A method for measuring a fermi level of a material based on ultraviolet photoelectron spectroscopy

Abstract

The application provides a method for measuring a material Fermi level based on ultraviolet photoelectron spectroscopy, and relates to the technical field of material analysis, and comprises the following steps: irradiating a to-be-measured sample with a photon beam of a target wavelength; constructing an ultraviolet photoelectron spectrum of the to-be-measured sample according to the distribution of photoelectrons of different kinetic energies emitted by the to-be-measured sample, wherein the photon beam belongs to the vacuum ultraviolet band; determining a Fermi edge region from the ultraviolet photoelectron spectrum of the to-be-measured sample and extracting shape information of the Fermi edge region; fitting the shape information of the Fermi edge region based on a convolution model previously constructed with the Fermi level of the to-be-measured sample as a to-be-fitted parameter, and determining the value of the Fermi level of the to-be-measured sample according to a fitting result. The fitting method has high automation degree, can quickly process a large amount of sample data, reduces the error of human judgment, and is especially suitable for high-throughput testing and online measurement.

Description

Technical Field

[0001] This invention relates to the field of materials analysis technology, specifically to a method for measuring the Fermi level of materials based on ultraviolet photoelectron spectroscopy. Background Technology

[0002] The Fermi level is a key physical parameter describing the electron distribution and electrochemical potential in solid materials, and it is crucial for understanding the electronic properties of materials, such as conductivity, work function, band structure, and interface level alignment. However, during measurement, limited instrument resolution can lead to some blurring of the measured photoelectron spectrum, affecting the analysis of the fine structure of the material surface, especially in the low-energy range where insufficient resolution is particularly pronounced. Specifically, spectral broadening makes it difficult to accurately locate the Fermi level, thus hindering in-depth analysis of the material's electronic structure.

[0003] According to the national recommended standard GB / T 41072-2021 "Guideline for Ultraviolet Photoelectron Spectroscopy in Surface Chemical Analysis", the commonly used Fermi edge localization method includes the "20%~80% intensity method", which estimates the Fermi level position by measuring the midpoint between the 20% and 80% intensity decrease regions in the photoelectron spectrum. However, this method does not take into account the influence of the instrument's energy resolution, and the resulting errors and broadening problems are still serious, leading to reduced accuracy and repeatability of the spectral analysis results and a large error. Summary of the Invention

[0004] This invention provides a method for measuring the Fermi level of a material based on ultraviolet photoelectron spectroscopy, aiming to solve the problems existing in the background art. To solve the above-mentioned technical problems, this invention is implemented as follows: In a first aspect, embodiments of the present invention provide a method for measuring the Fermi level of a material based on ultraviolet photoelectron spectroscopy, comprising: The sample to be tested is irradiated with a photon beam of the target wavelength. Based on the distribution of photoelectrons with different kinetic energies excited by the sample to be tested, the ultraviolet photoelectron spectrum of the sample to be tested is constructed. The photon beam belongs to the vacuum ultraviolet band. The horizontal axis of the ultraviolet photoelectron spectrum is the photoelectron kinetic energy, and the vertical axis is the photoelectron intensity. The Fermi edge region is determined from the ultraviolet photoelectron spectrum of the sample to be tested, and the shape information of the Fermi edge region is extracted. The Fermi edge region is a preset width range centered on the position of the Fermi edge. Based on a pre-constructed convolutional model using the Fermi level of the sample under test as the fitting parameter, and with the goal of minimizing the residual between the fitting function and the shape information, a genetic algorithm is used to fit the shape information of the Fermi edge region, and the value of the Fermi level of the sample under test is determined based on the fitting result. The convolutional model is used to describe thermal broadening and instrument broadening, and the influence of instrument broadening is subtracted by introducing the instrument broadening parameter.

[0005] Alternatively, the convolutional model can be constructed according to the following steps: A Fermi-Dirac distribution function is constructed to describe the thermal broadening effect of photoelectrons in the material of the sample under test; the Fermi level parameters contained in the Fermi-Dirac distribution function are used as unknown parameters to be fitted. Based on the spectral broadening corresponding to the pre-measured instrument response, a Gaussian function is constructed. The Gaussian function is used to describe the energy broadening effect introduced by the instrument's resolution. The instrument broadening parameter used in the Gaussian function is a pre-calibrated known value. The convolution model is obtained by performing a convolution operation between the Fermi-Dirac distribution function and the Gaussian function.

[0006] Optionally, using the Fermi level of the sample under test as the convolution model with parameters to be fitted, and aiming to minimize the residual between the fitting function and the shape information, a genetic algorithm is used to fit the shape information of the Fermi edge region, and the value of the Fermi level of the sample under test is determined based on the fitting result, including: The Fermi level parameters in the convolution model are used as the variables to be optimized in the genetic algorithm, and a fitness function is constructed with the goal of minimizing the residual between the fitting function and the shape information. Based on the fitness function, the genetic algorithm is driven to iteratively optimize the Fermi level parameters; Under the condition that the preset convergence condition is met, the optimal Fermi level parameter is output, and the optimal Fermi level parameter is determined as the value of the Fermi level of the sample to be tested.

[0007] Optionally, the sample to be tested is irradiated with a photon beam of the target wavelength, and the ultraviolet photoelectron spectrum of the sample to be tested is constructed based on the distribution of photoelectrons with different kinetic energies excited by the sample, including: The sample to be tested is irradiated with a photon beam of the target wavelength to obtain photoelectrons with different kinetic energies excited by the sample to be tested. Using a hemispherical energy analyzer, photoelectrons with different kinetic energies are screened from the photoelectrons with different kinetic energies excited by the sample under test. The signals of photoelectrons with different kinetic energies are amplified by a microchannel plate, and the corresponding light emission images are obtained on a fluorescent screen. The light emission images include pixels at multiple different positions. The luminescent image is captured using an industrial camera; All the light-emitting images captured by the industrial camera are superimposed, and the pixels with the same electron kinetic energy are integrated to obtain the ultraviolet photoelectron spectrum of the sample under test.

[0008] Optionally, before irradiating the sample to be tested with photon beams of different wavelengths, the method further includes: A reference sample is irradiated with an electron beam of target energy emitted by an electron gun to obtain photoelectrons excited in the reference sample; The hemispherical energy analyzer is used to filter out photoelectrons with different kinetic energies. The microchannel plate amplifies the signals of photoelectrons with different kinetic energies and obtains corresponding luminescent images on the fluorescent screen. The luminescent image is captured using an industrial camera; The energy calibration coefficient is calculated based on the correspondence between the pixel position and photoelectron kinetic energy of each pixel in the light emission imaging. The ultraviolet photoelectron spectrum of the sample under test is obtained by superimposing all the luminescent images captured by the industrial camera and integrating the pixels with the same electron kinetic energy, including: Based on the energy calibration coefficient, the pixel position of each pixel in the light emission imaging is converted into the corresponding photoelectron kinetic energy; The photoelectron kinetic energies corresponding to the pixel positions of each pixel in the light emission imaging are superimposed, and the data points with the same photoelectron kinetic energy are integrated to obtain the ultraviolet photoelectron spectrum of the sample under test.

[0009] Optionally, the Fermi edge region is determined from the ultraviolet photoelectron spectrum of the sample to be tested, and the shape information of the Fermi edge region is extracted, including: Calculate the first derivative of the ultraviolet photoelectron spectrum, and determine the position of the Fermi edge based on the first derivative; Centered on the position of the Fermi edge, a range of the preset width is selected as the Fermi edge region; Based on the maximum and minimum values ​​of photoelectron intensity within the Fermi edge region, the photoelectron intensity within the Fermi edge region is mapped to a standard intensity range to obtain the shape information.

[0010] Optionally, based on the fitness function, the genetic algorithm is driven to iteratively optimize the Fermi level parameters, including: Initialize a population containing multiple individuals, each individual in the population representing a candidate value for a Fermi level parameter; The fitness of each individual is calculated based on the fitness function, where the fitness is the sum of squared residuals between the predicted values ​​of the convolutional model and the shape information. Individuals are selected using a roulette wheel selection method based on their fitness to construct a mating pool; For individuals in the mating pool, a single-point crossover operation is performed according to a preset crossover probability; and for individuals after the single-point crossover operation, a mutation operation is performed according to a preset mutation probability. The N individuals with the highest fitness in the current population are retained in the next generation population, where N is an integer greater than 1; Repeat the above steps until the preset iteration conditions are met.

