Micro-nanoscale heat transfer simulation method and system for heterostructure

Abstract

The present application belongs to the technical field of micro-nano scale heat transfer simulation, and discloses a micro-nano scale heat transfer simulation method and system of a heterogeneous structure, comprising: obtaining material microcosmic phonon characteristic parameters through first principle calculation, constructing a defect scattering model in combination with the Massieu criterion, establishing an interface scattering boundary condition, and incorporating multiple key influencing factors into a unified phonon Boltzmann transport equation solving system, without relying on empirical thermal conductivity and interface thermal resistance parameters, so that local temperature distribution, heat flux density distribution, interface thermal conductivity, interface thermal resistance and other macro heat transfer parameters of the heterogeneous structure can be accurately obtained, and the accuracy, engineering applicability and cross-scene transferability of micro-nano scale heat transfer simulation are improved, and the problems of temperature rise abnormality and performance drift of a device caused by heat accumulation are effectively avoided.

Description

Technical Field

[0001] This invention belongs to the field of micro-nano scale heat transfer simulation technology, and relates to a micro-nano scale heat transfer simulation method and system for heterogeneous structures. Background Technology

[0002] Third-generation semiconductor heterostructures are increasingly used in high-power-density devices. However, at the micro-nano scale, the hotspots generated by the devices need to be transferred across multiple layers of materials and interfaces. Due to the limitations of the intrinsic thermal conductivity of materials, the thermal resistance of interfaces, and the prevalence of defects, heat is prone to accumulate, leading to abnormal temperature rise and performance drift of the devices. Therefore, accurately obtaining thermal parameters such as temperature field, heat flow distribution, and interface thermal conductivity has become the key to device design.

[0003] Current mainstream heat transfer simulation methods have significant technical shortcomings: Continuous medium models based on Fourier's law rely excessively on empirical thermal conductivity and interfacial thermal resistance parameters, resulting in significant prediction errors in micro / nano scenarios such as thin-layer structures and non-equilibrium heat transfer; while microscopic models based on phonon transport can describe complex heat transfer characteristics, they require input of microscopic parameters such as phonon dispersion and interfacial transmittance, which are difficult to obtain accurately through experiments, limiting their engineering applicability. More critically, point defects and dislocations in heterostructures significantly modulate phonon scattering, and this effect exhibits strong material specificity and mode dependence. Existing technologies cannot incorporate material microscopic properties, interfacial transmission behavior, and defect scattering mechanisms into a unified modeling framework, making it difficult to accurately characterize the "material-structure-defect" coupling effect. This leads to insufficient accuracy and cross-scenario transferability of simulation results, making it difficult to meet the practical needs of heat transfer prediction for heterostructures. Summary of the Invention

[0004] The purpose of this invention is to address the problems in the prior art, such as insufficient accuracy of continuous medium models in non-equilibrium heat transfer scenarios at the micro-nano scale of heterostructures, difficulty in obtaining the microscopic and interface parameters required by microscopic phonon models through experiments, and poor transferability of interface thermal parameters due to empirical fitting. This invention provides a micro-nano scale heat transfer simulation method and system for heterostructures.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] A micro / nano-scale heat transfer simulation method for heterostructures includes:

[0007] For each component material of the heterostructure to be simulated, the microscopic phonon characteristic parameters of the material are obtained by first-principles calculation; and a simulated phonon group is generated based on the microscopic phonon characteristic parameters of the material for solving phonon transport.

[0008] For material interfaces of heterostructures, the transmittance and reflectance of phonons at the interface are solved based on microscopic phonon characteristic parameters to obtain the phonon transmission characteristic parameters of the interface, and the corresponding interface scattering boundary conditions are established.

[0009] To address the defects present in heterostructures, a defect scattering model is constructed based on the Massen criterion. The average relaxation time of defect scattering corresponding to different phonon modes is calculated and then combined to obtain the equivalent total relaxation time.

[0010] Construct the geometric structure file of the heterogeneous structure and complete the spatial discretization, then set the initial conditions and boundary conditions, and mesh the geometric structure to obtain the computational grid cells;

[0011] Based on the simulated phonon group, equivalent total relaxation time, interface phonon transmission characteristic parameters, and computational grid cells, the phonon Boltzmann transport equation is solved, and the energy accumulation and heat transport contribution of phonons in each computational grid cell are statistically analyzed to obtain the local temperature distribution and heat flux density distribution of each computational grid cell.

[0012] Based on the local temperature distribution and heat flux density distribution, the macroscopic heat transfer parameters of the heterostructure are calculated and output, and the micro-nano scale heat transfer simulation of the heterostructure is completed.

[0013] A further improvement of the present invention is that:

[0014] Furthermore, for each component material of the heterostructure to be simulated, the microscopic phonon characteristic parameters of the materials are obtained through first-principles calculations; based on the microscopic phonon characteristic parameters, a simulated phonon group for solving phonon transport is generated, specifically as follows:

[0015] Step 1.1: Obtain the original unit cell structure of the target material and import the original unit cell structure into the first-principles calculation software to establish an initial calculation model;

[0016] Step 1.2: The initial calculation model is optimized using first-principles calculation software to obtain the optimized unit cell parameters and atomic coordinates;

[0017] Step 1.3: Based on the optimized cell structure, the second-order force constants are calculated and the phonon dispersion relation and / or phonon density of states are obtained by combining phonon calculation software and first-principles calculation software.

