Simulation method for rapid heavy ion track formation and evolution in semiconductor material
By combining first-principles calculations and a two-temperature model, the energy transfer simulations of the electronic subsystem and the lattice subsystem are performed separately, solving the problem of inaccurate simulation in the 2T-MD method and realizing accurate simulation and structural damage analysis of semiconductor materials subjected to rapid heavy ion incidence.
Patent Information
- Application Number
- CN202511336985.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-18
- Publication Date
- 2025-12-12
AI Technical Summary
The existing 2T-MD method is not effective in simulating fast heavy ion incident semiconductor materials. It cannot accurately describe the energy exchange process between the electronic subsystem and the lattice subsystem, resulting in simulation results that are seriously inconsistent with the actual situation.
Thermodynamic parameters of semiconductor materials are obtained using first-principles methods, and initial ionization energy is obtained through two-body collision methods. Combining a two-temperature model and classical molecular dynamics methods, energy transfer simulations of electronic subsystems and lattice subsystems are performed separately to avoid the influence of potential functions and time scales, and energy is directly distributed to lattice atoms for dynamic behavior simulation.
Accurate simulation of semiconductor materials subjected to rapid heavy ion incidence was achieved, simulation errors were reduced, the microscopic mechanism of structural damage was revealed, and the formation and evolution process of continuous tracks were provided.
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Figure CN121122437A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of material radiation damage simulation, in particular to a simulation method, device, equipment and medium for formation and evolution of a swift heavy ion track in a semiconductor material. BACKGROUND
[0002] When a swift heavy ion (SHI) is incident into a solid, a series of collisions occur between the ion and the lattice atoms, and a part of the energy is transferred to the atomic nuclei and electrons in the solid, causing energy loss of the incident ion, and further causing irradiation effects. For the swift heavy ion, the electron energy loss is dominant, and in the time scale of femtoseconds to picoseconds, strong ionization will induce structural damage, phase transition and damage recovery of different materials, forming an ion track with a diameter of about 1-10 nm and a length of about 10-100 μm. This change in system structure greatly affects the material properties, making SHI irradiation an effective means for modifying materials in the micron to nanometer scale. However, the research on the irradiation effects of materials has mainly focused on the energy transfer within the atomic subsystem, and little research has been done on the energy exchange process between the electronic subsystem and the atomic subsystem, resulting in many difficulties in understanding and simulating the electronic effects and damage evolution of various materials, especially semiconductor materials.
[0003] A two-temperature molecular dynamics (2T-MD) method developed by coupling a classical molecular dynamics (MD) and a two-temperature model (TTM) can simulate the irradiation damage process of a swift heavy ion. However, the 2T-MD method embeds the two-temperature model into the molecular dynamics simulation, and the potential function of the molecular dynamics simulation will affect the simulation results of the two-temperature model; and since the time scale of the two-temperature model simulation is much smaller than that of the molecular dynamics simulation, the results of long-time evolution will be seriously inconsistent with the actual situation. Therefore, the 2T-MD method has poor simulation effect on the swift heavy ion incident into a semiconductor material. SUMMARY
[0004] The purpose of the present application is to provide a simulation method, device, equipment and medium for formation and evolution of a swift heavy ion track in a semiconductor material, which can solve the problem of poor simulation effect of the existing 2T-MD method on the swift heavy ion incident into a semiconductor material.
[0005] To solve the above technical problems, an embodiment of the present application provides a simulation method for formation and evolution of a swift heavy ion track in a semiconductor material, comprising the following steps: Thermodynamic parameters of semiconductor materials are obtained using first-principles methods; The initial ionization energy generated instantaneously in the electronic subsystem of a semiconductor material during rapid heavy ion incident is obtained by a two-body collision method. Based on thermodynamic parameters and initial ionization energy, a two-temperature model is used to simulate the energy transfer process of electronic subsystems and lattice subsystems in semiconductor materials, so as to obtain the target energy generated when electronic subsystems and lattice subsystems reach thermal equilibrium; The target energy is allocated to each lattice atom in the lattice subsystem, and the dynamic behavior of each lattice atom is simulated using classical molecular dynamics methods based on the target energy of each lattice atom. Based on the continuous tracks formed by the dynamic behavior of lattice atoms in semiconductor materials, the structural damage caused by rapid heavy ion incident on semiconductor materials can be determined.
[0006] Furthermore, the method of obtaining the thermodynamic parameters of the semiconductor material using first-principles methods includes: Structural relaxation of semiconductor materials; Self-consistent calculations were performed on the semiconductor material after structural relaxation, and the electronic heat capacity of the semiconductor material was simulated with temperature by modifying the system temperature in the self-consistent calculation. Based on the trend of electronic heat capacity with temperature, the electronic heat capacity of semiconductor materials can be obtained using the following formula. C e : ;in, T e It is the temperature of the electrons. The electron temperature is T e Electronic heat capacity at time U The electron temperature of semiconductor materials is The internal energy of semiconductor materials; The electronic thermal conductivity of semiconductor materials can be obtained using the following formula. K e : , ;in, The electron temperature is Electronic thermal conductivity at that time The electron temperature is Electron diffusion rate at that time It is Boltzmann's constant. q It is electron charge. It is electron mobility; The electroacoustic coupling constant of semiconductor materials can be obtained from the following formula. g : ;in, The electron temperature is Electroacoustic coupling constant at time, It is the electron-phonon relaxation time; The lattice heat capacity of semiconductor materials can be obtained from the following formula. C l and lattice thermal conductivity K l : , ;in, The lattice temperature of a semiconductor material is The lattice heat capacity at that time The lattice temperature of a semiconductor material is The lattice thermal conductivity at that time is the molar volume of the semiconductor material; a, b, c, d, A, and B are characteristic parameters of different semiconductor materials obtained by fitting experimental data of semiconductor materials.