[0011] Optionally, the sample to be tested is irradiated with a photon beam of the target wavelength, including: Metal films with a purity higher than the preset value were used as the test samples; The surface of the sample to be tested is etched using an argon ion beam to remove the oxide layer and contaminants from the surface of the sample to be tested. The ultraviolet spectrum of the continuous band generated by the deuterium lamp is processed using a vacuum ultraviolet monochromator to obtain a photon beam of the target wavelength. In a vacuum sample chamber, the sample to be tested is irradiated with a photon beam of the target wavelength.

[0012] In a second aspect, embodiments of the present invention provide a Fermi level measurement system based on ultraviolet photoelectron spectroscopy, applied to the steps of the method described in the first aspect, including a light source module and an energy spectrum construction module; The light source module uses a photon beam of the target wavelength to irradiate the sample under test, and the photon beam belongs to the vacuum ultraviolet band; The energy spectrum construction module constructs the ultraviolet photoelectron energy spectrum of the sample under test based on the distribution of photoelectrons with different kinetic energies excited by the sample under test. The photon beam belongs to the vacuum ultraviolet band, and the horizontal axis of the ultraviolet photoelectron energy spectrum is the photoelectron kinetic energy, and the vertical axis is the photoelectron intensity. The Fermi edge region is determined from the ultraviolet photoelectron spectrum of the sample to be tested, and the shape information of the Fermi edge region is extracted. The Fermi edge region is a preset width range centered on the position of the Fermi edge. Construct a convolutional model to describe thermal broadening and instrument broadening; Based on a pre-built convolutional model that uses the Fermi level of the sample under test as the fitting parameter, the shape information of the Fermi edge region is fitted, and the value of the Fermi level of the sample under test is determined according to the fitting result; the convolutional model is used to describe thermal broadening and instrument broadening, and the influence of instrument broadening is subtracted by introducing the instrument broadening parameter.

[0013] Optionally, the light source module includes a deuterium lamp and a vacuum ultraviolet monochromator; The deuterium lamp is used to generate a continuous-wavelength ultraviolet spectrum; The vacuum ultraviolet monochromator is used to process the continuous-wavelength ultraviolet spectrum generated by the deuterium lamp to obtain a photon beam of the target wavelength. The energy spectrum construction module includes a hemispherical energy analyzer, a microchannel plate, a fluorescent screen, and an industrial camera; The hemispherical energy analyzer is used to filter out photoelectrons with different kinetic energies from the photoelectrons with different kinetic energies excited by the sample under test; The microchannel plate is used to amplify the signals of photoelectrons with different kinetic energies and obtain corresponding light emission images on a fluorescent screen. The light emission images include pixels at multiple different positions. The industrial camera is used to capture the luminescent image frame by frame according to a preset scanning step size; All the light-emitting images captured by the industrial camera are superimposed, and the pixels with the same electron kinetic energy are integrated to obtain the ultraviolet photoelectron spectrum of the sample under test.

[0014] The technical solutions provided by the embodiments of the present invention bring at least the following beneficial effects: This invention, by constructing a convolutional model of thermal broadening and instrument broadening, effectively distinguishes between electronic structure broadening caused by the material itself and broadening caused by instrument resolution. This allows the shape information of the Fermi edge region to more accurately reflect the actual electronic structure of the material, without being limited by instrument resolution. This invention uses a convolutional model to fit the shape of the Fermi edge region, effectively avoiding the measurement errors caused by the difficulty in accurately locating the Fermi level position and the failure to consider the influence of instrument resolution in related technologies. The fitting method of this invention has a high degree of automation, can quickly process large amounts of sample data, and reduces errors from human judgment, making it particularly suitable for high-throughput testing and online measurements. Attached Figure Description

[0015] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments of the present invention will be briefly introduced below.

[0016] Figure 1This is a schematic diagram of the steps of a method for measuring the Fermi level of a material based on ultraviolet photoelectron spectroscopy, provided in an embodiment of the present invention. Figure 2 This is a schematic diagram illustrating the fitting effect of ultraviolet photoelectron spectroscopy in Fermi level determination in one embodiment of the present invention; Figure 3 This is a schematic diagram of the genetic algorithm fitting iteration process in one embodiment of the present invention; Figure 4 This is a schematic diagram of the overall Fermi level determination method in one embodiment of the present invention; Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] Commonly used Fermi edge localization methods include the "20%~80% intensity method," which estimates the Fermi level position by measuring the midpoint between the 20% and 80% energies corresponding to the intensity decrease region in the photoelectron spectrum. However, this method struggles to accurately distinguish between electronic structure broadening caused by the material itself and broadening caused by instrument resolution. Especially in high-resolution measurements, the error and broadening problems remain significant due to the inability to completely eliminate instrument energy resolution, leading to reduced accuracy and repeatability of spectral analysis results and substantial errors. To address this issue, the core concept of this invention is to irradiate the sample under test with a photon beam in the vacuum ultraviolet band, exciting photoelectrons with different kinetic energies to construct an ultraviolet photoelectron spectrum. The Fermi edge region is extracted from the constructed ultraviolet photoelectron spectrum, and its shape information is obtained based on the photoelectron intensity information of the Fermi edge region. A convolution model is constructed to describe thermal broadening and instrument broadening, combining the Fermi-Dirac distribution function with a Gaussian function to describe the material's thermal broadening effect and the instrument resolution effect. A genetic algorithm is used to fit the shape information of the Fermi edge region, and the Fermi level of the sample under test is finally determined based on the fitting results. It is evident that this invention can separate the broadening effect caused by materials and instruments, thus improving the measurement accuracy of the Fermi level.

[0019] Figure 1 This is a schematic diagram illustrating the steps for measuring the Fermi level of a material based on ultraviolet photoelectron spectroscopy, as provided in one embodiment of the present invention. Figure 1 As shown, it includes: Step S11: Irradiate the sample to be tested with a photon beam of the target wavelength. Based on the distribution of photoelectrons with different kinetic energies excited by the sample to be tested, construct the ultraviolet photoelectron spectrum of the sample to be tested. The photon beam belongs to the vacuum ultraviolet band. The horizontal axis of the ultraviolet photoelectron spectrum is the photoelectron kinetic energy, and the vertical axis is the photoelectron intensity.

[0020] The sample under test is irradiated with a photon beam of the target wavelength, and an ultraviolet photoelectron spectrum is constructed based on the distribution of photoelectrons excited in the sample. A photon beam refers to electromagnetic radiation with a specific wavelength, belonging to the vacuum ultraviolet band. The photon beam interacts with the sample under test, exciting electrons in the sample and causing them to escape from the surface, thus generating photoelectrons.

[0021] During photoelectron emission, each photoelectron possesses a different kinetic energy due to the varying energy it absorbs when interacting with photons. The distribution of kinetic energy can reveal characteristics of the electronic structure within a sample. Therefore, the kinetic energy and corresponding intensity of photoelectrons are two important dimensions of the photoelectron spectrum, represented as the abscissa and ordinate of the ultraviolet photoelectron spectrum, respectively. Specifically, the ultraviolet photoelectron spectrum is obtained by measuring the kinetic energy distribution of photoelectrons emitted from the sample. Photoelectrons are excited from the sample by irradiating its surface with a photon beam from the vacuum ultraviolet region. By measuring the kinetic energy of the photoelectrons and displaying it in the ultraviolet photoelectron spectrum, the abscissa represents the kinetic energy of the photoelectrons, and the ordinate represents the corresponding photoelectron intensity, i.e., the number of photoelectrons detected at a given kinetic energy.

[0022] In an optional implementation, step S11 specifically includes steps S111 to S113: Step S111: Use a metal film with a purity higher than the preset value as the sample to be tested.

[0023] A high-purity (preferably ≥99.99%) metal thin film is selected as the sample to be tested. For example, a gold (Au) thin film can be used, with a thickness preferably between 20 nm and 100 nm. The sample to be tested has a smooth surface and is free of structural defects to ensure the representativeness of the photoelectron emission signal.

