Threshold calculation method

Abstract

To provide a threshold calculation method with which calculations are made safety without being affected by human act, and which, a simple method though, gives suggestions to the validity of error ranges or measurement ranges.SOLUTION: Provided is a threshold calculation method that makes calculations using an analysis device provided with a computing facility to compute a threshold μ0 from measured data, a storage facility, an input facility for inputting the measured data, and an output facility for outputting a threshold. The method includes: a step of inputting the measured data to the input facility; a measured data conversion step of converting the measured data on the basis of a data conversion expression having been preliminarily designed via the computing facility and the storage facility, and obtaining converted measured data in which μ is taken as a variable; a fitting step of fitting a Softplus function to the converted measured data, and obtaining a fitting Softplus function; and a step of outputting a threshold via the output facility in which μ0 of the fitting Softplus function is taken as the threshold.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a threshold calculation method. [Background technology]

[0002] In the analysis of physical phenomena, the threshold is a commonly used index. For example, in photoelectron yield spectroscopy (PYS), the horizontal axis represents the excitation energy of ultraviolet light irradiated onto a sample as excitation light, and the vertical axis represents the photoelectron yield emitted from the sample. The threshold is determined as the excitation energy at the point where the curve of the measurement data rises steeply. The obtained threshold is interpreted as the work function or ionization potential of the sample being measured.

[0003] Generally, the curve drawn by measurement data with a threshold is 0 up to the threshold in an ideal environment, and after the threshold is exceeded, it changes according to a function in accordance with the physical properties, such as proportional to the value on the horizontal axis or proportional to the square of the value. A method is used in which the vertical axis is set to the measurement value itself or the square root of the measurement value, and the curve is set so that after the threshold is exceeded, a straight line is drawn, and the straight line is extrapolated to find the intercept with the horizontal axis as the threshold.

[0004] This task, i.e., the task of setting a straight line and finding its intercept with the horizontal axis, is generally performed manually. Therefore, uncertainty and ambiguity due to the human effort are generated when setting the straight line. Attempts have been made to improve fitting accuracy by using the least squares method or the like to set the straight line, but since this method depends on the setting of the fitting target range, there is still a problem that it is still uncertain and ambiguous, although to a different degree than the human method. Patent Document 1 discloses a threshold calculation device, a calculation method, and a measurement device that improve the accuracy of PYS threshold calculation by improving regression analysis. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] JP 2020-160067 A Summary of the Invention [Problem to be solved by the invention]

[0006] An object of the present invention is to provide a threshold calculation method that is stable and not influenced by human intervention, is a simple method, and also provides a suggestion as to the validity of the error range and measurement range. [Means for solving the problem]

[0007] The configuration of the present invention for solving the problems is shown below. (Configuration 1) A threshold calculation method for calculating a threshold value μ0 from measurement data that is constructed by associating a plurality of measurement values ​​obtained from a sample with an environmental variable μ, which is one of the quantities representing an environment in which the sample is placed, with the environmental variable μ at that time, using an analysis device that includes a calculation device, a storage device, an input device for inputting the measurement data, and an output device for outputting the threshold value, the method comprising: inputting the measurement data into the input facility; a measurement data conversion step of converting the measurement data based on a pre-specified data conversion formula via the computing device and the storage device to obtain measurement conversion data with μ as an environmental variable; a fitting step of fitting the measurement conversion data with a Softplus function defined by equation (1) to obtain a fitted Softplus function; A threshold calculation method, comprising: setting μ0 of the fitting Softplus function as a threshold; and outputting the threshold via the output device. f=a×log e (1+exp((μ-μ0) / σ))+b Equation (1) where a and b are constants and σ represents the effective deviation. (Configuration 2) 2. The method for calculating a threshold value according to claim 1, wherein the fitting is performed by an absolute error method. (Configuration 3) 3. The threshold calculation method according to configuration 1 or 2, wherein the data conversion formula is one selected from the group consisting of a 1 / 2 power conversion formula, a 1 / 3 power conversion formula, a 2 / 5 power conversion formula, a 1 power conversion formula, and a 2 power conversion formula. (Configuration 4) 4. The threshold calculation method according to any one of configurations 1 to 3, wherein the measurement data is data obtained by measuring a physical phenomenon involving electrons. (Configuration 5) 4. The threshold calculation method according to any one of configurations 1 to 3, wherein the measurement data is measurement data of a phenomenon based on a Fermi-Dirac distribution. (Configuration 6) 4. The threshold calculation method according to any one of configurations 1 to 3, wherein the measurement data is measurement data obtained by photoelectron yield spectroscopy. Effect of the Invention

