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] This invention relates to a method for calculating thresholds. [Background technology]

[0002] In the analysis of physical phenomena, thresholds are commonly used indicators. For example, in photoelectron yield spectroscopy (PYS), the excitation energy of ultraviolet light irradiated onto the sample is plotted on the x-axis, and the photoelectron yield emitted from the sample is plotted on the y-axis. The excitation energy at the point where the curve drawn by the measurement data rises sharply is determined as the threshold. 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 value is 0 up to the threshold in an ideal environment, and after the threshold is exceeded, it changes according to a function that conforms to the material properties, such as being proportional to the value on the horizontal axis or proportional to its square. A method is employed in which the vertical axis is set to the measurement value itself or the square root of the measurement value, and the curve after the threshold value is set to be a straight line, and the intercept with the horizontal axis is obtained by extrapolating this straight line.

[0004] The process of setting a straight line and determining its intercept with the horizontal axis is generally performed manually. Therefore, human-induced uncertainty and ambiguity arise when setting the straight line. Attempts have been made to improve fitting accuracy by using methods such as the least squares method for setting the straight line, but these methods are dependent on the setting of the fitting range, and thus, although to a different degree, remain uncertain and ambiguous compared to manual methods. Furthermore, Patent Document 1 discloses a threshold calculation device, calculation method, and measurement device that improve the accuracy of PYS threshold calculation through improvements in regression analysis. [Prior art documents] [Patent Documents]

[0005] [Patent Document 1] Japanese Patent Publication No. 2020-160067 [Overview of the project] [Problems that the invention aims to solve]

[0006] The object of the present invention is to provide a threshold calculation method that is stable, independent of human error, simple to use, and provides insights into the validity of the error range and measurement range. [Means for solving the problem]

[0007] The configuration of the present invention for solving the problem is shown below. (Composition 1) A threshold calculation method comprising calculating a threshold μ0 from measurement data composed of multiple measurements obtained from a sample when an environment variable μ, which is one of the quantities representing the environment in which the sample is placed, is changed, and the environment variable μ at that time is associated with the current environment variable μ, using an analysis device equipped with a calculation device, a storage device, an input device for inputting the measurement data, and an output device for outputting the threshold, wherein The steps include inputting the measurement data into the input device, A measurement data conversion step involves performing a conversion of the measurement data based on a pre-specified data conversion formula via the aforementioned calculation equipment and storage equipment to obtain measurement conversion data in which μ is an environment variable, A fitting step to obtain a fitted Softplus function by fitting the Softplus function defined by equation (1) to the aforementioned measurement conversion data, A threshold calculation method that uses μ0 of the fitting Softplus function as the threshold value and outputs the threshold value via the output equipment. f = a × log e (1 + exp((μ - μ0) / σ)) + b Equation (1) a and b are constants, and σ represents the effective deviation. (Configuration 2) The fitting is the threshold calculation method described in Configuration 1, using the absolute error method. (Composition 3) 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 first power conversion formula, and a second power conversion formula, and the threshold value calculation method according to Configuration 1 or 2. (Configuration 4) The measurement data is data obtained by measuring a physical phenomenon mediated by electrons, and the threshold value calculation method according to any one of Configurations 1 to 3. (Configuration 5) The measurement data is data obtained by measuring a phenomenon based on the Fermi-Dirac distribution, and the threshold value calculation method according to any one of Configurations 1 to 3. (Configuration 6) The measurement data is data obtained by measuring photoelectron yield spectroscopy, and the threshold value calculation method according to any one of Configurations 1 to 3. [Advantages of the Invention]

[0008] According to the present invention, there is provided a method for calculating a threshold value that is stably calculated without being influenced by humans, is a simple method, and gives a suggestion on the validity of an error range and a measurement range. [Brief Description of the Drawings]

[0009] [Figure 1] It is a flowchart showing the processing flow of the present invention. [Figure 2] It is a configuration diagram showing the configuration of a threshold value calculation analysis device used in the present invention. [Figure 3] It is an explanatory diagram showing the relationship between each function. [Figure 4] It is an example when obtaining a threshold value for Cu-PYS measurement data, where (a) shows only the measurement data, (b) shows a measurement example by a person, and (c) shows an SP function fitting example. [Figure 5] It is an example when obtaining a threshold value for Al-PYS measurement data, where (a) shows only the measurement data, (b) shows a measurement example by a person, and (c) shows an SP function fitting example. [Figure 6] It is an example when obtaining a threshold value for Au-PYS measurement data, where (a) shows only the measurement data, (b) shows a measurement example by a person, and (c) shows an SP function fitting example. [Modes for carrying out the invention]

[0010] In the method of the present invention, the measurement data is converted according to a predetermined data conversion formula, and the Softplus function (hereinafter also referred to as the SP function) is fitted to the converted data, and a threshold value is calculated from the SP function. Here, the SP function is the function represented by the following equation (1). Its characteristics and features will be discussed later. f = a × log e (1 + exp((μ - μ0) / σ)) + b Equation (1) μ0 is the threshold. The environment variable is μ, which in the case of PYS measurement corresponds to the energy of the ultraviolet light irradiated onto the sample. The measurement result when the environment variable μ is 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 of the probability density function, which is the second derivative of the SP function (σ p 2 ) is (1 / 3) × (π × σ) 2 It is expressed as σ and is therefore called the effective deviation. p This is the deviation.

