Method for calculating heat transport performance of wide bandgap semiconductor based on deep learning potential

Abstract

The invention belongs to the field of high-power electric vacuum devices, relates to heat transport performance of an interface ceramic material in a high-power electric vacuum device, and particularly provides a deep learning potential-based wide bandgap semiconductor heat transport performance calculation method, which is used for solving various problems of existing methods. According to the method, firstly, the deep learning potential is constructed by adopting a first principle, then the deep learning potential is used as an empirical potential function, and the heat transport performance of the wide bandgap semiconductor is calculated through a molecular dynamics method, so that large-scale molecular dynamics simulation is realized, and a temperature conduction process and a heat transfer process of a long-time dimension can be accurately predicted; errors caused by empirical potential simulation calculation are avoided, and the time and operation cost of first principle calculation are greatly reduced.

Description

Technical Field

[0001] The present invention belongs to the field of high-power vacuum devices and relates to the thermal transport performance of interface ceramic materials in high-power vacuum devices. It specifically provides a method for calculating the thermal transport performance of wide-bandgap semiconductors based on deep learning potential. Background Art

[0002] In high-power vacuum devices, interfacial ceramic materials often serve as important components of packaging, support, or insulation structures, and their thermal conductivity plays a key role in the device's overall thermal management capabilities. Vacuum devices generate significant heat during operation, and failure to dissipate this heat in a timely and effective manner can easily lead to device overheating, performance degradation, and even failure. Therefore, improving the interfacial thermal conductivity of ceramic materials facilitates rapid heat conduction and diffusion, thereby ensuring stable device operation under high voltage, high current, and high frequency conditions. However, during the material exploration phase, measuring the thermal conductivity of candidate materials en masse consumes significant time and effort, resulting in a relative lack of data on the thermal transport properties of many materials.

[0003] At present, two methods have been proposed for calculating the thermal transport properties of wide-bandgap semiconductors. The first method is based on the Boltzmann transport equation and first principles, which can calculate the thermal conductivity of the system. It mainly uses first principles to extract the material's band structure, effective mass, phonon scattering information and other properties, and then combines explicit scattering mechanism modeling and Boltzmann transport theory based on relaxation time approximation to achieve efficient and accurate calculation of electronic thermal conductivity and related transport properties. However, when calculating large systems through first principles, huge errors will occur. The second is the classical molecular dynamics method based on empirical potential. This method uses the empirical interaction potential function to calculate the energy conduction rate and temperature gradient of the system, and then uses linear fitting to fit the slope of the temperature along the conduction direction. At the same time, combined with the energy transfer size of the cold and hot sources, the energy transfer size per unit time, that is, the energy transfer rate, is calculated. Then, the thermal conductivity of the system along the conduction direction can be obtained through the thermal conductivity calculation formula; however, this method is based on the empirical potential function, and the empirical potential function has relatively low accuracy at different temperatures and cannot accurately predict temperature changes. It mainly focuses on the motion process of the atomic nucleus and empirically processes the quantum properties of electrons, which affects the calculation of the overall thermal conductivity. Summary of the Invention

[0004] The purpose of the present invention is to provide a calculation method for the thermal transport performance of wide bandgap semiconductors based on deep learning potential, so as to solve the many problems existing in the existing methods. The present invention first adopts the first principles to construct the deep learning potential, and then uses the deep learning potential as the empirical potential function to calculate the thermal transport performance of wide bandgap semiconductors through the molecular dynamics method, realizing large-scale molecular dynamics simulation and accurately predicting the temperature conduction process and heat transfer process in the long time dimension. It not only avoids the errors caused by the empirical potential simulation calculation, but also greatly reduces the time and computational cost of the first principles calculation.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for calculating the thermal transport performance of wide bandgap semiconductors based on deep learning potential, characterized by comprising the following steps:

[0007] Step 1: Perform first-principles molecular dynamics simulation on the wide bandgap semiconductor material to be tested, record the equilibrium trajectory and obtain the atomic energy, atomic trajectory and force information of each step to form a training set;

[0008] Step 2: Perform deep learning potential function training based on the training set to obtain a deep learning potential function;

[0009] Step 3: Perform molecular dynamics simulation based on deep learning potential function to obtain the temperature gradient and energy transfer rate of the semiconductor system;

[0010] Step 4: Calculate the thermal conductivity of the wide bandgap semiconductor material to be tested in the heat conduction direction based on the temperature gradient and energy transfer rate of the semiconductor system.

