High-voltage electron gun brightness analysis method and related device

Abstract

The invention discloses a high-voltage electron gun brightness analysis method and a related device, and the method comprises the steps: building a high-voltage electron gun simulation model with a multi-stage acceleration lens, analyzing the influence of the thickness, spacing, inner diameter and other structural parameters of an electrode on the on-axis electric field distribution of the multi-stage acceleration lens, and building a fitting expression of the on-axis electric field distribution of the multi-stage acceleration lens. And based on a fitting expression, deducing the relationship between the structure parameter of the multistage accelerating lens and the spherical aberration coefficient, and further calculating the distribution of the brightness of the high-voltage electron gun along with the beam half angle. The analysis method can explore the relationship between the maximum brightness on the axis and the brightness under the specific beam half angle, and reveal the rule of the influence of the multistage accelerating lens on the brightness of the electron gun. And the method can also be used for multi-parameter optimization of a multi-stage accelerating lens so as to improve a brightness curve uniform area of the high-voltage electron gun.

Description

Technical Field

[0001] The present invention relates to the field of electronic optical systems, and in particular to a high-voltage electron gun brightness analysis method and related devices. Background Art

[0002] A multi-stage accelerating lens is a core component of a transmission electron microscope (TEM). Its function is to accelerate the electron beam to high energies (typically 100-300 keV). In addition to meeting high-voltage insulation and easy installation requirements, the multi-stage accelerating lens also needs to consider its impact on electron beam brightness. Brightness is defined as the electron beam current density per unit solid angle. This parameter comprehensively reflects important characteristics of the electron gun, such as beam intensity and uniformity, and directly affects the ultimate resolution of the TEM.

[0003] The inner diameter, thickness, and spacing of the electrodes in a multi-stage accelerating lens affect the electric field distribution between the electrodes, which in turn affects the transmission trajectory of the electron beam in the multi-stage accelerating section, and ultimately affects the brightness characteristics of the electron beam. Domestic and foreign scholars typically use simulation calculation methods for multi-stage accelerating structures. By constructing a simulation model and using numerical methods to simulate and calculate the trajectory of the electron beam in the multi-stage accelerating lens, etc., this method can obtain parameters such as the electron beam trajectory and aberrations, but it is difficult to explore the mechanism by which the electrode structure and excitation parameters affect the brightness of the electron beam. Therefore, constructing a method to analyze the mechanism by which the multi-stage accelerating lens structure and excitation parameters affect the brightness characteristics of the electron beam has important guiding significance for the design of high-resolution TEM electron guns.

[0004] Furthermore, when optimizing the electrode structure parameters of a multi-stage accelerating lens, the traditional method of setting up a test bench to measure the electrode structure's impact on brightness and then optimizing the electrode structure is time-consuming, while single-variable optimization methods struggle to find the optimal electrode structure. Therefore, it is crucial to perform multi-parameter optimization of the multi-stage accelerating lens based on the influence of the constructed multi-stage accelerating lens on the electron gun's brightness distribution curve. Summary of the Invention

[0005] In response to the current lack of analytical methods for the mechanism by which multi-stage accelerating lens structures and excitation parameters influence the brightness of electron guns, the present invention proposes an analytical method and related device for analyzing the influence of multi-stage accelerating lens structures on the brightness of electron guns by using a fitting expression for the electric field distribution on the axis of the multi-stage accelerating lens. The present invention can analyze the mechanism by which the multi-stage accelerating lens influences the brightness of electron guns, and can also be used for the multi-parameter optimization design of multi-stage accelerating lenses, thereby improving the efficiency of simulation design.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions: A method for analyzing the brightness of a high-voltage electron gun comprises the following steps: Step 1: Construct a multi-stage acceleration lens simulation model; Step 2: Based on the multi-stage accelerating lens simulation calculation model, construct a fitting expression for the electric field intensity on the multi-stage accelerating lens axis; Step 3: Calculate the third-order spherical aberration coefficient of the multi-stage accelerating lens based on the fitting expression of the electric field intensity on the multi-stage accelerating lens axis; Step 4: Based on the third-order spherical aberration coefficient of the multi-stage accelerating lens, the brightness expression of the high-voltage electron gun is obtained; Step 5: Based on the high-voltage electron gun brightness expression, the parameters affecting the electron gun brightness are analyzed, and a multi-parameter optimization design of the electron gun with a multi-stage acceleration structure is performed.

