Aluminum oxide coating secondary electron yield simulation method based on extended three-layer model

Abstract

The embodiment of the invention provides an aluminum oxide coating secondary electron yield simulation method based on an extended three-layer model. The aluminum oxide coating secondary electron yield simulation method comprises the following steps: obtaining a crystal structure of Al2O3 and Si; carrying out first principle calculation on the crystal structure to obtain a corresponding electronic structure; performing Monte Carlo simulation on Al2O3 and Si according to the interface potential barrier and the energy loss function to obtain an elastic average free path, a non-elastic average free path and a secondary electron yield of electrons transmitted in Al2O3 and Si; establishing an Al2O3 / Si double-layer structure model; carrying out Monte Carlo simulation on the Al2O3 / Si double-layer structure model by changing the thickness of the Al2O3 coating to obtain the secondary electron yield of the Al2O3 / Si double-layer structure; a SiO2 layer is added into the Al2O3 / Si double-layer structure, and an Al2O3 / SiO2 / Si three-layer structure model is established; and by changing the thickness of the Al2O3 coating, carrying out Monte Carlo simulation on the Al2O3 / SiO2 / Si three-layer structure model to obtain the secondary electron yield of the Al2O3 / SiO2 / Si three-layer structure. Therefore, the prediction precision of the secondary electron emission characteristic of the Al2O3 coating material is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the field of computational chemistry, and in particular to, but not limited to, a method for simulating the secondary electron yield of an aluminum oxide coating based on an extended three-layer model. Background Art

[0002] Secondary electron emission (SEE) is a basic physical process of the interaction between electrons and materials. It has been widely used in various electronic devices, including scanning electron microscopes, photomultiplier tubes, particle accelerators, and microchannel plate detectors. It is worth noting that in different applications, the effective modulation of the secondary electron yield (SEY) is crucial to meet the performance of different devices. For example, the detector requires a coating material with low SEY to achieve its high sensitivity. At the same time, low SEY materials can effectively suppress the electron cloud phenomenon in particle accelerators. However, microchannel plate-based photomultiplier tubes require high SEY material films to improve the photoelectron collection efficiency.

[0003] The semi-empirical SEE model of Dionne et al. is often used to describe the SEY of coating materials. However, the parameters of the Dionne model in mixed materials need to be determined by experimental data. In order to track the trajectory of electrons and study complex scattering processes, 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 of the invention

[0004] In order to overcome the limitations of the prior art and realize the calculation of secondary electron yield of multilayer structures without experimental data, the present invention provides a simulation method of secondary electron yield of aluminum oxide coatings based on an extended three-layer model.

[0005] The technical method of the embodiment of the present invention is implemented as follows:

[0006] In a first aspect, an embodiment of the present invention provides a method for simulating secondary electron yield of an aluminum oxide coating based on an extended three-layer model, the method comprising:

[0007] Get Al 2 O 3 and the crystal structure of Si;

[0008] Performing first-principles calculations on the crystal structures to obtain corresponding electronic structures; the electronic structures include Fermi level, state density, interface potential barrier and energy loss function;

[0009] According to the interface barrier and the energy loss function, 2 O 3 Monte Carlo simulation was performed with Si to obtain the electron 2 O 3 The elastic mean free path, inelastic mean free path and secondary electron yield of Si;

[0010] Establish Al 2 O 3 / Si double-layer structure model;

[0011] By changing Al 2 O 3 Coating thickness, for Al 2 O 3 The Monte Carlo simulation of the Al / Si double-layer structure model was performed to obtain 2 O 3 / Secondary electron yield of Si double-layer structure;

[0012] In Al 2 O 3 / Si double-layer structure with SiO 2 layer, build Al 2 O 3 / SiO 2 / Si three-layer structure model;

[0013] By changing Al 2 O 3 Coating thickness, for Al 2 O 3 / SiO 2 The Monte Carlo simulation of the Al / Si three-layer structure model was performed to obtain 2 O 3 / SiO 2 / Si three-layer structure.

[0014] In some embodiments, the Al 2 O 3 The crystal structure of Al and Si is 2 O 3 And the unit cell structure of P-doped Si.