[0024] Step S112: Use an argon ion beam to etch the surface of the sample to be tested in order to remove the oxide layer and contaminants on the surface of the sample to be tested.

[0025] The sample surface was etched using an argon ion beam. Specifically, an argon ion beam with an energy of 2keV was used, and the etching duration was 1 hour. The etching process thoroughly removed the surface oxide layer and organic contaminants, bringing the sample surface to an atomically clean state.

[0026] Step S113: Using a vacuum ultraviolet monochromator, the ultraviolet spectrum of the continuous band generated by the deuterium lamp is processed to obtain the photon beam of the target wavelength.

[0027] Turn on the deuterium lamp and preheat for 20 minutes to stabilize the light source output. Spectroscopically process the continuous ultraviolet spectrum generated by the deuterium lamp using a vacuum ultraviolet monochromator to select the target wavelength (example range: 115nm–400nm). Adjust the entrance and exit slits of the vacuum ultraviolet monochromator (preferably 0.5mm wide) to improve wavelength resolution and obtain a high monochromatic vacuum ultraviolet photon beam.

[0028] Step S114: In a sample chamber in a vacuum environment, the sample to be tested is irradiated with a photon beam of the target wavelength.

[0029] The cleaned sample to be tested is placed in an ultra-high vacuum sample chamber (vacuum level better than 5 × 10⁻⁶). -8 Pa), the target wavelength photon beam prepared in step S113 is used to vertically irradiate the sample surface.

[0030] In an optional implementation, step S11 further includes steps S115 to S119: Step S115: Irradiate the sample to be tested with a photon beam of the target wavelength to obtain photoelectrons with different kinetic energies excited by the sample to be tested.

[0031] A prepared beam of photons at the target wavelength is irradiated onto the surface of the sample under test. When the photon beam interacts with the sample surface, it transfers energy to electrons within the sample. These electrons are excited, and after gaining sufficient energy, they detach from the sample surface, forming photoelectrons. As mentioned earlier, since each photoelectron gains different amounts of energy when absorbing photons, their kinetic energies will also differ.

[0032] Step S116: Using a hemispherical energy analyzer, photoelectrons with different kinetic energies are screened out from the photoelectrons with different kinetic energies excited by the sample to be tested.

[0033] A hemispherical energy analyzer is used to screen photoelectrons emitted from the surface of the sample. The hemispherical energy analyzer is a common instrument for electron energy analysis. Its working principle is to separate the electron beam according to its kinetic energy using a combination of electric and magnetic fields. It consists of two hemispherical electrodes. After the photoelectron beam enters the hemispherical energy analyzer, the electric field between the electrodes separates the electrons according to their energy. By adjusting the strength of the electric field, photoelectrons with different kinetic energies can be screened. The hemispherical energy analyzer can measure the kinetic energy of photoelectrons and select photoelectrons within a specific kinetic energy range, which helps in the subsequent construction of a complete ultraviolet photoelectron spectrum, revealing the energy distribution of electrons in the sample.

[0034] Step S117: The signals of photoelectrons with different kinetic energies are amplified through a microchannel plate, and corresponding light emission images are obtained on a fluorescent screen. The light emission images include pixels at multiple different positions.

[0035] The signals of photoelectrons with different kinetic energies, filtered by a hemispherical energy analyzer, are amplified by a microchannel plate. A microchannel plate is a device composed of a series of tiny channels. Its working principle is that when photoelectrons flow through these channels, they excite the internal material to release secondary electrons, thereby amplifying the original photoelectron signal. This process significantly increases the signal intensity, allowing even weak photoelectron signals to be further detected and analyzed. The amplified photoelectron signal is displayed on a fluorescent screen as a light emission image. This light emission image on the fluorescent screen is generated by the light emission produced when photoelectrons collide with fluorescent material. Each luminous point on the screen corresponds to the detection signal of a photoelectron. Each luminous point represents an electron signal at a different location.

[0036] Step S118: Take a picture of the light emission using an industrial camera.

[0037] An industrial camera is used to capture images of the light emitted on a fluorescent screen. An industrial camera is a high-resolution, high-stability imaging device capable of accurately capturing the position and brightness of each light-emitting point on the screen. Each frame captured by the industrial camera represents a light emission image with different gating energies (kinetic energies), containing the brightness and position of each pixel, further improving measurement accuracy and data integrity.

[0038] Step S119: Superimpose all the light-emitting images captured by the industrial camera and integrate the pixels with the same electron kinetic energy to obtain the ultraviolet photoelectron spectrum of the sample to be tested.

[0039] All the luminescence imaging images captured by industrial cameras are superimposed to combine information from multiple images, obtaining more comprehensive signal data and ensuring no details are missed. After superimposing the images, the number of photoelectrons at each kinetic energy value is obtained by integrating pixels with the same photoelectron kinetic energy, i.e., the photoelectron intensity. The final ultraviolet photoelectron spectrum reflects the energy distribution of photoelectrons in the sample under test.

[0040] In an alternative embodiment, before irradiating the sample to be tested with photon beams of different wavelengths, the method further includes: Step S21: Irradiate the reference sample with an electron beam of target energy emitted by an electron gun to obtain photoelectrons excited by the reference sample.

[0041] An electron gun is used to emit an electron beam with a target energy to irradiate a reference sample. An electron gun is a device used to generate a high-energy electron beam. Its principle is to accelerate electrons to the target energy using an accelerating electric field, and then focus the electron beam onto the sample surface. The target energy is preset, and different values ​​can be selected according to experimental requirements. When the electron beam interacts with the surface of the reference sample, the electrons excite electrons in the reference sample, causing some of these electrons to gain sufficient energy and escape from the surface, forming photoelectrons. Therefore, the excited photoelectrons from the reference sample can provide a standard signal for calibrating the ultraviolet photoelectron spectrum of the sample under test.

[0042] Step S22: The photoelectrons with different kinetic energies are screened out using the hemispherical energy analyzer.

[0043] Step S23: The signals of photoelectrons with different kinetic energies are amplified through the microchannel plate, and corresponding luminescent images are obtained on the fluorescent screen.

[0044] Step S24: Take a picture of the light emission using an industrial camera.

[0045] The specific implementation methods of steps S22 to S24 are the same as or similar to those of steps S116 to S118, and will not be repeated here.

[0046] Step S25: Calculate the energy calibration coefficient based on the correspondence between the pixel position and photoelectron kinetic energy of each pixel in the light emission imaging.

[0047] The spatial coordinates of each pixel are extracted from the luminescent imaging data captured by an industrial camera. The spatial coordinates of each pixel represent its position on the fluorescent screen.

[0048] The photoelectron kinetic energy of each pixel is known. Using the position of each pixel and its corresponding photoelectron kinetic energy, an energy calibration coefficient is calculated. In this embodiment, the energy calibration coefficient is a parameter describing the mathematical relationship between pixel position and photoelectron kinetic energy, used to convert image coordinates into physical energy values. It can be understood that the energy calibration coefficient is an adjustment factor.

[0049] Step S119 specifically includes steps S1191 to S1192: Step S1191: Based on the energy calibration coefficient, convert the pixel position of each pixel in the light emission imaging into the corresponding photoelectron kinetic energy.

[0050] Using energy calibration coefficients obtained beforehand through reference sample calibration, the spatial coordinates of each pixel in the luminescent image captured by the industrial camera are converted into the corresponding photoelectron kinetic energy value. Specifically, based on the two-dimensional coordinates of the pixel on the fluorescent screen (such as row and column numbers), combined with the mapping relationship between pixel position and photoelectron kinetic energy defined by the energy calibration coefficients, mathematical calculations are used to convert the position information of each pixel into a physically meaningful photoelectron kinetic energy value, that is, to achieve a quantitative conversion from image spatial coordinates to energy physical quantities.

[0051] Step S1192: The photoelectron kinetic energies corresponding to the pixel positions of each pixel in the light emission imaging are superimposed, and the data points with the same photoelectron kinetic energy are integrated to obtain the ultraviolet photoelectron spectrum of the sample to be tested.