[0011] Furthermore, the specific process of step 1 is:

[0012] Step 1.1: In the MS (Material stdio) software, select the semiconductor system corresponding to the wide bandgap semiconductor material to be measured, and expand the semiconductor system to a lattice constant greater than And the initial semiconductor system is derived;

[0013] Step 1.2: In the VASP software, use the PBE functional to perform lattice optimization and energy self-consistency on the initial semiconductor system to obtain the optimized semiconductor system;

[0014] Step 1.3: In the VASP software, set the time step to 1 fs, the number of steps to 6000-10000 steps, and the temperature range to be measured to 300K-500K. Perform molecular dynamics simulations under the canonical ensemble (NVT ensemble). During the simulation, record the equilibrium trajectory and the atomic energy, atomic trajectory, and force information of each step to form a training set.

[0015] Furthermore, the specific process of step 2 is:

[0016] DeePMD-kit software is used as the deep learning potential function training software. During the deep learning potential function training process, the loss function L is set as:

[0017]

[0018] Where N represents the number of atoms, F i represents the atomic force of atom i, E represents the energy of the semiconductor system, Δ represents the difference between the training data and the DP prediction, and the pre-factor p e With p f ΔE 2 and |ΔF i | 2 The weight value of

[0019] The atomic position information mapping descriptor is:

[0020]

[0021] in, Represents mapping descriptor, representing local structural features; R ij represents the Euclidean distance between atoms i and j, R cs Indicates the smooth cutoff radius, R c Indicates the maximum cutoff radius; x ij 、y ij 、z ij They represent the coordinate component differences of atom j relative to atom i on the x, y, and z axes, respectively.

[0022] Furthermore, the specific process of step 3 is:

[0023] Step 3.1: In the LAMMPS software, expand the optimized semiconductor system to a cell with more than 2000 atoms. After expansion, divide the semiconductor system into 20 to 30 blocks evenly along the direction of heat conduction to be measured.

[0024] Step 3.2: Minimize the energy of the semiconductor system and then perform thermodynamic relaxation of the system for 30 ps to 50 ps within the temperature range to be measured.

[0025] Step 3.3: Set the cold and hot sources to the lowest and highest temperatures in the temperature range to be measured, respectively. Perform a thermodynamic molecular dynamics simulation of the middle block using the NVE ensemble to calculate and record the temperature of the middle block and the energy transferred by the cold and hot sources.

[0026] Furthermore, the specific process of step 4 is as follows:

[0027] Step 4.1: Time average the temperature of each intermediate block:

[0028]

[0029] Among them, T n represents the average temperature of block n, T n,t represents the temperature of block n at time t, t tol represents the simulation time;

[0030] Step 4.2: Calculate the slope of the conduction direction based on the average temperature of each block to obtain the rate of change of temperature with the conduction direction R:

[0031]

[0032] Step 4.3: Calculate the energy transfer rate dQ based on the total energy transferred by the cold and hot sources:

[0033]

[0034] Where Q represents the total energy transferred by the cold and heat sources;

[0035] Step 4.4: Calculate the thermal conductivity κ based on the rate of change of temperature with conduction direction R and the energy transfer rate dQ: κ = dQ × R.

[0036] Based on the above technical solution, the beneficial effects of the present invention are:

[0037] The present invention provides a method for calculating the thermal transport performance of wide-bandgap semiconductors based on deep learning potential. First, a training data set is constructed using first principles, and then a deep learning potential is constructed based on the training data set. The deep learning potential is used as an empirical potential function, and the thermal transport performance of the wide-bandgap semiconductor is calculated by molecular dynamics method. Large-scale molecular dynamics simulation is realized, and the temperature conduction process and heat transfer process in the long-term dimension can be accurately predicted. It not only avoids the errors caused by empirical potential simulation calculations, but also greatly reduces the time and computational cost of first-principles calculations. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Schematic diagram of the flow chart of the method for calculating the thermal transport performance of wide bandgap semiconductors based on deep learning potential in the present invention.