[0008] According to the present invention, there is provided a method for calculating a threshold value which is stable and not influenced by human intervention, is a simple method, and yet provides a suggestion as to the validity of the error range and measurement range. [Brief description of the drawings]

[0009] [Figure 1] FIG. 2 is a flow chart showing a processing flow of the present invention. [Diagram 2] FIG. 2 is a configuration diagram showing the configuration of a threshold calculation analysis device used in the present invention. [Diagram 3] FIG. 2 is an explanatory diagram showing the relationship between functions. [Figure 4] These are examples of calculating a threshold value for Cu-PYS measurement data. (a) shows only the measurement data, (b) shows an example of measurement by a human, and (c) shows an example of SP function fitting. [Diagram 5] These are examples of calculating a threshold for Al-PYS measurement data. (a) shows measurement data only, (b) shows an example of measurement by a human, and (c) shows an example of SP function fitting. [Figure 6] These are examples of determining a threshold value for Au-PYS measurement data. (a) shows measurement data only, (b) shows an example of measurement by a human, and (c) shows an example of SP function fitting. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] In the method of the present invention, a Softplus function (hereinafter also referred to as an SP function) is fitted to converted data obtained by converting measurement data according to a pre-specified data conversion formula, and a threshold value is calculated from the SP function. Here, the SP function is a function expressed by the following formula (1). The characteristics and features of the function will be described later. f=a×log e (1+exp((μ-μ0) / σ))+b Equation (1) μ0 is the threshold value. The environmental variable is μ, which in the case of PYS measurement corresponds to the energy of the ultraviolet light irradiated on the sample. The measurement result at that environmental variable μ, i.e., the photoelectron yield in the case of PYS measurement, is f. a and b are constants, and σ represents the effective deviation. σ is the variance (σ p 2 ) is (1 / 3) × (π × σ) 2 Since it is expressed as σ, it is called the effective deviation. p is the deviation.

[0011] The threshold calculation procedure of the present invention will be described with reference to the flow chart of FIG. 1 and the configuration diagram of FIG. First, measurement data acquired by a measurement device is prepared and input to the input facility 11 of the threshold calculation analysis device 101 in Fig. 2 (step S11 in Fig. 1). Here, the data may be accumulated in a batch format and all data may be input, or the measurement device and the threshold calculation analysis device 101 may be connected online and the data may be input one by one for each measurement.

[0012] 2, the threshold calculation analysis device 101 comprises an input facility 11, a calculation facility 14, a memory facility 15, an information path 16, and an output facility 17, and is configured such that measurement data (input data) 12 is input to the input facility 11 and output data (such as thresholds) 18 is output from the output facility 17 in response to an instruction from a data conversion formula 13. Therefore, the threshold calculation process of the present invention is not performed manually but is performed by a device. Here, the computing equipment 14 is a computing device mainly composed of semiconductor computing devices such as a CPU, an MPU, and a GPU, and the memory equipment 15 is composed of memory devices such as temporary memory devices such as DRAM and SRAM, and long-term memory devices (storage) such as FLASH memory, FRAM (registered trademark), EPROM, hard disks, floppy disks, and magnetic tapes. It is not necessary to have a long-term memory device, but it is useful as an option when performing advanced analysis of threshold data, such as a data reference function. It is also possible to configure the memory equipment 15 only with a long-term memory device without a temporary memory device, but in that case, it takes time to transfer data. Therefore, it is preferable to have both a temporary memory device and a long-term memory device. The information path 16 is a facility that connects the input facility 14, the calculation facility 14, the memory facility 15, and the output facility 17 to transmit data and information, and is generally made up of wiring (optical interconnects are also acceptable).

[0013] An instruction to designate a data conversion formula is input to the input facility 11 of the threshold calculation analysis device 101 (step S12). Here, the data conversion formula is a formula for converting measurement data, keeping in mind that after the threshold is exceeded, the data changes according to a function in accordance with physical properties, such as proportional or squared proportional, as the environmental variable increases, and is preferably selected from the group consisting of a 1 / 2 power conversion formula, a 1 / 3 power conversion formula, a 2 / 5 power conversion formula, a 1 power conversion formula, and a 2 power conversion formula.

