Angle resolution photoelectron spectroscopy detection system and photoelectron spectroscopy detection method

Abstract

The invention provides an angle-resolved photoelectron spectroscopy detection system, which is used for analyzing a quantum material and comprises a light source, a vacuum chamber, a sample table, an electron energy analyzer, a source meter, a first working mode and a second working mode. Wherein the light source is used for providing photon excitation, and light irradiates a sample. The vacuum chamber is used for providing a vacuum environment. The sample table is arranged in the vacuum chamber and used for bearing a sample to be analyzed, and the sample table comprises a cryostat, a cold head, an insulating sheet, a copper block and a sample support from top to bottom. The electron energy analyzer is used for detecting the emitting angle of electrons in the inclination angle direction, the emitting angle of the electrons in the azimuth angle direction, kinetic energy and the corresponding number of the electrons after the sample is illuminated under bias voltage, and the electrons are emitted into the detection range of the electron energy analyzer. And on the basis of the analysis, the momentum in the x direction, the momentum in the y direction and the electron binding energy corresponding to electrons in the sample are analyzed.

Description

Technical Field

[0001] The present invention relates to the field of optoelectronic technology, in particular to photoelectron spectroscopy technology, and more particularly to an angle-resolved photoelectron energy spectrum detection system and a photoelectron energy spectrum detection method. Background Art

[0002] Photoelectron spectroscopy is an experimental technique with a long history, its origins dating back to the groundbreaking discoveries of the photoelectric effect by Hertz, Holvax, and Lenard in the late 19th century, and the subsequent ingenious interpretation by Einstein. About half a century later, Kai Siegbahn developed this phenomenon into a practical and reliable experimental method, which over time evolved into what is known today as angle-resolved photoemission spectroscopy (ARPES). Today, ARPES has become one of the most powerful and widely used techniques for probing the electronic structure of materials. ARPES directly measures the energy (E) and momentum (k) of electrons within a material, two quantities that are key to analyzing the electronic structure of quantum materials and understanding the properties of matter. Numerous experimental results and theoretical concepts have been discussed in review articles and authoritative textbooks.

[0003] When a beam of light hits a solid, the electrons in the material can absorb the energy of the photons and overcome the work function (also known as the work function). ) escape from the sample surface as photoelectrons. By measuring the energy and number of photoelectrons at different emission angles, the energy and momentum of the electrons within the material, as well as the corresponding physical information, can be recovered. ARPES technology has achieved significant and continuous improvements, particularly in energy resolution, momentum resolution, and detection efficiency. These improvements are primarily driven by advances in energy analyzer and light source technology. Initially, electron energy analyzers could only detect electrons in a single angular direction (0D) at a time. Now, they can detect electrons in multiple angular directions along a line (1D) and on a surface (2D), resulting in a significant improvement in detection efficiency. Laser ARPES, which uses lasers as light sources, has further revolutionized this field. The technology described in patent application CN1995996B offers several significant advantages, including extremely high energy and momentum resolution, low manufacturing cost, bulk sensitivity, and compatibility with ultrafast speeds.

[0004] Although ARPES technology has made great progress in the past few decades, modern ARPES technology is still greatly limited in the angular detection range of photoelectrons. The mainstream hemispherical electron energy analyzer can simultaneously detect the angle of The angular range of electrons, however, the emitted photoelectron range includes the entire The spatial extent of the solid angle ( ), so in reality, only a small part of the photoelectrons are detected, and most of the emitted photoelectrons are wasted, which leads to very low detection efficiency. The angular range of the hemispherical spectrometer makes the corresponding momentum space range very small, especially for the laser ARPES system. Therefore, for the traditional ARPES system, if you want to obtain the area of ​​interest, you need to perform a lot of acquisitions through mechanical rotation and stitch the results together. This is not only very time-consuming, but multiple mechanical rotations will introduce mechanical errors, changes in transition scattering geometry and sample degradation. Therefore, a new solution is urgently needed to expand the observation range of the hemispherical spectrometer to improve the single detection efficiency, and eventually even reach Full range detection of solid angle.

[0005] It should be noted that this background information is provided solely to introduce relevant information of the present invention to facilitate understanding of the technical solution of the present invention. It does not necessarily constitute prior art. In the absence of evidence demonstrating that the relevant information was disclosed prior to the filing date of the present invention, the relevant information should not be considered prior art. Summary of the Invention

[0006] The purpose of the present invention is to overcome the above-mentioned defects of the prior art and provide a new angle-resolved photoelectron spectroscopy detection system and method.

[0007] According to a first aspect of the present invention, an angle-resolved photoelectron spectroscopy detection system is provided for analyzing quantum materials. The system comprises a light source, a vacuum chamber, a sample stage, an electron energy analyzer, a source meter, and a first operating mode and a second operating mode. The light source provides photon excitation, irradiating the sample stage with light. The vacuum chamber provides a vacuum environment. The sample stage is set in the vacuum chamber and is used to carry the sample to be analyzed. In order from top to bottom, the sample stage includes: a low-temperature thermostat, a cold head, an insulating sheet, a copper block, and a sample holder, wherein: the low-temperature thermostat is used to provide a low-temperature environment; the cold head is connected to the bottom end of the low-temperature thermostat; the cold head is connected to one end of the copper block through the insulating sheet, and the other end of the copper block is connected to the sample holder, or the cold head is connected to one end of the copper block, and the other end of the copper block is connected to the sample holder through the insulating sheet, and the sample holder is used to directly carry the quantum material sample to be detected; or the cold head is connected to one end of the copper block, and the other end of the copper block is connected to the sample holder, and the insulating sheet is inserted between the sample holder and the quantum material sample to be detected carried by it; the sample holder is externally connected to a source meter with adjustable voltage, and the source meter is used to apply a bias voltage to the sample to form an electric field between the sample stage and the electron energy analyzer. After light is irradiated on the sample surface, the electrons absorb photon energy to overcome the work function ( ) escapes and is emitted into the detection range of the electron energy analyzer. The electron energy analyzer is disposed in a vacuum chamber and is used to detect the emission angle in the tilt angle direction, the emission angle in the azimuth angle direction, the kinetic energy, and the corresponding number of electrons emitted from the sample into its detection range after photon irradiation under bias. The electron energy analyzer is configured with a first operating mode and a second operating mode, wherein: in the first operating mode, the electron energy analyzer extracts the energy distribution curve of the electron cone bottom based on the detected electron cone, obtains the distance between the two peaks through differentiation, and analyzes the sample work function according to a first preset analysis model; in the second operating mode, the electron energy analyzer analyzes the x-direction momentum, y-direction momentum, and electron binding energy values ​​corresponding to the electrons in the sample based on the detected electron emission angle in the tilt angle direction, the electron emission angle in the azimuth angle direction, and the kinetic energy, combined with the sample work function, according to a second preset analysis model.