[0052] All converted photoelectron kinetic energy data are superimposed and integrated. Then, the intensity of data points with the same photoelectron kinetic energy value in the superimposed data is integrated, and the photoelectron signal intensity corresponding to all pixels with the same kinetic energy value is statistically analyzed. For each data point with photoelectron kinetic energy, the total photoelectron intensity of all pixels with the same kinetic energy value is accumulated. Traversing the entire kinetic energy range, a relationship curve is plotted with photoelectron kinetic energy as the x-axis and the integrated photoelectron intensity as the y-axis to obtain the ultraviolet photoelectron spectrum of the sample under test.

[0053] By using the energy calibration coefficient, the spatial position of each pixel (i.e., its position on the fluorescent screen) can be mapped to the corresponding photoelectron kinetic energy value, ensuring that each data point in the final energy spectrum corresponds to the actual photoelectron kinetic energy, thus avoiding errors caused by inaccurate mapping between spatial position and energy.

[0054] Step S12: Determine the Fermi edge region from the ultraviolet photoelectron spectrum of the sample to be tested, and extract the shape information of the Fermi edge region, wherein the Fermi edge region is a preset width range centered on the position of the Fermi edge.

[0055] The Fermi edge region is extracted from the ultraviolet photoelectron spectrum of the sample under test, and its shape information is obtained. The Fermi edge refers to the electron energy range near the Fermi level in the ultraviolet photoelectron spectrum; typically, at zero temperature, the Fermi level is at the highest point of the electron spectrum. The electron intensity information near the Fermi level can provide crucial information about the electronic structure and surface state of the sample under test. First, the Fermi edge region in the ultraviolet photoelectron spectrum is identified by determining its location. Next, a preset width range centered on the Fermi edge is selected as the Fermi edge region. Finally, the photoelectron intensity within this Fermi edge region is processed and mapped to a standard intensity range to extract the shape information of the region.

[0056] In one optional implementation, step S12 specifically includes steps S121 to S123: Step S121: Calculate the first derivative of the ultraviolet photoelectron spectrum and determine the position of the Fermi edge based on the first derivative.

[0057] The Fermi edge in ultraviolet (UV) photoelectron spectroscopy typically appears as a region of abrupt or rapid change. To accurately pinpoint this change, the location of the abrupt change can be identified by calculating the first derivative of the UV photoelectron spectrum. The first derivative reflects the rate of intensity change in the UV photoelectron spectrum and can clearly indicate the region of fastest intensity change, corresponding to the location of the Fermi edge.

[0058] Step S122: Using the position of the Fermi edge as the center, select an interval of the preset width range as the Fermi edge region.

[0059] A preset width range centered on the Fermi edge is selected as the Fermi edge region. The selection of the preset width range is based on experience or theoretical models, aiming to ensure that all important information near the Fermi edge is covered. For example, a region of ±1 eV centered on the Fermi edge can be selected. The Fermi edge region covers the electron energy range near the Fermi edge location, effectively capturing the characteristics of the Fermi edge and avoiding the omission of key information that may affect subsequent analysis.

[0060] Step S123: Based on the maximum and minimum values ​​of photoelectron intensity within the Fermi edge region, map the photoelectron intensity within the Fermi edge region to a standard intensity range to obtain the shape information.

[0061] Maximum photoelectron intensity ( The photoelectron intensity is the highest intensity value among all data points within the Fermi edge region, corresponding to the saturation signal of electronically occupied states below the Fermi level. The minimum photoelectron intensity ( The value is the lowest intensity among all data points within the Fermi edge region, corresponding to the background noise of unoccupied states above the Fermi level. The standard intensity range is a normalized intensity range fixed at [0,1], where 0 represents... ,1 represents The normalized spectral curve retains key features such as the slope and broadening of the Fermi edge, while eliminating intensity deviations introduced by instrument gain or light source fluctuations.

[0062] Searching for the global extremum within the Fermi edge region:

[0063]

[0064] The position of the first derivative peak in step S121 is determined (e.g., for gold samples). ).

[0065] The original intensity of each energy point E within the region Normalization is performed to obtain shape information. That is, the normalized ultraviolet photoelectron spectrum:

[0066] This invention characterizes the formation mechanism of the Fermi edge in ultraviolet photoelectron spectroscopy by establishing a physics-driven convolution model. The convolution model simultaneously considers the intrinsic electron thermal distribution of the material (Fermi-Dirac distribution) and the broadening introduced by instrument resolution (Gaussian function). Its convolution result matches the measured ultraviolet photoelectron spectrum, thereby achieving high-precision inversion of the Fermi level. The convolution model constructed in this invention overcomes the subjective errors of traditional manual interpretation methods, providing a theoretical basis for automated fitting.

[0067] Figure 2 This is a schematic diagram illustrating the fitting effect of ultraviolet photoelectron spectroscopy in Fermi level determination in one embodiment of the present invention. Figure 2 Plotting photoelectron kinetic energy (eV) on the horizontal axis and normalized intensity on the vertical axis, the ultraviolet photoelectron spectrum of a standard gold (Au) sample as the test sample is displayed under specific testing conditions. The solid line in the figure represents the measured photoelectron energy distribution data. These data points cover the Fermi level (…). The region near 300K temperature and 7.7eV ultraviolet light represents the area under these conditions. hν Photoelectron kinetic energy distribution on the surface of a gold sample under excitation of 7.7 eV. The positions of the circles indicate the intensity distribution from the high-energy region ( The value of ) is approximately constant, and it rapidly decreases to the low-energy region ( The near-zero value of the Fermi-Dirac distribution forms a typical steep drop at the Fermi edge. However, the measured points do not exhibit an ideal step, but rather a smooth transition, reflecting the combined effects of electron thermal motion (Fermi-Dirac distribution) and instrument noise. The theoretical fitting curve (dashed line) represents the output of the theoretical convolution model, i.e., the convolution result of the Fermi-Dirac distribution function and the Gaussian function. This curve closely matches the experimental data points, with only a slight deviation near the Fermi edge (the residual is extremely small). The Fermi-Dirac distribution part describes 300K ( T Statistical thermal distribution of electrons at 300K. Fermi-Dirac distribution (partial). The smooth slope (rather than a vertical drop) reflects temperature-induced broadening. The Gaussian function portion is used to simulate instrument resolution broadening. Figure 2 It can be seen that the present invention can achieve highly reliable Fermi level determination under standard industrial conditions.

[0068] In one alternative implementation, the convolutional model is constructed according to the following steps: Step S31: Construct the Fermi-Dirac distribution function, which is used to describe the thermal broadening effect of photoelectrons in the material of the sample to be tested; the Fermi level parameters contained in the Fermi-Dirac distribution function are used as unknown parameters to be fitted.

[0069] The Fermi-Dirac distribution function is constructed to describe the thermal broadening effect of photoelectrons in the material of the sample under test. It reflects the occupation of electrons under thermal equilibrium, especially at low temperatures, where the energy distribution of electrons follows this distribution law.

[0070] Specifically, thermal broadening is caused by the temperature of the material. Temperature changes lead to an expansion of the kinetic energy of electrons near the Fermi level, manifested as a wider distribution range of photoelectrons in the energy spectrum. The Fermi-Dirac distribution function can accurately describe the influence of thermal effects on the photoelectron spectrum based on the temperature information of the sample. Ideally, all states below the Fermi level are occupied, while states above the Fermi level are empty. In actual measurements, due to finite temperature, the Fermi edge is no longer an ideal vertical step, but rather a smooth transition, the degree of which is determined by the Fermi-Dirac distribution. The parameters of thermal broadening can be obtained through the Fermi-Dirac distribution function and incorporated into subsequent convolutional models.

[0071] The Fermi-Dirac distribution function has the following functional form:

[0072] In the formula, It is the kinetic energy of electrons; The Fermi level to be fitted; Boltzmann constant ( eV / K); The experimental temperature can be obtained by monitoring the sample stage in real time using a temperature sensor.

[0073] Step S32: Based on the spectral broadening corresponding to the pre-measured instrument response, a Gaussian function is constructed. The Gaussian function is used to describe the energy broadening effect introduced by the resolution of the instrument. The instrument broadening parameter used in the Gaussian function is a pre-calibrated known value.