[0014] Next, the measurement data is converted based on the designated data conversion formula using the calculation facility 14 and the storage facility 15 (step S13). Meanwhile, the SP function shown in equation (1) is prepared (step S14), and the SP function is fitted to the data-converted measured values ​​(step S15). The fitting process involves varying the parameter values ​​in various ways to refine the parameters of the SP function so that the difference between the SP function value f and the corresponding data-converted measured values ​​is minimized for a wide range of environmental variables μ. As a result of examining various methods, including the least squares method, for minimizing the fitting process, it was found that the absolute error method is best used for the fitting process. This is because the absolute error method is a method that is less affected by outliers, and is particularly effective when there are few measurement points or when there is a lot of measurement noise (noise such as a Gaussian distribution cannot be assumed).

[0015] Thereafter, μ0 of the fitted SP function is output or displayed from the output device 17 as a threshold value (18) (step S16), and the process ends (S17).

[0016] Next, the characteristics of the SP function will be described with reference to FIG. As mentioned earlier, the SP function 1 is the function shown in equation (1), and is mathematically a function of the same series as the logistic function. In addition, the threshold for PYS is I p It can also be expressed as equation (2). f=a×log e (1+exp((xI p ) / (κ B ×T)))+b Formula (2) Here, κ B is the Boltzmann constant and T is the effective temperature. The first derivative of the SP function is the Sigmoid function, which is distribution 2 in Figure 3 (cumulative distribution function).

[0017] In addition, almost all physical phenomena involving electrons can be analyzed by attributing them to the Fermi-Dirac distribution (FD distribution), and the FD distribution can also be handled by the Sigmoid function, which is a function of the same series as the Logistic function. Therefore, the threshold calculation method of the present invention can be applied not only to PYS, but also to the measurement of phenomena based on the Fermi-Dirac distribution, in other words, to the measurement of phenomena involving electrons.

[0018] The second derivative of the SP function is the probability density function (PDF) (3 in Figure 3). The average value of the PDF (which is also the maximum value) is μ0 (I p ), variance of PDF (σ p 2 ) is (1 / 3) × (π × σ) 2 (The variance in the case of conforming to Equation 2 is (1 / 3) × (π × κ B ×T) 2 ). The PDF is a waveform distribution similar to a normal distribution, analytically 1σ p is 72.0%, 2σ p is 94.8%, and 3σ p gives a probability of 99.1%. That is, the threshold (average value) I p from ±1σ p The range of I indicates a probability range of 72.0%. p +3σ p A wider measurement range will provide sufficient accuracy. For reference, Figure 3 also shows the ReLU function 4, which has a function shape similar to that used when manually calculating a threshold value.

[0019] From the above, the present method makes it possible to analytically calculate the threshold value of a physical phenomenon involving electrons, such as a physical phenomenon based on the Fermi-Dirac distribution, such as PYS, simply and stably, while eliminating artificial factors. Furthermore, this method makes it possible to evaluate and suggest the validity of the error range (deviation) of the threshold and the measurement range. EXAMPLES

[0020] Example 1 In Example 1, the results of calculating the PYS thresholds of copper (Cu), aluminum (Al) and gold (Au) using the threshold calculation analysis device 101 shown in Fig. 2 will be described. For reference, the results of the artificial method will also be briefly mentioned. However, it should be noted that the present invention is not limited to such a specific form, and the technical scope of the present invention is defined by the claims.

[0021] The measurement data for PYS of Cu, Al, and Au were obtained as follows. Cu, Al, and Au are polycrystalline samples with a purity of 99.5% or more. Before the measurement, each sample was washed with ethanol to expose a clean surface. It is believed that a natural oxide film has formed on the surface. The PYS measurement was performed in an air environment at room temperature using an AC-3 (Riken Keiki Co., Ltd.) The measurement results for Cu, Al, and Au are shown in Figures 4(a), 5(a), and 6(a), respectively.

[0022] The thresholds were determined by artificially drawing straight lines on the PYS measurement results, i.e., by a human being, for Cu, Al, and Au, and the results are shown in Figure 4(b), Figure 5(b), and Figure 6(b), respectively. There were two subjects, so that the differences between subjects could be seen. There was a large variability in the measurement results.