[0018] Step 1.4: Based on the optimized cell structure, the third-order force constants are calculated using both anharmonic force constant calculation software and first-principles software.

[0019] Step 1.5: Based on the second-order and third-order force constants, calculate the intrinsic thermal conductivity and / or phonon relaxation time of the material using Boltzmann transport equation solving software, and determine whether the phonon spectrum and / or intrinsic thermal conductivity are consistent with the experimental data; if inconsistent, adjust the first-principles calculation parameters and / or optimize the model structure and return to step 1.2 to re-execute until the preset consistency criterion is met;

[0020] Step 1.6: After satisfying the consistency criterion, output the microscopic phonon characteristic parameters of the target material, and generate a simulated phonon group for subsequent phonon transport solutions.

[0021] Furthermore, the first principle calculation software is at least one of VASP, Quantum ESPRESSO, ABINIT, and CASTEP; the phonon calculation software is at least one of Phonopy and / or ALAMODE; the anharmonic constant calculation software is at least one of Phono3py, thirdorder.py, and / or ALAMODE; the Boltzmann transport equation solving software is at least one of ShengBTE and / or almaBTE; and the microscopic phonon characteristic parameters include at least phonon dispersion relation, phonon density of states, group velocity, mode specific heat, and / or intrinsic phonon relaxation time.

[0022] Furthermore, for the material interface of the heterostructure, the transmittance and reflectance of phonons at the interface are solved based on the microscopic phonon characteristic parameters to obtain the interface phonon transmission characteristic parameters, and the corresponding interface scattering boundary conditions are established, specifically as follows:

[0023] Based on phonon dispersion relations, group velocity and / or phonon density of states, construct the phonon mode set of the materials on both sides of the interface;

[0024] The transmittance and reflectance of different phonon modes at the interface are calculated using scattering mismatch theory and / or acoustic mismatch model, and / or the phonon transmission coefficient at the interface is calculated using the non-equilibrium Green's function method.

[0025] When a phonon particle reaches the interface, it is transmitted into the material on the other side with a probability of transmittance T, and reflected back to the raw material with a probability of reflectance R. After transmission / reflection, the phonon branch and propagation direction are updated.

[0026] The calculation of the non-equilibrium Green's function method is implemented by a self-written program or by at least one of the NEGF calculation frameworks; the scattering mismatch theory is the DMM model and the acoustic mismatch model is the AMM model.

[0027] Furthermore, regarding the defects present in the heterostructure, a defect scattering model is constructed based on the Massen criterion. The average relaxation time of defect scattering corresponding to different phonon modes is calculated, and the results are combined to obtain the equivalent total relaxation time, thereby achieving a quantitative characterization of the influence of defects on phonon transport. Specifically:

[0028] The defects include one or more of point defects, dislocations, impurities, vacancies, substitutional atoms and / or interface roughness defects, and corresponding scattering rate expressions are established for each defect type, and the defect scattering relaxation time of each phonon mode is calculated.

[0029] The scattering rates of point defect scattering and dislocation scattering are:

[0030]

[0031]

[0032] in, Represents phonon frequency, For the phonon group velocity, Indicates temperature. The average volume of atoms For the first The relative concentration of seed site defects, This represents the average atomic mass in the undoped case. It is the first atomic mass of seed point defects and The difference For dislocation surface density, For Burgers vector, Grüneisen constant, Used to describe the range of the stress field caused by dislocations;

[0033] The scattering rate of the polycrystalline grain boundary scattering process is:

[0034]

[0035]

[0036]

[0037]

[0038] in, This represents the scattering rate of polycrystalline grain boundary scattering; The characteristic size of the grain is defined as the average distance between adjacent grain boundaries in a heterostructure. The grain boundary scattering intensity is related to the phonon frequency. Related variables; These correspond to point defects and extended defects near grain boundaries, respectively. For the first Scattering intensity coefficient of defects For the first The density of this type of defect near the grain boundary characterizes the distribution concentration of this type of defect in the grain boundary region; To match the phonon frequency Relevant characteristic variables; For temperature; The average volume of atoms; Boltzmann's constant; To reduce Planck's constant; The equivalent diameter of the region affected by the extended defect characterizes the spatial influence range of the extended defect near the grain boundary; Phonon characteristic variables The critical value;

[0039] The Masison criterion is used to combine the relaxation times of different types of defect scattering to obtain the equivalent total relaxation time; where the equivalent total relaxation time is:

[0040]

[0041] in, The average defect scattering relaxation time is given. For the first Defect-like scattering relaxation time.

[0042] Furthermore, the process involves constructing a geometric structure file for the heterogeneous structure and performing spatial discretization, then setting initial and boundary conditions, and meshing the geometric structure to obtain computational grid cells. Specifically:

[0043] A geometric model of a heterogeneous structure is established and a geometric structure file is generated. The geometric model includes at least two material layers and their interface locations. The contact interface is one or more of the following: ideal planar contact, rough contact surface, and surface with artificial microstructure.