[0074] Based on the spectral broadening corresponding to the instrument response, a Gaussian function is constructed to describe the energy broadening effect caused by instrument resolution. In actual measurements, due to the inherent resolution limitations of the instrument, the measured photoelectron spectrum exhibits a certain degree of broadening, which typically displays a Gaussian shape. To simulate this effect, a Gaussian function is constructed; the Gaussian distribution is a mathematical function widely used to describe random and measurement errors. The standard form of the Gaussian function describes the distribution of photoelectron energy, and its width is proportional to the instrument resolution. By measuring the actual instrument response (using known spectral lines), the broadening information introduced by the instrument can be obtained, and this effect can be quantified using the Gaussian function.

[0075] The Gaussian function has the following functional form:

[0076] In the formula, The spectral broadening corresponding to the pre-measured instrument response is also known as the instrument broadening standard deviation. The half-width at half-maximum (WHM) of the Gaussian function is known, and the WHM and standard deviation are related. The relationship is:

[0077] Step S33: Perform a convolution operation between the Fermi-Dirac distribution function and the Gaussian function to obtain the convolution model, which includes the Fermi level parameters to be fitted.

[0078] By convolving the previously constructed Fermi-Dirac distribution function with a Gaussian function, a comprehensive convolution model is obtained. Convolution is a common mathematical method for combining two signals or functions. This operation integrates thermal broadening and instrument broadening effects, resulting in a comprehensive energy spectrum broadening model. Through convolution, the effects of thermal and instrument effects are combined, producing a new function that represents the final broadening of the photoelectron spectrum under these two effects. The convolution model accurately describes the photoelectron spectrum of the sample under test, taking into account the combined effects of temperature and instrument resolution.

[0079] Fermi-Dirac distribution With Gaussian expansion Convolution is performed to obtain the convolution model. :

[0080] In the formula, E F The parameters of the Fermi level to be fitted are denoted as . and As a known constant input; The integral variable represents the initial kinetic energy of the photoelectrons before they broaden.

[0081] Step S13: Based on a pre-constructed convolutional model using the Fermi level of the sample to be tested as the fitting parameter, with the goal of minimizing the residual between the fitting function and the shape information, a genetic algorithm is used to fit the shape information of the Fermi edge region, and the value of the Fermi level of the sample to be tested is determined based on the fitting result.

[0082] Understandably, this invention treats the instrument as known (through prior calibration) and the sample to be tested as unknown, aiming to solve for the Fermi level of the material. That is, the ultraviolet photoelectron spectrometer is considered a measurement tool with known characteristics, and its instrument broadening parameters corresponding to its energy resolution are obtained through pre-calibration. Based on this, a convolutional model coupling the intrinsic thermal broadening of the material and the instrument broadening is constructed. In the convolutional model, the instrument broadening parameter is used as a known constant input to subtract the interference of the instrument on the measurement results; while the Fermi level of the sample to be tested is used as the only unknown parameter to be fitted, contained in the Fermi-Dirac distribution function describing the electron thermal distribution. By acquiring the ultraviolet photoelectron spectrum of the sample to be tested, extracting the shape information of the Fermi edge region, and using an optimization algorithm to fit the convolutional model, the true Fermi level value of the material to be tested can be directly derived. This invention, by subtracting the influence of the instrument as a fixed background, can effectively eliminate the broadening effect of instrument resolution on the measurement results, thereby significantly improving the accuracy of the determination of the material's Fermi level.

[0083] Because the spectral shape of the Fermi edge region is extremely sensitive to the location of the Fermi level, the fitted residual function often exhibits multiple local minima in the parameter space to be optimized. Traditional methods relying on gradients or iteration step sizes are highly dependent on initial guesses and are prone to getting trapped in local optima, leading to deviations in the determination of the Fermi level. Therefore, in one embodiment of this invention, a genetic algorithm is proposed for global fitting. The genetic algorithm, by simulating the selection, crossover, and mutation processes in nature, maintains a set of candidate solutions (population) in the parameter space and performs parallel searches, effectively escaping local minima traps and approaching the global optimum without relying on external initial values. Using the sum of squared residuals between the convolutional model's predicted values ​​and the measured Fermi edge shape information as the fitness function, and driving the genetic algorithm iterative optimization with the goal of minimizing the residuals, it can automatically converge to the optimal Fermi level parameters.

[0084] Based on the previously constructed convolutional model, the shape information of the Fermi edge region of the sample is fitted to determine the sample's Fermi level. First, a genetic algorithm is used to optimize and adjust the Fermi level parameters in the convolutional model. By minimizing the residual between the fitted function and the experimental data, an optimal fitting result is obtained. Finally, based on the optimal Fermi level parameters in the fitting result, the Fermi level value of the sample is determined.

[0085] In an optional implementation, step S13 specifically includes steps S131 to S133: Step S131: The Fermi level parameters in the convolution model are used as the variables to be optimized in the genetic algorithm, and a fitness function is constructed with the goal of minimizing the residual between the fitting function and the shape information.

[0086] To establish the mapping relationship between the genetic algorithm and the physical convolutional model, the problem of solving the Fermi level is transformed into a definite optimization problem. First, the variables to be optimized and their boundaries are determined: the Fermi level in the convolutional model is used as the sole decision variable in the genetic algorithm, and its search interval is set according to the material properties of the sample. In the convolutional model, the instrument broadening parameter and experimental temperature are pre-calibrated or measured known constants and do not participate in the optimization search.

[0087] After defining the variable space, a fitness function is constructed to evaluate the excellence of an individual. The core objective of this invention is to minimize the residual between the predicted curve of the convolutional model and the Fermi edge shape information extracted experimentally. Within the Fermi edge region, for each energy point... The predicted value of the convolutional model is The normalized shape information extracted in the experiment is Define the sum of squared residuals as the optimization objective function:

[0088] The summation sign applies to all energy points within the Fermi edge region. A smaller SSR indicates a higher degree of agreement between the theoretical curve and the measured data for the corresponding candidate Fermi level.

[0089] Step S132: Based on the fitness function, drive the genetic algorithm to iteratively optimize the Fermi level parameters.

[0090] A genetic algorithm is used to perform global optimization in the search space of Fermi level parameters. The genetic algorithm simulates the selection, crossover, and mutation mechanisms in biological evolution, performing a parallel search in the parameter space on a population basis. In each generation, the fitness function is used to evaluate the quality of individuals, and the algorithm gradually approaches the global optimum through a process of natural selection.

[0091] In an optional implementation, step S132 specifically includes steps S1321 to S1326: Step S1321: Initialize a population containing multiple individuals, where each individual in the population represents a candidate value for a Fermi level parameter.

[0092] Figure 3 This is a schematic diagram of the genetic algorithm fitting iteration process in one embodiment of the present invention. Please refer to [link / reference]. Figure 3The initial population is constructed by first determining a reasonable range of values ​​for the Fermi level parameters (e.g., the target energy range where the Fermi level of a metallic material lies). Based on the target energy range, a predefined number of candidate solutions (i.e., individuals) are randomly generated, each representing a possible value of the Fermi level. The generation of initial solutions follows a uniform distribution principle to ensure that the solution space is fully covered and to avoid local optima traps caused by the clustering of initial solutions. The population size is usually set according to the problem complexity; too small a population will reduce search efficiency, while too large a population will increase computational burden. The initialization process considers the parameter encoding method. If floating-point direct encoding is used, each individual is a single real value; if binary encoding is used, the gene string length is set to match the parameter precision requirements. The final initial population should have sufficient diversity to provide ample evolutionary potential for genetic operations.

[0093] Step S1322: Calculate the fitness of each individual according to the fitness function, where the fitness is the sum of squared residuals between the predicted value of the convolutional model and the shape information.

[0094] For each individual in the current population, the candidate Fermi level value it represents is denoted as... The candidate Fermi level values ​​are substituted into the mapping relationship established in step S131, i.e., into the pre-constructed convolution model, where the instrument broadening and temperature are known constants, and the Fermi level parameters to be fitted are... Take the candidate value of the current individual Generate the theoretical Fermi edge shape curve corresponding to the candidate value, and extract the experimentally normalized Fermi edge shape information obtained in step S12. Within the Fermi edge region, for each energy point Calculate the intensity difference between the theoretical curve and the experimental data point by point, and apply the fitness function defined in step S131, i.e., the formula for the sum of squared residuals (SSR):

[0095] The sum of the squared differences across all data points yields the residual sum of squares (SSR) for that individual. This SSR is the fitness quantification index for that individual. A smaller SSR indicates a higher degree of agreement between the theoretical prediction and experimental data for the candidate Fermi level, signifying stronger fitness and a greater probability of preservation and propagation in subsequent evolutionary processes.