[0007] Furthermore, the method of obtaining the initial ionization energy generated instantaneously in the electronic subsystem of a semiconductor material by rapid heavy ion incident on it via a two-body collision includes: Based on Monte Carlo simulation software, a three-dimensional model of semiconductor materials was established, and the three-dimensional model was meshed at the nanoscale. The ionization energy of fast heavy ions incident on semiconductor materials was simulated by a two-body collision method. The ionization energy distribution of the fast heavy ions in each grid after incident on the semiconductor material was obtained, and the ionization energy distribution of the three-dimensional model after grid division was used as the initial ionization energy.
[0008] Furthermore, based on thermodynamic parameters and initial ionization energy, a two-temperature model is used to simulate the energy transfer process of the electronic subsystem and lattice subsystem in the semiconductor material, including: Based on thermodynamic parameters and initial ionization energy, the two differential thermal diffusion equations of the two-temperature model are numerically solved, and the energy transfer process of electronic subsystems and lattice subsystems in semiconductor materials is simulated through the solution process.
[0009] Furthermore, the distribution of the target energy to each lattice atom in the lattice subsystem includes: Based on the principle that the statistical distribution of the kinetic energy of each lattice atom conforms to a Gaussian distribution and the statistical distribution of the momentum of each lattice atom conforms to a uniform distribution, the target energy is distributed to each lattice atom in the lattice subsystem.
[0010] Furthermore, based on the target energy of each lattice atom, the dynamic behavior of each lattice atom is simulated using classical molecular dynamics methods, including: Convert the target energy of each lattice atom into the initial kinetic energy of each lattice atom, and simulate the kinetic behavior of each lattice atom according to the initial kinetic energy of each atom by using the molecular dynamics method.
[0011] Further, before simulating the kinetic behavior of each lattice atom, further comprising: Expand the cell structure of each lattice atom to form a supercell structure, and relax the supercell structure.
[0012] Embodiments of the application also provide a simulation device for rapid heavy ion track formation and evolution in a semiconductor material, comprising: A parameter acquisition module configured to acquire thermodynamic parameters of the semiconductor material by a first-principle method; An energy acquisition module configured to acquire initial ionization energy generated in an electron subsystem of the semiconductor material by a two-body collision method when the rapid heavy ion is incident on the semiconductor material; A two-temperature model simulation module configured to simulate energy transfer processes of the electron subsystem and a lattice subsystem of the semiconductor material by a two-temperature model according to the thermodynamic parameters and the initial ionization energy, to obtain target energy generated when the electron subsystem and the lattice subsystem reach thermal equilibrium; A molecular dynamics simulation module configured to distribute the target energy to each lattice atom in the lattice subsystem, and simulate kinetic behavior of each lattice atom by a classical molecular dynamics method according to the target energy of each lattice atom; A damage determination module configured to determine a structural damage condition caused by the rapid heavy ion incident on the semiconductor material according to a continuous track formed by kinetic behavior of the lattice atoms in the semiconductor material.
[0013] Embodiments of the application also provide a computer device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the simulation method for rapid heavy ion track formation and evolution in a semiconductor material.
[0014] Embodiments of the application also provide a computer-readable storage medium storing a computer program, and the computer program is executed by a processor to implement the simulation method for rapid heavy ion track formation and evolution in a semiconductor material.
[0015] The simulation method for rapid heavy ion track formation and evolution in a semiconductor material provided by the application has at least the following beneficial effects: The present application is based on the thermodynamic properties of semiconductor materials, and then the first principle calculation is used to obtain the thermodynamic parameters of semiconductor materials, and the initial ionization energy generated in the electronic subsystem of semiconductor materials by the fast heavy ion incident semiconductor materials is obtained by the two-body collision method. After that, the two-temperature model simulation (energy transfer process of the electronic subsystem and the lattice subsystem in the semiconductor material) is carried out to obtain the target energy generated when the electronic subsystem and the lattice subsystem reach thermal equilibrium. Then, the target energy is distributed to each lattice atom in the lattice subsystem, and then the molecular dynamics simulation (dynamic behavior of each lattice atom) is carried out. Therefore, according to the continuous track formed by the dynamic behavior of the lattice atoms in the semiconductor material, the structure damage caused by the fast heavy ion incident semiconductor material can be determined. The above process decouples the two-temperature model simulation and the molecular dynamics simulation, and they are carried out separately, which avoids the problems that the two-temperature model simulation is affected by the potential function of the molecular dynamics simulation and the simulation results are inaccurate due to the different time scales of the two-temperature model simulation and the molecular dynamics simulation in the 2T-MD method. BRIEF DESCRIPTION OF DRAWINGS
[0016] The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiments of the application and together with the description serve to explain the application. In the drawings:
[0017] Figure 1 A schematic diagram of a semiconductor material fast heavy ion track formation and evolution simulation method provided by the present application; Figure 2 A schematic diagram of the calculation results of the electronic heat capacity of a β-Ga2O3 material provided by the present application; Figure 3 A schematic diagram of the fitting results of the lattice heat capacity of a β-Ga2O3 material provided by the present application; Figure 4 A schematic diagram of the initial ionization energy generated in the electronic system of a β-Ga2O3 material by a 467 MeV Kr ion incident in the material at a moment provided by the present application; Figure 5 A schematic diagram of the energy deposited into the lattice atoms of a β-Ga2O3 material by a 467 MeV Kr ion incident in the material at a moment provided by the present application; Figure 6 A schematic diagram of the melting zone radius of a β-Ga2O3 material at 1 ps and 350 ps by a 467 MeV Kr ion incident in the material provided by the present application; DETAILED DESCRIPTION
[0018] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions of the present application will be described below in connection with specific embodiments of the present application and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative labor fall within the protection scope of the present application.