[0044] Set initial and boundary conditions, and apply interface scattering boundary conditions at the contact interface; mesh the geometric model to obtain computational mesh elements;

[0045] The boundary conditions include at least one or more of the following: isothermal boundary, adiabatic boundary, heat flux boundary, and / or heat source boundary; the mesh type is a structured mesh and / or an unstructured mesh, used to statistically analyze the contribution of phonons to the temperature and heat flux of the local mesh region.

[0046] The heat flux density at the heat source boundary satisfies

[0047]

[0048] in, For heat source power, The area of ​​the heat source.

[0049] Furthermore, based on the simulated phonon group, equivalent total relaxation time, interface phonon transmission characteristic parameters, and computational grid cells, the phonon Boltzmann transport equation is solved, and the energy accumulation and thermal transport contribution of phonons in each computational grid cell are statistically analyzed to obtain the local temperature distribution and heat flux density distribution of each computational grid cell. Specifically:

[0050] Step 2.1: Based on the geometric model, boundary conditions and mesh generation results, import the material microscopic phonon characteristic parameters and equivalent total relaxation time;

[0051] Step 2.2: Emit a single phonon particle from the isothermal boundary and / or heat source boundary, drive the phonon particle to fly within the computational domain, and determine and execute phonon-phonon scattering events based on the equivalent total relaxation time; simultaneously, determine and execute phonon-boundary scattering events based on boundary conditions, and determine and execute phonon-interface scattering events based on interface scattering boundary conditions; wherein, the determination is based on spatial position: if the entire flight process remains within the computational domain and does not encounter a boundary, phonon-phonon scattering occurs; if it encounters a boundary, phonon-boundary scattering occurs; if it encounters an interface, phonon-interface scattering occurs.

[0052] Step 2.3: After a scattering event occurs, update the frequency, group velocity direction, and / or energy weight of the phonon particles, and accumulate the contribution of the phonon flight process to the local temperature and heat flux density of the grid cells.

[0053] Step 2.4: Determine whether the phonon particle has reached the preset maximum scattering threshold and / or reached the isothermal boundary; if either condition is met, terminate the phonon particle tracking; otherwise, return to step 2.3 to continue tracking.

[0054] Step 2.5: Determine whether the number of phonon particles that have been emitted and tracked has reached the maximum number of phonons set in the simulation; if not, return to step 2.2 to continue emitting new phonon particles; if the maximum number has been reached, output the temperature distribution and heat flux density distribution of each grid cell in the computational domain.

[0055] The frequency, polarization branch, and initial flight direction of the phonon particles are determined based on the Bose-Einstein distribution and / or importance sampling.

[0056]

[0057] in, To reduce Planck's constant, Boltzmann's constant, For the boundary temperature, The frequency of the phonon;

[0058] The flight time of phonons is sampled using an exponential distribution, specifically:

[0059]

[0060] in, A random number between 0 and 1; For the flight time of phonons; Let be the equivalent total relaxation time of the phonon.

[0061] Furthermore, the calculation and output of macroscopic heat transfer parameters of the heterostructure based on local temperature distribution and heat flux density distribution specifically includes:

[0062] Select statistical regions of preset thickness on both sides of the interface, calculate the average temperature on both sides of the interface, and obtain the interface temperature difference. ;Statistical analysis of steady-state heat flux density across the interface along the interface normal direction ;

[0063] Based on interface temperature difference With steady-state heat flux density Calculate the thermal conductivity of the interface With interfacial thermal resistance ,satisfy

[0064]

[0065]

[0066] Output the temperature distribution, heat flux density distribution, and / or equivalent thermal conductivity corresponding to the interface thermal conductivity and interface thermal resistance.

[0067] A micro / nano-scale heat transfer simulation system with a heterostructure includes:

[0068] The calculation module calculates the microscopic phonon characteristic parameters of each component material of the heterostructure to be simulated using first-principles calculations; and generates a simulated phonon group for solving phonon transport problems based on the microscopic phonon characteristic parameters.

[0069] The construction module, for the material interface of the heterostructure, solves the transmittance and reflectance of phonons at the interface based on the microscopic phonon characteristic parameters, obtains the interface phonon transmission characteristic parameters, and establishes the corresponding interface scattering boundary conditions.

[0070] The merging module addresses the defects present in the heterostructure by constructing a defect scattering model based on the Massen criterion, calculating the average relaxation time of defect scattering corresponding to different phonon modes, and merging them to obtain the equivalent total relaxation time.

[0071] The partitioning module constructs a geometric structure file of the heterogeneous structure and performs spatial discretization. Then, it sets initial conditions and boundary conditions and performs mesh partitioning of the geometric structure to obtain computational mesh cells.

[0072] The acquisition module, based on the simulated phonon group, equivalent total relaxation time, interface phonon transmission characteristic parameters, and computational grid cells, solves the phonon Boltzmann transport equation, statistically analyzes the energy accumulation and heat transport contribution of phonons in each computational grid cell, and obtains the local temperature distribution and heat flux density distribution of each computational grid cell.