[0007] Furthermore, the multi-stage accelerating lens simulation calculation model includes an emission unit and a multi-stage accelerating unit. The emission unit is a thermal field emission electron gun, including a cathode, a suppressor, and an absorber. The cathode is arranged along the main optical axis of the electron gun. The suppressor is arranged outside the cathode and is arranged on one side of the cathode at a distance of 250 μm from the cathode gun tip. A voltage of -300 V is applied relative to the cathode. The absorber is arranged on the other side of the cathode at a distance of 500 μm from the cathode gun tip. A voltage of 4000 V is applied relative to the cathode. The multi-stage acceleration unit includes a plurality of acceleration unit electrodes, which are arranged between the emission unit and the exit plane along the main optical axis of the electron gun. The outer boundaries between the acceleration unit electrodes and the exit plane serve as boundaries for simulation calculation.

[0008] Furthermore, based on the multi-stage accelerating lens simulation calculation model, a fitting expression for the electric field intensity on the multi-stage accelerating lens axis is constructed, specifically: The electric field intensity on the axis of the multi-stage accelerating lens is fitted using Fourier series. The fitting expression is as follows:

[0009] in, z is the distance between the main optical axis of the electron gun and the cathode gun tip, unit: m; harmonic coefficient , n is the harmonic order; L, R, and H are the structural parameters of the multi-stage accelerating lens, where L is the thickness of the accelerating unit electrode, unit: m; R is the distance between adjacent accelerating unit electrodes, unit: m; H is the inner diameter of the accelerating unit electrode, unit: m; N is the maximum value of the harmonic order; is the amplitude of the field distribution, unit: V / m; K is the slope of the linear function of the field strength; D is the length of a single acceleration unit, and D=L+R, unit: m.

[0010] Furthermore, the third-order spherical aberration coefficient of the multi-stage accelerating lens is calculated based on the fitting expression of the electric field intensity on the axis of the multi-stage accelerating lens, specifically: Substituting the fitting expression of the electric field intensity on the multi-stage accelerating lens axis into the integral formula of the spherical aberration coefficient and ignoring high-order harmonics, we get:

[0011] Further rewritten as:

[0012] The relationship between the third-order spherical aberration coefficient of the multi-stage accelerating lens and the structural parameters of the multi-stage accelerating lens is expressed as:

[0013] Where, k 1. k 2 is the proportional factor introduced to consider the voltage division of adjacent electrodes of the multi-stage accelerating lens and the influence of the emission unit on the electric field distribution of the multi-stage accelerating unit.

[0014] Furthermore, the brightness expression of the high-voltage electron gun is expressed as follows:

[0015] Where, is the current, unit: A; is the beam half angle, unit: mrad; is the radius of the virtual source considering the influence of spherical chromatic aberration, unit: nm; is the virtual source diameter, unit: nm; is the cathode effective emission area, unit: nm 2 ; is the angular current density, unit: A / srad; in,

[0016]

[0017] Where, is the radius of the virtual source without considering the influence of spherical chromatic aberration, unit: nm; is the radius of the blur circle caused by spherical aberration, unit: nm; is the radius of the blur circle caused by chromatic aberration, unit: nm; is the third-order spherical aberration coefficient, unit: mm; is the half-order central chromatic aberration coefficient, unit: mm; is the first-order central chromatic aberration coefficient, unit: mm; is the energy dispersion of the electron beam when it is emitted, unit: eV; It is the highest energy of electrons in a high-brightness electron gun, unit: eV.

[0018] Furthermore, keeping the emission unit structure and excitation parameters unchanged, the structural parameters R, L and H of the multi-stage accelerating lens are changed in sequence to obtain the maximum brightness on the axis when the above structural parameters are changed. , blur circle radius affected by chromatic aberration , virtual source radius without considering the influence of spherical chromatic aberration Basically does not change with the change of structural parameters. 、 and The average value of the simulation calculation is substituted into the expression of the electron gun brightness, and the beam half angle is The brightness at the axis is expressed as the maximum brightness The proportional relationship:

[0019]

[0020] In the formula The maximum brightness on the axis, unit: A / cm 2 .srad; The beam half angle is Brightness at the time, unit: A / cm 2 .srad; is the maximum angular current density on the axis, unit: A / srad.

[0021] Furthermore, based on the high-voltage electron gun brightness expression, the parameters affecting the electron gun brightness are analyzed, and the multi-parameter design of the electron gun with a multi-stage acceleration structure is optimized, specifically: The maximum brightness and the uniform area of the brightness curve are used as parameters to examine the brightness of the electron gun; Based on the influence of different multi-stage acceleration units on the uniform area of the brightness curve, a multi-parameter optimization design of the electron gun with a multi-stage acceleration unit is carried out to improve the uniform area of the brightness curve; The uniform area of the brightness curve is defined as the beam half angle occupied by 90% of the maximum brightness, and the beam half angle is defined as half of the solid angle opened by the electron beam.