[0015] In some embodiments, the Al 2 O 3 The double-layer structure model of P-doped Si substrate is Al-coated 2 O 3 coating.

[0016] In some embodiments, by changing Al 2 O 3Coating thickness, for Al 2 O 3 The Monte Carlo simulation of the Al / Si double-layer structure model was performed to obtain 2 O 3 In the secondary electron yield of the Al / Si double-layer structure, the 2 O 3 The coating thicknesses are 1nm, 3nm, 5nm, and 7nm respectively.

[0017] In some embodiments, the Al 2 O 3 / SiO 2 The three-layer structure of P-doped Si substrate and Al 2 O 3 The coating contains SiO 2 Middle layer.

[0018] In some embodiments, by changing Al 2 O 3 Coating thickness, for Al 2 O 3 / SiO 2 The Monte Carlo simulation of the Al / Si three-layer structure model was performed to obtain 2 O 3 / SiO 2 In the secondary electron yield of the Al / Si three-layer structure, 2 O 3 The coating thickness is h+0.6nm, and h is 1nm, 3nm, 5nm, and 7nm.

[0019] The Al based on the extended three-layer model provided in the embodiment of the present invention 2 O 3 The simulation method of secondary electron yield of coating significantly improves the 2 O 3 The prediction accuracy of the secondary electron emission characteristics of coating materials; on the one hand, by introducing the extended three-layer model, the electron transport and scattering process inside the coating can be described more carefully, including the interaction between the coating and the substrate interface, so as to more accurately reflect the secondary electron emission behavior of the actual material under electron beam bombardment; on the other hand, by simulating the Al 2 O 3 The secondary electron yield of the coating can optimize the design parameters of the coating, such as coating thickness, component ratio, etc., to meet the requirements of specific applications for secondary electron emission characteristics. In addition, the Monte Carlo simulation method of the present invention is efficient and flexible; 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 applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a schematic flow chart of a method for simulating the secondary electron yield of an aluminum oxide coating based on an extended three-layer model provided in an embodiment of the present invention;

[0021] Figure 2 is a schematic diagram of a unit cell of P-doped Si provided in an embodiment of the present invention;

[0022] Figure 3 It is Al provided in the embodiment of the present invention 2 O 3 / Schematic diagram of Si double-layer structure model;

[0023] Figure 4 It is Al provided in the embodiment of the present invention 2 O 3 SEY comparison diagram of / Si double-layer structure and experimental results;

[0024] Figure 5 It is Al provided in the embodiment of the present invention 2 O 3 / SiO 2 Schematic diagram of the three-layer structure model of / Si;

[0025] Figure 6 The embodiment of the present invention provides different Al 2 O 3 Coating thickness, Al 2 O 3 / SiO 2 SEY diagram of the / Si three-layer structure model and experimental results. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings. The described embodiments should not be regarded as limiting the present invention. All other embodiments obtained by ordinary technicians in the field without making creative work are within the scope of protection of the present invention.

[0027] In the following description, reference is made to "some embodiments", which describe a subset of all possible embodiments, but it is understood that "some embodiments" may be the same subset 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 present invention have the same meaning as those commonly understood by those skilled in the art to which the embodiments of the present invention pertain. The terms used in the embodiments of the present invention are only for the purpose of describing the embodiments of the present invention and are not intended to limit the present invention.

[0028] The embodiment of the present invention provides an Al based on an extended three-layer model2 O 3 For simulation methods of secondary electron yield of coatings, see Figure 1 , Figure 1 is a flow chart of a method for simulating the secondary electron yield of an aluminum oxide coating based on an extended three-layer model provided by an embodiment of the present invention, which is combined with Figure 1 The steps shown are explained.

[0029] Step S110, obtaining Al 2 O 3 and the crystal structure of Si.

[0030] Here, the crystal structure may include unit cell parameters.

[0031] In this embodiment, Al 2 O 3 The unit cell structure of P-doped Si material is used to obtain the input file of the first principle calculation. Compared with the experimental data, the P-doped Si substrate structure is often used, such as Figure 2 shown.