[0073] The output module calculates and outputs the macroscopic heat transfer parameters of the heterostructure based on the local temperature distribution and heat flux density distribution, thereby completing the micro-nano scale heat transfer simulation of the heterostructure.

[0074] Compared with the prior art, the present invention has the following beneficial effects:

[0075] This invention obtains the microscopic phonon characteristic parameters of materials through first-principles calculations, constructs a defect scattering model by combining it with the Massen criterion, establishes interface scattering boundary conditions, and incorporates multiple key influencing factors into a unified phonon Boltzmann transport equation solution system. It does not rely on empirical thermal conductivity and interface thermal resistance parameters, and can accurately obtain the local temperature distribution, heat flux density distribution, and macroscopic heat transfer parameters such as interface thermal conductivity and interface thermal resistance of heterostructures. This improves the accuracy, engineering applicability, and cross-scenario transferability of micro- and nano-scale heat transfer simulations, and provides accurate thermal parameter support for the thermal design of high-power-density devices with third-generation semiconductor heterostructures, effectively avoiding abnormal temperature rise and performance drift caused by heat accumulation in the devices. Attached Figure Description

[0076] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0077] Figure 1 This is a schematic flowchart of the micro-nano scale heat transfer simulation method for heterostructures of the present invention.

[0078] Figure 2 This is a flowchart illustrating the process of obtaining the microscopic phonon characteristic parameters of materials based on first-principles calculations according to the present invention.

[0079] Figure 3 This is a flowchart illustrating the phonon Boltzmann transport equation solved using the phonon Monte Carlo method of this invention.

[0080] Figure 4 This is a schematic diagram of the micro-nano scale heat transfer simulation system with heterostructure of the present invention;

[0081] Figure 5 A schematic diagram showing the calculated thermal conductivity of GaN and diamond at different temperatures for example, and a comparison with experimental results;

[0082] Figure 6 This is a temperature distribution diagram of the GaN / diamond heterostructure when the defect concentration is 0% in the example.

[0083] Figure 7 This is a schematic diagram illustrating the changes in the interface thermal conductivity of a GaN / diamond heterostructure when the diamond contains defects with different vacancy concentrations, as shown in the example. Detailed Implementation

[0084] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0085] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0086] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0087] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper," "lower," "horizontal," or "inner" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of the invention is in use, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Furthermore, terms such as "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0088] Furthermore, the use of the term "horizontal" does not imply that the component must be absolutely horizontal, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0089] In the description of the embodiments of the present invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention according to the specific circumstances.

[0090] The present invention will now be described in further detail with reference to the accompanying drawings:

[0091] See Figure 1 This invention discloses a micro-nano scale heat transfer simulation method for heterostructures, comprising:

[0092] S101, For each component material of the heterostructure to be simulated, the microscopic phonon characteristic parameters of the material are obtained by first-principles calculation; based on the microscopic phonon characteristic parameters of the material, a simulated phonon group is generated for phonon transport solution;

[0093] See Figure 2 S101.1 Obtain the original cell structure of the target material and import the original cell structure into the first-principles calculation software to establish an initial calculation model;

[0094] S101.2, First-principles calculation software is used to optimize the cell structure of the initial calculation model to obtain the optimized cell parameters and atomic coordinates;

[0095] S101.3, based on the optimized unit cell structure, combined with phonon calculation software and first-principles calculation software, calculates the second-order force constant and obtains the phonon dispersion relation and / or phonon density of states;

[0096] S101.4, based on the optimized cell structure, the third-order force constants are obtained by combining anharmonic force constant calculation software and first-principles software;

[0097] S101.5, based on the second-order and third-order force constants, uses Boltzmann transport equation solving software to calculate the intrinsic thermal conductivity and / or phonon relaxation time of the material, and determines whether the phonon spectrum and / or intrinsic thermal conductivity are consistent with experimental data; if inconsistent, adjust the first-principles calculation parameters and / or optimize the model structure and return to S101.2 to re-execute until the preset consistency criterion is met;

[0098] S101.6 After satisfying the consistency criterion, output the microscopic phonon characteristic parameters of the target material, and generate a simulated phonon group for subsequent phonon transport solutions.

[0099] The first principle calculation software is at least one of VASP, Quantum ESPRESSO, ABINIT, and CASTEP; the phonon calculation software is at least one of Phonopy and / or ALAMODE; the anharmonic constant calculation software is at least one of Phono3py, thirdorder.py, and / or ALAMODE; the Boltzmann transport equation solving software is at least one of ShengBTE and / or almaBTE; and the microscopic phonon characteristic parameters include at least phonon dispersion relation, phonon density of states, group velocity, mode specific heat, and / or intrinsic phonon relaxation time.

[0100] S102, For the material interface of heterostructure, the transmittance and reflectance of phonons at the interface are solved based on the microscopic phonon characteristic parameters to obtain the interface phonon transmission characteristic parameters and establish the corresponding interface scattering boundary conditions.