[0019] Currently, the inelastic thermal spike model (iTS) is mainly used to describe the interaction between strong ionizing radiation and solids at femtosecond scale under the irradiation of fast heavy ions into a material system. The most common application of the iTS model is the two-temperature model formula, in which all physical fields are described as a set of two differential heat diffusion equations coupled through an exchange term and an additional source term in the equation of the electron subsystem:
[0020] In the formula, the subscripts e and l represent the electron and lattice subsystems, T e,l is the temperature, C e,l and K e,l are the heat capacity and thermal conductivity, is the electron-phonon coupling, is the initial energy deposition term of the fast heavy ion incident into the material system.
[0021] At the nanometer (nm) spatial scale, the application of classical molecular dynamics at the nanosecond (ns) time scale after irradiation has made a major contribution to the understanding of damage evolution and residual damage after ion irradiation. However, the classical molecular dynamics method has the limitation of not being able to incorporate the effect of electron energy loss, which leads to the fact that this method can only be used to study the irradiation category that interacts with atomic nuclei in the material, such as low-energy ions. For high-energy ion incidence, the electron energy loss is dominant, and the cross section of nuclear collision is very small, in which case the classical molecular dynamics method is not suitable for simulating the irradiation damage process of fast heavy ions.
[0022] To address this limitation, Duffy and Rutherford coupled classical molecular dynamics with a two-temperature model, developing the two-temperature molecular dynamics 2T-MD method. The 2T-MD model describes the energy exchange between atomic and electronic subsystems, while also considering electron blocking and electro-acoustic coupling interactions. A frictional term is added as an energy loss coefficient to the classical molecular dynamics equations simulating ion motion, replacing the differential thermal diffusion equations (2) of the lattice subsystems in the original two-temperature model.
[0023] In the formula, and Let m represent the electron blocking constant and the electroacoustic coupling constant, respectively. i and v i These represent the mass and velocity of the atom, respectively. This represents the force acting on atom i at time t due to its interaction with surrounding atoms. (Random force term) This includes the energy gained from interacting with electrons, determined by the local electron temperature. Friction term. Includes an electronic anti-friction term and an electroacoustic coupling friction term With electron blocking constant and electroacoustic coupling constant related, and They are represented as:
[0024] In the formula, It is the electron blocking constant. It is the electroacoustic coupling constant. N The volume is ΔV The total number of atoms in the CET cell. N' The speed in this cell is greater than v c The number of atoms, k B Represents the Boltzmann constant. Electrons resist friction. It is an electroacoustic coupling friction force. In 2T-MD, the finite difference method is used to simultaneously perform numerical integration on the thermal diffusion equation and the molecular dynamics equation describing the electronic subsystem, and energy exchange occurs between the two subsystems within each molecular dynamics time step.
[0025] The existing 2T-MD method is a simulation method that couples a two-temperature model with molecular dynamics. The limitation of this coupling method is that it cannot directly map the lattice temperature and energy obtained from the two-temperature model simulation to the atomic information input for molecular dynamics simulation. Therefore, the two-temperature model equation (2), representing the energy transfer characteristics of the lattice subsystem, is directly modified to a stochastic force term (4) representing interatomic interactions in molecular dynamics simulation, to adapt to the widely used molecular dynamics simulation software. This substitution is also because the 2T-MD method cannot obtain accurate thermodynamic properties of semiconductor materials; it can only extract all material properties of the lattice subsystem in the original two-temperature model equation (2), such as lattice heat capacity. C l and lattice thermal conductivity K l All of them are integrated into the friction force term, which does not have a unified and defined standard.
[0026] In the 2T-MD method, since the two-temperature model and molecular dynamics simulation are performed simultaneously, the two-temperature model process is greatly affected by the potential function used in the molecular dynamics simulation. The potential function describes the interatomic forces, and different potential functions in the molecular dynamics simulation emphasize different interatomic interaction forces. In addition, this method takes into account all material properties of the lattice system in the original two-temperature model equation (2), such as lattice heat capacity. C l and lattice thermal conductivity K l Integrating everything into a single friction term inherently introduces errors, and the resulting friction term... and There is no unified standard for determining the parameters, and they involve significant subjectivity and uncertainty. Most importantly, the thermodynamic parameters required in the two-temperature model are all quantities that change with temperature. However, in the 2T-MD method, the electronic heat capacity, a thermodynamic parameter of the electronic subsystem... C e Electronic thermal conductivity K e Electron blocking constant Electroacoustic coupling constant and lattice heat capacity C l and lattice thermal conductivity K l Integrated friction term These thermodynamic parameters are almost all taken as constant values, which makes the final simulation results have a large error with the actual situation.