[0022] A high-voltage electron gun brightness analysis system, comprising: Model building module: used to build a multi-stage acceleration lens simulation calculation model; Expression building module: used to build the fitting expression of the electric field intensity on the axis of the multi-stage accelerating lens based on the multi-stage accelerating lens simulation calculation model; The first calculation module is used to calculate the third-order spherical aberration coefficient of the multi-stage accelerating lens based on the fitting expression of the electric field intensity on the multi-stage accelerating lens axis; The second calculation module is used to obtain the brightness expression of the high-voltage electron gun based on the third-order spherical aberration coefficient of the multi-stage accelerating lens; Analysis module: used to analyze the parameters affecting the brightness of the electron gun based on the brightness expression of the high-voltage electron gun, and to perform multi-parameter optimization design of the electron gun with a multi-stage acceleration structure.

[0023] A computer device comprises a memory, a processor and a computer program stored in the memory and runnable on the processor. When the processor executes the computer program, the steps of the high-voltage electron gun brightness analysis method are realized.

[0024] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the high-voltage electron gun brightness analysis method are implemented.

[0025] Compared with the prior art, the present invention has the following beneficial technical effects: The present invention proposes a method for analyzing the brightness of a high-voltage electron gun. This method first establishes a fitting expression for the on-axis electric field of a multi-stage accelerating lens. The method then uses this fitting expression to derive a relationship between the influence of the multi-stage accelerating lens structure on the third-order spherical aberration coefficient and the brightness of the electron gun. This method facilitates the study of the influence of the multi-stage accelerating lens structure of a high-voltage electron gun on the maximum brightness and the distribution of brightness with beam half-angle, and can further be used to optimize the brightness of the electron gun. Compared with traditional methods that study the influence of the multi-stage accelerating structure on the brightness of the electron gun through simulation calculations and experimental testing, the method of the present invention, by establishing a relationship expression for the influence of the multi-stage accelerating lens structure on the brightness of the electron gun, can quickly obtain the key structural parameters of the electron gun. This method can not only analyze the mechanism of the influence of the electron gun multi-stage accelerating structure parameters on characteristics such as spherical aberration, electron gun brightness distribution, and virtual source size from a physical perspective, but also avoid the complex processes of model establishment, meshing, simulation solution, and other numerical calculations, thereby improving the efficiency of electron gun brightness analysis and optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The drawings in the specification are used to provide further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0027] Figure 1 It is a schematic diagram of the overall structure of the electron gun; Figure 2 It is a schematic diagram of the transmitting unit structure; Figure 3 It is a schematic diagram of the structure of a multi-stage acceleration unit; Figure 1-Figure 3In the figure, 101, emission unit; 102, multi-stage acceleration unit; 103, main optical axis of electron gun; 104, acceleration unit electrode; 105, boundary of simulation calculation; 201, cathode; 202, suppression electrode; 203, absorption electrode; Figure 4 is the electric field intensity in the Z direction under different electrode partial pressures; Figure 5 is the electric field intensity in the Z direction at different electrode spacings; Figure 6 is the electric field intensity in the Z direction under different electrode thicknesses; Figure 7 is the electric field intensity in the Z direction under different electrode inner diameters; Figure 8 is the comparison of the field distribution between fitting and simulation calculations; Figure 9 It is the change of maximum brightness and uniform range of brightness curve when the inner diameter of the electrode changes; Figure 10 is the variation of angular current density with structural parameters; Figure 11 is the change of blur circle diameter caused by spherical chromatic aberration with structural parameters; Figure 12 is the variation of the third-order spherical aberration coefficient with the structural parameters; Figure 13 Model 1 simulation and brightness curve calculated according to the formula; Figure 14 It is the change during the optimization process of electrode structure size; Figure 15 It is the change during the optimization process of the uniform area of the brightness curve; Figure 16 is the change in the third-order spherical aberration coefficient during the optimization process; Figure 17 It is the brightness curve of the multi-stage accelerated lens optimization change; Figure 18 It is a flow chart of the high-voltage electron gun brightness analysis method of the present invention. DETAILED DESCRIPTION

