to Equation 7, which is used as an example.

[0081]

number

[0082] In step S9 (posterior distribution estimation step), the posterior distribution is estimated by performing kernel density estimation. In this embodiment, a Gaussian function is used as the kernel to perform kernel density estimation for multiple sample values ​​27b of the time constant, and the time constant (τ i We estimate the posterior distribution 28b of ). Note that the kernel used when estimating the kernel density is not limited to the example Gaussian function.

[0083] As will be shown in Example 1 later, the time constant (τ) obtained by this posterior distribution estimation step is compared with the Laplace DLTS method. i The posterior distribution 28b of ) has high time constant resolution. As a result, according to the analysis device 1 of one embodiment, high time constant resolution can be obtained even if the signal-to-noise ratio of the signal related to the change in transient capacitance is low.

[0084] Preferably, in step S9, the measured temperature and the time constant are plotted on a plane (1 / T-lnτT 2 Two-dimensional kernel density estimation can be performed on multiple sample values ​​27b of the time constant in ), and the posterior distribution 28b of the time constant can be estimated.

[0085] In other embodiments, in step S9, the measured temperature and the magnitude of the change in transient capacitance (ΔC) of the capacitance signal 23 are measured. i By performing two-dimensional kernel density estimation on multiple sample values ​​27a of the magnitude of the volume change in a plane plotted between (T-ΔC plane) and (T-ΔC plane), the posterior distribution 28a of the magnitude of the volume change can be estimated.

[0086] Figure 10 is a diagram illustrating the posterior distribution estimation step. As shown by the plotted points in the graph of Figure 10, the sample values ​​obtained by Bayesian estimation are not the distribution itself, but rather values ​​sampled from the distribution. In the posterior distribution estimation step, the posterior distribution (kernel density function), which is drawn by the solid line indicated by symbol 83 in the graph of Figure 10, is estimated from the multiple sample values.

[0087] Step S10 (posterior distribution display step) displays the posterior distribution in heatmap format. The deep level evaluation method using transient capacitance clarifies the relationship between the time constant of capacitance change and temperature. In steps S1 to S9, the time constant is determined from the transient capacitance change at a certain temperature. In this step S10, the relationship between the time constant of capacitance change and temperature is appropriately displayed. Therefore, transient capacitance signals at multiple temperatures are acquired and used for the final evaluation of the deep level.

[0088] In step S10, preferably, the measured temperature and the time constant are plotted on a plane (1 / T-lnτT). 2 In the plot, the posterior distribution of the time constant 28b is displayed in heatmap format. This allows the three-dimensional data of the measured temperature, the time constant τ, and the posterior distribution of the time constant to be displayed in two dimensions using the intensity of the heatmap. The heatmap allows the probability values ​​of the posterior distribution to be represented by intensity, enabling a display that takes advantage of the benefits of Bayesian estimation.

[0089] In other embodiments, the measured temperature and the magnitude of the capacity change (ΔC) are used. iIn the plot of the plane (T-ΔC plane) where the temperature and the transient capacitance change are plotted, the posterior distribution 28a of the capacitance change can be displayed in heatmap format. This allows the three-dimensional data of the measured temperature, the magnitude of the transient capacitance change (ΔC) of the capacitance signal, and the posterior distribution of the capacitance signal to be displayed in two dimensions by the intensity of the heatmap.

[0090] Figure 11 is an example of a schematic diagram showing the posterior distribution of the time constant in heatmap format. (A) is the case when the number of energy levels is 1, and (B) is the case when the number of energy levels is 2. As shown in (A) and (B), the relationship between the time constant τ and temperature T (τT) is given by (τT 2 Since an Arrhenius plot of ) results in a straight line, this method is used to evaluate deep energy levels. Figure 12 is an example of a schematic diagram showing the posterior distribution of the magnitude of capacity change in heatmap format. (A) is the case when there is one type of energy level, and (B) is the case when there are two types of energy levels. The posterior distribution of the magnitude of capacity change 28 can also be displayed in heatmap format, similar to the heatmap of the posterior distribution of the time constant shown in Figure 11.