[0027] This invention aims to achieve: By decoupling the 2T-MD method, a multi-scale simulation method for instantaneous deposition (first-principles calculation - two-temperature model simulation - molecular dynamics simulation) was invented. This method eliminates the need to consider interatomic interactions in molecular dynamics simulation, the influence of potential functions on the two-temperature model simulation, and the equivalent of friction terms. Starting from the thermodynamic properties of semiconductor materials, this invention, based on the thermodynamic parameters of semiconductor materials obtained through first-principles calculations, numerically solves the two-temperature model equations to obtain the energy of instantaneous deposition of rapidly incident heavy ions in semiconductor materials. This deposition energy, according to the principle of "Gaussian distribution of kinetic energy and uniform distribution of momentum," directly corresponds to each atom in the material system. The processed atomic information is then directly used as the initial input condition for subsequent molecular dynamics simulations to undergo long-term molecular dynamics evolution.
[0028] Based on this, this invention proposes a universal method that simultaneously considers the ultrafast energy transfer behavior of electron subsystems at the femtosecond scale and the dynamic evolution of material systems at the picosecond scale. This method starts by calculating the thermodynamic properties of semiconductor materials using first-principles methods, minimizing the accumulation of errors from subjective data. A numerical solution program for the two-temperature model equations is developed, directly mapping the deposition energy obtained from the two-temperature model simulation to the atomic information in subsequent molecular dynamics simulations. Then, long-term molecular dynamics evolution is performed to establish a multi-scale spatiotemporal evolution model of semiconductor materials subjected to rapid heavy ion incidence. This gradually reveals the microscopic mechanisms of structural damage caused by continuous track formation and defect evolution in semiconductor materials subjected to rapid heavy ion incidence.
[0029] The technical solutions provided by the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
[0030] One embodiment of the present invention relates to a simulation method for the formation and evolution of fast heavy ion tracks in semiconductor materials. The specific process of the simulation method for the formation and evolution of fast heavy ion tracks in semiconductor materials in this embodiment can be as follows: Figure 1 As shown, it includes: Step 101: Obtain the thermodynamic parameters of the semiconductor material using a first-principles method.
[0031] Specifically, the electronic heat capacity of semiconductor materials is obtained through first-principles calculations, i.e. C e : First-principles calculation software was used to perform structural relaxation on the unit cell of the semiconductor material system; based on the structural relaxation, self-consistent calculations were performed; and the electronic heat capacity of the semiconductor material was calculated according to equation (7). C e : In the formula: T eIt is the temperature of the electrons. The electron temperature is T e Electronic heat capacity at time U The electron temperature of semiconductor materials is The internal energy of a semiconductor material.
[0032] Calculate the electronic thermal conductivity of semiconductor materials K e and electroacoustic coupling constant g : Calculate the electronic thermal conductivity of semiconductor materials based on equations (8) and (9): In the formula: The electron temperature is Electronic thermal conductivity at that time The electron temperature is Electron diffusion rate at that time It is Boltzmann's constant. q It is electron charge. It is electron mobility.
[0033] The electroacoustic coupling constant of the semiconductor material is calculated according to equation (10): In the formula: The electron temperature is Electroacoustic coupling constant at time, It is the electron-phonon relaxation time.
[0034] Based on experimental data, the lattice heat capacity of semiconductor materials was fitted. C l and lattice thermal conductivity K l : Different semiconductor materials have different lattice heat capacities and lattice thermal conductivities. However, in a higher temperature range, the overall lattice properties of semiconductor materials show the same trend. The fitted lattice heat capacity equation (11) and lattice thermal conductivity equation (12) are as follows: In the formula: The lattice temperature of a semiconductor material is The lattice heat capacity at that time The lattice temperature of a semiconductor material is The lattice thermal conductivity at that time is the molar volume of the semiconductor material; a, b, c, d, A, and B are characteristic parameters of different semiconductor materials obtained by fitting experimental data of semiconductor materials.
[0035] Step 102: Obtain the initial ionization energy generated instantaneously in the electronic subsystem of the semiconductor material by rapid heavy ion incident on the semiconductor material using a two-body collision method.
[0036] Based on Monte Carlo simulation software, a three-dimensional model of semiconductor material was established, and the three-dimensional model was meshed at the nanoscale. The fast heavy ion incident on the semiconductor material was simulated by the two-body collision method, and the ionization energy of the fast heavy ion in each mesh after incident on the semiconductor material was obtained. The ionization energy distribution of the meshed three-dimensional model was used as the initial ionization energy.
[0037] Step 103: Based on thermodynamic parameters and initial ionization energy, a two-temperature model is used to simulate the energy transfer process of the electronic subsystem and lattice subsystem in the semiconductor material, so as to obtain the target energy generated when the electronic subsystem and lattice subsystem reach thermal equilibrium.