[0028] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0029] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0030] A method for analyzing the brightness of a high-voltage electron gun, such as Figure 18 As shown, including: The first step is to build a simulation model of a multi-stage accelerating lens. The multi-stage accelerating lens is a typical axisymmetric electrostatic lens used in the acceleration section of a high-voltage electron gun. The simulation model is as follows: Figure 1 As shown in Figure 1 . This simulation model primarily consists of an emission unit 101 and a multi-stage acceleration unit 102. The emission unit is a thermal field emission electron gun, consisting of a cathode 201, a suppressor 202, and an extractor 203. The cathode 201 is made of a tungsten wire coated with zirconium oxide. In the simulation model, the cathode 201 is arranged along the main optical axis 103 of the electron gun. The suppressor 202 is located outside the cathode 201, on the left side of the cathode 201, 250 μm from the cathode gun tip, with a voltage of -300 V applied relative to the cathode. The extractor 203 is located on the right side of the cathode 201, 500 μm from the cathode gun tip, with a voltage of 4000 V applied relative to the cathode. The acceleration unit electrode 104 has a similar structure and is arranged along the main optical axis 103 of the electron gun, between the right side of the emission unit 101 and the exit plane. The voltage between the electrodes of the multi-stage accelerating lens is Vd = 3000V. The electrode structural parameters are electrode thickness L (unit: mm), electrode inner diameter H (unit: mm), and electrode spacing R (unit: mm). The length of a single accelerating unit is defined as D = L + R (unit: mm). The electron beam is accelerated through six stages, raising its energy to 200 kV. The outer boundary between the accelerating unit electrodes 104 and the exit plane serve as the boundary 105 for the simulation calculation.

[0031] The second step is to construct a fitting expression for the electric field intensity on the axis of the multi-stage accelerating lens. Based on the structural parameters and excitation parameters of the emitting unit and accelerating unit electrodes, a numerical method is used to calculate the surface current density of the emitting unit cathode, the spatial electric field distribution, and the electron beam trajectory. At the same time, the influence of the space charge effect is considered and the electric field distribution is corrected. This cycle is repeated until the calculation results converge. During the calculation process, the isoparametric finite element method is used to deal with irregular electrode structures and obtain the value of the field distribution. The thickness of the accelerating unit electrode, the distance between adjacent accelerating unit electrodes, and the inner diameter of the accelerating unit electrode are changed in turn, and the corresponding electric field distribution change law when the structural parameters of each accelerating unit electrode are changed is simulated and calculated. Figure 6 Taking the axial electric field under different accelerating unit electrode thicknesses L as an example, the axial electric field distribution is periodic, and the overall electric field distribution shows an upward trend. The electric field distribution under different accelerating unit electrode voltages Vd, different accelerating unit electrode spacings R, and different accelerating unit electrode inner diameters H presents similar characteristics. Therefore, the present invention uses Fourier series fitting to obtain the electric field strength. The fitting formula is as follows: (1) Where, z is the distance between the main optical axis of the electron gun and the cathode gun tip, unit: m; harmonic coefficient , n is the harmonic order; L, R, and H are the structural parameters of the multi-stage accelerating lens, where L is the thickness of the accelerating unit electrode, unit: m; R is the distance between adjacent accelerating unit electrodes, unit: m; H is the inner diameter of the accelerating unit electrode, unit: m; N is the maximum value of the harmonic order; is the amplitude of the field distribution, unit: V / m; K is the slope of the linear function of field strength; D is the length of a single acceleration unit (D=L+R), unit: m.

[0032] Step 3. Calculate the third-order spherical aberration coefficient of the multi-stage accelerating lens. Substitute the fitting expression of the electric field intensity on the axis of the multi-stage accelerating lens obtained in the second step into the integral formula of the spherical aberration coefficient and ignore the high-order harmonics to obtain (2) When is small, the exponential term can be linearly approximated, and formula (2) can be rewritten as (3) The relationship between the third-order spherical aberration coefficient and the electrode structure parameters in the multi-stage accelerating lens simulation model can be expressed as (4) In the formula k 1. k2 is the proportional factor introduced by considering the voltage division of adjacent electrodes of the multi-stage accelerating lens and the influence of the emission unit on the electric field distribution of the multi-stage accelerating unit. It can be determined by fixing the electrode structure and excitation of the emission unit, fixing the voltage division of the multi-stage accelerating lens electrodes, changing the electrode structure parameters of the multi-stage accelerating lens, and using the least squares fitting method.

[0033] The fourth step is to calculate the brightness of the electron gun. The formula for calculating the brightness of the electron gun is as follows: (5) Where, is the current (unit: A); is the beam half angle (unit: mrad); is the radius of the virtual source considering the influence of spherical chromatic aberration (unit: nm); is the virtual source diameter (unit: nm); is the cathode effective emission area (unit: nm 2 ); is the angular current density (unit: A / srad).