[0008] Preferably, the light source further includes a light source focusing system for focusing the light beam.

[0009] Preferably, the sample stage further comprises a copper braid, and the copper block is connected to the sample holder via the copper braid.

[0010] Preferably, the insulating sheet is made of sapphire or Kapton plastic.

[0011] Preferably, the electron energy analyzer is a hemispherical analyzer.

[0012] Preferably, the first preset model is:

[0013] in, is the surface work function of the sample, represents the photon energy, is the measured internal Fermi level of the sample, is the measured energy value corresponding to the value of kinetic energy of 0 in the emitted electron, and are the two peaks of the cone bottom energy distribution curve, is the distance between the two peaks, and the symbols in the formula represent the superscript Represents Detector.

[0014] Preferably, when the electron energy analyzer detects the electron's emission angle in the tilt angle direction, the electron's emission angle in the azimuth angle direction, and the kinetic energy in the second working mode, it eliminates energy distortion on the data and then analyzes the momentum of the electrons in the x-direction, the momentum in the y-direction, and the electron binding energy value inside the sample according to the second preset analysis model, wherein the energy distortion elimination processing is performed in the following manner: the first step is to use image edge recognition to identify the edge of the matrix in the energy direction, and obtain the corresponding energy position as the new energy baseline; the second step is to integrate and normalize the small energy area near the previously generated baseline, and eliminate the regional intensity enhancement caused by the energy band intensity; the third step is to identify the normalized image edge and obtain the final energy baseline.

[0015] Preferably, the second preset model is:

[0016] in,

[0017] in, is the kinetic energy value detected by the electron energy analyzer, with the superscript Represents Detector, is the kinetic energy value of the sample surface, the superscript Representative Sample, is the effective electric field potential energy, is the elementary charge, is the energy of the photon in the photoelectric effect, is Planck's constant, is the photon frequency, is the sample work function, is the internal electron binding energy of the material to be solved, is the reduced Planck constant, defined as , is the rest mass of the free electron, The internal electrons of the material to be solved are Momentum in direction, The internal electrons of the material to be solved are Momentum in direction, is the bias voltage applied to the sample, is the instrument work function, is the electron emission angle in the tilt angle direction detected by the electron energy analyzer, is the emission angle of the electron detected by the analyzer in the azimuthal direction. is the conversion factor, where is the analyzer angle limit conversion coefficient, is the analyzer position limit conversion coefficient, is the linear correlation coefficient. For the convenience of writing, the dimensionless parameter is defined .

[0018] Preferably, the second preset model further includes an intensity correction term to map the angle space to the momentum space:

[0019] Among them, each partial differential component is:

[0020] in,

[0021] The formula Used to indicate or One of them.

[0022] According to a second aspect of the present invention, there is provided a photoelectron spectroscopy detection method based on the angle-resolved photoelectron spectroscopy detection system according to the first aspect of the present invention, characterized in that the method comprises: Place the sample to be tested on the sample holder of the angle-resolved photoelectron spectroscopy detection system; Turn on the light source to illuminate the sample and apply a bias voltage through the power supply connected to the sample holder; The electron energy analyzer of the angle-resolved photoelectron spectroscopy detection system detects the complete electron cone of photoelectrons in a first working mode and detects the emission angle of electrons in the tilt angle direction, the emission angle of electrons in the azimuth angle direction, and the kinetic energy within the detection range in a second working mode; The sample work function is obtained according to the electron cone by the angle-resolved photoelectron spectroscopy detection system; The angle-resolved photoelectron spectroscopy detection system obtains the momentum of electrons in the x-direction, the momentum in the y-direction, and the electron binding energy values ​​inside the sample based on the electron emission angle in the tilt angle direction, the electron emission angle in the azimuth angle direction, the kinetic energy, and the sample work function.

[0023] Compared with the existing technology, the advantages of the present invention are: the present invention realizes an ultra-low-cost, stable, efficient and universal ARPES bias increase scheme, further realizes the expansion of ARPES detection range, and greatly improves detection efficiency; the present invention expands the ability of ARPES to measure work function, and provides a new method to realize high-precision detection of sample work function and realize spatial resolution of work function; the present invention retains the high-resolution detection advantage of ARPES, especially laser ARPES, and can realize high-precision detection of electronic structure. In the absence of bias, it has the same measurement method and resolution as conventional ARPES and has universal applicability; the scheme of the present invention has the ability to detect weak signals. After the momentum detection range is expanded, the measurement statistics will also be enhanced. The same statistical signal detection can be achieved with weaker light intensity, and the enhanced statistical effect can be achieved for samples with weak signals; the scheme of the present invention can be extended to ultrafast light sources to achieve compatibility with ultrafast research. At the same time, by replacing the appropriate light source, two-photon research on the unoccupied state electronic structure of the sample can be realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The embodiments of the present invention are further described below with reference to the accompanying drawings, in which: Figure 1 This is a schematic diagram of the physical quantity information of the measured material under ideal conditions; Figure 2 Schematic diagram of the system structure of the angle-resolved photoelectron spectroscopy detection system according to an embodiment of the present invention; Figure 3 Schematic diagram of the traditional ARPES system structure; Figure 4 Schematic diagram of the hardware structure of the angle-resolved photoelectron spectroscopy detection system according to an embodiment of the present invention; Figure 5 Schematic diagram of the principle of measuring work function by the angle-resolved photoelectron spectroscopy detection system according to an embodiment of the present invention; Figure 6 2 is a schematic diagram of a work function measurement process according to an embodiment of the present invention; Figure 7 is a schematic diagram of the corresponding relationship between the measurement parameters and the maximum detectable emission angle according to an embodiment of the present invention; Figure 8 A schematic diagram of a measurement process according to an embodiment of the present invention; Figure 9 Schematic diagram comparing the momentum space range covered by a single measurement of the original laser ARPES and the single measurement range provided by the solution of the present invention; Figure 10 This is a schematic diagram of all emitted electron information collected by performing a single measurement on a typical cage quantum material CsV3Sb5 using the solution of the present invention according to an embodiment of the present invention; Figure 11 Schematic diagram of measurement results of a typical copper oxide superconductor Bi2212 under different polarization states according to an embodiment of the present invention. DETAILED DESCRIPTION

[0025] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below through specific embodiments in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0026] Before introducing the solution of the present invention, some relevant background knowledge is first introduced.