[0032] Step S120, performing first-principles calculations on the crystal structures to obtain corresponding electronic structures; the electronic structures include Fermi levels, state density, interface potential barriers, and energy loss functions.

[0033] In some embodiments, the Fermi level is a key parameter used to determine the conductivity of a material.

[0034] In some embodiments, density of states refers to a function that describes the energy distribution of electrons.

[0035] In some embodiments, the interface barrier refers to the energy obstacle encountered by electrons at the interface of materials, which determines whether the electrons can easily pass through the interface and the energy loss that may occur when passing through.

[0036] In some embodiments, the energy loss function describes the energy lost by electrons as they travel through a material due to interactions with atoms in the material, and is usually related to the energy of the electrons and the properties of the material.

[0037] In this embodiment, all first-principles calculations were performed using Quantum ESPRESSO7.1. The generalized gradient approximation (GGA) (Perdew-Burke-Ernzerhof, PBE) method was used in the calculation to consider the exchange correlation potential in the interaction between electrons. The electron wave function was expanded by the plane wave basis vector group, and an ultrasoft pseudopotential was used to describe the interaction between the ion core and the valence electron. According to the state density, it can be known that the Fermi level W of the P-doped Si structure isF Entering the conduction band, the value is 7.13eV, which can be calculated as a conductor. The interface barrier of the material is different in conductors and non-conductors. For conductive materials, the barrier height is the work function For non-conducting materials, the barrier height is the electron affinity The energy loss function ELF is the reciprocal of the imaginary part of the material's dielectric function ε(q,ω). The energy loss function based on momentum transfer in different directions determines the energy lost by electrons in the material and the inelastic mean free path, thereby affecting the generation of internal secondary electrons and the probability of them passing through the potential barrier.

[0038] In some embodiments, the interface barrier is different in conductive and non-conductive materials. For conductive materials, the barrier height is the work function; for non-conductive materials, the barrier height is the electron affinity.

[0039] Step S130, according to the interface barrier and the energy loss function, 2 O 3 Monte Carlo simulation was performed with Si to obtain the electron 2 O 3 The elastic mean free path, inelastic mean free path and secondary electron yield of electrons transported in and Si.

[0040] In some embodiments, Monte Carlo simulation is a statistical method based on random sampling, which is suitable for simulating the transmission process of electrons in materials. According to the simulation results, the elastic mean free path and inelastic mean free path of electrons in the material are calculated. The elastic mean free path is the average distance that electrons travel during elastic scattering, only changing the scattering angle without losing energy; the inelastic mean free path is the average distance that electrons travel when inelastic scattering occurs, losing energy and changing the scattering angle, and there is a certain probability of generating internal secondary electrons.

[0041] In this embodiment, the Monte Carlo method simulates the scattering collision process of incident electrons in the material, and takes elastic scattering and inelastic scattering into consideration.

[0042] Elastic mean free path λ el The average distance that electrons travel during elastic scattering without losing energy but only changing the scattering angle is:

[0043]

[0044] in, 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 Avogadro's constant, and ρ is the density of the substance.

[0045] Inelastic mean free path λ in When electrons are inelastically scattered, the average distance they travel through loses energy and changes the scattering angle. There is a certain probability that internal secondary electrons will be generated:

[0046]

[0047] in, is the energy loss, a 0 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 electrons move in a material, the energy loss of the electrons can be expressed by the stopping power:

[0049]

[0050] in, To stop the ability, is the upper frequency limit.

[0051] When the incident electron undergoes an inelastic collision inside the material, the probability of the internal secondary electron being generated is related to the joint state density of the free electrons. When the internal secondary electron reaches the material interface, the probability of crossing the interface barrier and becoming a secondary electron is:

[0052]

[0053] Among them, W 0 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 and the surface normal when it reaches the surface, and U 0 is the interface barrier.

[0054] Step S140, establish A1 2 O 3 / Si double-layer structure model.

[0055] In some embodiments, when constructing the model, it is necessary to consider Al 2 O 3 The interface characteristics between Si and Si, such as interface roughness, interface chemical bonds, etc., may have an important impact on the secondary electron yield.