[0034] in (6) (7) (8) In the formula is the radius of the virtual source considering the effects of spherical and chromatic aberrations, unit: nm; is the radius of the virtual source without considering the influence of spherical chromatic aberration, unit: nm; is the radius of the blur circle caused by spherical aberration, unit: nm; is the radius of the blur circle caused by chromatic aberration, unit: nm; is the third-order spherical aberration coefficient, unit: mm; is the half-order central chromatic aberration coefficient, unit: mm; is the first-order central chromatic aberration coefficient, unit: mm; is the energy dispersion of the electron beam when it is emitted, unit: eV; is the electron gun acceleration voltage, unit: V.

[0035] Step 5: Explore the maximum brightness on the axis based on the brightness expression and beam half angle Brightness The relationship between them can be analyzed based on which the parameters affecting the brightness of the electron gun can be analyzed. The multi-parameter optimization of the electrode structure parameters of the multi-stage acceleration unit can also be performed according to the change of brightness with beam half-angle to improve the uniform area of the brightness curve.

[0036] (9) (10) In the formula The maximum brightness on the axis, unit: A / cm 2 .srad; The beam half angle is Brightness at the time, unit: A / cm 2 .srad; is the maximum angular current density on the axis, unit: A / srad. 、 、r、 The parameters can be determined by the following method: keep the emission unit structure and excitation parameters unchanged, change the structural parameters R, L and H of the multi-stage acceleration lens, and obtain the maximum brightness on the axis when the above structural parameters change. , blur circle radius affected by chromatic aberration , virtual source radius without considering the influence of spherical chromatic aberration Basically does not change with the change of structural parameters. 、 、 and The average value of the simulation calculation is substituted into the expression of the electron gun brightness, and a certain beam half angle can be The brightness at the axis is expressed as the maximum brightness proportional relationship.

[0037] High-voltage electron guns are usually equipped with an aperture, that is, there is a fixed beam half-angle on the beam path, which intercepts a part of the electrons with higher overall brightness in the brightness distribution curve with beam half-angle. Therefore, the maximum brightness and the uniform area of the brightness curve (defined as the beam half-angle occupied by 90% of the maximum brightness) can be used as parameters to examine the brightness of the electron gun, and the brightness under a fixed beam half-angle (such as 2mrad, 5mrad, etc.) can also be examined. At this time, in the brightness calculation formula, the beam half-angles of different structural models are consistent, which can be used to analyze the influence of the spherical chromatic aberration coefficient on the actual effective emission area and give the distribution law of brightness with beam half-angle. In addition, based on the influence of different multi-stage accelerating lenses on the uniform area of the brightness curve, a multi-parameter optimization design of the electron gun with a multi-stage accelerating lens can also be performed to improve the uniform area of the brightness curve ( Figure 17 ).

[0038] Example 1 This paper takes the calculation of the field distribution of the 6-stage accelerating structure in a 200kV thermal field emission electron gun as an example to illustrate, and explores the influence of the parameter changes of the multi-stage accelerating lens structure on the angular current density, spherical aberration coefficient and brightness of the electron gun.

[0039] The emission unit is a thermal field emission electron gun with a cathode curvature radius of 0.5μm. A 4kV voltage is applied to the absorption electrode relative to the cathode to cause electrons to be emitted from the tungsten cathode coated with zirconium oxide. A -300V voltage is applied to the suppression electrode to suppress large-angle electron emission. The first and second anodes serve to pre-focus the electron beam. The multi-stage accelerating lens uses a 6-stage equipotential gradient acceleration method to accelerate the electron beam to 200kV. The simulation calculation model of the multi-stage accelerating lens is as follows: Figure 1 The electrode structures of the multi-stage acceleration section are the same except for the first acceleration stage. Here, three multi-stage acceleration lens calculation models are set. The parameters of model 1 (i.e. the initial model) are: acceleration unit electrode spacing R = 16.6mm, acceleration unit electrode thickness L = 7.3mm, acceleration unit electrode inner diameter H = 10.4mm. Figure 3 According to the above scheme, the voltage divider Vd of two adjacent accelerating unit electrodes in the multi-stage accelerating section, the distance R between the accelerating unit electrodes, the thickness L of the accelerating unit electrodes, and the inner diameter H of the accelerating unit electrodes are changed in sequence to obtain the curve of the on-axis field distribution as the above structural parameters change (as shown in Figure 4-Figure 7 ). According to the influence of electrode structure and voltage on the on-axis field distribution, the values of various parameters in the fitting expression of the on-axis field distribution of the multi-stage accelerating lens are determined. In order to verify the accuracy of the analytical expression, in addition to the above-mentioned multi-stage accelerating stage structure, the structural dimensions of model 2: accelerating unit electrode spacing R = 17.4mm, accelerating unit electrode thickness L = 7.1mm, accelerating unit electrode inner diameter H = 11.2mm and model 3: accelerating unit electrode spacing R = 19.5mm, accelerating unit electrode thickness L = 7.8mm, accelerating unit electrode inner diameter H = 11.8mm are selected. The on-axis electric field distribution calculated by the fitting expression and the on-axis electric field distribution calculated by numerical simulation are shown as follows Figure 8 It can be seen that the error between the two is less than or equal to 5%, indicating that the fitting expression of the field distribution on the multi-stage accelerating lens axis is basically consistent with the actual field distribution.