[0027] In an experiment, it is hoped that ARPES can provide Figure 1 The electronic band structure information shown, Figure 1 It shows the information of a three-dimensional space, including momentum 、 and energy The physical quantity we want to obtain is the electron inside the material corresponding to each ( , , ) spatial coordinates, and further analysis yields the single-particle spectrum function. This physical quantity reflects the electron's band structure information, the interaction information within the material, and how this information changes with the environment (such as temperature, doping, pressure, etc.). After decades of development, the ARPES hemispherical electron energy analyzer, the latest generation of Scienta Da30L analyzers, can detect a small area in angular space ( angular detection range), if a larger angle is detected, the sample needs to be mechanically rotated. However, as mentioned in the background technology section, the use of mechanical rotation to expand the observation space will introduce changes in the transition scattering geometry, thereby resulting in the loss of key transition matrix element information.

[0028] As is well known, a hemispherical energy analyzer consists of two parts: an electron lens at the front and a hemispherical analyzer at the back. The electron lens shapes the incident electrons, converting the angular information of the outgoing electrons relative to the focal point into their position information before entering the hemispherical analyzer, similar to the principle of imaging with an optical lens. However, the size of the electron lens is limited, with an angle of only ±15° relative to the sample at the entrance. Therefore, the analyzer can only measure an angular range of ±15° at a time. When electrons enter the hemispherical analyzer, due to the different radii of motion caused by the centripetal force, electrons of different energies will impact different locations on the hemispherical analyzer. The photon energy of laser ARPES is generally low, typically less than 11 eV, resulting in a relatively low kinetic energy. Therefore, within the ±15° range of the electron energy analyzer, the angular range of a single measurement is extremely small, and the resulting momentum space is accordingly extremely small.

[0029] It should be noted that the hemispherical energy analyzer has a slit structure, which is located between the electron lens and the hemispherical analyzer mentioned above. Electrons corresponding to different angles along the slit direction will eventually hit the other direction of the hemispherical analyzer along different radial directions. Therefore, each detection displays an image in the two-dimensional coordinates of angle-energy on the electron energy analyzer, and the physical information is contained in the intensity corresponding to each point. The latest generation of DA30L electron energy analyzer can obtain information about electrons in the direction perpendicular to the slit by deflecting electrons, that is, by applying up and down deflection voltages through the electron lens, so that electrons in the vertical direction are deflected and fly into the slit so that they can be detected, thus realizing the measurement of the equivalent two-dimensional angular range. When the bias is applied, an electric field is constructed between the sample and the analyzer, and the emitted photoelectrons are deflected by the electric field, so that electrons at a larger angle are deflected into the analyzer, realizing the detection of a larger emission angle. By applying a sufficiently large bias, the entire laser ARPES can be collected. Electrons within a solid angle (±90°) can perfectly address the aforementioned issue of limited single-shot laser ARPES detection range. Based on this, the present invention proposes a universal solution for expanding laser ARPES detection, aiming to improve the detection efficiency of hemispherical spectrometers. The basic physical principle of this solution is that by applying a bias voltage to the sample, an electric field is created between the sample and the analyzer. Electrons escaping from the sample surface are deflected by the electric field. Electrons at large angles are deflected into the analyzer within a ±15° detection angle, thus enabling wide-range measurement.

[0030] The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0031] According to one embodiment of the present invention, the present invention provides an angle-resolved photoelectron spectroscopy detection system for analyzing the electronic structure in quantum materials, such as Figure 2 As shown, the system includes a light source, a vacuum chamber, a sample stage, an electron energy analyzer, and a source meter. The light source uses a laser, which irradiates the sample. The vacuum chamber provides a vacuum environment, and the sample stage is located within the vacuum chamber to support the sample to be analyzed. The electron energy analyzer is arranged in a vacuum chamber, and is used to detect the emission angle in the tilt angle direction, the emission angle in the azimuth angle direction, the kinetic energy and the corresponding number of electrons emitted from the sample into its detection range after laser irradiation under bias; the electron energy analyzer is configured with a first working mode and a second working mode, wherein: in the first working mode, the electron energy analyzer extracts the energy distribution curve of the electron cone bottom based on the detected electron cone, obtains the distance between the two peaks through differentiation, and analyzes the work function of the sample according to the first preset analysis model; in the second working mode, the electron energy analyzer analyzes the momentum in the x direction, the momentum in the y direction, and the electron binding energy corresponding to the sample's emitted electrons according to the detected electron emission angle in the tilt angle direction, the emission angle in the azimuth angle direction, and the kinetic energy, combined with the sample work function, according to the second preset analysis model. The source meter is used to apply a bias to the sample to form an electric field between the sample stage and the electron energy analyzer. If no bias is applied to the sample, such as Figure 3 As shown, in the traditional structure, there is no electric field between the electron energy analyzer and the sample stage, and the electron energy analyzer can only detect electrons within a limited range.

[0032] According to one embodiment of the present invention, the light source further includes a light source focusing system for focusing the laser.

[0033] According to one embodiment of the present invention, Figure 4 As shown, the sample stage, in order from top to bottom, includes: a low-temperature thermostat, a cold head, an insulating sheet, a copper block, and a sample holder, wherein: the low-temperature thermostat is used to provide a low-temperature environment. The low-temperature thermostat is used to provide a low-temperature environment; the cold head is connected to the bottom end of the low-temperature thermostat; the cold head is connected to one end of the copper block via an insulating sheet, and the other end of the copper block is connected to the sample holder, or the cold head is directly connected to one end of the copper block, and the other end of the copper block is connected to the sample holder via an insulating sheet, and the sample holder is used to directly carry the quantum material sample to be detected; or the cold head is connected to one end of the copper block, and the other end of the copper block is connected to the sample holder, and the insulating sheet is inserted between the sample holder and the quantum material sample to be detected carried by it; the sample holder is externally connected to a source meter with adjustable voltage, and the source meter is used to apply a bias voltage to the sample to form an electric field between the sample stage and the electron energy analyzer. After the laser is irradiated on the sample surface, electrons absorb light energy and escape and emit it into the detection range of the electron energy analyzer. According to one embodiment of the present invention, still referring to Figure 4The sample stage also includes a copper braid, and the copper block is connected to the sample holder via the copper braid.

