Alumina coating secondary electron yield simulation method based on extended three-layer model
By extending the three-layer model and using Monte Carlo simulation methods, the problem of accurately calculating the secondary electron yield of alumina coatings was solved, achieving efficient and accurate coating design optimization to meet different application requirements.
Patent Information
- Application Number
- CN202510224497.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-27
- Publication Date
- 2025-12-12
- Estimated Expiration
- 2045-02-27
AI Technical Summary
Existing technologies make it difficult to accurately calculate the secondary electron yield of multilayer structures, especially the secondary electron yield of alumina coatings, without experimental data.
Using an extended three-layer model approach, combining first-principles calculations and Monte Carlo simulations, three-layer structural models of Al2O3/Si and Al2O3/SiO2/Si are established by obtaining the crystal structure, electronic structure, interface barrier, and energy loss function. Monte Carlo simulations are then performed to predict the secondary electron yield.
It significantly improves the prediction accuracy of secondary electron emission characteristics of alumina coating materials, can more accurately describe electron transport and scattering processes, optimize coating design parameters, meet specific application requirements, and provide rapid simulation feedback.
Smart Images
Figure CN119943201B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of computational chemistry, and relates to, but is not limited to, an aluminum oxide coating secondary electron yield simulation method based on an extended three-layer model. BACKGROUND
[0002] Secondary electron emission (SEE) is a fundamental physical process of electron-material interaction, which has been widely applied in various electronic devices, including scanning electron microscopes, photomultiplier tubes, particle accelerators, and microchannel plate detectors. It is worth noting that in different application scenarios, the effective modulation of secondary electron yield (SEY) is crucial to meet the performance of different devices. For example, a detector needs a low SEY coating material to achieve its high sensitivity, and a low SEY material can effectively suppress the electron cloud phenomenon in a particle accelerator. However, a photomultiplier tube based on a microchannel plate needs a high SEY material film to improve the photoelectron collection efficiency.
[0003] The semi-empirical SEE model of Dionne et al. is commonly used to describe the SEY of coating materials. However, the Dionne model parameters in mixed materials need to be determined by experimental data. In order to track the electron trajectory and study the complex scattering process, the Monte Carlo (MC) method is a good choice. In addition, density functional theory (DFT) as a first-principles calculation method based on quantum mechanics can deeply understand the electronic structure and properties of materials. SUMMARY
[0004] In order to solve the limitations of the prior art and realize the calculation of the secondary electron yield of a multi-layer structure without experimental data, the present application provides an aluminum oxide coating secondary electron yield simulation method based on an extended three-layer model.
[0005] The technical method of the embodiment of the present application is realized as follows:
[0006] In a first aspect, the embodiment of the present application provides an aluminum oxide coating secondary electron yield simulation method based on an extended three-layer model, which comprises:
[0007] obtaining the crystal structure of Al2O3 and Si;
[0008] performing first-principles calculation on the crystal structure respectively to obtain the corresponding electronic structure; the electronic structure includes Fermi level, state density, interface potential barrier, and energy loss function;
[0009] According to the interface barrier and the energy loss function, a Monte Carlo simulation is performed on Al2O3 and Si to obtain elastic mean free path, inelastic mean free path and secondary electron yield of electrons in Al2O3 and Si;
[0010] An Al2O3 / Si double-layer structure model is established;
[0011] A Monte Carlo simulation is performed on the Al2O3 / Si double-layer structure model by changing the thickness of the Al2O3 coating layer to obtain the secondary electron yield of the Al2O3 / Si double-layer structure;
[0012] An Al2O3 / SiO2 / Si three-layer structure model is established by adding a SiO2 layer to the Al2O3 / Si double-layer structure;
[0013] A Monte Carlo simulation is performed on the Al2O3 / SiO2 / Si three-layer structure model by changing the thickness of the Al2O3 coating layer to obtain the secondary electron yield of the Al2O3 / SiO2 / Si three-layer structure.
[0014] In some embodiments, the crystal structure of the Al2O3 and Si is the unit cell structure of Al2O3 and P-doped Si.
[0015] In some embodiments, the Al2O3 / Si double-layer structure model is an Al2O3 coating layer coated on a P-doped Si substrate.