[0096] It should be noted that the fitness function optimizes by minimizing the deviation between prediction and actual results. Its mathematical form is concise and computationally efficient, making it easy to quickly evaluate hundreds or thousands of candidate solutions during large-scale iterations of genetic algorithms.

[0097] Step S1323: Based on the fitness of each individual, individuals are selected using roulette wheel selection to construct a mating pool.

[0098] The selection process simulates the "survival of the fittest" principle, selecting high-quality individuals to participate in reproduction. A roulette wheel selection method is used to achieve probabilistic selection. First, the sum of squared residuals (SSR) of all individuals is converted into a fitness value. Since a smaller SSR indicates better performance, it is transformed into a value proportional to fitness through a reciprocal or linear transformation.

[0099] The fitness of each individual is calculated as a proportion of the total fitness; this proportion determines the sector area it occupies on the virtual roulette wheel. Higher fitness results in a larger sector area and a higher probability of selection. Random numbers are generated to simulate roulette wheel rotation, and individuals are selected based on the sector area where the random number lands. This process is repeated until the mating pool reaches a preset size. This ensures that high-fitness individuals have a higher chance of being retained, while low-fitness individuals still have a chance of being selected (avoiding premature convergence). Selection pressure can be dynamically controlled by adjusting the fitness scaling ratio to balance the algorithm's exploration and development capabilities.

[0100] Step S1324: Perform a single-point crossover operation on individuals in the mating pool according to a preset crossover probability, and perform a mutation operation on individuals after the single-point crossover operation according to a preset mutation probability.

[0101] Crossover and mutation operations simulate biological genetic variation to generate a new generation of solutions. Single-point crossover (recombination) involves randomly pairing individuals (parents) from a mating pool and determining whether to perform crossover based on a preset probability. If performed, a breakpoint is randomly selected in the solution representation sequence, and gene segments after that breakpoint are exchanged between the two parent individuals, generating two new individuals (offspring). For example, gene positions are exchanged in binary encoding, while arithmetic crossover can be used in floating-point encoding.

[0102] The mutation operation involves randomly modifying some gene values ​​of the offspring individuals after crossover according to a preset mutation probability. Mutation methods include small perturbations (adding Gaussian noise to floating-point encoding) and bit flips (binary encoding). The mutation intensity is controlled within a reasonable range; too strong a mutation will destroy high-quality solutions, while too weak a mutation will reduce population diversity.

[0103] Crossover promotes high-quality gene combinations, while mutation introduces new genes to explore unknown regions. Together, they drive the solution space towards better regions while maintaining population diversity and avoiding local optima.

[0104] Step S1325: The N individuals with the highest fitness in the current population are retained in the next generation population, where N is an integer greater than 1.

[0105] To ensure algorithm stability, an elite retention strategy is introduced, identifying the top N individuals with the highest fitness in the current population. These elite individuals are then directly copied to the next generation of the population without crossover or mutation. The biological significance of elite retention lies in protecting the discovered optimal solution from being destroyed by random operations, ensuring the convergence of the algorithm. Its core idea is to prevent the loss of high-quality genes due to selection randomness and to accelerate the convergence process, especially when the fitness terrain is complex. This provides an anchor point for subsequent searches, guiding the population to evolve towards the region where the elite solution is located.

[0106] Step S1326: Repeat the above steps until the preset iteration conditions are met.

[0107] Merge elite individuals with newly generated offspring to form a new generation of complete population. Check if preset termination conditions are met, including: the fitness SSR of the current best individual is lower than the preset accuracy requirement, or the number of iterations has reached the maximum allowed number of iterations. If the iteration conditions are not met, return to step S1312 for next-generation evaluation and evolution; otherwise, exit the loop and output the Fermi level value corresponding to the current best individual.

[0108] In other words, the iterative process drives the population to asymptotically approach the global optimum through continuous selection-crossover-mutation-elite retention. After the genetic algorithm terminates, the final output Fermi level parameter is the measurement result after separating the instrument broadening and thermal broadening effects.

[0109] Step S133: If the preset convergence condition is met, output the optimal Fermi level parameter and determine the optimal Fermi level parameter as the value of the Fermi level of the sample to be tested.

[0110] The Fermi level parameters are iteratively adjusted until the residuals converge to a preset threshold. This preset threshold is a pre-defined error range, indicating that the fitting accuracy has met requirements. When the residuals converge to this preset threshold, the algorithm stops iterating, obtaining a fitting result that includes the optimal Fermi level parameters. At this point, the fitting result is close to the optimal solution and can be used for subsequent analysis. The obtained optimal Fermi level parameters are the Fermi level values ​​of the sample to be tested.

[0111] Figure 4 This is a schematic diagram of the overall Fermi level determination method in one embodiment of the present invention. Please refer to [link / reference]. Figure 4First, the Fermi level measurement process is initiated. A deuterium lamp and an ultraviolet monochromator generate vacuum ultraviolet light of the target wavelength, irradiating the sample in an ultra-high vacuum environment to excite photoelectrons. Photoelectrons with different kinetic energies are screened using a hemispherical energy analyzer, and the signal is amplified by a microchannel plate and imaged on a fluorescent screen. Further, an industrial camera captures images frame by frame, and the images are superimposed and integrated with pixels of the same kinetic energy to form an ultraviolet photoelectron spectrum. Next, the first derivative of the spectrum is calculated to locate the Fermi edge, and the Fermi edge region is selected as the analysis region. The photoelectron intensity within the Fermi edge region is normalized to the [0,1] interval to eliminate the influence of intensity fluctuations. Further, a convolutional model is constructed, and a genetic algorithm is used for nonlinear least-squares fitting. The optimal Fermi level is determined by minimizing the residual between the model and the experimental data. When the residual converges to a threshold, the optimal parameters are output as the Fermi level value. Finally, the measurement is completed, and the Fermi level value is returned.

[0112] This invention effectively distinguishes between electronic structure broadening caused by the material itself and broadening caused by instrument resolution by constructing a convolutional model of thermal broadening and instrument broadening. This allows the shape information of the Fermi edge region to more accurately reflect the actual electronic structure of the material, without being affected by instrument resolution limitations. The invention uses a convolutional model to fit the shape of the Fermi edge region, effectively avoiding the problems of difficulty in accurately locating the Fermi edge position and susceptibility to instrument resolution issues in related technologies, which can lead to measurement errors. The fitting method of this invention has a high degree of automation, can quickly process large amounts of sample data, and reduces errors from human judgment, making it particularly suitable for high-throughput testing and online measurements.

[0113] This invention also provides a Fermi level measurement system based on ultraviolet photoelectron spectroscopy, the system being used to perform the steps described above, including a light source module and an energy spectrum construction module.

[0114] The light source module uses a photon beam of the target wavelength to irradiate the sample under test, and the photon beam belongs to the vacuum ultraviolet band.

[0115] The sample under test is irradiated with a photon beam of the target wavelength, and an ultraviolet photoelectron spectrum is constructed based on the distribution of photoelectrons excited in the sample. The photon beam interacts with the sample, exciting electrons in the sample and causing them to escape from the surface, thereby generating photoelectrons.

[0116] The energy spectrum construction module constructs the ultraviolet photoelectron energy spectrum of the sample under test based on the distribution of photoelectrons with different kinetic energies excited by the sample. The photon beam belongs to the vacuum ultraviolet band, and the horizontal axis of the ultraviolet photoelectron energy spectrum is the photoelectron kinetic energy, and the vertical axis is the photoelectron intensity.

[0117] During photoelectron emission, each photoelectron possesses a different kinetic energy due to the varying energy it absorbs when interacting with a photon. Therefore, the kinetic energy and corresponding intensity of photoelectrons are two important dimensions of the photoelectron spectrum, represented as the abscissa and ordinate of the ultraviolet (UV) photoelectron spectrum, respectively. Specifically, the UV photoelectron spectrum is obtained by measuring the kinetic energy distribution of photoelectrons emitted from the sample. Photoelectrons are excited from the sample by irradiating its surface with a photon beam from the vacuum ultraviolet region. The kinetic energy of the photoelectrons is measured and displayed in the UV photoelectron spectrum; the abscissa represents the kinetic energy, and the ordinate represents the corresponding photoelectron intensity, i.e., the number of photoelectrons detected at a given kinetic energy.