[0034] By inserting an insulating sheet into the cooling path, the present invention isolates the sample's potential from the rest of the sample stage, facilitating electrical operations. Furthermore, the insulating sheet still serves as a heat conductor, so an insulator with good thermal conductivity or an ultra-thin insulating sheet should be used, such as the sapphire or ultra-thin plastic sheet mentioned below. The present invention is highly universal and can be implemented in a variety of cooling paths simply by adding an insulating structure to the cooling path. For example, in the previous embodiment, a traditional four-axis design without a copper braid, directly connected to the sample holder with a copper block, can achieve the same effect by inserting a sapphire sheet between the cold head and the copper block. Furthermore, the sapphire sheet can also be inserted into the cooling path of mechanically movable or detachable structures, such as between the copper braid and the sample holder, or between the sample holder and the sample, achieving the same effect. The sapphire sheet can also be replaced with a different insulating material, such as an ultra-thin Kapton plastic sheet. In the electrical connection structure directly connected to the sample, a wire is connected to the source meter outside the vacuum for biasing or grounding. The remaining components should remain grounded. It is particularly noted that the type of the sample holder, whether it is a flat plate holder, a Unisoku holder, or a self-designed sample holder, does not affect the solution of the present invention.

[0035] According to one embodiment of the present invention, the system is equipped with a hemispherical electron spectrometer DA30L (Scienta-Omicron), the light source is a tripled frequency Nd:YVO4 laser (Vanguard, Spectra Physics), the laser repetition rate is 80MHz, the maximum power is 4W, After the (KBBF) frequency doubling, a vacuum deep ultraviolet (VUV) laser of 6.994 eV is generated. After being focused by the Micro-Lens, the laser forms a diameter of about The source meter uses Keithley-2450 source meter, with a maximum bias voltage of , the insulation method is to insert a sapphire sheet between the cold head and the copper braid. The thickness of the sapphire sheet is .

[0036] Compared with the traditional ARPES, the system of the present invention has the following differences: 1. The physical models used are different. In conventional ARPES, electron trajectories before entering the analyzer are straight lines, using a point-divergence model. Therefore, the angle obtained by the analyzer is the actual emission angle. However, in this invention, electron trajectories change after emission due to the electric field. Therefore, the electron energy analyzer uses a parallel metal plate capacitor model for measurement.

[0037] 2. Different detection methods. Since the electron trajectory of traditional ARPES is a straight line, the receiving angle of the analyzer is limited, generally , so if you want to collect more than The sample with a degree angle needs to be rotated; the present invention adopts the parallel metal plate capacitor model to describe the physical process in the measurement. By adjusting the voltage, the detection range is changed. When the voltage is increased, the electric field between the sample and the analyzer is larger, so the electrons are deflected more, and a larger angle of electron deflection can be entered. The voltage is large enough, 2 All emitted electrons in the solid angle can be collected, far exceeding the operational range of mechanical rotation. Not only that, this method greatly improves the detection efficiency, does not change the scattering geometry, and thus makes the data more reliable. It can simultaneously measure the work function and monitor the photocurrent, and introduces the possibility of electrical measurement.

[0038] 3. The data processing method is different. Due to the different physical models, the formulas used in the process of converting the momentum of the data obtained by the electron energy analyzer and finally obtaining the desired physical quantity are different. Traditional ARPES uses polycrystalline Au as a way to calibrate the Fermi energy of the analyzer, but this method is now invalid. The solution of the present invention uses an algorithm that directly finds the Fermi energy from the sample information. Traditional ARPES ignores the important role of the work function in the spectral process and usually operates it as 4.3eV. In fact, the 4.3eV obtained by measuring the kinetic energy value through the Fermi energy of polycrystalline gold or the sample is the instrument work function. If there is a difference between the sample work function and the instrument work function, in traditional ARPES, an electric field will still be constructed between the sample and the instrument, affecting the electron trajectory, and the sample work function still needs to be accurately measured before the experiment.

[0039] To better understand the present invention, let us first briefly explain why the laser detection range is relatively small. The photoelectric process and the traditional ARPES conversion physical model are:

[0040] is the sample work function, and The internal electrons of the materials to be solved are Direction and Momentum in direction, is the internal electron binding energy of the material to be solved, and is the angle of the emitted electron detected by the analyzer (before entering the analyzer in traditional ARPES, the electron trajectory is a straight line, which is a point divergence model, so the angle obtained by the analyzer is the actual emission angle), is the photon energy. It can be seen that the photon energy of the light source used in laser ARPES is usually low ( ), while the analyzer can only detect The electronic angle range of the angle, so the corresponding detection momentum or Therefore, in the present invention, a bias voltage is applied to the sample to deflect the electrons emitted at a large angle into the analyzer, which is equivalent to increasing the effective and In addition, the present invention can not only expand the laser ARPES detection range and greatly improve the detection efficiency, but also expand the ability of laser ARPES to measure work function.

[0041] Then, the physical model adopted by the present invention is introduced according to the physical principle on which the present invention is based. As described in the previous embodiment, the basic physical principle on which the present invention is based is that by applying a bias voltage to the sample, an electric field is constructed between the sample and the analyzer. Under the action of the electric field, electrons are deflected. Electrons with large angles are deflected into the In the angle detection analyzer, the parallel metal plate capacitor model can well explain this physical process. After mathematical derivation, a reliable analytical model can be obtained as follows:

[0042] in,

[0043]

[0044] in, is the kinetic energy value detected by the electron energy analyzer, with the superscript Represents Detector, is the kinetic energy value of the sample surface, the superscript Representative Sample, is the effective electric field potential energy, according to the formula definition, is the elementary charge, is the bias voltage applied to the sample, is the instrument work function, which is determined by the kinetic energy value obtained by the corresponding measurement of the Fermi energy of polycrystalline gold or sample. is the energy of the photon in the photoelectric effect, is Planck's constant, is the photon frequency, and the scheme of the present invention uses 6.994eV, is the sample work function, is the internal electron binding energy of the material to be solved (Binding Energy), is the reduced Planck constant, defined as , is the rest mass of the free electron, The internal electrons of the material to be solved are Momentum in direction, The internal electrons of the material to be solved are Momentum in direction, is the electron emission angle in the tilt angle direction detected by the electron energy analyzer, is the emission angle of the electron detected by the analyzer in the azimuthal direction. is the conversion factor, where is the electronic energy analyzer angle limit conversion coefficient, Electronic energy analyzer position limit conversion coefficient, is the linear correlation coefficient.