[0038] Specifically, based on thermodynamic parameters and initial ionization energy, the two differential thermal diffusion equations of the two-temperature model are numerically solved, and the energy transfer process of electronic subsystems and lattice subsystems in semiconductor materials is simulated through the solution process.
[0039] Step 104: Distribute the target energy to each lattice atom in the lattice subsystem, and simulate the dynamic behavior of each lattice atom using classical molecular dynamics methods based on the target energy of each lattice atom.
[0040] Specifically, firstly, based on the principle that the statistical distribution of the kinetic energy of each lattice atom conforms to a Gaussian distribution and the statistical distribution of the momentum of each lattice atom conforms to a uniform distribution, the target energy is allocated to each lattice atom in the lattice subsystem. Then, the target energy of each lattice atom is converted into the initial kinetic energy of each lattice atom, and based on the initial kinetic energy of each atom, the dynamic behavior of each lattice atom is simulated using molecular dynamics methods.
[0041] Step 105: Determine the structural damage caused by rapid heavy ion incident on the semiconductor material based on the continuous tracks formed by the dynamic behavior of lattice atoms in the semiconductor material.
[0042] In the specific implementation, firstly, the electronic and lattice thermodynamic parameters obtained above ( C e , K e , g , C l ,K l The initial ionization energy of the SHI incident semiconductor material system was obtained, and a program was written to numerically solve the two-temperature model equations (1) and (2). The solution process describes in detail the time evolution and radial spatial distribution of temperature and energy of the electron / lattice system, and obtains the energy of rapid heavy ion incident on the material system deposited into the lattice atoms within a femtosecond. Then, molecular dynamics software was used to perform atomic-scale molecular dynamics simulation on the semiconductor material, and structural relaxation was performed at room temperature to obtain a relatively stable ground state structure. Finally, the energy obtained after rapid heavy ion incident and deposited into the lattice atoms within a femtosecond time was mapped to the structurally relaxed lattice atoms according to the principles of kinetic energy Gaussian distribution and momentum uniform distribution, as the initial input condition for molecular dynamics simulation.
[0043] Atomic-scale molecular dynamics simulations were performed using molecular dynamics software with periodic boundary conditions and isothermal layers in both the X and Y directions (perpendicular to the XOY plane and parallel to the Z direction). The simulation step size and duration can be adjusted according to the characteristics of the simulated material, with simulation duration ranging from ps to ns. During the molecular dynamics simulation, the atomic information output at the set step size is viewed in an atomic visualization tool, allowing observation of changes in atomic positions, the formation of dislocation defects, and the evolution of ion incident tracks throughout the simulation. This provides a complete understanding of the microscopic mechanism by which rapid heavy ion incidence in semiconductor materials forms continuous trajectories that cause structural damage.
[0044] Compared with the prior art, the present invention has the following beneficial effects: First, this invention separates the dual-temperature model simulation process from the molecular dynamics simulation process. It adopts a method of instantaneous energy deposition in a fast heavy ion incident material system. First, a program is written to perform complete numerical calculations of the dual-temperature model, and then the dynamic evolution at the atomic scale of molecular dynamics is performed. This avoids the problem of the dual-temperature model process being affected by the potential function of molecular dynamics simulation in the 2T-MD method.
[0045] First, regarding the thermodynamic parameters (electronic heat capacity) of the electronic subsystem and lattice system required in the two-temperature model equations... C e Electronic thermal conductivity K e Electroacoustic coupling constant g lattice heat capacity C l lattice thermal conductivity K l ), starting from the thermodynamic properties of the material itself, quantitative calculations are performed, avoiding the errors caused by equating the thermodynamic parameters of the crystal system to friction terms in the 2T-MD method.
[0046] Secondly, the thermodynamic properties of all semiconductor materials in this invention take temperature changes into account, and the numerical solution program for the dual-temperature model equations uses thermodynamic parameters that evolve with temperature, thus minimizing simulation errors to the greatest extent.
[0047] In some embodiments, the electronic thermal capacity of the semiconductor material in step 101 C e The calculation can be performed using other methods to solve the equations, such as: In the formula, T e It is the temperature of the electrons. The electron temperature is T e Electronic heat capacity at time It refers to the energy level where the electron resides. The electron temperature is T e Chemical potential at time It is at the energy level The electronic state density, It is the Fermi-Dirac distribution function. k B It is the Boltzmann constant.
[0048] Electronic thermal conductivity of semiconductor materials K e and electroacoustic coupling constant g The calculation can be performed using other methods to solve the equations, such as: In the formula, It is the reduced Planck constant. k B It is Boltzmann's constant. It is the phonon frequency. This represents the interaction strength of the electroacoustic coupling. It refers to the energy level where the electron resides. It is at the energy level The electronic state density, It is the Fermi level. It is the electronic density of states at the Fermi level. It is the Fermi-Dirac distribution function.
[0049] In the formula, It is the electroacoustic coupling constant. N The number of atoms in the unit cell. k B Boltzmann's constant, atomic mass Let V be the volume of an atomic unit cell. For electron-phonon relaxation time.