[0016] In some embodiments, in the Monte Carlo simulation of the Al2O3 / Si double-layer structure model by changing the thickness of the Al2O3 coating layer to obtain the secondary electron yield of the Al2O3 / Si double-layer structure, the thickness of the Al2O3 coating layer is 1 nm, 3 nm, 5 nm, and 7 nm, respectively.
[0017] In some embodiments, the Al2O3 / SiO2 / Si three-layer structure is a P-doped Si substrate with a SiO2 intermediate layer between the Al2O3 coating layer.
[0018] In some embodiments, in the Monte Carlo simulation of the Al2O3 / SiO2 / Si three-layer structure model by changing the thickness of the Al2O3 coating layer to obtain the secondary electron yield of the Al2O3 / SiO2 / Si three-layer structure, the thickness of the Al2O3 coating layer is h+0.6 nm, and h is 1 nm, 3 nm, 5 nm, and 7 nm.
[0019] The Al2O3 coating secondary electron yield simulation method based on the extended three-layer model provided by the embodiment of the application significantly improves the prediction accuracy of the secondary electron emission characteristics of the Al2O3 coating material. On the one hand, by introducing the extended three-layer model, the electron transmission and scattering process inside the coating can be described in more detail, including the interaction between the coating and the substrate, so that the actual material under electron beam bombardment can more accurately reflect the secondary electron emission behavior. On the other hand, by simulating the secondary electron yield of the Al2O3 coating under different conditions, the design parameters of the coating, such as the coating thickness and the composition ratio, can be optimized to meet the needs of specific applications for secondary electron emission characteristics. In addition, the Monte Carlo simulation method of the application has high efficiency and flexibility; by adjusting the simulation parameters and input conditions, the secondary electron emission characteristics of different coating structures and electron beam conditions can be quickly obtained, providing rapid feedback and guidance for experimental research and engineering application. BRIEF DESCRIPTION OF DRAWINGS
[0020] Figure 1 is a flowchart of the Al2O3 coating secondary electron yield simulation method based on the extended three-layer model provided by the embodiment of the application;
[0021] Figure 2 is a schematic diagram of the unit cell of P-doped Si provided by the embodiment of the application;
[0022] Figure 3 is a schematic diagram of the Al2O3 / Si double-layer structure model provided by the embodiment of the application;
[0023] Figure 4 is a comparison diagram of the SEY of the Al2O3 / Si double-layer structure and the experimental results provided by the embodiment of the application;
[0024] Figure 5 is a schematic diagram of the Al2O3 / SiO2 / Si three-layer structure model provided by the embodiment of the application;
[0025] Figure 6 is a SEY diagram of the Al2O3 / SiO2 / Si three-layer structure model and the experimental results under different Al2O3 coating thicknesses provided by the embodiment of the application. DETAILED DESCRIPTION
[0026] In order to make the purpose, technical scheme and advantages of the application more clear, the application will be further described in detail below in combination with the drawings. The described embodiments should not be regarded as limiting the application, and all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the application.
[0027] In the following description, references to "some embodiments" refer to a subset of all possible embodiments; however, it is understood that "some embodiments" may be the same or different subsets of all possible embodiments and may be combined with each other without conflict. Unless otherwise defined, all technical and scientific terms used in the embodiments of the invention have the same meaning as commonly understood by one of ordinary skill in the art to which the embodiments of the invention pertain. The terminology used in the embodiments of the invention is for the purpose of describing the embodiments of the invention only and is not intended to limit the invention.
[0028] This invention provides a method for simulating the secondary electron yield of Al2O3 coatings based on an extended three-layer model. (See also...) Figure 1 , Figure 1 This is a flowchart illustrating the secondary electron yield simulation method for alumina coatings based on an extended three-layer model provided in this embodiment of the invention. Figure 1 The steps shown are explained.
[0029] Step S110: Obtain the crystal structures of Al2O3 and Si.
[0030] Here, crystal structure can include unit cell parameters.
[0031] In this embodiment, the cell structures of Al2O3 and P-doped Si materials were obtained, and the input files for first-principles calculations were derived from these cell structures. Compared to experimental data, the P-doped Si substrate structure is frequently used, such as... Figure 2 As shown.
[0032] Step S120: Perform first-principles calculations on the crystal structure to obtain the corresponding electronic structure; the electronic structure includes Fermi level, density of states, interface barrier and energy loss function.