[0045] At the same time, a strength correction factor is also required , to map the angle space to the momentum space. The correction in intensity comes from the different sizes of the corresponding volume elements when the two parameter spaces are converted to each other, that is, , which mathematically corresponds to the Jacobian determinant:

[0046] Among them, each partial differential component is:

[0047] in,

[0048] The formula Used to indicate or The rest of the parameters in the intensity parameter are the same as defined before.

[0049] Therefore, from the physical model formula, it can be seen that the entire physical process of light entering and electrons exiting can be simplified as follows: input: light , voltage U; the analyzer measures the physical quantity: kinetic energy ,angle and ; The physical quantities to be determined inside the quantum material need to be converted, including the physical quantity work function , binding energy ,momentum and , as well as the spectral intensity obtained for each corresponding physical quantity after correction, these information are further analyzed to obtain information such as single-particle spectral functions and interactions.

[0050] The physical model used in the scheme of the present invention is described above. The following describes another new functional improvement of the scheme of the present invention, that is, the present invention provides a more convenient and accurate method for measuring the work function, and the accuracy of the work function measurement is controlled to The following is a detailed introduction to the sample work function.

[0051] First, let me explain why we need to measure the work function. The work function is an intrinsic physical quantity of the material. Accurately measuring the work function is of great significance in materials science, condensed matter physics, and device engineering. The work function helps understand the degree of electron confinement on the surface of the material and is a key parameter for understanding the distribution of electronic states. The work function can be used to help design and optimize electronic devices and help solve material engineering problems, such as in the semiconductor and optoelectronic industries. The work function helps provide surface states, such as distinguishing different cleavage planes and judging whether the sample is aging during the experiment. The work function is an important physical quantity in the low-energy ARPES process. As shown in the previous formula, the sample work function It is a very important physical quantity that affects the subsequent data processing and conversion of the experiment. As can be seen from the previous examples, even at 0 bias, The existence of this correction term, therefore, physically, even without bias, if there is a difference between the sample work function and the instrument work function, a built-in electric field will be constructed. For the example of the present invention, the instrument work function is measured to be 4.3eV, and the sample work function is generally in the range of 0.7-7eV, so this Built-in electric fields around 3V can affect electron trajectories, leading to inaccurate measurements. This significantly impacts the accuracy of ARPES, especially laser ARPES. For example, the photon energy used in synchrotron ARPES is typically 100eV, and the kinetic energy of the emitted electrons is at least >90eV. Therefore, an electric field of around 3V has little effect on the measurement. However, in laboratory laser ARPES, the energy of the photons is typically 6-11eV, and the kinetic energy of the emitted electrons is typically only 1-6eV, resulting in a significant impact. This demonstrates the importance of accurately measuring the work function for accurately understanding and obtaining material parameters.

[0052] Secondly, let's explain why conventional ARPES cannot measure the work function of a sample. As previously explained, even without a bias voltage, the difference between the sample and the work function will result in a built-in electric field between the sample and the analyzer. If the sample work function is greater than the instrument work function, this electric field will accelerate the emitted electrons, and all of them will be collected by the analyzer, thus obtaining work function information. If the sample work function is less than the instrument work function, this electric field will decelerate the electrons, preventing lower-energy electrons from reaching the analyzer and decelerating to zero. Therefore, the work function information falls outside the analyzer's collection energy window, making it impossible to obtain valid work function information. On the other hand, if the physical model does not consider the existence of the built-in electric field, the measurement accuracy will be affected. Therefore, conventional ARPES cannot obtain high-precision work function information for all samples.

[0053] Third, let me introduce how to obtain the work function under the existing technology. Method 1 uses KPFM (Kelvin probe force microscopy) to measure the contact potential difference (CPD) between the sample and the probe to obtain the work function difference. However, this method only measures the relative work function difference and requires calibration of standard samples. It is greatly affected by the environment and probe contamination and requires a complex feedback system. Method 2 uses the thermal electron emission method (Thermionic emission). By heating the sample to a high temperature, the electrons gain thermal energy and jump out of the material. The work function is inferred based on the Richardson equation. However, this method has low accuracy and it is difficult to obtain thermal stability. It is affected by surface cleanliness and emission area. Method 3 uses XPS (X-ray photoemission), which is also a relatively common method. It uses X-rays to irradiate the sample, collects the sample binding energy spectrum, and determines the low kinetic energy cutoff by measuring the kinetic energy of the escaped electrons, thereby Calculating the work function is often done in XPS, but the typical operating mode is similar to the transmission mode used in ARPES analyzers, integrating all electrons entering the analyzer. This mode suffers from poor accuracy, typically only a few hundred meV. However, the present invention combines a micro-spot to obtain work function information for different cleavage plane regions. This approach is also compatible with ARPES experiments, allowing both work function and electronic structure measurements to be performed in the same sample cleavage state, yielding more physical information.

[0054] The following describes in detail how the electron energy analyzer in the solution of the present invention measures the work function of a sample with reference to the accompanying drawings.