[0091] Finally, the energy levels and capture cross-sections used for evaluating deep levels can be determined by the following procedure. In the heatmap of the posterior distribution of time constants exemplified in Figure 11, a straight line is drawn along the high-probability portion distributed on a straight line, the energy levels are determined from the slope, and the capture area is determined from the intercept. Similarly, in the heatmap of the posterior distribution of the magnitude of capacity change exemplified in Figure 12, a straight line is drawn along the high-probability portion distributed on a straight line with zero slope, and the density is determined from the intercept. Note that these data processing operations can be performed analytically by the estimation unit 17.

[0092] As described above, the analysis device 1 according to one embodiment of the present invention can obtain high time constant resolution even when the signal-to-noise ratio of the signal relating to the change in transient capacitance is low. As will be shown in Example 1 described later in comparison with the Laplace DLTS method, the posterior distribution 28b of the time constant obtained by the posterior distribution estimation step has high resolution. The resolution of the obtained time constant is high, and it is particularly excellent in its ability to distinguish between multiple deep levels. Furthermore, high time constant resolution can be obtained even when the signal-to-noise ratio of the measurement signal is low, and the measurement device 90 (transient capacitance signal measurement device) does not require an enormous number of measurements.

[0093] [Other forms] Although the present invention has been described above with reference to specific embodiments, the present invention is not limited to the embodiments described above.

[0094] Temperature dependence model of the time constant Figure 13 is a diagram illustrating the characteristics of the physical model used in the analysis method according to another embodiment of the present invention and the advantages of dividing it into temperature regions. In the analysis method according to the other embodiment, a temperature dependence model of the time constant is introduced into the physical model. Unless otherwise specified, the analysis method according to the other embodiment that introduces a temperature dependence model of the time constant into the physical model is the same as the analysis method according to the first embodiment that does not introduce a temperature dependence model of the time constant into the physical model, so redundant explanations are omitted.

[0095] As shown in Figure 13, the temperature-dependent model of the time constant assumes that certain energy levels affect transient capacitance changes only in specific temperature ranges. Based on this assumption, the model and data are divided into multiple temperature ranges, and Bayesian estimation is performed for each divided temperature range. In each temperature range, the number of types n of energy levels that affect transient capacitance changes is limited, thereby reducing the number of types n of energy levels that need to be considered in the Bayesian estimation.

[0096] Refer to Figure 13. For example, assume that for a transient capacitance change in a certain capacitance signal, each of the four levels 1 to 4 affects only a specific temperature range. In the example shown in Figure 13, it is assumed that only level 1 affects the transient capacitance change at the lowest temperature, only level 4 affects the transient capacitance change at the highest temperature, and for multiple intermediate temperature ranges between low and high temperatures, at most, for example, two levels overlap and affect the transient capacitance change.

[0097] When introducing a temperature-dependent time constant model into a physical model, attempting to reproduce all energy levels using a single model results in a large number of energy levels to consider in Bayesian estimation. In contrast, dividing the data into multiple temperature regions allows only the energy levels influencing those regions to be considered. In the example shown in Figure 13, there are a total of four energy levels, but when divided into multiple temperature regions, a maximum of two energy levels need to be considered in Bayesian estimation.

[0098] The temperature-dependent model of the time constant introduced into the physical model is described. In other embodiments, the time constant of the transient capacitance change included in the physical model is temperature-dependent, and the capacitance signal C(t) relating to the time change of transient capacitance is a signal measured at multiple measurement temperatures. In other embodiments, transient capacitance changes due to multiple types of deep levels are represented by the following equations 8 and 9, which further introduce temperature dependence to the time constant τ of equation 2 in one embodiment. Here α i ,β i is a parameter. T is the temperature (absolute temperature).

[0099]

number

[0100] Therefore, when using a model that assumes additive white Gaussian noise as the physical model, similar to Equation 3 in one embodiment, the physical models used in other embodiments are represented by the following Equations 10 and 11.

[0101]

number

[0102] Note that Equation 8 is the same as Equation 2, and Equation 10 is the same as Equation 3. Equations 9 and 11 show the temperature dependence of the time constant.