[0039] Figure 2 This is a comparison chart of the energy predicted by the deep learning potential function in the present invention and the results of first-principles molecular dynamics calculations.

[0040] Figure 3 This is a comparison chart of the x-direction force predicted by the deep learning potential function in the present invention and the results of the first-principles molecular dynamics calculations.

[0041] Figure 4 This is a comparison chart of the y-direction force predicted by the deep learning potential function in the present invention and the results of first-principles molecular dynamics calculations.

[0042] Figure 5 This is a comparison chart of the z-direction force predicted by the deep learning potential function in the present invention and the results of the first-principles molecular dynamics calculations.

[0043] Figure 6 This is a diagram showing the calculation results of the thermal transport performance of wide bandgap semiconductors (w-AlN) based on deep learning potential in the present invention. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical solutions and beneficial effects of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0045] This embodiment provides a method for calculating the thermal transport properties of wide-bandgap semiconductors based on deep learning potential, which is used to calculate the thermal conductivity of wurtzite AlN (w-AlN); the software involved includes: MS software, VASP software, LAMMPS software, and DeePMD-kit software. Among them, the number of w-AlN atoms used for first-principles molecular dynamics calculations is 64, and the number of atoms used for deep potential molecular dynamics simulations is 2400.

[0046] The calculation method of wide bandgap semiconductor thermal transport performance based on deep learning potential is as follows Figure 1 As shown, the specific steps include:

[0047] Step 1: Perform first-principles molecular dynamics simulation on the wide bandgap semiconductor material to be tested, record the equilibrium trajectory, and obtain the atomic energy, atomic trajectory, and force information for each step to form a training set. The specific process is as follows:

[0048] Step 1.1: In the MS (Material stdio) software, select the semiconductor system corresponding to the wide bandgap semiconductor material to be measured, and expand the semiconductor system to a lattice constant greater than And the initial semiconductor system is derived;

[0049] Step 1.2: In the VASP software, use the PBE functional to perform lattice optimization and energy self-consistency on the initial semiconductor system to obtain the optimized semiconductor system;

[0050] Step 1.3: In the VASP software, set the time step to 1 fs, the number of steps to 6000, and the temperature range to be measured to 300K–500K. Perform molecular dynamics simulations (thermodynamic equilibrium) in the canonical ensemble (NVT ensemble). During the simulation, record the equilibrium trajectory and the atomic energy, atomic trajectory, and force information for each step to form the training set.

[0051] Step 2: Perform deep learning potential function training based on the training set to obtain a deep learning potential function;

[0052] This embodiment uses DeePMD-kit software, which is used as deep learning potential function training software. It can implement multi-body potential training with almost no loss of accuracy. Specifically:

[0053] During the deep learning potential function training process, the loss function L is set to:

[0054]

[0055] Where N represents the number of atoms, F i represents the atomic force of atom i, E represents the energy of the semiconductor system, Δ represents the difference between the training data and the DP prediction, and the pre-factor p e With p f ΔE 2 and |ΔF i | 2 The weight value of

[0056] At the same time, the atomic position information mapping descriptor is:

[0057]

[0058] in, Represents mapping descriptor, representing local structural features; R ij represents the Euclidean distance between atoms i and j, R cs Indicates the smooth cutoff radius, R c Indicates the maximum cutoff radius, atoms outside this range will be ignored; x ij 、y ij 、z ij Represent the coordinate component differences of atom j relative to atom i on the x, y, and z coordinate axes respectively;

[0059] The training data (atomic energy, atomic trajectory and force information) in step 1 are trained and fitted using the DeePMD-kit software; the cutoff radius is set to The descriptor is selected as 'se_e2_a', the embedding layer and fitting layer networks are set to {25, 50, 100} and {240, 240, 240} respectively, and the number of training steps is set to 2 million to ensure the accuracy of the results. After the training is completed, the deep learning potential function is obtained;

[0060] like Figure 2 The figure shows a comparison between the energy predicted by the deep learning potential function and the results of the first-principles molecular dynamics calculations, as shown in Figures 3 to 5 The following are comparisons of the forces in the x, y, and z directions predicted by the deep learning potential function and the results of the first-principles molecular dynamics calculations. It can be seen from the figure that the energy and force predicted by the deep learning potential function trained in this embodiment are close to the results of the first-principles molecular dynamics calculations, and the root mean square errors are 0.0006 eV / atom and 0.0006 eV / atom, respectively. This indicates that the deep learning potential function in this invention has achieved the computational accuracy of first-principles molecular dynamics.