[0055] The work function is defined as the minimum energy required to extract an electron from the Fermi level inside the material to the vacuum level. Therefore, to obtain the work function, the core physical quantity that needs to be obtained is the maximum kinetic energy of the emitted electron. To obtain this quantity, we need to understand the following process: First, after applying the bias voltage, if the voltage is appropriate, all 2 The photoelectrons emitted from the solid angle, all the electrons collected should be an electron cone, this cone is in the form of a three-dimensional hyperbolic function, Figure 5 Small Figure 5 a-5e shows the section of the cone along the energy direction, i.e., the isoenergetic surface. It can be seen that as the binding energy deepens, the electron collection range gradually shrinks, reflecting a conical shape. Figure 5 Small Figure 5 f-5j Figure 5 Small Figure 5 The slice of the electron cone corresponding to the momentum position of the red line marked in a shows a parabolic cone shape. The physics of the electron cone can be understood. Physically, the kinetic energy of the bottom of the electron cone is 0 when it is emitted. The upper plane of the cone corresponds to the Fermi energy obtained by measurement, which corresponds to the position of maximum kinetic energy when it is emitted. Therefore, the key to obtaining the work function lies in accurately extracting the values ​​of these two. It can be seen that the choice of the cone bottom for different slices is very critical. Therefore, if only one slice is measured, the choice of the cone bottom is very unfavorable (the acquisition method of the hemispherical ARPES analyzer is to collect a line in the momentum space each time, and then use the electron optical deflector function to piece together the momentum area, that is, the time-series acquisition is similar to a small Figure 5 f-5j slice diagram, and then pieced together into a complete electron cone), the more accurate the cone bottom is, the more accurate the work function is, so there are two ways to process the data. Figure 5 Small Figure 5 k is shown in the figure. The line in the figure is for small Figure 5 From the curves obtained by integrating f-5j and the entire electron cone, we can see that the Fermi cutoff on the right is very sharp and can be read accurately, but the secondary electron cutoff on the left, that is, the measurement energy position corresponding to the zero kinetic energy of the emission, is not easy to find (usually, in order to avoid interference from stray electrons, the midpoint of this cutoff is read as its value). The total integral of the electron cone is similar to the curve of the work function obtained by XPS, that is, the current status of work function measurement. Therefore, by taking advantage of the angular resolution, we can extract Figure 5 Small and medium Figure 5 The curve in l, that is, the small Figure 5 The curve at the center of the f-5j angle. It is obvious that the secondary electron cutoff is more obvious, and the midpoint value can be easily read. A more accurate approach is to find the center slice and differentiate the curve once at this cutoff minimum, such as Figure 5 Small and medium Figure 5 As shown in m, the peak values ​​of the two peaks on the left and right are fitted and the formula can be used.

[0056] Calculate the value of the work function, is the surface work function of the sample, represents the photon energy, is the measured internal Fermi level of the sample, that is, the peak on the right side read out by small figure k, This is the measured energy value corresponding to the kinetic energy of 0 in the emitted electron, that is, the peak on the left read out in small figure k. and are the two peaks of the cone bottom energy distribution curve, is the distance between the two peaks, and the symbols in the formula represent the superscript Represents Detector.

[0057] According to one embodiment of the present invention, Figure 6 As shown, when using the system of the present invention to measure the work function, first apply a suitable bias value, then test the complete electron cone, extract the energy distribution curve (EDC) at the bottom of the cone, perform a differential, read the distance between the two peaks, and finally use Calculate the work function. Among them, because the specific value of the work function of the sample is unknown, a bias voltage needs to be added to the sample to ensure that low-energy secondary electrons can be collected. The bias value is set on the one hand to obtain a suitable voltage for measurement, and on the other hand, the work function value can be simply estimated in the data display window of the analyzer. Experimentally, there are two ways to find a suitable bias value: one is to gradually increase the applied bias value (negative value) by a small amount, and continuously adjust the central energy and measurement window of the corresponding analyzer until the applied bias value can reach the bottom of the electron cone. The other is to directly set the voltage to -20V or -30V. Due to the crystal stability requirements, the work function must be greater than 0, so in theory, as long as the voltage value is greater than the photon energy, the bottom of the cone can be detected. Some margin can be set here. After seeing the bottom of the cone through the above method, a simple estimate of the work function value is made. Using the formula introduced in the parallel metal plate model, the bias value corresponding to the complete deflection of 90-degree electrons into the analyzer can be estimated, such as Figure 7 As shown in the figure, the horizontal axis represents the applied voltage, the vertical axis represents the sample work function, and the color and contour lines in the figure represent the maximum emission angle that can be collected. Of course, to complete the work function measurement task, it is not necessary to see the entire electron cone. It is only necessary to scan a few slices near the cone bottom area. However, for the sake of data integrity, it is recommended to measure the complete electron cone shape once. After obtaining the electron cone data, there are two ways to extract the cone bottom, such as Figure 5 As shown in the work function principle diagram, the first method is as follows Figure 5 As shown in a-5d, by continuously reducing the binding energy, it can be seen that the size of the electron cone gradually narrows and eventually forms a point, namely the bottom of the electron cone. Therefore, the binding energy can be adjusted until the point with the smallest electron cone area is found. At this momentum position, a distribution curve along the energy in the electron cone matrix is ​​taken, namely the curve of the cone bottom (normal emission). The second method, such as Figure 5 As shown in f-5i, a small area near the bottom of the cone is sliced ​​along a certain momentum direction, and the curve corresponding to the center of the slice is taken out. The lowest curve at the left truncation of the curve is found, which is the cone bottom curve. Regardless of the selection method, the obtained cone bottom curve should contain the same information. The next step is to take a differential of the obtained curve. Since the edges on both sides of the curve are very sharp, two peaks can be obtained. By fitting the positions of these two peaks, the two peak position values ​​are read out. Position(left)= That is, the energy corresponding to the secondary electron cutoff, Position (right) = That corresponds to the Fermi level. Finally, after obtaining two peaks, we can use the formula Calculate the work function. Using this process, we can obtain the work function value with sub-meV accuracy, which is much higher than the sample work function in the existing technology.

[0058] According to one embodiment of the present invention, Figure 8 As shown, measurements using the system of the present invention include the following steps: measuring the work function, determining the appropriate bias voltage, performing a coarse scan, eliminating energy distortion, and converting coordinates using a conversion formula (a physical model of a flat metal plate). As can be seen from the previous embodiments, the work function is a critical physical quantity for subsequent data processing during measurement. Therefore, the testing method of the present invention begins by measuring the work function using the methods described in the previous embodiments. The experiment is then designed and conducted based on the experimental requirements and the desired physical information. For example, if the experimental objective requires visualization of finer band structure details, a lower bias voltage can be used. If a wide range of band information is desired, a higher bias voltage is required. The optimal bias voltage is selected to collect all emitted electrons. This is because the analyzer has a fixed angular resolution. Electrons entering the analyzer at more angles than ±15° are equivalent to a decrease in effective angular resolution. Therefore, from this perspective, the present invention is equivalent to attaching a variable-focal-length lens to a fixed-focal-length analyzer, enabling experiments with high angular resolution while measuring a wider momentum range.