[0040] Taking the change of electrode thickness L as an example, Figure 9 Simulation calculations show that as the electrode structure parameters L*H / R / R increase, the maximum brightness changes little, while the uniform area of the brightness curve increases. To further analyze the relationship between the uniform area of the brightness curve and the electrode structure of the multi-stage acceleration unit, a fixed beam half-angle of 5mrad was selected. Simulation calculations show that the angular current density at 5mrad basically does not change with changes in the structure parameters L*H / R / R (e.g. Figure 10 ), the main parameter affecting the brightness at a 5mrad beam half angle is the virtual source diameter (e.g. Figure 11 ), as the structural parameters L*H / R / R increase, the diameter of the blur circle caused by chromatic aberration changes little, while the diameter of the blur circle caused by spherical aberration decreases. As the structural parameters L*H / R / R increase, the third-order spherical aberration coefficient gradually decreases (such as Figure 12). According to the influence of the electrode structure on the third-order spherical aberration coefficient, the expression of the third-order spherical aberration coefficient can be fitted and deduced as follows: (11) The third-order spherical aberration coefficient fitting expression considering the influence of electrode structure size is substituted into the brightness calculation formula to analyze the brightness characteristics. Taking model 1 as an example, the brightness calculated by the formula and the brightness calculated by simulation are as follows Figure 13 It can be seen that the two are basically consistent, which shows that the third-order spherical aberration coefficient is the main factor affecting the brightness distribution curve with beam half angle.

[0041] Through this formula, we can easily analyze the influence of the multi-stage acceleration structure parameters on the third-order spherical aberration coefficient. That is, the smaller the third-order spherical aberration coefficient of the multi-stage acceleration unit, the smaller the diameter of the blur circle caused by spherical aberration under a certain beam half-angle, and the larger the uniform area of the brightness curve.

[0042] Example 2 The optimization of the structural parameters of the multi-stage acceleration unit of a 200kV high-voltage electron gun is used as an example to illustrate the improvement of the uniform area of the brightness curve.

[0043] The cathode electrons are in the form of thermal field emission, and the cathode curvature radius is 0.8μm. A voltage of 7kV is applied to the absorption stage relative to the cathode, and a voltage of -300V is applied to the suppression stage relative to the cathode. The multi-stage acceleration stage is 7-stage acceleration, and the voltage between two adjacent electrodes is 20kV. The electrode spacing R=20mm, electrode thickness L=8mm, and electrode inner diameter H=12mm of the multi-stage acceleration unit. According to the above scheme, the relationship between the brightness of the electron gun and the beam half-angle can be obtained by simulation calculation. Similar to Example 1, the multi-stage acceleration unit does not affect the maximum brightness on the axis, but only affects the uniform area of the brightness curve. Subsequently, a multi-parameter optimization method is used to optimize the electrode structure parameters of the multi-stage acceleration lens to improve the brightness characteristics of the electron gun. After 7 steps of optimization, the final structure of the multi-stage acceleration lens obtained is an electrode spacing R=16.7mm, an electrode thickness L=6.9mm, and an electrode inner diameter H=9.1mm. Under the conditions of the emission unit and electrode voltage divider, the third-order spherical aberration coefficient is calculated by fitting: (12) The changes of electrode structural parameters during the optimization process are as follows: Figure 14 , the change of the uniform area of the brightness curve is as follows Figure 15 , the change of the third-order spherical aberration coefficient is as follows Figure 16 It can be seen that the essence of optimizing the multi-stage accelerating lens is to reduce the third-order spherical aberration coefficient, thereby increasing the uniform area of the brightness curve. After the optimized design, the third-order spherical aberration coefficient is smaller, and the uniform area of the brightness curve occupies a larger beam half-angle range (such as Figure 17This provides ideas and directions for the optimization design of multi-stage acceleration systems. The process of optimizing the multi-stage acceleration lens is essentially the process of reducing the third-order spherical aberration coefficient of the multi-stage acceleration lens. Based on this rule, multi-parameter optimization design can simultaneously optimize the electrode inner diameter H, electrode thickness L, and electrode spacing R. The optimization process iteratively converges quickly, improving the efficiency of simulation design.