[0033] In some embodiments, the Fermi level is used as a key parameter to determine the electrical conductivity of a material.
[0034] In some embodiments, the density of states is a function describing the distribution of electron energy.
[0035] In some embodiments, the interface barrier refers to the energy barrier encountered by electrons at the material interface, which determines whether electrons can easily pass through the interface and the energy loss that may occur during the passage.
[0036] In some embodiments, the energy loss function describes the energy lost by electrons as they travel through a material due to their interactions with the atoms of the material. It is typically related to the energy of the electrons and the properties of the material.
[0037] In this embodiment, all first-principles calculations are completed by Quantum ESPRESSO 7.1. In the calculation, the (Perdew-Burke-Ernzerhof, PBE) method of Generalized Gradient Approximation (GGA) is used to consider the exchange correlation potential in the interaction between electrons, the electron wave function is expanded by the plane wave basis set, and the ultra-soft pseudo-potential is used to describe the interaction between the ion core and the valence electrons. According to the state density, the Fermi energy W of the P-doped Si structure is in the conduction band, and the value is 7.13 eV, which can be calculated as a conductor. The interface potential barrier of the material is different in the conductor and the non-conductor. For the conductor material, the barrier height is the work function F , and for the non-conductor material, the barrier height is the electron affinity The energy loss function ELF is the reciprocal of the imaginary part of the dielectric function ε(q, ω) of the material. The energy loss function based on the momentum transfer in different directions determines the energy loss and the inelastic mean free path of the electron in the material, thereby affecting the generation of the secondary electron and the probability of the secondary electron passing through the barrier.
[0038] In some embodiments, the interface potential barrier is different in the conductor and the non-conductor material. For the conductor material, the barrier height is the work function; and for the non-conductor material, the barrier height is the electron affinity.
[0039] In step S130, according to the interface potential barrier and the energy loss function, Monte Carlo simulation is performed on Al2O3 and Si to obtain the elastic mean free path, the inelastic mean free path, and the secondary electron yield of the electron transmission in Al2O3 and Si.
[0040] In some embodiments, the Monte Carlo simulation is a statistical method based on random sampling, which is suitable for simulating the transmission process of the electron in the material. According to the simulation results, the elastic mean free path and the inelastic mean free path of the electron transmission in the material are calculated. The elastic mean free path is the average distance that the electron passes through in the elastic scattering process, only changing the scattering angle without losing energy; the inelastic mean free path is the average distance that the electron passes through when the electron loses energy and changes the scattering angle in the inelastic scattering process, and there is a certain probability of generating the secondary electron.
[0041] In this embodiment, the Monte Carlo method simulates the scattering and collision process of the incident electron in the material, and considers the elastic scattering and the inelastic scattering.
[0042] The elastic mean free path λ el is the average distance that the electron passes through in the elastic scattering process, only changing the scattering angle without losing energy:
[0043]
[0044] where, is the differential elastic cross section, σ el is the elastic scattering cross section, A is the relative mass of the atom, θ is the scattering angle, N A is the Avogadro constant, ρ is the density of the material.
[0045] The inelastic mean free path λ in is the average distance that an electron travels when it undergoes inelastic scattering, losing energy and changing scattering angle, with a certain probability of generating an inner secondary electron:
[0046]
[0047] where, is the energy loss, a0 is the Bohr radius, q is the momentum, is the reduced Planck constant, W is the electron energy, m is the electron mass, λ in is the inelastic mean free path.
[0048] When an electron moves in a material, the energy loss of the electron can be expressed by the stopping power:
[0049]
[0050] where, is the stopping power, is the upper limit frequency.
[0051] When an incident electron undergoes inelastic collision inside the material, the probability of generating an inner secondary electron is proportional to the joint state density of the free electrons When the inner secondary electron reaches the material interface, the probability of overcoming the interface potential barrier to become a secondary electron emitted is:
[0052]
[0053] where, W0 is the initial energy of the free electron, W F is the Fermi level, W is the electron energy, β is the angle between the secondary electron reaching the surface and the surface normal, U0 is the interface potential barrier.
[0054] Step S140, establish an Al2O3 / Si double-layer structure model.
[0055] In some embodiments, when constructing the model, the interface properties between Al2O3 and Si, such as interface roughness, interface chemical bonds, etc., which may have important effects on the secondary electron yield, need to be considered.