[0059] Experimental process: Figure 8 As shown in the figure, for bias ARPES measurement, as mentioned above, first, the work function of the sample needs to be measured. This step is to prepare for subsequent data processing. At the same time, the work function can also help determine the sample cleavage surface, surface reconstruction and other information. Second, after determining the work function of the sample, combined with the theoretical model described above, and Figure 7The corresponding calculations should be tailored to the actual experimental requirements to select an appropriate bias voltage. For example, if you want to detect a large amount of band structure information, you need to use a high voltage to increase the detection range. Conversely, if the experimental goal is to observe fine electronic band structure, a lower voltage and better momentum resolution are required. Therefore, different voltages should be selected depending on the experimental objectives. Third, a rough scan is performed. Through a quick scan, the voltage is confirmed to be appropriate, whether the desired data information and data range are obtained, and whether the sample-light source-analyzer parameters are correctly selected. For example, the polarization orientation of the light source can include linear polarization of different directions and circular polarization of different handedness. The sample orientation and scattering geometry directly affect the spectral intensity distribution. The analyzer can adjust the energy resolution by setting different measurement modes and slit sizes. By adjusting the scan energy range and acquisition time, it is possible to confirm that the experimental conditions are optimized. Fourth, a formal scan can be performed. By changing the environment and experimental settings, the desired physical properties can be investigated, such as the relationship between temperature, light polarization, and doping. Fifth, after obtaining the data, the effects of energy distortion must be eliminated. Energy distortion primarily arises from two sources. First, due to the electron optics and slit shape, the collected iso-energy positions are not straight lines, but rather curved iso-energy lines. After data acquisition, the analyzer applies a linear correction algorithm using its own software. For conventional ARPES, this algorithm works well because the analyzer's ideal electron optics meet these conditions. However, for biased ARPES experiments, electrons subjected to electric field interference may not fully satisfy the software's inherent correction relationship, as the electron optics are highly sensitive to electron angular variations. This requires additional correction. Second, the energy values ​​corresponding to different angular positions of the electron energy analyzer can vary slightly, a consequence of the analyzer's electron optics accuracy. Conventional ARPES can typically correct for subtle differences in Fermi energy at different locations using methods for measuring polycrystalline gold. However, the experimental process presented in this paper renders these previous methods ineffective, requiring the extraction of Fermi level information from the intrinsic information in the experimental data. The goal of energy distortion correction is to eliminate these inaccuracies in the two energy directions and restore the curved iso-energy lines to a reasonable straight line. The present invention utilizes a unique algorithm, which is similar to the method in the field of image recognition. The processing is divided into three steps. The first step is to use image edge recognition to identify the edge of the matrix in the energy direction and obtain the corresponding energy position as the new energy baseline. For most data, the threshold dichotomy recognition method can complete this task well, that is, a mask is generated with data greater than the threshold set to 1 and less than the threshold set to 0 and multiplied with the original three-dimensional data, and then the energy value corresponding to the edge is identified.However, for data with energy bands at the Fermi energy, due to the existence of the energy bands, the number of measured electrons in this small area will be high, that is, the matrix element value in this area will be enlarged, so simple edge recognition will cover this feature. Therefore, in the second step, the small energy area near the previously generated baseline is integrated and normalized to eliminate the regional intensity enhancement caused by the energy band intensity. Finally, the normalized image edge is identified and the final energy baseline is obtained. The Fermi energy obtained from the experimental data is corrected back to the energy baseline. The Fermi energy flatness obtained by this method can reach less than 1meV and is applicable to most experimental measurements. Sixth, the aforementioned physical models and formulas are used for coordinate transformation to obtain the energy and momentum intrinsic information inside the quantum material.

[0060] In order to verify the effect of the present invention, the following is explained in conjunction with experiments.

[0061] like Figure 9 As shown, Figure 9 a is the momentum space range covered by a single measurement of the original laser ARPES, Figure 9 b is the single measurement range provided by the solution of the present invention. It can be seen that the measurement space is expanded by about 9 times and the measurement efficiency is improved by about 36 times.

[0062] Figure 10 This figure shows all the information collected from the emitted electrons in a single measurement of the typical caged quantum material CsV3Sb5 using the solution of the present invention. As can be seen, a single measurement can obtain all the physical information about the emitted electrons, expanding our comprehensive understanding of the material's electronic properties.

[0063] Figure 11 Using the present invention's technical solution, measurements of the typical copper oxide superconductor Bi2212 under different polarization states reveal clear variations in the matrix response with varying experimental conditions, a feat previously unattainable with conventional ARPES. This overcomes the limitation of previous laser ARPES techniques, which relied solely on mechanical sample rotation for testing, providing experimental technical support for studying matrix elements and potentially opening up new possibilities for studying the fine structure of electrons.

[0064] Through the above embodiments, it can be seen that the scheme of the present invention can achieve the following purposes: the present invention realizes an ultra-low-cost, stable, efficient and universal laser ARPES bias increase scheme, further realizes the expansion of the laser ARPES detection range, and greatly improves the detection efficiency; the present invention expands the ability of laser ARPES to measure work function, and provides a new method to realize high-precision detection of sample work function, and realizes the spatial resolution capability of work function; the present invention retains the high-resolution detection advantage of laser ARPES, and can realize the detection of high-precision electronic structure. In the absence of bias, it has the same measurement method and resolution as conventional laser ARPES and has universal applicability; the scheme of the present invention has the ability to detect weak signals. After the momentum detection range is expanded, the measurement statistics will also be enhanced. The same statistical signal detection can be achieved with weaker light intensity, and the enhanced statistical effect can be achieved for samples with weak signals; the scheme of the present invention can be extended to ultrafast light sources to achieve compatibility with ultrafast research. At the same time, by replacing the appropriate light source, two-photon research on the unoccupied state electronic structure of the sample can be realized.

[0065] It should be noted that although the above describes the various steps in a specific order, it does not mean that the steps must be performed in the above specific order. In fact, some of these steps can be executed concurrently or even in a different order as long as the required functions can be achieved.