[0011] The threshold calculation procedure of the present invention will be explained with reference to the flowchart in Figure 1 and the configuration diagram in Figure 2. First, the measurement data acquired by the measuring device is prepared and input into the input equipment 11 of the threshold calculation and analysis device 101 shown in Figure 2 (step S11 in Figure 1). Here, the data may be accumulated in a batch and input all at once, or the measuring device and the threshold calculation and analysis device 101 may be connected online and the data may be input sequentially for each measurement.

[0012] As shown in Figure 2, the threshold calculation and analysis device 101 comprises an input device 11, a calculation device 14, a storage device 15, an information path 16, and an output device 17. The device is configured to receive measurement data (input data) 12 into the input device 11 and instructions from the data conversion formula 13, after which output data (such as thresholds) 18 is output from the output device 17. Therefore, the threshold calculation process of the present invention is performed by the device, not by human intervention. Here, the computing equipment 14 is a computing device mainly composed of semiconductor computing devices such as a CPU, MPU, and GPU, and the storage equipment 15 consists of storage devices such as temporary storage devices like DRAM and SRAM, and long-term storage devices (storage) such as FLASH memory, FRAM (registered trademark), EPROM, hard disks, floppy disks, and magnetic tapes. Long-term storage devices are not necessarily required, but they are useful as an option when performing advanced analysis of threshold data, such as data reference functions. It is also possible to configure the storage equipment 15 with only long-term storage devices without temporary storage devices, but in that case, data transfer will take a long time. Therefore, it is preferable to have both temporary storage devices and long-term storage devices. The information path 16 is a device that transmits data and information between the input equipment 14, the processing equipment 14, the storage equipment 15, and the output equipment 17, and generally consists of wiring (it may also be an optical interconnect).

[0013] An instruction to specify a data conversion formula is input to the input equipment 11 of the threshold calculation and 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, it changes according to a function that conforms to the physical properties, such as being proportional or proportional to the square, as the environment variable increases. Preferably, it is selected from 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.

[0014] Next, the measurement data is converted using the calculation equipment 14 and the storage equipment 15 based on the instructed data conversion formula (step S13). On the one hand, the SP function shown in Equation (1) is prepared (Step S14), and the SP function is fitted to the measurement values that have been data-converted (Step S15). The fitting process is a process of determining the parameters of the SP function by varying the values of the parameters so that the difference between the value f of the SP function and the corresponding data-converted measurement values is minimized for a wide range of environmental variables μ. As a result of examining various processes including the least squares method as the minimization process of the fitting, it was found that it is advisable to use the absolute error method for the fitting process. This is because the absolute error method is a method that is less affected by outliers and is effective particularly when the number of measurement points is small or when the measurement noise is large (noise such as a Gaussian distribution cannot be assumed).

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

[0016] Next, the characteristics of the SP function will be described while referring to FIG. 3. As described above, the SP function 1 is the function shown in Equation (1) and is a function in the same series as the Logistic function mathematically. Note that the threshold value in the case of PYS can be expressed as Equation (2) with I p as follows. f = a×log e (1 + exp((x - I p ) / (κ B ×T))) + b Equation (2) Here, κ B is the Boltzmann constant, and T is the effective temperature. The function obtained by differentiating the SP function once is the Sigmoid function, which is the distribution (cumulative distribution function) 2 in FIG. 3.

[0017] Furthermore, while almost all physical phenomena involving electrons can be analyzed by attributing them to the Fermi-Dirac distribution (FD distribution), the FD distribution can also be handled by the Sigmoid function, which is a function in 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 function obtained by taking the second derivative of the SP function is the probability density distribution function, shown in Figure 3 (PDF: Probability density function). The average value (which is also the local maximum) of a PDF is μ0 (I if following Equation 2). p ), PDF distribution (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 ). PDF is a waveform distribution similar to a normal distribution, analytically equivalent to 1σ. p 72.0%, 2σ p It is 94.8%, and 3σ p This gives a 99.1% probability. That is, the threshold (mean value) I p ±1σ p The range represents a 72.0% probability range. Also, threshold I p +3σ p A wider measurement range will result in sufficient accuracy. For reference, Figure 3 also includes the ReLU function 4, which has a function form similar to that used when determining the threshold manually.