[0061] Step 3: Perform molecular dynamics simulation based on deep learning potential function to obtain the temperature gradient and energy transfer rate of the semiconductor system; the specific process is as follows:

[0062] Step 3.1: In LAMMPS, expand the optimized semiconductor system to a cell size greater than 2000 atoms. Partition the expanded semiconductor system into 20 to 30 blocks evenly spaced along the direction of heat conduction to be measured. During this process, fix the atoms at both ends of the heat conduction direction (i.e., the two ends of the semiconductor system) to prevent temperature loss during the simulation. Set up hot and cold sources. The hot source will continuously conduct heat, while the cold source will continuously lose heat, resulting in a temperature gradient.

[0063] Step 3.2: Minimize the energy of the semiconductor system and then perform thermodynamic relaxation of the system for 30 ps to 50 ps within the temperature range to be measured.

[0064] Step 3.3: Set the cold and hot sources to the lowest and highest temperatures in the temperature range to be measured, respectively. Perform a thermodynamic molecular dynamics simulation on the middle block (along the heat conduction direction, all blocks except the first and last blocks are considered middle blocks) using the NVE ensemble. Calculate and record the temperature of the middle block and the energy transferred by the cold and hot sources.

[0065] In this embodiment, through the code interface between DeePMD-kit and LAMMPS, molecular dynamics simulation based on deep learning potential can be directly implemented. By setting the cold source and the heat source, the temperature change with the propagation direction can be obtained by simulation.

[0066] Step 4: Calculate the thermal conductivity of the wide bandgap semiconductor material to be tested in the heat conduction direction based on the temperature gradient and energy transfer rate of the semiconductor system. The specific process is as follows:

[0067] Step 4.1: Perform a time-average on the temperature of each intermediate block to avoid temperature peculiarities, specifically:

[0068]

[0069] Among them, T n represents the average temperature of block n, T n,t represents the temperature of block n at time t, then ∑t n,t is the total temperature, t tol represents the simulation time;

[0070] Step 4.2: Calculate the slope of the conduction direction based on the average temperature of each block, thereby obtaining the rate of change R of temperature along the conduction direction (z direction in this embodiment), specifically:

[0071]

[0072] Step 4.3: Calculate the energy transfer rate dQ based on the total energy transferred by the cold and hot sources, specifically:

[0073]

[0074] Where Q represents the total energy transferred by the cold and heat sources, t tol represents the simulation time;

[0075] Step 4.4: Calculate the thermal conductivity κ based on the rate of change of temperature with the conduction direction R and the energy transfer rate dQ, specifically: κ = dQ × R; the thermal conductivity of w-AlN is calculated as follows: Figure 6 As shown, from left to right and from top to bottom, the first figure shows the loss of heat source energy and the absorption of cold source energy. The second figure shows the temperature change along the direction of heat conduction: the fitted slope is -0.3904. The third figure shows the change of heat flow per unit area over time: the heat flow tends to equilibrium over time. The fourth figure shows the change of thermal conductivity over time: it tends to equilibrium over time and stabilizes at 300W / (m·K).

[0076] In summary, the present invention proposes a calculation method for the thermal transport properties of wide-bandgap semiconductors based on deep learning potential, which takes into account both the calculation accuracy of first-principles molecular dynamics and the calculation speed of classical molecular dynamics simulation, fundamentally solving the problem of mismatch between calculation efficiency and calculation accuracy; the time saved when using deep potential calculation is 2 orders of magnitude less than the time spent on empirical potential calculation, and at the same time, it is 3 orders of magnitude less than the time spent on first-principles calculation, indicating that the present invention has a significant improvement in calculation speed compared with the two existing methods.