[0101] Based on phonon dispersion relations, group velocity and / or phonon density of states, construct the phonon mode set of the materials on both sides of the interface;

[0102] The transmittance and reflectance of different phonon modes at the interface are calculated using scattering mismatch theory and / or acoustic mismatch model, and / or the phonon transmission coefficient at the interface is calculated using the non-equilibrium Green's function method.

[0103] When a phonon particle reaches the interface, it is transmitted into the material on the other side with a probability of transmittance T, and reflected back to the raw material with a probability of reflectance R. After transmission / reflection, the phonon branch and propagation direction are updated.

[0104] The calculation of the non-equilibrium Green's function method is implemented by a self-written program or by at least one of the NEGF calculation frameworks; the scattering mismatch theory is the DMM model and the acoustic mismatch model is the AMM model.

[0105] S103. To address the defects present in heterostructures, a defect scattering model is constructed based on the Massen criterion. The average relaxation time of defect scattering corresponding to different phonon modes is calculated and combined to obtain the equivalent total relaxation time.

[0106] The defects include one or more of point defects, dislocations, impurities, vacancies, substitutional atoms and / or interface roughness defects, and corresponding scattering rate expressions are established for each defect type, and the defect scattering relaxation time of each phonon mode is calculated.

[0107] The scattering rates of point defect scattering and dislocation scattering are:

[0108]

[0109]

[0110] in, Represents phonon frequency, For the phonon group velocity, Indicates temperature. The average volume of atoms, For the first The relative concentration of seed site defects, This represents the average atomic mass in the undoped case. It is the first atomic mass of seed point defects and The difference, For dislocation surface density, For Burgers vector, Grüneisen constant, Used to describe the range of the stress field caused by dislocations;

[0111] The scattering rate of the polycrystalline grain boundary scattering process is:

[0112]

[0113]

[0114]

[0115]

[0116] in, This represents the scattering rate of polycrystalline grain boundary scattering; The characteristic size of the grain is defined as the average distance between adjacent grain boundaries in a heterostructure. The grain boundary scattering intensity is related to the phonon frequency. Related variables; These correspond to point defects and extended defects near grain boundaries, respectively. For the first Scattering intensity coefficient of defects For the first The density of this type of defect near the grain boundary characterizes the distribution concentration of this type of defect in the grain boundary region; To match the phonon frequency Relevant characteristic variables; For temperature; The average volume of atoms; Boltzmann's constant; To reduce Planck's constant; The equivalent diameter of the region affected by the extended defect characterizes the spatial influence range of the extended defect near the grain boundary; Phonon characteristic variables The critical value;

[0117] The Masison criterion is used to combine the relaxation times of different types of defect scattering to obtain the equivalent total relaxation time; where the equivalent total relaxation time is:

[0118]

[0119] in, The average defect scattering relaxation time is given. For the first Defect-like scattering relaxation time.

[0120] S104: Construct the geometric structure file of the heterogeneous structure and complete the spatial discretization. Then set the initial conditions and boundary conditions, and perform mesh generation on the geometric structure to obtain the computational mesh element.

[0121] A geometric model of a heterogeneous structure is established and a geometric structure file is generated. The geometric model includes at least two material layers and their interface locations. The contact interface is one or more of an ideal planar contact, a rough contact surface, and a surface with artificial microstructures. The geometric structure file is manually written using the actual structure and includes dimensions and material information such as computational domain size, interface, boundary location, and material type.

[0122] Set initial and boundary conditions, and apply interface scattering boundary conditions to the contact interface; mesh the geometric model to obtain computational grid cells; the initial conditions include: macroscopic temperature, heat flux distribution, and heat flux distribution of the initial computational domain;

[0123] The boundary conditions include at least one or more of the following: isothermal boundary, adiabatic boundary, heat flux boundary, and / or heat source boundary; the mesh type is a structured mesh and / or an unstructured mesh, used to statistically analyze the contribution of phonons to the temperature and heat flux of the local mesh region.

[0124] The heat flux density at the heat source boundary satisfies

[0125]

[0126] in, For heat source power, The area of ​​the heat source.

[0127] S105, based on the simulated phonon group, equivalent total relaxation time, interface phonon transmission characteristic parameters and computational grid cells, solves the phonon Boltzmann transport equation, and statistically analyzes the energy accumulation and heat transport contribution of phonons in each computational grid cell to obtain the local temperature distribution and heat flux density distribution of each computational grid cell.

[0128] See Figure 3S105.1, based on the geometric model, boundary conditions and mesh generation results, and importing the material micro phonon characteristic parameters and equivalent total relaxation time;

[0129] S105.2, a single phonon particle is emitted from the isothermal boundary and / or the heat source boundary, driving the phonon particle to fly within the computational domain, and a phonon-phonon scattering event is determined and executed based on the equivalent total relaxation time; simultaneously, a phonon-boundary scattering event is determined and executed based on the boundary conditions, and a phonon-interface scattering event is determined and executed based on the interface scattering boundary conditions; wherein, the determination is based on the spatial position: if the entire flight process remains within the computational domain and does not encounter a boundary, phonon-phonon scattering occurs; if a boundary is encountered, phonon-boundary scattering occurs; if an interface is encountered, phonon-interface scattering occurs.