[0066] While various embodiments of the present invention have been described above, the above descriptions are intended to be illustrative, non-exhaustive, and not limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is selected to best explain the principles of the embodiments, their practical applications, or technological improvements in the marketplace, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. An angle-resolved photoelectron spectroscopy detection system for analyzing quantum materials, characterized in that: The system includes a light source, a vacuum chamber, a sample stage, an electron energy analyzer, a source meter, a first operating mode, and a second operating mode, wherein: The light source is used to provide photon excitation, and the light shines on the sample; The vacuum chamber is used to provide a vacuum environment; The sample stage is set in the vacuum chamber and is used to carry the sample to be analyzed. In order from top to bottom, the sample stage includes: a cryostat, a cold head, an insulating sheet, a copper block, and a sample holder, among which: A cryostat is used to provide a low temperature environment; The cold head is connected to the bottom end of the cryostat; The cold head is connected to one end of the copper block via an insulating sheet, and the other end of the copper block is connected to the sample holder, or the cold head is connected to one end of the copper block, and the other end of the copper block is connected to the sample holder via an insulating sheet, and the sample holder is used to directly carry the quantum material sample to be detected; or the cold head is connected to one end of the copper block, and the other end of the copper block is connected to the sample holder, and the insulating sheet is inserted between the sample holder and the quantum material sample to be detected; The sample holder is connected to a source meter with adjustable voltage. The source meter is used to apply bias voltage to the sample to form an electric field between the sample stage and the electron energy analyzer. When light is irradiated on the sample surface, electrons absorb the light energy and escape into the detection range of the electron energy analyzer. The electron energy analyzer is disposed in a vacuum chamber and is used to detect the emission angle in the tilt angle direction, the emission angle in the azimuth angle direction, the kinetic energy, and the corresponding number of electrons emitted from the sample within its detection range after the sample is illuminated under bias. The electron energy analyzer is configured with a first operating mode and a second operating mode, wherein: In the first working mode, the electron energy analyzer extracts the electron cone bottom energy distribution curve based on the detected electron cone, obtains the distance between the two peaks through differentiation, and analyzes the sample work function according to the first preset analysis model; In the second working mode, the electron energy analyzer analyzes the momentum in the x-direction, the momentum in the y-direction, and the electron binding energy values ​​corresponding to the electrons inside the sample according to the second preset analysis model based on the detected electron emission angle in the tilt angle direction, the electron emission angle in the azimuth angle direction, and the kinetic energy, combined with the sample work function.

2. The angle-resolved photoelectron spectroscopy detection system according to claim 1, characterized in that: The light source further comprises a light source focusing system for focusing the light beam.

3. The angle-resolved photoelectron spectroscopy detection system according to claim 1, characterized in that: The sample stage further comprises a copper braid, and the copper block is connected to the sample holder via the copper braid.

4. The angle-resolved photoelectron spectroscopy detection system according to any one of claims 1 to 3, characterized in that: The insulating sheet is made of sapphire or Kapton plastic.

5. The angle-resolved photoelectron spectroscopy detection system according to claim 1, characterized in that: The electron energy analyzer is a hemispherical analyzer.

6. The angle-resolved photoelectron spectroscopy detection system according to claim 1, characterized in that: The first preset model is: in, is the surface work function of the sample, represents the photon energy, is the measured internal Fermi level of the sample, is the measured energy value corresponding to the value of kinetic energy of 0 in the emitted electron, and are the two peaks of the cone bottom energy distribution curve, is the distance between the two peaks, and the symbols in the formula represent the superscript Represents Detector.

7. The angle-resolved photoelectron spectroscopy detection system according to claim 5, characterized in that: When the electron energy analyzer detects the electron emission angle in the tilt angle direction, the electron emission angle in the azimuth angle direction, and the kinetic energy in the second operating mode, it performs energy distortion elimination processing on the data and then analyzes the momentum of the sample's emitted electrons in the x-direction, the momentum in the y-direction, and the electron binding energy value according to the second preset analysis model. The energy distortion elimination processing is performed in the following manner: The first step is to use image edge recognition to identify the edge of the matrix in the energy direction and obtain the corresponding energy position as the new energy baseline; The second step is to integrate and normalize the small energy region near the previously generated baseline, and eliminate the regional intensity enhancement caused by the band intensity; The third step is to identify the edges of the normalized image and obtain the final energy baseline.

8. The angle-resolved photoelectron spectroscopy detection system according to claim 7, characterized in that: The second preset model is: in, in, is the kinetic energy value detected by the electron energy analyzer, with the superscript Represents Detector, is the kinetic energy value of the sample surface, the superscript Representative Sample, is the effective electric field potential energy, is the basic charge, is the energy of the photon in the photoelectric effect, is Planck's constant, is the photon frequency, is the sample work function, is the internal electron binding energy of the material to be solved, is the reduced Planck constant, defined as , is the rest mass of the free electron, The internal electrons of the material to be solved Momentum in direction, The internal electrons of the material to be solved Momentum in direction, is the bias voltage applied to the sample, is the instrument work function, is the electron emission angle in the tilt angle direction detected by the electron energy analyzer, is the emission angle of the electron detected by the analyzer in the azimuthal direction. is the conversion factor, where is the analyzer angle limit conversion coefficient, is the analyzer position limit conversion coefficient, is the linear correlation coefficient. For the convenience of writing, the dimensionless parameter is defined .

9. The angle-resolved photoelectron spectroscopy detection system according to claim 8, characterized in that: The second preset model also includes an intensity correction term to map the angle space to the momentum space: Among them, each partial differential component is: in, The formula Used to indicate or One of them.

10. A photoelectron spectroscopy detection method based on the angle-resolved photoelectron spectroscopy detection system according to any one of claims 1 to 9, characterized in that: The method comprises: Place the sample to be tested on the sample holder of the angle-resolved photoelectron spectroscopy detection system; Turn on the light source to illuminate the sample and apply a bias voltage through the power supply connected to the sample holder; The electron energy analyzer of the angle-resolved photoelectron spectroscopy detection system detects the complete electron cone of photoelectrons in a first working mode and detects the emission angle of electrons in the tilt angle direction, the emission angle of electrons in the azimuth angle direction, and the kinetic energy within the detection range in a second working mode; The sample work function is obtained according to the electron cone by the angle-resolved photoelectron spectroscopy detection system; The angle-resolved photoelectron spectroscopy detection system obtains the momentum of electrons in the x-direction, the momentum in the y-direction, and the electron binding energy values ​​inside the sample based on the electron emission angle in the tilt angle direction, the electron emission angle in the azimuth angle direction, the kinetic energy, and the sample work function.

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