[0050] In step 102, the initial ionization energy generated instantaneously in the electronic subsystem by fast heavy ion incident on the semiconductor material can be calculated using other equations, such as: In the formula, It is the initial ionization energy deposition term generated instantaneously within the electronic subsystem of a semiconductor material by rapid heavy ion incidence. It is the spatial distribution term of the initial depositional energy. It is an exponential factor. r It is the radius of the ionization track. r m It is the maximum radius of the simulated semiconductor material system. S e It is the electron energy loss value of the incident ions. t It's time.
[0051] In the formula, It is the initial ionization energy deposition term generated instantaneously within the electronic subsystem of a semiconductor material by rapid heavy ion incidence. A 0 is an adjustable parameter. It is the spatial distribution term of the initial depositional energy. It is the electron energy deposition time. t It is time. It is the standard deviation of the Gaussian distribution.
[0052] In the formula, t It's about thickness. It is deposited on a thickness of t Energy within a coaxial cylindrical shell, N It is the number of atoms in the system. e It is electron charge. It is the effective charge of the system's atoms. It is an adjustable parameter that depends on the velocity of the incident particle. , c It's the speed of light. m It is electronic quality. T It is the maximum range of ion-injected semiconductor material systems. It determines the electron range at a given energy level.
[0053] In the formula, It is the initial ionization energy deposition term generated instantaneously within the electronic subsystem of a semiconductor material by rapid heavy ion incidence. It is the spatial term of the initial ionization energy deposition. It is the time term of the initial ionization energy deposition. It is the unit mesh volume. It is the electron energy loss value of the SHI incident semiconductor material system. It is the standard deviation of the Gaussian distribution, with a value of 1. r It is the radius of the semiconductor material's spatial location from the incident ion trajectory. t It refers to time, since the calculation is based on the initial ionization energy deposition. Here it is set to 0. This is the electron energy deposition time, with a value of 10. -15 s.
[0054] In one example, the energy deposited into the lattice atoms within a femtosecond time after rapid heavy ion incidence is used as the initial input condition for molecular dynamics simulation. Alternatively, regions and atomic groups can be divided in the molecular dynamics software, and the temperature deposited into the lattice system within a femtosecond time after rapid heavy ion incidence can be converted into the atomic velocity and used as the initial input condition for molecular dynamics simulation.
[0055] To facilitate understanding, this invention uses 467MeV Kr ion incident β-Ga2O3 material as an example to detail a simulation method for the formation and evolution of fast heavy ion tracks in semiconductor materials: Step S1: Calculate the electronic heat capacity of β-Ga2O3 material using first-principles methods. C e .
[0056] Step S1.1: Use first-principles calculation software to perform structural relaxation on the β-Ga2O3 unit cell; Step S1.2: Based on structural relaxation, perform self-consistent calculations; Step S1.3: Calculate the electronic heat capacity of β-Ga2O3 material according to equation (7), and the calculation results are as follows. Figure 2 As shown.
[0057] Step S2: Calculate the electronic thermal conductivity of β-Ga2O3 material K e and electroacoustic coupling constant g .
[0058] Step S2.1: Calculate the electronic thermal conductivity of β-Ga2O3 material according to equations (8) and (9); Step S2.2: Calculate the electroacoustic coupling constant of β-Ga2O3 material according to equation (10); Step S3: Fit the lattice heat capacity of β-Ga2O3 material based on experimental data. C l and lattice thermal conductivity K l .
[0059] Step S3.1: Fit the lattice heat capacity of β-Ga2O3 material based on experimental data and equation (11). The fitting result is as follows: Figure 3 As shown; Step S3.2: Fit the lattice thermal conductivity of β-Ga2O3 material according to equation (12); Step S4: Calculate the initial ionization energy generated instantaneously in the electronic subsystem by fast heavy ion incident on the semiconductor material. A(r,t) .
[0060] Step S4.1: Based on the Monte Carlo simulation software GEANT4, construct the β-Ga2O3 target material and divide the target material into 133×133×9 grids at the nanoscale; Step S4.2: Set up a target source, i.e., an incident Kr ion point source, outside the target material target body along the center of the top surface. Ions are incident on the target material along the Z direction. Step S4.3: Simulate the incidence of 467 MeV Kr ions into β-Ga2O3 material using the two-body collision method to obtain the ionization energy of fast heavy ions within each grid of the β-Ga2O3 target material. Use the ionization energy distribution of the meshed 3D model as the initial ionization energy. The calculation results are as follows: Figure 4 As shown.
[0061] Step S5: The electronic and lattice thermodynamic parameters obtained in steps S1-4 ( C e , K e , g , C l , K l The initial ionization energy of the 467MeV Kr ion incident on the β-Ga2O3 material system was substituted into equations (1) and (2) to numerically solve the two-temperature model equations. This solution process describes in detail the time evolution and radial spatial distribution of temperature and energy in the electronic / lattice subsystem, obtaining the energy deposited into the lattice atoms when the electronic subsystem and lattice system of the 467MeV Kr ion incident on the β-Ga2O3 material reach thermal equilibrium, such as... Figure 5 As shown.
[0062] Step S6: Perform atomic-scale molecular dynamics simulations on the β-Ga2O3 system using molecular dynamics software, and perform structural relaxation at room temperature to obtain a relatively stable ground state structure.