[0130] S105.3 After a scattering event occurs, update the frequency, group velocity direction and / or energy weight of the phonon particles, and accumulate the contribution of the phonon flight process to the local temperature and heat flux density of the grid cells.

[0131] S105.4 Determine whether the phonon particle has reached the preset maximum scattering threshold and / or reached the isothermal boundary; if either condition is met, terminate the phonon particle tracking, otherwise return to S105.3 to continue tracking;

[0132] S105.5 determines whether the number of phonon particles that have been emitted and tracked has reached the maximum number of phonons set in the simulation; if not, it returns to S105.2 to continue emitting new phonon particles; if it has reached the maximum number, it outputs the temperature distribution and heat flux density distribution of each grid cell in the computational domain.

[0133] The frequency, polarization branch, and initial flight direction of the phonon particles are determined based on the Bose-Einstein distribution and / or importance sampling.

[0134]

[0135] in, To reduce Planck's constant, Boltzmann's constant, For the boundary temperature, The frequency of the phonon;

[0136] The flight time of phonons is sampled using an exponential distribution, specifically:

[0137]

[0138] in, A random number between 0 and 1; For the flight time of phonons; Let be the equivalent total relaxation time of the phonon.

[0139] S106 calculates and outputs the macroscopic heat transfer parameters of heterostructures based on local temperature distribution and heat flux density distribution, thus completing the micro-nano scale heat transfer simulation of heterostructures.

[0140] Select statistical regions of preset thickness on both sides of the interface, calculate the average temperature on both sides of the interface, and obtain the interface temperature difference. ;Statistical analysis of steady-state heat flux density across the interface along the interface normal direction ;

[0141] Based on interface temperature difference With steady-state heat flux density Calculate the thermal conductivity of the interface With interfacial thermal resistance ,satisfy

[0142]

[0143]

[0144] Output the temperature distribution, heat flux density distribution, and / or equivalent thermal conductivity corresponding to the interface thermal conductivity and interface thermal resistance.

[0145] See Figure 4 This invention discloses a micro / nano-scale heat transfer simulation system with a heterostructure, comprising:

[0146] The calculation module calculates the microscopic phonon characteristic parameters of each component material of the heterostructure to be simulated using first-principles calculations; and generates a simulated phonon group for solving phonon transport problems based on the microscopic phonon characteristic parameters.

[0147] The construction module, for the material interface of the heterostructure, solves the transmittance and reflectance of phonons at the interface based on the microscopic phonon characteristic parameters, obtains the interface phonon transmission characteristic parameters, and establishes the corresponding interface scattering boundary conditions.

[0148] The merging module addresses the defects present in the heterostructure by constructing a defect scattering model based on the Massen criterion, calculating the average relaxation time of defect scattering corresponding to different phonon modes, and merging them to obtain the equivalent total relaxation time.

[0149] The partitioning module constructs a geometric structure file of the heterogeneous structure and performs spatial discretization. Then, it sets initial conditions and boundary conditions and performs mesh partitioning of the geometric structure to obtain computational mesh cells.

[0150] The acquisition module, based on the simulated phonon group, equivalent total relaxation time, interface phonon transmission characteristic parameters, and computational grid cells, solves the phonon Boltzmann transport equation, statistically analyzes the energy accumulation and heat transport contribution of phonons in each computational grid cell, and obtains the local temperature distribution and heat flux density distribution of each computational grid cell.

[0151] The output module calculates and outputs the macroscopic heat transfer parameters of the heterostructure based on the local temperature distribution and heat flux density distribution, thereby completing the micro-nano scale heat transfer simulation of the heterostructure.

[0152] Example:

[0153] Taking GaN / diamond heterostructure as an example, according to Figure 1 The process shown is used to perform micro-nano scale heat transfer simulation and obtain the interfacial thermal conductivity results under different vacancy defect concentrations.

[0154] First, first-principles and phonon property calculations were performed on GaN and diamond materials, respectively. First-principles calculations were performed using VASP software, with the LDA functional chosen for the exchange-correlation functional and the plane-wave cutoff energy set to 520 eV. To obtain the force constants and reduce finite-size effects, supercells were constructed for GaN and diamond, with dimensions of 4×4×4 and 5×5×5, respectively. After optimizing the cell structure, the second-order force constants were calculated using Phonopy combined with VASP output; the third-order force constants were calculated using thirdorder.py combined with VASP output.

[0155] The second and third force constants were then input into almaBTE to calculate the phonon dispersion, phonon density of states, group velocity, specific heat, and intrinsic relaxation time of GaN and diamond, among other microscopic phonon characteristics. The q-mesh was set to 15×15×15 in the almaBTE calculations. Under this parameter setting, the intrinsic thermal conductivity of the two materials was further calculated, and its consistency with experimental / literature calibration values ​​was verified. The verification results in this embodiment are as follows: Figure 5 As shown, the calculation parameters and force constant extraction process can obtain reasonable thermal conductivity of materials under different temperature conditions, thus ensuring the reliability of subsequent heat transfer prediction for heterostructures. Finally, the microscopic phonon characteristic parameters of GaN and diamond are output, and a simulated phonon group is constructed based on these parameters for subsequent Monte Carlo solutions.