[0103] The data processing procedure performed in the analysis method according to other embodiments will be explained in more detail. As explained with reference to Figure 13, in the analysis method according to other embodiments, a temperature dependence model of the time constant is introduced into the physical model. Therefore, the capacitance signal C(t) relating to the time change of transient capacitance is a signal measured at multiple measurement temperatures.

[0104] In the analysis method according to other embodiments, preferably, in step S3 (capacitance signal conversion step), the capacitance signal 23(ΔC(t)) relating to the time change of transient capacitance can be normalized. By using the normalized transient capacitance change, the magnitude of the capacitance change becomes a constant that does not depend on temperature, and the number of parameters that need to be considered in the analysis from step S3 onward can be reduced.

[0105] The transient capacity change is expressed by Equation 12, and the density can be determined from ΔC in Equation 12. The determined density is shown in Equation 13.

[0106]

number

[0107]

number

[0108] Here, N D is doping density, C R This is the steady-state capacitance under reverse bias in DLTS measurements. Density N T Since it is constant regardless of temperature, the transient capacitance change is compared to the steady-state capacitance C under reverse bias. RBy dividing by this, the normalized transient capacity change can be calculated.

[0109] In the analysis methods according to the other embodiments described above, a temperature-dependent model of the time constant is introduced into the physical model. In order to distinguish between multiple types of deep levels, the analysis apparatus according to the other embodiments performs Bayesian estimation based on a physical model that includes capacitance signals C(t) measured at multiple measurement temperatures obtained from the measurement device 90, the magnitude of the transient capacitance change, and its time constant, and the physical model in which the time constant has temperature dependence, and estimates the posterior distribution of the time constant τ of the capacitance signal C(t) obtained from the measurement device 90.

[0110] As will be compared and examined in the embodiments described later, according to the posterior distribution of the time constant τ estimated by the analysis method of other embodiments, it is possible to obtain a high time constant resolution that can distinguish between multiple types (e.g., four types) of deep levels, even when the signal-to-noise ratio of the capacitance signal is relatively low.

[0111] In the above embodiment, the analysis device 1 analyzes the transient capacitance signal measured by the DLTS measuring device 90, but the signal that the analysis device 1 analyzes is not limited to transient capacitance signals. The signal that the analysis device 1 analyzes is not limited to transient capacitance changes related to deep levels formed in the semiconductor, but can be any signal with some kind of exponential change.

[0112] In the above embodiment, a Gaussian distribution is used for the noise distribution, but the noise distribution assumed in the physical model, etc., is not limited to a Gaussian distribution. Any distribution can be used for the noise distribution assumed in the physical model, etc., as long as the distribution can be statistically described.

[0113] In the above embodiment, a capacitive signal conversion step is performed in step S3 and a capacitive signal selection step is performed in step S6. However, these steps are optional processes, and either or both steps can be omitted. For example, if the capacitive signal conversion step is omitted in step S3, the data processing that was performed on the converted capacitive signal 23(ΔC(t)) in subsequent steps can be performed on the (unconverted) capacitive signal 21(C(t)).

[0114] The variance estimation step S4 can be omitted. Instead, the variance and time constant can be estimated simultaneously by adding a variance parameter in the Bayesian estimation step S8.

[0115] In the data fitting step S7 for calculating the optimal solution, any form of data fitting method can be applied, not just the Trust Region Reflective method exemplified.

[0116] In the Bayesian estimation step S8, it is not necessary to use the Markov Chain Monte Carlo (MCMC) method; the MCMC method is optional. In that case, the posterior distribution estimation step S9 can be omitted.

[0117] The posterior distribution estimation step S9 can be omitted. In that case, the display in the posterior distribution display step S10 will be in histogram format.

[0118] The heatmap display in the posterior distribution display step S10 is not limited to the posterior distribution; for example, a DLTS spectrum or a time constant spectrum obtained by Laplace DLTS may also be used.

[0119] In the above embodiment, the analysis device 1 is connected to the measuring device 90 via a network 9, but the connection method between the analysis device 1 and the measuring device 90 is not limited thereto. The analysis device 1 may also be integrated with a control console that controls the measurement operation of the measuring device 90.