[0063] Step S7: The energy of the 467MeV Kr ions obtained in step S5 that are deposited into the β-Ga2O3 lattice atoms within a femtosecond time after incident on the β-Ga2O3 material is mapped to the atoms after structural relaxation in step S6 in the form of a Gaussian distribution of kinetic energy and a uniform distribution of momentum, and used as the initial conditions for molecular dynamics simulation.
[0064] Step S8: Perform atomic-scale molecular dynamics simulations in molecular dynamics software, using periodic boundary conditions, and set isothermal layers in both the X and Y directions (perpendicular to the XOY plane and parallel to the Z direction).
[0065] Step S9: View the atomic information output at the set step size during the molecular dynamics simulation in step S8 in the atomic visualization tool, observe the changes in atomic positions, the formation of dislocation defects, and the evolution of ion incident tracks throughout the simulation time, and fully reveal the microscopic mechanism of structural damage caused by the formation of continuous trajectories in β-Ga2O3 material by rapid heavy ion incident.
[0066] Figure 6 The diagram shows the molten zone formed at the track center of β-Ga2O3 material when 467MeV Kr ions are incident on it at 1ps and 350ps.
[0067] The steps of the various methods described above are only for clarity. In practice, they can be combined into one step or some steps can be split into multiple steps. As long as they include the same logical relationship, they are all within the protection scope of this invention. Adding insignificant modifications or introducing insignificant designs to the algorithm or process, without changing the core design of the algorithm and process, are also within the protection scope of this invention.
[0068] Another embodiment of the present invention relates to a simulation device for the formation and evolution of fast heavy ion tracks in semiconductor materials. The implementation details of this simulation device are described below. The following details are provided for ease of understanding and are not essential for implementing this solution. The simulation device for the formation and evolution of fast heavy ion tracks in semiconductor materials in this embodiment includes: The parameter acquisition module is used to acquire the thermodynamic parameters of semiconductor materials using first-principles methods. The energy harvesting module is used to harvest the initial ionization energy generated instantaneously in the electronic subsystem of a semiconductor material by rapid heavy ion incident on the semiconductor material via a two-body collision method. The dual-temperature model simulation module is used to simulate the energy transfer process of the electronic subsystem and lattice subsystem in semiconductor materials based on thermodynamic parameters and initial ionization energy, so as to obtain the target energy generated when the electronic subsystem and lattice subsystem reach thermal equilibrium. The molecular dynamics simulation module is used to allocate the target energy to each lattice atom in the lattice subsystem, and to simulate the dynamic behavior of each lattice atom using classical molecular dynamics methods based on the target energy of each lattice atom. The damage determination module is used to determine the structural damage caused by rapid heavy ion incidence on semiconductor materials based on the continuous tracks formed by the dynamic behavior of lattice atoms in the semiconductor material.
[0069] It is not difficult to see that this embodiment is a device embodiment corresponding to the above method embodiments, and this embodiment can be implemented in conjunction with the above method embodiments. The relevant technical details and technical effects mentioned in the above embodiments are still valid in this embodiment, and will not be repeated here to reduce repetition. Accordingly, the relevant technical details mentioned in this embodiment can also be applied to the above embodiments.
[0070] It is worth mentioning that all modules involved in this embodiment are logical modules. In practical applications, a logical unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. Furthermore, to highlight the innovative aspects of this invention, this embodiment does not introduce units that are not closely related to solving the technical problem proposed by this invention; however, this does not mean that other units are absent from this embodiment.
[0071] Another embodiment of the present invention relates to a computer device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the simulation method for rapid heavy ion track formation and evolution in semiconductor materials in the above embodiments.
[0072] The memory and processor are connected via a bus, which can include any number of interconnecting buses and bridges, connecting various circuits of one or more processors and memories. The bus can also connect various other circuits, such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be described further herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over the wireless medium via an antenna, which further receives data and transmits it to the processor.
[0073] The processor manages the bus and general processing, and also provides various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory is used to store data used by the processor during operation.
[0074] Another embodiment of the present invention relates to a computer-readable storage medium storing a computer program. When executed by a processor, the computer program implements the method embodiments described above.
[0075] That is, those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.
[0076] Those skilled in the art will understand that the above embodiments are specific embodiments for implementing the present invention, and in practical applications, various changes can be made to them in form and detail without departing from the spirit and scope of the present invention.
Claims
1. A simulation method for the formation and evolution of rapid heavy ion tracks in semiconductor materials, characterized in that, The method includes: Thermodynamic parameters of semiconductor materials are obtained using first-principles methods; The initial ionization energy generated instantaneously in the electronic subsystem of a semiconductor material during rapid heavy ion incident is obtained by a two-body collision method. Based on thermodynamic parameters and initial ionization energy, a two-temperature model is used to simulate the energy transfer process of electronic subsystems and lattice subsystems in semiconductor materials, so as to obtain the target energy generated when electronic subsystems and lattice subsystems reach thermal equilibrium; The target energy is allocated to each lattice atom in the lattice subsystem, and the dynamic behavior of each lattice atom is simulated using classical molecular dynamics methods based on the target energy of each lattice atom. Based on the continuous tracks formed by the dynamic behavior of lattice atoms in semiconductor materials, the structural damage caused by rapid heavy ion incident on semiconductor materials can be determined.