[0156] After obtaining the microscopic phonon characteristic parameters of GaN and diamond, the transmittance and reflectance of phonons at the GaN / diamond interface are calculated, and interface scattering boundary conditions are constructed accordingly. Specifically, based on the phonon dispersion, group velocity, and density of states of the two materials, a set of phonon modes on both sides of the interface is established, and frequency-dependent transmittance and reflectance are calculated using scattering mismatch theory (DMM). Subsequently, T and R are transformed into probabilistic boundary conditions for interface events in Monte Carlo solutions: when a phonon particle reaches the interface, it is transmitted into the other material with probability T and reflected back to the original material with probability R, and the branching and propagation direction of the particle are updated after transmission / reflection.

[0157] To characterize the impact of defects on interfacial heat transfer, this embodiment considers vacancy defects present in the material and sets different vacancy defect concentrations as comparative conditions. See [link to relevant documentation]. Figure 6 A defect scattering model was established for vacancy defects, the defect scattering relaxation time corresponding to the phonon mode was calculated, and the equivalent total relaxation time was obtained by combining the results using the Massen criterion.

[0158] Subsequently, a geometric model of the GaN / diamond heterostructure was constructed, and the initial and boundary conditions required for heat transfer calculations were set. The boundary conditions included isothermal boundaries (303 K for the hot end and 297 K for the cold end), and an interface scattering boundary condition was applied at the GaN / diamond interface. To statistically analyze the contributions of local temperature and heat flux, the geometric model was meshed; in this embodiment, the mesh size was set to 20×100×20 (corresponding to the number of discrete meshes in the three directions of the computational domain), used for subsequent Monte Carlo statistical analysis of the temperature field and heat flux density distribution at the mesh scale.

[0159] After mesh generation and parameter import, the Monte Carlo method was used to solve the phonon Boltzmann transport equation, and the energy accumulation and heat transport contribution of phonons in each mesh cell were statistically analyzed to obtain the local temperature distribution and heat flux density distribution. In this embodiment, the maximum number of phonons in the Monte Carlo simulation was set to 6 × 10⁻⁶. 5 .

[0160] After obtaining the steady-state temperature distribution and heat flux density distribution, the interfacial thermal parameters are further extracted. Specifically, statistical regions of preset thickness are selected on both sides of the interface, the average temperature on both sides of the interface is calculated to obtain the interfacial temperature difference, and the steady-state heat flux density passing through the interface along the interface normal is statistically analyzed. Based on this, the interfacial thermal conductivity and interfacial thermal resistance are calculated.

[0161] Repeating the above calculation process and changing the vacancy defect concentration, the variation of interfacial thermal conductivity under different vacancy defect concentrations in diamond was obtained; the interfacial thermal conductivity results in this embodiment are as follows. Figure 7As shown, the method of this invention can couple the microscopic phonon properties of materials, interface transmission behavior, and defect scattering mechanisms within a unified framework, and output interface thermal conductivity parameters that can be directly used for thermal design and interface engineering evaluation of heterostructures.

[0162] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for simulating heat transfer at the micro / nano scale in heterogeneous structures, characterized in that, include: For each component material of the heterostructure to be simulated, the microscopic phonon characteristic parameters of the material are obtained by first-principles calculations. A simulated phonon group for solving phonon transport problems is generated based on the material's microscopic phonon characteristic parameters. For material interfaces of heterostructures, the transmittance and reflectance of phonons at the interface are solved based on microscopic phonon characteristic parameters to obtain the phonon transmission characteristic parameters of the interface, and the corresponding interface scattering boundary conditions are established. To address the defects present in heterostructures, a defect scattering model is constructed based on the Massen criterion. The average relaxation time of defect scattering corresponding to different phonon modes is calculated and then combined to obtain the equivalent total relaxation time. Construct the geometric structure file of the heterogeneous structure and complete the spatial discretization, then set the initial conditions and boundary conditions, and mesh the geometric structure to obtain the computational grid cells; Based on the simulated phonon group, equivalent total relaxation time, interface phonon transmission characteristic parameters, and computational grid cells, the phonon Boltzmann transport equation is solved, and the energy accumulation and heat transport contribution of phonons in each computational grid cell are statistically analyzed to obtain the local temperature distribution and heat flux density distribution of each computational grid cell. Based on the local temperature distribution and heat flux density distribution, the macroscopic heat transfer parameters of the heterostructure are calculated and output, and the micro-nano scale heat transfer simulation of the heterostructure is completed.