[0120] In the above embodiment, the analysis device 1 is implemented as a single unit, but the analysis device 1 does not need to be a single unit; the processor, memory, auxiliary storage device 20, etc., may be located separately and connected to each other via a network. Similarly, the input device 31 and the display screen 32 do not necessarily need to be located in the same place; they may be located separately and connected to each other via a network 9 for communication.

[0121] In the above embodiment, each functional block of the analysis device 1 is executed by a single processor, but these functional blocks do not necessarily need to be executed by a single processor; they may be processed in a distributed manner across multiple processors. Alternatively, an FPGA (Field Programmable Gate Array) may perform the processing instead of a processor, or a GPU (Graphics Processing Unit) may be used as an accelerator to assist the parallel processing performed by the processor. In other words, processing performed by a processor includes processing performed by the processor or FPGA using an accelerator such as a GPU.

[0122] In the above embodiment, each functional block 11 to 17 constituting the data processing unit 10 is implemented by software, but each of these functional blocks 11 to 17 may be partially or entirely implemented as hardware. The processing of each functional block 11 to 17 constituting the data processing unit 10 does not need to be processed by a single processor, but may be distributed and processed by multiple processors. Each of the functional blocks 11 to 17 constituting the data processing unit 10 and the data items 21 to 26, 27a, 27b, 28a, 28b in the auxiliary storage device 20 may be partially or entirely cloudified on another server device (not shown) connected via the communication I / F unit 33.

[0123] The following examples illustrate the features of the present invention. Unless otherwise specified, the term "analysis method of the present invention" refers to the analysis method described in the above examples. [Examples]

[0124] In Example 1, the analysis method of the present invention was compared with the Laplace DLTS method in terms of the resolution of the time constant. The analysis method of the present invention was the analysis method according to one embodiment described above. The Laplace DLTS method used for comparison was the method disclosed in Non-Patent Document 1. The simulation conditions are shown in Equation 14.

[0125]

number

[0126] Figure 14 shows the simulation results comparing the time constant resolution of the analysis method of the present invention and the Laplace DLTS method. (A) is the capacitance change to be simulated, and the capacitance change was simulated for several different signal-to-noise ratios. (B) is the Laplace DLTS signal obtained by applying the Laplace DLTS method to the capacitance change shown in (A). (C) is the probability density of the posterior distribution of the time constant obtained by applying the analysis method of the present invention to the capacitance change shown in (A).

[0127] As shown in Figure 14, according to the Laplace DLTS method, the signal-to-noise ratio (SNR) required to separate the two time constants τ1 and τ2 was approximately 1000. The Laplace DLTS method could not separate the two time constants τ1 and τ2 when the SNR of the capacitance signal was 100 or 10. In contrast, the analysis method of the present invention was able to separate the two time constants τ1 and τ2 even when the SNR of the capacitance signal was 10.

[0128] Figure 15 is a graph showing the minimum signal-to-noise ratio (SNR) required to separate the two time constants. As shown in Figure 15, the analysis method of the present invention significantly reduces the minimum SNR required to separate the time constants compared to the Laplace DLTS method. The analysis method of the present invention shows that the minimum SNR required to separate the time constants is approximately 1 / 10 to 1 / 100 of that required by the Laplace DLTS method. [Examples]

[0129] In Example 2, as in Example 1, the analysis method of the present invention was compared with the Laplace DLTS method in terms of the resolution of the time constant. The analysis method of the present invention adopted the analysis method of the other embodiment described above and introduced a temperature dependence model of the time constant into the physical model. For the Laplace DLTS method used for comparison, a method was adopted that further added a moving average processing to the method disclosed in Non-Patent Document 1.

[0130] Simulation data was used for comparison. Similar to Example 1, the capacitance change was simulated for several different signal-to-noise ratios, and the resolution of the time constant was compared between the two methods by applying the analysis method of the present invention and the Laplace DLTS method to the capacitance changes obtained from the simulation.