[0056] In this example, the double-layer model structure is a P-doped Si substrate coated with Al 2 O 3 Coating, such as Figure 3As shown, if the energy of the incident electron is low, the internal secondary electrons excited by the inelastic collision are almost all located in the Al 2 O 3 In contrast, if the energy of the incident electrons is high enough, they may penetrate the Al 2 O 3 The coating excites the internal secondary electrons in the P-doped Si substrate. During the movement, the internal secondary electrons may cross the interface barrier and escape from the coating surface to become secondary electrons. 2 O 3 / Si double-layer model, the interface barrier depends on the band structures of the two materials. 2 O 3 During coating, not all electrons have enough energy to overcome the interface barrier due to energy loss during scattering.

[0057] Step S150, by changing Al 2 O 3 Coating thickness, for Al 2 O 3 The Monte Carlo simulation of the Al / Si double-layer structure model was performed to obtain 2 O 3 / Si double-layer structure.

[0058] In this example, Al 2 O 3 The coating thicknesses in the / Si double-layer structure model are 1nm, 3nm, 5nm, and 7nm respectively. Figure 4 The double-layer structure SEY shown and the experimental results show that the double-layer structure model constructed in this example still needs to be further optimized.

[0059] In this example, according to the experimental results in the related art, 2 O 3 The TiN coating on the substrate contains TiO 2 Therefore, in this example, it is assumed that Al 2 O 3 There is SiO between the coating and the P-doped Si substrate 2 Element.

[0060] like Figure 5 As shown, Al 2 O 3 / SiO 2 The three-layer structure model of P-doped Si substrate and Al 2 O 3 The coating contains SiO 2 Middle layer.

[0061] Step S160, at A12 O 3 / Si double-layer structure with SiO 2 layer, build Al 2 O 3 / SiO 2 / Si three-layer structure model.

[0062] In this embodiment, SiO 2 The layer may act as a buffer layer or transition layer to improve the Al 2 O 3 The interface characteristics between Si and Si affect the secondary electron yield. This step helps to deeply understand the interface characteristics between SiO 2 The role of the middle layer in the multilayer structure.

[0063] Step S170, by changing Al 2 O 3 Coating thickness, for Al 2 O 3 / SiO 2 The Monte Carlo simulation of the Al / Si three-layer structure model was performed to obtain 2 O 3 / SiO 2 / Si three-layer structure.

[0064] In this example, because the Al 2 O 3 The thickness of the coating cannot be accurately determined to 1nm, 3nm, 5nm, and 7nm, so this example sets Al 2 O 3 The coating thickness is h+0.6nm, and h is 1nm, 3nm, 5nm, and 7nm. Figure 6 The comparison diagram of the calculation results of the present invention and the experimental measurement results shows that the secondary electron yield obtained by the present invention is consistent with the experimental measurement results, thereby proving the effectiveness of the method of the present invention.

[0065] The Al based on the extended three-layer model provided in the embodiment of the present invention 2 O 3 The simulation method of secondary electron yield of coating significantly improves the 2 O 3 The prediction accuracy of the secondary electron emission characteristics of coating materials; on the one hand, by introducing the extended three-layer model, the electron transport and scattering process inside the coating can be described more carefully, including the interaction between the coating and the substrate interface, so as to more accurately reflect the secondary electron emission behavior of the actual material under electron beam bombardment; on the other hand, by simulating the Al 2 O 3The secondary electron yield of the coating can optimize the design parameters of the coating, such as coating thickness, component ratio, etc., to meet the requirements of specific applications for secondary electron emission characteristics. In addition, the Monte Carlo simulation method of the present invention is efficient and flexible; 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 applications.

[0066] In some embodiments, the Al 2 O 3 The crystal structure of Al and Si is 2 O 3 And the unit cell structure of P-doped Si.

[0067] In some embodiments, the Al 2 O 3 The double-layer structure model of P-doped Si substrate is Al-coated 2 O 3 coating.