[0019] Based on the above, this method allows for the simple and stable calculation of electron-mediated physical phenomena, such as the threshold of PYS, based on the Fermi-Dirac distribution, while excluding artificial factors and analyzing the process analytically. Furthermore, this method makes it possible to evaluate and suggest the validity of the threshold error range (deviation) and the measurement range. [Examples]

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

[0021] The PYS measurement data for Cu, Al, and Au were obtained as follows. The Cu, Al, and Au samples are polycrystalline with a purity of 99.5% or higher. Before measurement, each sample was washed with ethanol to expose a clean surface. It is assumed that a native oxide film is formed on the surface. A PYS measuring device, AC-3 (manufactured by Riken Keiki Co., Ltd.), was used for measurements in an atmospheric environment at room temperature. The measurement results for Cu, Al, and Au are shown in Figures 4(a), 5(a), and 6(a), respectively.

[0022] Figures 4(b), 5(b), and 6(b) show the results of manually drawing straight lines on the PYS measurement results to determine thresholds for Cu, Al, and Au, respectively. Two subjects were used in each case to allow for comparison of differences between subjects. Significant variability is observed in the measurement results.

[0023] The method of the present invention was applied to PYS of Cu, Al, and Au to determine thresholds. The application method is described in detail below. For the measurement data, a power of 1 / 2 was applied to the photoelectron yield (measured intensity) from a theoretical model. Softplus function fitting was then performed using the absolute error method on the intensity to which the power of 1 / 2 had been applied. Here, the Softplus function used was of the form shown in equation (2). The fitting process yields Ip and T. Ip becomes the threshold, and the variance is calculated from T. The value of the variance (σ) p 2 The square root of ) is the deviation (σ p ) becomes ±σ relative to the threshold. p This range represents the error margin, and a deviation of ±3 times is considered the minimum acceptable measurement range.

[0024] The results are shown in Figures 4(c), 5(c), and 6(c), respectively. The threshold for Cu's PYS is 5.56 eV, and the deviation σ p The threshold for Al is 0.30 eV, the calculated minimum valid measurement range is 4.66 to 6.46 eV, the threshold for Al's PYS is 6.14 eV, and the deviation σ p The threshold for PYS of Au is 0.24 eV, the calculated minimum valid measurement range is 5.42-6.86 eV, and the PYS threshold for Au is 5.36 eV, with a deviation of σ. p The reading was 0.41 eV, and the calculated reasonable minimum measurement range was 4.13 to 6.59 eV. The method of the present invention made it possible to obtain a threshold that fits well to the measured value, eliminates human error, is highly stable, and provides insights into the error and measurement range. [Industrial applicability]

[0025] This invention goes beyond simply calculating PYS thresholds. It enables the analysis of physical states such as the band gap determined by absorbance measurements (transmission and reflection) and the Schottky barrier barrier determined by current-voltage measurements. Using these states, it allows for the stable, simple, and unaffected calculation of thresholds that serve as indicators for managing the state and quality of materials and devices. Furthermore, the calculated thresholds also suggest the validity of the error range and measurement range. Therefore, this method is expected to contribute to the advancement of science and technology, as well as to the improvement of product quality and performance, and thus to the development of industry. [Explanation of symbols]

[0026] 1: Softplus function (SP function) 2: Sigmoid function (Softplus first derivative function, cumulative distribution function) 3: Probability Density Function (Softplus Second 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 pathway (information path) 17: Output equipment 18: Output data (threshold) 101: Threshold calculation and analysis device

Claims

1. When the environment variable μ, which is one of the quantities representing the environment in which the sample is placed, is changed, multiple measurement values ​​obtained from the sample are associated with the environment variable μ at that time, and a threshold μ is constructed from the measurement data. ０ The calculation equipment, storage equipment, input equipment for inputting the measurement data, and the threshold μ ０ A threshold calculation method calculated using an analysis device equipped with output equipment that outputs the following: The aforementioned environment variable μ corresponds to the energy of ultraviolet light irradiated onto the sample in photoelectron yield spectroscopy measurements. The steps include inputting the measurement data into the input device, A measurement data conversion step involves performing a conversion of the measurement data based on a pre-specified data conversion formula via the aforementioned calculation equipment and storage equipment to obtain measurement conversion data in which μ is an environment variable, A fitting step to obtain a fitted Softplus function by fitting the Softplus function defined by equation (1) to the measurement conversion data, The μ of the aforementioned fitting Softplus function ０ A threshold calculation method that uses a threshold value and outputs the threshold value via the output equipment. 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 fitting is performed using the absolute error method, according to the threshold calculation method of claim 1.

3. The threshold calculation method according to claim 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.

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

5. 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 from photoelectron yield spectroscopy.

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