[0131] In the simulation of capacity changes, the semiconductor material was assumed to be silicon carbide 4H-SiC, and the four levels were assumed to be as follows. Energy levels: 0.385eV, 0.406eV, 0.417eV, and 0.429eV • Capture cross-sectional area: All are the same (1 x 10) -16 cm 2 ) • Density: All are the same (determined by the signal-to-noise ratio). • Time constant τ at 200K: approximately 0.3 seconds, 1 second, 2 seconds, and 4 seconds The measurement temperature was assumed to be as follows: • Laplace DLTS method: 200K (Kelvin) • Analysis method of the present invention: 200K±10K / 1K (Centered around 200K, with increments of ±10K)

[0132] Figure 16 shows simulation results comparing the time constant resolution of the analysis method of the present invention and the Laplace DLTS method. (A) is the Laplace DLTS signal obtained by applying the Laplace DLTS method to the simulation data of capacitance change. (B) is the probability density of the posterior distribution of the time constant obtained by applying the analysis method of the present invention to the simulation data of capacitance change.

[0133] As shown in Figure 16(A), the Laplace DLTS method failed to separate the four time constants τ1 to τ4 corresponding to the four energy levels, regardless of whether the signal-to-noise ratio (SNR) of the capacitance signal being analyzed was between 100 and 1000. In particular, it failed to separate the two time constants τ2 and τ3. In contrast, according to the analysis method of the present invention, as shown in Figure 16(B), when the SNR of the capacitance signal is 180 or higher, the four time constants τ1 to τ4 corresponding to the four energy levels could be clearly separated. [Examples]

[0134] In Example 3, we confirmed whether multiple levels could be separated by applying the analysis method of the present invention to the capacitance signal that was actually measured. The analysis method of the present invention employs the analysis method of the other embodiment described above, and a temperature-dependent model of the time constant is introduced into the physical model.

[0135] Figure 17 shows the DLTS signal to be analyzed in Example 3. The DLTS signal shown in Figure 17 is the signal actually measured by a DLTS measuring device for defects generated by irradiating silicon carbide 4H-SiC with an electron beam.

[0136] It is known that when 4H-SiC is irradiated with an electron beam, only carbon atoms (C) are displaced at irradiation energies of approximately 100 keV or higher, while both carbon atoms (C) and silicon atoms (Si) are displaced at irradiation energies of approximately 220 keV or higher. Therefore, in the data with an irradiation energy of approximately 116 keV, the peak at approximately 200 K (Kelvin) is a peak obtained from a single energy level. In contrast, in the data with an irradiation energy of approximately 400 keV, the peak at approximately 200 K (Kelvin) is a peak obtained from multiple energy levels, indicating that it is a peak where multiple peaks obtained from multiple energy levels are mixed together. In Example 3, we applied the analysis method of the present invention to DLTS signal data with an irradiation energy of approximately 400 keV, which contains multiple peaks in this manner, to confirm whether it is actually possible to separate the multiple energy levels.

[0137] Figure 18 shows Arrhenius plots obtained by applying the analysis method of the present invention to the DLTS signals shown in Figure 17. (A) is the Arrhenius plot of the analysis results for data with an irradiation energy of approximately 116 keV. (B) is the Arrhenius plot of the analysis results for data with an irradiation energy of approximately 400 keV.

[0138] As shown in the Arrhenius plot (A), in the analysis of data with an irradiation energy of approximately 116 keV, the DLTS data for each temperature were roughly aligned on a single straight line. This confirmed that the data for approximately 116 keV was obtained from a single peak originating from a single energy level.

[0139] As shown in the Arrhenius plot (B), in the analysis results for data with an irradiation energy of approximately 400 keV, we were able to confirm the arrangement of four lines corresponding to each of the four energy levels. Therefore, it was confirmed that the analysis method of the present invention can actually separate each of the four energy levels from DLTS signal data with an irradiation energy of approximately 400 keV. [Explanation of Symbols]