[0068] In some embodiments, by changing Al 2 O 3 Coating thickness, for Al 2 O 3 The Monte Carlo simulation of the Al / Si double-layer structure model was performed to obtain 2 O 3 In the secondary electron yield of the Al / Si double-layer structure, the 2 O 3 The coating thicknesses are 1nm, 3nm, 5nm, and 7nm respectively.

[0069] In some embodiments, the Al 2 O 3 / SiO 2 The three-layer structure of P-doped Si substrate and Al 2 O 3 The coating contains SiO 2 Middle layer.

[0070] In some embodiments, by changing Al 2 O 3 Coating thickness, for Al 2 O 3 / SiO 2 The Monte Carlo simulation of the Al / Si three-layer structure model was performed to obtain 2 O 3 / SiO 2 In the secondary electron yield of the Al / Si three-layer structure, 2 O 3The coating thickness is h+0.6nm, and h is 1nm, 3nm, 5nm, and 7nm.

[0071] The above description is only an embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement and improvement made within the spirit and scope of the present invention are included in the protection scope of the present invention.

[0072] It should be understood that "one embodiment" or "an embodiment" mentioned throughout the specification means that specific features, structures or characteristics related to the embodiment are included in at least one embodiment of the present invention. Therefore, "in one embodiment" or "in an embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. In addition, these specific features, structures or characteristics can be combined in one or more embodiments in any suitable manner. It should be understood that in various embodiments of the present invention, the size of the serial number of the above-mentioned processes does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of the present invention. The serial numbers of the above-mentioned embodiments of the present invention are only for description and do not represent the advantages and disadvantages of the embodiments.

[0073] It should be noted that, in this article, the terms "comprise", "include" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method or device including a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method or device. In the absence of further restrictions, an element defined by the statement "comprises one..." does not exclude the presence of other identical elements in the process, method, article or device including the element. In several embodiments provided by the present invention, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation, such as: multiple 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 is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for simulating the secondary electron yield of an aluminum oxide coating based on an extended three-layer model, characterized in that: The method comprises: Obtain the crystal structure of Al2O3 and Si; Performing first-principles calculations on the crystal structures to obtain corresponding electronic structures; the electronic structures include Fermi level, state density, interface potential barrier and energy loss function; According to the interface potential barrier and the energy loss function, a 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 electrons transmitted in Al2O3 and Si; Establish Al2O3 / Si double-layer structure model; By changing the thickness of Al2O3 coating, the Monte Carlo simulation of Al2O3 / Si double-layer structure model was carried out to obtain the secondary electron yield of Al2O3 / Si double-layer structure; Add SiO2 layer to Al2O3 / Si double-layer structure to establish Al2O3 / SiO2 / Si three-layer structure model; By changing the thickness of the Al2O3 coating, the Monte Carlo simulation of the Al2O3 / SiO2 / Si three-layer structure model was carried out, and the secondary electron yield of the Al2O3 / SiO2 / Si three-layer structure was obtained.

2. The method according to claim 1, characterized in that The crystal structure of Al2O3 and Si is a unit cell structure of Al2O3 and P-doped Si.

3. The method according to claim 1, characterized in that The Al2O3 / Si double-layer structure model is a P-doped Si substrate coated with an Al2O3 coating.

4. The method according to claim 1, characterized in that: The Al2O3 / Si double-layer structure model is subjected to Monte Carlo simulation by changing the thickness of the Al2O3 coating, and the secondary electron yield of the Al2O3 / Si double-layer structure is obtained. The thickness of the Al2O3 coating is 1nm, 3nm, 5nm, and 7nm, respectively.

5. The method according to claim 1, characterized in that The Al2O3 / SiO2 / Si three-layer structure has a SiO2 intermediate layer between the P-doped Si substrate and the Al2O3 coating.

6. The method according to claim 1, characterized in that The Al2O3 / SiO2 / Si three-layer structure model is subjected to Monte Carlo simulation by changing the thickness of the Al2O3 coating, and the secondary electron yield of the Al2O3 / SiO2 / Si three-layer structure is obtained. The thickness of the Al2O3 coating is h+0.6nm, and h is 1nm, 3nm, 5nm, and 7nm.

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