[0056] In this example, the double-layer model structure is an Al2O3 coating coated on a P-doped Si substrate, such as... Figure 3 As shown, if the energy of the incident electrons is low, almost all the internal secondary electrons excited by inelastic collisions reside within the Al2O3 coating. Conversely, if the energy of the incident electrons is high enough, they may penetrate the Al2O3 coating and excite internal secondary electrons in the P-doped Si substrate. During their movement, these internal secondary electrons may cross the interface barrier and escape from the coating surface as secondary electrons. For the Al2O3 / Si bilayer model, the interface barrier depends on the band structure of both materials. When electrons enter the Al2O3 coating, due to energy loss during scattering, not all electrons have sufficient energy to overcome the interface barrier.
[0057] Step S150: By changing the Al2O3 coating thickness, a Monte Carlo simulation is performed on the Al2O3 / Si bilayer structure model to obtain the secondary electron yield of the Al2O3 / Si bilayer structure.
[0058] In this example, the coating thicknesses in the Al2O3 / Si bilayer structure model are 1 nm, 3 nm, 5 nm, and 7 nm. (The text then abruptly shifts to a seemingly unrelated topic: "Through examples...") Figure 4 The results of the SEY double-layer structure shown and the experimental results indicate that the double-layer structure model constructed in this example still needs further optimization.
[0059] In this example, based on experimental results from related technologies, TiO2 is present in the TiN coating on the Al2O3 substrate. Therefore, it is assumed in this example that SiO2 is present between the Al2O3 coating and the P-doped Si substrate.
[0060] like Figure 5 As shown, the Al2O3 / SiO2 / Si three-layer structure model has a SiO2 intermediate layer between the P-doped Si substrate and the Al2O3 coating.
[0061] Step S160: Add a SiO2 layer to the Al2O3 / Si bilayer structure to establish an Al2O3 / SiO2 / Si trilayer structure model.
[0062] In this embodiment, the SiO2 layer may serve as a buffer or transition layer, improving the interfacial properties between Al2O3 and Si, thereby affecting the secondary electron yield. This step helps to deepen the understanding of the role of the SiO2 intermediate layer in multilayer structures.
[0063] Step S170: By changing the thickness of the Al2O3 coating, a Monte Carlo simulation is performed on the Al2O3 / SiO2 / Si three-layer structure model to obtain the secondary electron yield of the Al2O3 / SiO2 / Si three-layer structure.
[0064] In the present example, because the thickness of the Al2O3 coating in the actual experiment cannot be accurately 1 nm, 3 nm, 5 nm and 7 nm, the thickness of the Al2O3 coating in the present example is set to h+0.6 nm, and h is 1 nm, 3 nm, 5 nm and 7 nm. Figure 6 For the comparison chart of the calculation results of the present application and the experimental measurement results, it can be seen that the secondary electron yield obtained by using the present application is more consistent with the experimental measurement results, thereby proving the effectiveness of the method of the present application.
[0065] The Al2O3 coating secondary electron yield simulation method based on the extended three-layer model provided by the embodiments of the present application significantly improves the prediction accuracy of the secondary electron emission characteristics of the Al2O3 coating material; on the one hand, by introducing the extended three-layer model, the electron transport and scattering process inside the coating can be described in more detail, including the interaction between the coating and the substrate, thereby more accurately reflecting the secondary electron emission behavior of the actual material under electron beam bombardment; on the other hand, by simulating the secondary electron yield of the Al2O3 coating under different conditions, the design parameters of the coating, such as the coating thickness, the composition ratio, etc., can be optimized to meet the needs of the secondary electron emission characteristics for specific applications. In addition, the Monte Carlo simulation method of the present application has high efficiency and flexibility; by adjusting the simulation parameters and input conditions, the secondary electron emission characteristics under different coating structures and electron beam conditions can be quickly obtained, providing rapid feedback and guidance for experimental research and engineering application.
[0066] In some embodiments, the crystal structure of the Al2O3 and Si is the unit cell structure of Al2O3 and P-doped Si.
[0067] In some embodiments, the Al2O3 / Si double-layer structure model is an Al2O3 coating coated on a P-doped Si substrate.
[0068] In some embodiments, in the Monte Carlo simulation of the Al2O3 / Si double-layer structure model by changing the thickness of the Al2O3 coating, the thickness of the Al2O3 coating is 1 nm, 3 nm, 5 nm and 7 nm, respectively.