[0140] 1 Analysis device 9 Network 10 Data Processing Unit 11 Capacitive signal acquisition section 12 Temperature signal acquisition section 13 Capacitance signal conversion section 14 Variance estimation part 15. Signal-to-noise ratio calculation unit (SNR calculation unit) 16 Capacitance signal selection unit 17 Estimation part 171 Optimal Solution Calculation Unit 172 Bayesian Estimation Unit 173 Posterior distribution estimation part 174 Posterior distribution display section 20 Auxiliary storage 21 Capacitance signal 22 Temperature signal 23. Converted Capacitive Signal 24 Dispersion 25 Signal-to-noise ratio 26 Optimal Solution Sets 27(27a,27b) Sample values 28(28a,28b) Posterior distribution 31 Input devices 32 Display screen 33. Communication Interface Section (Communication I / F Section) 90 DLTS measuring device 91 Transient capacitance meter 92 Temperature Controller 93 Temperature-Variable Probe 94 electrode 95 probes 99 samples P Analysis Program

Claims

1. A capacitance signal acquisition step to acquire a capacitance signal relating to the time change of transient capacitance, An estimation step in which Bayesian estimation is performed based on the capacitance signal and a physical model including the magnitude and time constant of the transient capacitance change, to estimate the posterior distribution of the time constant of the capacitance signal, A method for analyzing transient capacity changes, including [specific details omitted].

2. The analysis method according to claim 1, wherein the capacitance signal is a capacitance signal relating to the time change of the transient capacitance.

3. A variance estimation step is performed to estimate the statistical noise variance of the aforementioned capacitance signal, A signal-to-noise ratio (SNR) calculation step, which calculates the signal-to-noise ratio based on the capacitance signal and the noise dispersion, It further includes, The analysis method according to claim 1, wherein the estimation step is performed on the capacitance signal among a plurality of capacitance signals in which the signal-to-noise ratio is greater than or equal to a predetermined threshold.

4. The transient capacitance is a transient capacitance relating to a deep level formed in the semiconductor, The estimation step described above is: An optimal solution calculation step involves performing data fitting on the capacitance signal and calculating the optimal solution set of the number of deep levels that reproduce the capacitance signal and the optimal values ​​of the parameters. A Bayesian estimation step involves generating initial values ​​based on the set of optimal solutions, performing the Bayesian estimation using the generated initial values, and extracting multiple sample values ​​of the time constant. A posterior distribution estimation step involves performing kernel density estimation on the multiple sample values ​​of the time constant and estimating the posterior distribution of the time constant. The analysis method according to claim 3, including the method described in claim 3.

5. The capacitance signal is a signal measured at multiple measurement temperatures. The method further includes a temperature signal acquisition step of acquiring a temperature signal relating to the measured temperature, The aforementioned posterior distribution estimation step further, The analysis method according to claim 4, comprising performing two-dimensional kernel density estimation on a plane plotting the measured temperature and the time constant, and estimating the preceding and succeeding distribution of the time constant.

6. The capacitance signal is a signal measured at multiple measurement temperatures. The process further includes a temperature signal acquisition step of acquiring a temperature signal relating to the measured temperature, The Bayesian estimation step further extracts multiple sample values ​​of the magnitude of the transient capacity change, The aforementioned posterior distribution estimation step further, The analysis method according to claim 4, comprising performing two-dimensional kernel density estimation on the plurality of sample values ​​of the capacitance signal in a plane plotting the measured temperature and the change in the transient capacitance of the capacitance signal, and estimating the posterior distribution of the capacitance signal.

7. The estimation step described above is: In the plot, a posterior distribution display step is performed, in which the posterior distribution of the time constant or the posterior distribution of the capacitance signal is displayed in heatmap format. The analysis method according to claim 5, further comprising:

8. The time constant of the transient capacitance change included in the physical model has a temperature dependence. The analysis method according to any one of claims 1 to 7, wherein the capacitance signal is a signal measured at multiple measurement temperatures.

9. A capacitance signal acquisition unit acquires a capacitance signal relating to the time change of transient capacitance, An estimation unit that performs Bayesian estimation based on the capacitance signal and a physical model including the magnitude and time constant of the transient capacitance change, and estimates the posterior distribution of the time constant of the capacitance signal. A device for analyzing transient capacitance changes, including [specific component / feature].

10. On the computer, A capacitance signal acquisition function that acquires a capacitance signal relating to the time change of transient capacitance, An estimation function that performs Bayesian estimation based on the capacitance signal and a physical model including the magnitude and time constant of the transient capacitance change, and estimates the posterior distribution of the time constant of the capacitance signal, A program to achieve this.

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