JP-7854712-B2 - Threshold calculation method

Inventors

• 柳生 進二郎
• 吉武 道子
• 長田 貴弘
• 知京 豊裕

Assignees

• 国立研究開発法人物質・材料研究機構

Dates

Publication Date

20260507

Application Date

20220822

Claims (6)

1. A threshold calculation method comprising 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 μ0, wherein the threshold μ0 is calculated from measurement data configured by associating multiple measurement values obtained from the sample with the environment variable μ, which is one of the quantities representing the environment in which the sample is placed, when the environment variable μ is changed, 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, A threshold calculation method that uses μ 0 of the fitting Softplus function as the threshold and outputs the threshold via the output equipment. f=a×log e (1+exp((μ-μ 0 )/σ))+b Formula (1) a and b are constants, and σ represents the effective deviation.
2. The fitting is performed using the absolute error method, as described in 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 the Fermi-Dirac distribution.
6. The threshold calculation method according to claim 1, wherein the measurement data is measurement data from photoelectron yield spectroscopy.

Description

This invention relates to a method for calculating thresholds. 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 formed by these 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. Generally, the curve traced by measurement data with a threshold, in an ideal environment, is zero up to the threshold, and after exceeding the threshold, it changes according to a function based on 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 represent the measurement value itself or its square root, and the curve after exceeding the threshold is set to form a straight line. This straight line is then extrapolated, and the intercept with the horizontal axis is used to determine the threshold. 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. Japanese Patent Publication No. 2020-160067 This is a flowchart illustrating the processing flow of the present invention.This is a diagram showing the configuration of the threshold calculation and analysis device used in the present invention.This is an explanatory diagram showing the relationships between the functions.This is an example of determining a threshold value for Cu-PYS measurement data, where (a) shows only the measurement data, (b) shows an example of measurement by a human, and (c) shows an example of SP function fitting.This is an example of determining a threshold for Al-PYS measurement data, where (a) shows only the measurement data, (b) shows an example of measurement by a human, and (c) shows an example of SP function fitting.This is an example of determining a threshold for Au-PYS measurement data, where (a) shows only the measurement data, (b) shows an example of measurement by a human, and (c) shows an example of SP function fitting. In the method of the present invention, a Softplus function (hereinafter also referred to as the SP function) is fitted to the converted data, which is obtained by converting the measurement data according to a predetermined data conversion formula, 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-μ 0 )/σ))+b Formula (1) μ 0 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 called the effective deviation because the variance (σ p 2 ) of the probability density function, which is the second derivative of the SP function, is expressed as (1/3) × (π × σ) 2. Note that σ p is the deviation. 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. 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, and output data (such