[0069] In some embodiments, the Al2O3 / SiO2 / Si three-layer structure model is a P-doped Si substrate with an Al2O3 coating containing a SiO2 intermediate layer in the middle.
[0070] In some embodiments, in the Monte Carlo simulation of the Al2O3 / SiO2 / Si three-layer structure model by changing the thickness of the Al2O3 coating, the thickness of the Al2O3 coating is h+0.6 nm, and h is 1 nm, 3 nm, 5 nm and 7 nm.
[0071] The above merely provides an example of the present application, but is not intended to limit the protection scope of the present application. Any modification, equivalent replacement, and improvement within the spirit and scope of the present application shall be included in the protection scope of the present application.
[0072] It should be understood that the reference to “one embodiment” or “an embodiment” throughout the specification means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the application. Therefore, appearances of the phrases “in one embodiment” or “in an embodiment” in various places throughout the specification are not necessarily referring to the same embodiment. Furthermore, the particular features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. It should be understood that the sequence of the processes described above does not mean the execution order, and the execution order of the processes should be determined according to the functions and inherent logic, and should not constitute any limitation on the implementation process of the embodiments of the application. The sequence of the above embodiments of the application is only for description, and does not represent the advantages or disadvantages of the embodiments.
[0073] It should be noted that, in this document, the terms “comprises”, “comprising”, or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without more limitations, the element defined by the statement “comprises a” does not exclude the presence of additional identical elements in the process, method, article, or apparatus that includes the element. In several embodiments provided by the present application, it should be understood that the disclosed devices and methods can be implemented in other ways. The above described device embodiments are only schematic, for example, the division of the units is only a logical function division, and actual implementation can be another division, for example, a plurality of units or components can be combined, or can be integrated into another system, or some features can be ignored or not executed.
[0074] The above merely provides an example of the present application, but is not intended to limit the protection scope of the present application. Any modification, equivalent replacement, and improvement within the technical range disclosed by the present application, which can be easily thought by those skilled in the art, shall be included in the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.
Claims
1. A method for simulating the secondary electron yield of an Al2O3 coating based on an extended three-layer model, characterized in that, The method comprises: obtaining crystal structures of Al2O3 and Si; performing first-principle calculation on the crystal structures respectively to obtain corresponding electronic structures; the electronic structures include Fermi level, state density, interface potential barrier and energy loss function; performing Monte Carlo simulation on Al2O3 and Si according to the interface potential barrier and the energy loss function to obtain elastic mean free path, inelastic mean free path and secondary electron yield of electron transmission in Al2O3 and Si; establishing an Al2O3 / Si double-layer structure model; performing Monte Carlo simulation on the Al2O3 / Si double-layer structure model by changing the thickness of the Al2O3 coating to obtain secondary electron yield of the Al2O3 / Si double-layer structure; adding a SiO2 layer in the Al2O3 / Si double-layer structure to establish an Al2O3 / SiO2 / Si three-layer structure model; performing Monte Carlo simulation on the Al2O3 / SiO2 / Si three-layer structure model by changing the thickness of the Al2O3 coating to obtain secondary electron yield of the Al2O3 / SiO2 / Si three-layer structure; the crystal structures of Al2O3 and Si are unit cell structures of Al2O3 and P-doped Si; the Al2O3 / Si double-layer structure model is an Al2O3 coating on a P-doped Si substrate; the Al2O3 / SiO2 / Si three-layer structure is a P-doped Si substrate with a SiO2 intermediate layer between the Al2O3 coating.
2. The method of claim 1, wherein, In the step of performing Monte Carlo simulation on the Al2O3 / Si double-layer structure model by changing the thickness of the Al2O3 coating to obtain secondary electron yield of the Al2O3 / Si double-layer structure, the thickness of the Al2O3 coating is 1 nm, 3 nm, 5 nm or 7 nm.
3. The method of claim 1, wherein, In the step of performing Monte Carlo simulation on the Al2O3 / SiO2 / Si three-layer structure model by changing the thickness of the Al2O3 coating to obtain secondary electron yield of the Al2O3 / SiO2 / Si three-layer structure, the thickness of the Al2O3 coating is h+0.6 nm, and h is 1 nm, 3 nm, 5 nm or 7 nm.