[0044] Example 3 This embodiment provides a high-voltage electron gun brightness analysis system, including: Model building module: used to build a multi-stage acceleration lens simulation calculation model; Expression building module: used to build the fitting expression of the electric field intensity on the axis of the multi-stage accelerating lens based on the multi-stage accelerating lens simulation calculation model; The first calculation module is used to calculate the third-order spherical aberration coefficient of the multi-stage accelerating lens based on the fitting expression of the electric field intensity on the multi-stage accelerating lens axis; The second calculation module is used to obtain the brightness expression of the high-voltage electron gun based on the third-order spherical aberration coefficient of the multi-stage accelerating lens; Analysis module: used to analyze the parameters affecting the brightness of the electron gun based on the brightness expression of the high-voltage electron gun, and to perform multi-parameter optimization design of the electron gun with a multi-stage acceleration structure.

[0045] Example 4 This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the high-voltage electron gun brightness analysis method are implemented.

[0046] Example 5 This embodiment provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the steps of the high-voltage electron gun brightness analysis method are implemented.

[0047] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit its scope of protection. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that after reading the present invention, those skilled in the art may still make various changes, modifications or equivalent substitutions to the specific implementation methods of the invention, but these changes, modifications or equivalent substitutions are all within the scope of protection of the pending claims of the invention.

Claims

1. A method for analyzing the brightness of a high-voltage electron gun, characterized in that: The steps include: Step 1: Construct a multi-stage acceleration lens simulation model; Step 2: Based on the multi-stage accelerating lens simulation calculation model, construct a fitting expression for the electric field intensity on the multi-stage accelerating lens axis; Step 3: Calculate the third-order spherical aberration coefficient of the multi-stage accelerating lens based on the fitting expression of the electric field intensity on the multi-stage accelerating lens axis; Step 4: Based on the third-order spherical aberration coefficient of the multi-stage accelerating lens, the brightness expression of the high-voltage electron gun is obtained; Step 5: Based on the high-voltage electron gun brightness expression, analyze the parameters that affect the electron gun brightness, and perform multi-parameter optimization design of the electron gun with a multi-stage acceleration structure.

2. A high-voltage electron gun brightness analysis method according to claim 1, characterized in that: The multi-stage accelerating lens simulation calculation model comprises an emitting unit (101) and a multi-stage accelerating unit (102); the emitting unit (101) is a thermal field emission electron gun, comprising a cathode (201), a suppressor (202) and an absorber (203); the cathode (201) is arranged along the main optical axis (103) of the electron gun; the suppressor (202) is arranged outside the cathode (201) and is arranged on one side of the cathode (201) at a distance of 250 μm from the cathode gun tip, and a voltage of -300 V is applied relative to the cathode (201); the absorber (203) is arranged on the other side of the cathode (201) at a distance of 500 μm from the cathode gun tip, and a voltage of 4000 V is applied relative to the cathode (201); The multi-stage acceleration unit (102) includes a plurality of acceleration unit electrodes (104), which are arranged between the emission unit (101) and the exit plane along the main optical axis (103) of the electron gun, and the outer boundary between the acceleration unit electrodes (104) and the exit plane serve as the boundary (105) of the simulation calculation.

3. A high-voltage electron gun brightness analysis method according to claim 2, characterized in that: Based on the multi-stage accelerating lens simulation calculation model, a fitting expression for the electric field intensity on the multi-stage accelerating lens axis is constructed, specifically: The electric field intensity on the axis of the multi-stage accelerating lens is fitted using Fourier series. The fitting expression is as follows: in, z is the distance between the main optical axis of the electron gun and the cathode gun tip, unit: m; harmonic coefficient , n is the harmonic order; L, R, and H are the structural parameters of the multi-stage accelerating lens, where L is the thickness of the accelerating unit electrode, unit: m; R is the distance between adjacent accelerating unit electrodes, unit: m; H is the inner diameter of the accelerating unit electrode, unit: m; N is the maximum value of the harmonic order; is the amplitude of the field distribution, unit: V / m; K is the slope of the linear function of the field strength; D is the length of a single acceleration unit, and D=L+R, unit: m.