2. The simulation method for rapid heavy ion track formation and evolution in semiconductor materials according to claim 1, characterized in that, The method of obtaining the thermodynamic parameters of semiconductor materials using first-principles methods includes: Structural relaxation of semiconductor materials; Self-consistent calculations were performed on the semiconductor material after structural relaxation, and the electronic heat capacity of the semiconductor material was simulated with temperature by modifying the system temperature in the self-consistent calculation. Based on the trend of electronic heat capacity with temperature, the electronic heat capacity of semiconductor materials can be obtained using the following formula. C e : ;in, T e It is the temperature of the electrons. The electron temperature is T e Electron heat capacity at time U The electron temperature of semiconductor materials is The internal energy of semiconductor materials; The electronic thermal conductivity of semiconductor materials can be obtained using the following formula. K e : , ;in, The electron temperature is Electronic thermal conductivity at that time The electron temperature is Electron diffusion rate at that time It is Boltzmann's constant. q It is electron charge. It is electron mobility; The electroacoustic coupling constant of semiconductor materials can be obtained from the following formula. g : ;in, The electron temperature is Electroacoustic coupling constant at time, It is the electron-phonon relaxation time; The lattice heat capacity of semiconductor materials can be obtained from the following formula. C l and lattice thermal conductivity K l : , ;in, The lattice temperature of a semiconductor material is The lattice heat capacity at that time The lattice temperature of a semiconductor material is The lattice thermal conductivity at that time is the molar volume of the semiconductor material; a, b, c, d, A, and B are characteristic parameters of different semiconductor materials obtained by fitting experimental data of semiconductor materials.
3. The simulation method for the formation and evolution of fast heavy ion tracks in semiconductor materials according to claim 1, characterized in that, The method of obtaining the initial ionization energy generated instantaneously in the electronic subsystem of a semiconductor material by rapid heavy ion incidence via a two-body collision includes: Based on Monte Carlo simulation software, a three-dimensional model of semiconductor materials was established, and the three-dimensional model was meshed at the nanoscale. The ionization energy of fast heavy ions incident on semiconductor materials was simulated by a two-body collision method. The ionization energy distribution of the ionized heavy ions in each grid after incident on the semiconductor material was obtained, and the ionization energy distribution of the three-dimensional model after grid division was used as the initial ionization energy.
4. The simulation method for rapid heavy ion track formation and evolution in semiconductor materials according to claim 1, characterized in that, The energy transfer process of the electronic subsystem and lattice subsystem in semiconductor materials is simulated using a two-temperature model based on thermodynamic parameters and initial ionization energy, including: Based on thermodynamic parameters and initial ionization energy, the two differential thermal diffusion equations of the two-temperature model are numerically solved, and the energy transfer process of electronic subsystems and lattice subsystems in semiconductor materials is simulated through the solution process.
5. The simulation method for the formation and evolution of fast heavy ion tracks in semiconductor materials according to claim 1, characterized in that, The process of distributing the target energy to the individual lattice atoms in the lattice subsystem includes: Based on the principle that the statistical distribution of the kinetic energy of each lattice atom conforms to a Gaussian distribution and the statistical distribution of the momentum of each lattice atom conforms to a uniform distribution, the target energy is distributed to each lattice atom in the lattice subsystem.
6. The simulation method for rapid heavy ion track formation and evolution in semiconductor materials according to claim 1, characterized in that, The simulation of the dynamic behavior of each lattice atom, based on the target energy of each lattice atom, using classical molecular dynamics methods, includes: The target energy of each lattice atom is converted into the initial kinetic energy of each lattice atom, and the dynamic behavior of each lattice atom is simulated using classical molecular dynamics methods based on the initial kinetic energy of each atom.
7. The simulation method for rapid heavy ion track formation and evolution in semiconductor materials according to claim 1, characterized in that, Before simulating the dynamic behavior of each lattice atom, the following is also included: The primitive cell structure of each lattice atom is expanded to form a supercell structure, and the supercell structure is then relaxed.
8. A simulation device for the formation and evolution of rapid heavy ion tracks in semiconductor materials, characterized in that, The device includes: The parameter acquisition module is used to acquire the thermodynamic parameters of semiconductor materials using first-principles methods. The energy harvesting module is used to harvest the initial ionization energy generated instantaneously in the electronic subsystem of a semiconductor material by rapid heavy ion incident on the semiconductor material via a two-body collision method. The dual-temperature model simulation module is used to simulate the energy transfer process of the electronic subsystem and lattice subsystem in semiconductor materials based on thermodynamic parameters and initial ionization energy, so as to obtain the target energy generated when the electronic subsystem and lattice subsystem reach thermal equilibrium. The molecular dynamics simulation module is used to allocate the target energy to each lattice atom in the lattice subsystem, and to simulate the dynamic behavior of each lattice atom using classical molecular dynamics methods based on the target energy of each lattice atom. The damage determination module is used to determine the structural damage caused by rapid heavy ion incidence on semiconductor materials based on the continuous tracks formed by the dynamic behavior of lattice atoms in the semiconductor material.
9. A computer device, characterized in that, include: At least one processor; And a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform a simulation method for rapid heavy ion track formation and evolution in semiconductor materials as claimed in any one of claims 1 to 7.
10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements a simulation method for the formation and evolution of rapid heavy ion tracks in semiconductor materials as described in any one of claims 1 to 7.