[0023] The method of the present invention was applied to PYS of Cu, Al and Au to determine the threshold value. The application method is detailed below. For the measured data, a power of 1 / 2 was applied to the photoelectron yield (measured intensity) from the theoretical model. The intensity to which the power of 1 / 2 was applied was fitted with the Softplus function using the absolute error method. Here, the Softplus function used was in the form of Equation (2). As a result of fitting, Ip and T are obtained. Ip is the threshold value, and the variance is calculated from T. The variance value (σ p 2 ) is the square root of the deviation (σ p ) with respect to the threshold value. p This area is the error range, and a deviation of ±3 times is the minimum reasonable measurement range.

[0024] The results are shown in Figure 4(c), Figure 5(c) and Figure 6(c), respectively. The threshold of PYS for Cu is 5.56 eV, with a deviation of σ p is 0.30 eV, the calculated minimum reasonable measurement range is 4.66 to 6.46 eV, the PYS threshold of Al is 6.14 eV, and the deviation σ p is 0.24 eV, the calculated minimum reasonable measurement range is 5.42 to 6.86 eV, and the threshold of PYS of Au is 5.36 eV, with a deviation of σ p was 0.41 eV, and the calculated minimum reasonable measurement range was 4.13 to 6.59 eV. The method of the present invention enabled us to obtain threshold values ​​that fit well to the measured values, eliminated artifacts, were highly stable, and provided indications of error and measurement range. [Industrial Applicability]

[0025] The present invention is not limited to calculating the PYS threshold value. It is possible to stably and easily calculate the threshold value, which is an index for managing the state and quality of materials and devices, by analyzing the physical state such as the band gap based on absorbance measured by transmission and reflection measurement and the Schottky barrier based on current-voltage measurement, without being influenced by human intervention. Furthermore, the calculated threshold value also indicates the validity of the error range and measurement range. Therefore, it is believed that this method will contribute to the development of science and technology, as well as to the improvement of product quality and performance, that is, to the development of industry. [Explanation of symbols]

[0026] 1: Softplus function (SP function) 2: Sigmoid function (Softplus first differential function, cumulative distribution function) 3: Probability density function (Softplus quadratic differential function) 4: ReLU (Rectified Linear Unit) function 11: Input equipment 12: Measurement data (input data) 13: Data conversion formula 14: Computing equipment 15: Storage equipment 16: Information path 17: Output equipment 18: Output data (threshold) 101: Threshold calculation and analysis device

Claims

1. A threshold value μ is calculated from measurement data that is constructed by associating a plurality of measurement values obtained from the sample with the environmental variable μ, which is one of the quantities representing the environment in which the sample is placed, when the environmental variable μ is changed. ０ A threshold calculation method for calculating a threshold μ using an analysis device including a calculation facility, a storage facility, an input facility for inputting the measurement data, and an output facility for outputting the threshold μ 0, inputting the measurement data into the input facility; a measurement data conversion step of converting the measurement data based on a pre-specified data conversion formula via the calculation facility and the storage facility to obtain measurement conversion data with μ as an environmental variable; a fitting step of fitting the measurement conversion data with a Softplus function defined by equation (1) to obtain a fitted Softplus function; μ of the fitting Softplus function ０ a threshold value, and outputs the threshold value via the output facility. f = a×log ｅ (1 + exp((μ - μ ０ ) / σ)) + b Equation (1) a and b are constants, and σ represents the effective deviation.

2. The threshold calculation method according to claim 1 , wherein the fitting is performed by an absolute error method.

3. 3. The threshold calculation method according to claim 1, wherein the data transformation formula is one selected from the group consisting of a ½ power transformation formula, a ⅓ power transformation formula, a ⅔ power transformation formula, a 1 power transformation formula, and a 2 power transformation formula.

4. 2. The threshold calculation method according to claim 1, wherein the measurement data is data obtained by measuring a physical phenomenon involving electrons.

5. 2. The threshold calculation method according to claim 1, wherein the measurement data is measurement data of a phenomenon based on a Fermi-Dirac distribution.

6. The threshold calculation method according to claim 1 , wherein the measurement data is measurement data obtained by photoelectron yield spectroscopy.

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