4. A high-voltage electron gun brightness analysis method according to claim 3, characterized in that: The third-order spherical aberration coefficient of the multi-stage accelerating lens is calculated based on the fitting expression of the electric field intensity on the multi-stage accelerating lens axis, specifically: Substituting the fitting expression of the electric field intensity on the multi-stage accelerating lens axis into the integral formula of the spherical aberration coefficient and ignoring high-order harmonics, we get: Further rewritten as: The relationship between the third-order spherical aberration coefficient of the multi-stage accelerating lens and the structural parameters of the multi-stage accelerating lens is expressed as: Where, k 1. k 2 is the proportional factor introduced to consider the voltage division of adjacent electrodes of the multi-stage accelerating lens and the influence of the emission unit on the electric field distribution of the multi-stage accelerating unit.

5. A high-voltage electron gun brightness analysis method according to claim 4, characterized in that: The brightness expression of the high-voltage electron gun is as follows: Where, is the current, unit: A; is the beam half angle, unit: mrad; is the radius of the virtual source considering the influence of spherical chromatic aberration, unit: nm; is the virtual source diameter, unit: nm; is the cathode effective emission area, unit: nm 2 ; is the angular current density, unit: A / srad; in, Where, is the radius of the virtual source without considering the influence of spherical chromatic aberration, unit: nm; is the radius of the blur circle caused by spherical aberration, unit: nm; is the radius of the blur circle caused by chromatic aberration, unit: nm; is the third-order spherical aberration coefficient, unit: mm; is the half-order central chromatic aberration coefficient, unit: mm; is the first-order central chromatic aberration coefficient, unit: mm; is the energy dispersion of the electron beam when it is emitted, unit: eV; It is the highest energy of electrons in a high-brightness electron gun, unit: eV.

6. A high-voltage electron gun brightness analysis method according to claim 5, characterized in that: Keeping the emission unit structure and excitation parameters unchanged, the structural parameters R, L and H of the multi-stage accelerating lens are changed in sequence to obtain the maximum brightness on the axis when the above structural parameters are changed. , blur circle radius affected by chromatic aberration , virtual source radius without considering the influence of spherical chromatic aberration Basically does not change with the change of structural parameters. 、 and The average value of the simulation calculation is substituted into the expression of the electron gun brightness, and the beam half angle is The brightness at the axis is expressed as the maximum brightness The proportional relationship: In the formula The maximum brightness on the axis, unit: A / cm 2 .srad; The beam half angle is Brightness at the time, unit: A / cm 2 .srad; is the maximum angular current density on the axis, unit: A / srad.

7. The method for analyzing brightness of a high-voltage electron gun according to claim 5, wherein: Based on the high-voltage electron gun brightness expression, the parameters affecting the electron gun brightness are analyzed, and the multi-parameter design of the electron gun with a multi-stage acceleration structure is optimized, specifically: The maximum brightness and the uniform area of the brightness curve are used as parameters to examine the brightness of the electron gun; Based on the influence of different multi-stage acceleration units on the uniform area of the brightness curve, a multi-parameter optimization design of the electron gun with a multi-stage acceleration unit is carried out to improve the uniform area of the brightness curve; The uniform area of the brightness curve is defined as the beam half angle occupied by 90% of the maximum brightness, and the beam half angle is defined as half of the solid angle opened by the electron beam.

8. A high-voltage electron gun brightness analysis system, characterized in that: include: Model building module: used to build a multi-stage acceleration lens simulation calculation model; Expression building module: used to build the fitting expression of the electric field intensity on the axis of the multi-stage accelerating lens based on the multi-stage accelerating lens simulation calculation model; The first calculation module is used to calculate the third-order spherical aberration coefficient of the multi-stage accelerating lens based on the fitting expression of the electric field intensity on the multi-stage accelerating lens axis; The second calculation module is used to obtain the brightness expression of the high-voltage electron gun based on the third-order spherical aberration coefficient of the multi-stage accelerating lens; Analysis module: used to analyze the parameters affecting the brightness of the electron gun based on the brightness expression of the high-voltage electron gun, and perform multi-parameter optimization design of the electron gun with a multi-stage acceleration structure.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the high-voltage electron gun brightness analysis method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the high-voltage electron gun brightness analysis method according to any one of claims 1 to 7 are implemented.

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