[0118] The Fermi edge region is determined from the ultraviolet photoelectron spectrum of the sample to be tested, and the shape information of the Fermi edge region is extracted. The Fermi edge region is a preset width range centered on the position of the Fermi edge.

[0119] The Fermi edge region is extracted from the ultraviolet photoelectron spectrum of the sample under test, and its shape information is obtained. First, the Fermi edge region in the ultraviolet photoelectron spectrum is identified by determining the location of the Fermi edge. Next, a preset width range centered on the Fermi edge is selected as the Fermi edge region. Finally, the photoelectron intensity within the Fermi edge region is processed and mapped to a standard intensity range to extract the shape information of the region.

[0120] Construct a convolutional model to describe thermal broadening and instrument broadening.

[0121] This invention characterizes the formation mechanism of the Fermi edge in ultraviolet photoelectron spectroscopy by establishing a physics-driven convolution model. The convolution model simultaneously considers the intrinsic electron thermal distribution of the material (Fermi-Dirac distribution) and the broadening introduced by instrument resolution (Gaussian function). Its convolution result matches the measured ultraviolet photoelectron spectrum, thereby achieving high-precision inversion of the Fermi level. The convolution model constructed in this invention overcomes the subjective errors of traditional manual interpretation methods, providing a theoretical basis for automated fitting.

[0122] Based on a pre-built convolutional model that uses the Fermi level of the sample under test as the fitting parameter, the shape information of the Fermi edge region is fitted, and the value of the Fermi level of the sample under test is determined according to the fitting result; the convolutional model is used to describe thermal broadening and instrument broadening, and the influence of instrument broadening is subtracted by introducing the instrument broadening parameter.

[0123] Based on the previously constructed convolutional model, the shape information of the Fermi edge region of the sample is fitted to determine the sample's Fermi level. First, a genetic algorithm is used to optimize and adjust the Fermi level parameters in the convolutional model. By minimizing the residual between the fitted function and the experimental data, an optimal fitting result is obtained. Finally, based on the optimal Fermi level parameters in the fitting result, the Fermi level value of the sample is determined.

[0124] In one alternative implementation, the light source module includes a deuterium lamp and a vacuum ultraviolet monochromator; The deuterium lamp is used to generate a continuous-wavelength ultraviolet spectrum.

[0125] First, the vacuum ultraviolet deuterium lamp is controlled to generate a continuous ultraviolet spectrum covering the vacuum ultraviolet band. The deuterium lamp is a commonly used ultraviolet light source, particularly suitable for providing high-brightness and highly stable ultraviolet spectra. In practice, the deuterium lamp is activated by adjusting the power supply and control system. During emission, the deuterium lamp produces continuous ultraviolet light within the vacuum ultraviolet band. The output spectrum will include light of multiple different wavelengths.

[0126] The vacuum ultraviolet monochromator is used to process the continuous-wavelength ultraviolet spectrum generated by the deuterium lamp to obtain a photon beam of the target wavelength.

[0127] The continuous-wavelength ultraviolet beam generated by the deuterium lamp is fed into a vacuum ultraviolet monochromator, where it is further filtered and output as monochromatic light of a specific target wavelength. A vacuum ultraviolet monochromator is a device capable of separating and outputting a specific wavelength from the spectrum; its core working principle is based on the dispersion effect of light. The vacuum ultraviolet monochromator contains optical elements such as gratings, lenses, or prisms to separate light of different wavelengths. By adjusting the angle of the grating, the desired target wavelength is selected. After the filtered beam emitted by the deuterium lamp enters the ultraviolet monochromator, the optical elements selectively separate the light of the desired wavelength according to the preset target wavelength, while filtering out other components outside the target wavelength range. Through this process, the vacuum ultraviolet monochromator can output monochromatic light of the target wavelength, that is, obtain a photon beam of the target wavelength.

[0128] The energy spectrum construction module includes a hemispherical energy analyzer, a microchannel plate, a fluorescent screen, and an industrial camera.

[0129] The hemispherical energy analyzer is used to filter out photoelectrons with different kinetic energies from the photoelectrons with different kinetic energies excited by the sample under test.

[0130] A hemispherical energy analyzer is used to screen photoelectrons emitted from the surface of the sample. After the photoelectron beam enters the hemispherical energy analyzer, the electric field between the electrodes separates the electrons according to their energy. By adjusting the strength of the electric field, photoelectrons with different kinetic energies can be screened out. The hemispherical energy analyzer can measure the kinetic energy of the photoelectrons and select photoelectrons within a specific kinetic energy range, which helps in the subsequent construction of a complete ultraviolet photoelectron spectrum, revealing the energy distribution of electrons in the sample.

[0131] The microchannel plate is used to amplify the signals of photoelectrons with different kinetic energies and obtain corresponding luminescent images on a fluorescent screen. The luminescent images include pixels at multiple different locations.

[0132] The signals of photoelectrons with different kinetic energies, filtered by a hemispherical energy analyzer, are amplified by a microchannel plate. This process significantly increases the signal intensity, allowing even weak photoelectron signals to be further detected and analyzed. The amplified photoelectron signals are displayed on a fluorescent screen as a light emission image. This light emission image on the screen is generated by the light emission produced when photoelectrons collide with fluorescent material; each luminous point on the screen corresponds to the detection signal of one photoelectron. Each luminous point represents an electron signal at a different location.

[0133] The industrial camera is used to capture the luminescent image frame by frame according to a preset scanning step size.

[0134] An industrial camera is used to capture frame-by-frame images of the luminescent images generated on the fluorescent screen. The industrial camera is a high-resolution, high-stability imaging device capable of precisely capturing the position and brightness of each luminescent point on the screen. To ensure data accuracy and completeness, the imaging process follows a preset scan step size, meaning the camera moves a certain distance each time to capture one frame. This method ensures that all luminescent images on the fluorescent screen are captured continuously and comprehensively. Each frame represents the luminescent image at a different time point, containing the brightness and position of each pixel, further improving measurement accuracy and data completeness.

[0135] All the light-emitting images captured by the industrial camera are superimposed, and the pixels with the same electron kinetic energy are integrated to obtain the ultraviolet photoelectron spectrum of the sample under test.

[0136] All the luminescence imaging images captured by industrial cameras are superimposed to combine information from multiple images, obtaining more comprehensive signal data and ensuring no details are missed. After superimposing the images, the number of photoelectrons at each kinetic energy value is obtained by integrating pixels with the same photoelectron kinetic energy, i.e., the photoelectron intensity. The final ultraviolet photoelectron spectrum reflects the energy distribution of photoelectrons in the sample under test.

[0137] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, apparatus, electronic devices, and media. Therefore, embodiments of the present invention can take the form of entirely hardware embodiments, entirely software embodiments, or embodiments combining software and hardware aspects. Furthermore, embodiments of the present invention can take the form of a computer program product embodied on one or more computer-readable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0138] Embodiments of the present invention are described with reference to flowchart illustrations and / or block diagrams of methods and apparatus according to embodiments of the present invention. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing terminal equipment to cause a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0139] Although preferred embodiments of the present invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present invention.

[0140] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the term "comprising" or any other variations thereof is intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element. The foregoing has provided a detailed description of a method and system for determining Fermi levels based on ultraviolet photoelectron spectroscopy provided by this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and its core ideas; at the same time, for those skilled in the art, based on the ideas of this invention, there will be changes in specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A method for determining the Fermi level based on ultraviolet photoelectron spectroscopy, characterized in that, include: The sample to be tested is irradiated with a photon beam of the target wavelength. Based on the distribution of photoelectrons with different kinetic energies excited by the sample to be tested, the ultraviolet photoelectron spectrum of the sample to be tested is constructed. The photon beam belongs to the vacuum ultraviolet band. The horizontal axis of the ultraviolet photoelectron spectrum is the photoelectron kinetic energy, and the vertical axis is the photoelectron intensity. The Fermi edge region is determined from the ultraviolet photoelectron spectrum of the sample to be tested, and the shape information of the Fermi edge region is extracted. The Fermi edge region is a preset width range centered on the position of the Fermi edge. Based on a pre-constructed convolutional model using the Fermi level of the sample under test as the fitting parameter, and with the goal of minimizing the residual between the fitting function and the shape information, a genetic algorithm is used to fit the shape information of the Fermi edge region, and the value of the Fermi level of the sample under test is determined based on the fitting result. The convolutional model is used to describe thermal broadening and instrument broadening, and the influence of instrument broadening is subtracted by introducing the instrument broadening parameter.