[0077] The above description is only a specific embodiment of the present invention. Any feature disclosed in this specification, unless otherwise stated, can be replaced by other equivalent or alternative features with similar purposes; all disclosed features, or all steps in the methods or processes, except for mutually exclusive features and / or steps, can be combined in any way.

Claims

1. A method for calculating the thermal transport properties of wide bandgap semiconductors based on deep learning potential, characterized in that: The following steps are involved: Step 1: Perform first-principles molecular dynamics simulation on the wide bandgap semiconductor material to be tested, record the equilibrium trajectory and obtain the atomic energy, atomic trajectory and force information of each step to form a training set; Step 2: Perform deep learning potential function training based on the training set to obtain a deep learning potential function; Step 3: Perform molecular dynamics simulation based on deep learning potential function to obtain the temperature gradient and energy transfer rate of the semiconductor system; Step 4: Calculate the thermal conductivity of the wide bandgap semiconductor material to be tested in the heat conduction direction based on the temperature gradient and energy transfer rate of the semiconductor system.

2. The method for calculating the thermal transport performance of wide bandgap semiconductors based on deep learning potential according to claim 1, characterized in that: The specific process of step 1 is: Step 1.1: In the MS (Material stdio) software, select the semiconductor system corresponding to the wide bandgap semiconductor material to be measured, and expand the semiconductor system to a lattice constant greater than And the initial semiconductor system is derived; Step 1.2: In the VASP software, use the PBE functional to perform lattice optimization and energy self-consistency on the initial semiconductor system to obtain the optimized semiconductor system; Step 1.3: In the VASP software, set the time step to 1 fs, the number of steps to 6000-10000 steps, and the temperature range to be measured to 300K-500K. Perform molecular dynamics simulations under the canonical ensemble (NVT ensemble). During the simulation, record the equilibrium trajectory and the atomic energy, atomic trajectory, and force information of each step to form a training set.

3. The method for calculating the thermal transport performance of wide bandgap semiconductors based on deep learning potential according to claim 1, characterized in that: The specific process of step 2 is: DeePMD-kit software is used as the deep learning potential function training software. During the deep learning potential function training process, the loss function L is set as: Where N represents the number of atoms, F i represents the atomic force of atom i, E represents the energy of the semiconductor system, Δ represents the difference between the training data and the DP prediction, and the pre-factor p e With p f ΔE 2 and |ΔF i | 2 The weight value of The atomic position information mapping descriptor is: in, Represents mapping descriptor, representing local structural features; R ij represents the Euclidean distance between atoms i and j, R cs Indicates the smooth cutoff radius, R c Indicates the maximum cutoff radius; x ij 、y ij 、z ij They represent the coordinate component differences of atom j relative to atom i on the x, y, and z axes, respectively.

4. The method for calculating the thermal transport performance of wide bandgap semiconductors based on deep learning potential according to claim 1, characterized in that: The specific process of step 3 is: Step 3.1: In the LAMMPS software, expand the optimized semiconductor system to a cell with more than 2000 atoms. After expansion, divide the semiconductor system into 20 to 30 blocks evenly along the direction of heat conduction to be measured. Step 3.2: Minimize the energy of the semiconductor system and then perform thermodynamic relaxation of the system for 30 ps to 50 ps within the temperature range to be measured. Step 3.3: Set the cold and hot sources to the lowest and highest temperatures in the temperature range to be measured, respectively. Perform a thermodynamic molecular dynamics simulation of the middle block using the NVE ensemble to calculate and record the temperature of the middle block and the energy transferred by the cold and hot sources.

5. The method for calculating the thermal transport performance of wide bandgap semiconductors based on deep learning potential according to claim 1, characterized in that: The specific process of step 4 is: Step 4.1: Time average the temperature of each intermediate block: Among them, T n represents the average temperature of block n, T n,t represents the temperature of block n at time t, t tol represents the simulation time; Step 4.2: Calculate the slope of the conduction direction based on the average temperature of each block to obtain the rate of change of temperature with the conduction direction R: Step 4.3: Calculate the energy transfer rate dQ based on the total energy transferred by the cold and hot sources: Where Q represents the total energy transferred by the cold and heat sources; Step 4.4: Calculate the thermal conductivity κ based on the rate of change of temperature with conduction direction R and the energy transfer rate dQ: κ = dQ × R.

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