2. The method according to claim 1, characterized in that, Construct the convolutional model according to the following steps: A Fermi-Dirac distribution function is constructed to describe the thermal broadening effect of photoelectrons in the material of the sample under test; the Fermi level parameters contained in the Fermi-Dirac distribution function are used as unknown parameters to be fitted. Based on the spectral broadening corresponding to the pre-measured instrument response, a Gaussian function is constructed. The Gaussian function is used to describe the energy broadening effect introduced by the instrument's resolution. The instrument broadening parameter used in the Gaussian function is a pre-calibrated known value. The convolution model is obtained by performing a convolution operation between the Fermi-Dirac distribution function and the Gaussian function.

3. The method according to claim 2, characterized in that, Using the Fermi level of the sample under test as the fitting parameter in a convolutional model, with the objective of minimizing the residual between the fitting function and the shape information, a genetic algorithm is used to fit the shape information of the Fermi edge region, and the value of the Fermi level of the sample under test is determined based on the fitting result, including: The Fermi level parameters in the convolution model are used as the variables to be optimized in the genetic algorithm, and a fitness function is constructed with the goal of minimizing the residual between the fitting function and the shape information. Based on the fitness function, the genetic algorithm is driven to iteratively optimize the Fermi level parameters; Under the condition that the preset convergence condition is met, the optimal Fermi level parameter is output, and the optimal Fermi level parameter is determined as the value of the Fermi level of the sample to be tested.

4. The method according to claim 1, characterized in that, The sample to be tested is irradiated with a photon beam of the target wavelength. Based on the distribution of photoelectrons with different kinetic energies excited by the sample, the ultraviolet photoelectron spectrum of the sample is constructed, including: The sample to be tested is irradiated with a photon beam of the target wavelength to obtain photoelectrons with different kinetic energies excited by the sample to be tested. Using a hemispherical energy analyzer, photoelectrons with different kinetic energies are screened from the photoelectrons with different kinetic energies excited by the sample under test. The signals of photoelectrons with different kinetic energies are amplified by a microchannel plate, and the corresponding light emission images are obtained on a fluorescent screen. The light emission images include pixels at multiple different positions. The luminescent image is captured using an industrial camera; All the light-emitting images captured by the industrial camera are superimposed, and the pixels with the same electron kinetic energy are integrated to obtain the ultraviolet photoelectron spectrum of the sample under test.

5. The method according to claim 4, characterized in that, Before irradiating the sample under test with photon beams of different wavelengths, the method further includes: A reference sample is irradiated with an electron beam of target energy emitted by an electron gun to obtain photoelectrons excited in the reference sample; The hemispherical energy analyzer is used to filter out photoelectrons with different kinetic energies. The microchannel plate amplifies the signals of photoelectrons with different kinetic energies and obtains corresponding luminescent images on the fluorescent screen. The luminescent image is captured using an industrial camera; The energy calibration coefficient is calculated based on the correspondence between the pixel position and photoelectron kinetic energy of each pixel in the light emission imaging. The ultraviolet photoelectron spectrum of the sample under test is obtained by superimposing all the luminescent images captured by the industrial camera and integrating the pixels with the same electron kinetic energy, including: Based on the energy calibration coefficient, the pixel position of each pixel in the light emission imaging is converted into the corresponding photoelectron kinetic energy; The photoelectron kinetic energies corresponding to the pixel positions of each pixel in the light emission imaging are superimposed, and the data points with the same photoelectron kinetic energy are integrated to obtain the ultraviolet photoelectron spectrum of the sample under test.

6. The method according to claim 1, characterized in that, The Fermi edge region is determined from the ultraviolet photoelectron spectrum of the sample to be tested, and the shape information of the Fermi edge region is extracted, including: Calculate the first derivative of the ultraviolet photoelectron spectrum, and determine the position of the Fermi edge based on the first derivative; Centered on the position of the Fermi edge, a range of the preset width is selected as the Fermi edge region; Based on the maximum and minimum values ​​of photoelectron intensity within the Fermi edge region, the photoelectron intensity within the Fermi edge region is mapped to a standard intensity range to obtain the shape information.

7. The method according to claim 3, characterized in that, Based on the fitness function, the genetic algorithm is driven to iteratively optimize the Fermi level parameters, including: Initialize a population containing multiple individuals, each individual in the population representing a candidate value for a Fermi level parameter; The fitness of each individual is calculated based on the fitness function, where the fitness is the sum of squared residuals between the predicted values ​​of the convolutional model and the shape information. Individuals are selected using a roulette wheel selection method based on their fitness to construct a mating pool; For individuals in the mating pool, a single-point crossover operation is performed according to a preset crossover probability; and for individuals after the single-point crossover operation, a mutation operation is performed according to a preset mutation probability. The N individuals with the highest fitness in the current population are retained in the next generation population, where N is an integer greater than 1; Repeat the above steps until the preset iteration conditions are met.

8. The method according to claim 1, characterized in that, Irradiating the sample under test with a photon beam of the target wavelength, including: Metal films with a purity higher than the preset value were used as the test samples; The surface of the sample to be tested is etched using an argon ion beam to remove the oxide layer and contaminants from the surface of the sample to be tested. The ultraviolet spectrum of the continuous band generated by the deuterium lamp is processed using a vacuum ultraviolet monochromator to obtain a photon beam of the target wavelength. In a vacuum sample chamber, the sample to be tested is irradiated with a photon beam of the target wavelength.

9. A Fermi level determination system based on ultraviolet photoelectron spectroscopy, characterized in that, The method applied to perform the steps of any one of claims 1-8 includes a light source module and an energy spectrum construction module; The light source module uses a photon beam of the target wavelength to irradiate the sample under test, and the photon beam belongs to the vacuum ultraviolet band; The energy spectrum construction module constructs the ultraviolet photoelectron energy spectrum of the sample under test based on the distribution of photoelectrons with different kinetic energies excited by the sample under test. The photon beam belongs to the vacuum ultraviolet band, and the horizontal axis of the ultraviolet photoelectron energy spectrum is the photoelectron kinetic energy, and the vertical axis is the photoelectron intensity. The Fermi edge region is determined from the ultraviolet photoelectron spectrum of the sample to be tested, and the shape information of the Fermi edge region is extracted. The Fermi edge region is a preset width range centered on the position of the Fermi edge. Construct a convolutional model to describe thermal broadening and instrument broadening; Based on a pre-built convolutional model that uses the Fermi level of the sample under test as the fitting parameter, the shape information of the Fermi edge region is fitted, and the value of the Fermi level of the sample under test is determined according to the fitting result; the convolutional model is used to describe thermal broadening and instrument broadening, and the influence of instrument broadening is subtracted by introducing the instrument broadening parameter.

10. The system according to claim 9, characterized in that, The light source module includes a deuterium lamp and a vacuum ultraviolet monochromator; The deuterium lamp is used to generate a continuous-wavelength ultraviolet spectrum; The vacuum ultraviolet monochromator is used to process the continuous-wavelength ultraviolet spectrum generated by the deuterium lamp to obtain a photon beam of the target wavelength. The energy spectrum construction module includes a hemispherical energy analyzer, a microchannel plate, a fluorescent screen, and an industrial camera; The hemispherical energy analyzer is used to filter out photoelectrons with different kinetic energies from the photoelectrons with different kinetic energies excited by the sample under test; The microchannel plate is used to amplify the signals of photoelectrons with different kinetic energies and obtain corresponding light emission images on a fluorescent screen. The light emission images include pixels at multiple different positions. The industrial camera is used to capture the luminescent image frame by frame according to a preset scanning step size; All the light-emitting images captured by the industrial camera are superimposed, and the pixels with the same electron kinetic energy are integrated to obtain the ultraviolet photoelectron spectrum of the sample under test.

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