2. The micro / nano-scale heat transfer simulation method for heterogeneous structures according to claim 1, characterized in that, For each component material of the heterostructure to be simulated, the microscopic phonon characteristic parameters of the materials are obtained through first-principles calculations; based on the microscopic phonon characteristic parameters, a simulated phonon group is generated for phonon transport solutions, specifically: Step 1.1: Obtain the original unit cell structure of the target material and import the original unit cell structure into the first-principles calculation software to establish an initial calculation model; Step 1.2: First-principles calculation software is used to optimize the cell structure of the initial calculation model to obtain the optimized cell parameters and atomic coordinates; Step 1.3: Based on the optimized cell structure, the second-order force constants are calculated and the phonon dispersion relation and / or phonon density of states are obtained by combining phonon calculation software and first-principles calculation software. Step 1.4: Based on the optimized cell structure, the third-order force constants are calculated using both anharmonic force constant calculation software and first-principles software. Step 1.5: Based on the second-order and third-order force constants, calculate the intrinsic thermal conductivity and / or phonon relaxation time of the material using Boltzmann transport equation solving software, and determine whether the phonon spectrum and / or intrinsic thermal conductivity are consistent with the experimental data; if inconsistent, adjust the first-principles calculation parameters and / or optimize the model structure and return to step 1.2 to re-execute until the preset consistency criterion is met; Step 1.6: After satisfying the consistency criterion, output the microscopic phonon characteristic parameters of the target material, and generate a simulated phonon group for subsequent phonon transport solutions.

3. The micro / nano-scale heat transfer simulation method for heterogeneous structures according to claim 2, characterized in that, The first principle calculation software is at least one of VASP, Quantum ESPRESSO, ABINIT, and CASTEP; the phonon calculation software is at least one of Phonopy and / or ALAMODE; the anharmonic constant calculation software is at least one of Phono3py, thirdorder.py, and / or ALAMODE; the Boltzmann transport equation solving software is at least one of ShengBTE and / or almaBTE; and the microscopic phonon characteristic parameters include at least phonon dispersion relation, phonon density of states, group velocity, mode specific heat, and / or intrinsic phonon relaxation time.

4. The micro / nano-scale heat transfer simulation method for heterogeneous structures according to claim 3, characterized in that, For the material interface of the heterostructure, the transmittance and reflectance of phonons at the interface are solved based on the microscopic phonon characteristic parameters to obtain the interface phonon transmission characteristic parameters, and the corresponding interface scattering boundary conditions are established, specifically as follows: Based on phonon dispersion relations, group velocity and / or phonon density of states, construct the phonon mode set of the materials on both sides of the interface; The transmittance and reflectance of different phonon modes at the interface are calculated using scattering mismatch theory and / or acoustic mismatch model, and / or the phonon transmission coefficient at the interface is calculated using the non-equilibrium Green's function method. When a phonon particle reaches the interface, it is transmitted into the material on the other side with a probability of transmittance T, and reflected back to the raw material with a probability of reflectance R. After transmission / reflection, the phonon branch and propagation direction are updated. The calculation of the non-equilibrium Green's function method is implemented by a self-written program or by at least one of the NEGF calculation frameworks; the scattering mismatch theory is the DMM model and the acoustic mismatch model is the AMM model.

5. The micro / nano-scale heat transfer simulation method for heterogeneous structures according to claim 4, characterized in that, To address the defects present in heterostructures, a defect scattering model is constructed based on the Massen criterion. The average relaxation time of defect scattering corresponding to different phonon modes is calculated, and the results are combined to obtain the equivalent total relaxation time, thereby achieving a quantitative characterization of the impact of defects on phonon transport. Specifically: The defects include one or more of point defects, dislocations, impurities, vacancies, substitutional atoms and / or interface roughness defects, and corresponding scattering rate expressions are established for each defect type, and the defect scattering relaxation time of each phonon mode is calculated. The scattering rates of point defect scattering and dislocation scattering are: in, Represents phonon frequency, For the phonon group velocity, Indicates temperature. The average volume of atoms, For the first The relative concentration of seed site defects, This represents the average atomic mass in the undoped case. It is the first atomic mass of seed point defects and The difference, For dislocation surface density, For Burgers vector, Grüneisen constant, Used to describe the range of the stress field caused by dislocations; The scattering rate of the polycrystalline grain boundary scattering process is: in, This represents the scattering rate of polycrystalline grain boundary scattering; The characteristic size of the grain is defined as the average distance between adjacent grain boundaries in a heterostructure. The grain boundary scattering intensity is related to the phonon frequency. Related variables; These correspond to point defects and extended defects near grain boundaries, respectively. For the first Scattering intensity coefficient of defects For the first The density of this type of defect near the grain boundary characterizes the distribution concentration of this type of defect in the grain boundary region; To be related to phonon frequency Relevant characteristic variables; For temperature; The average volume of atoms; Boltzmann's constant; To reduce Planck's constant; The equivalent diameter of the region affected by the extended defect characterizes the spatial influence range of the extended defect near the grain boundary; Phonon characteristic variables The critical value; The Masison criterion is used to combine the relaxation times of different types of defect scattering to obtain the equivalent total relaxation time; where the equivalent total relaxation time is: in, The average defect scattering relaxation time is given. For the first Defect-like scattering relaxation time.

6. The micro / nano-scale heat transfer simulation method for heterogeneous structures according to claim 5, characterized in that, The process involves constructing a geometric structure file for the heterogeneous structure, spatially discretizing it, setting initial and boundary conditions, and then meshing the geometric structure to obtain computational grid cells. Specifically: A geometric model of a heterogeneous structure is established and a geometric structure file is generated. The geometric model includes at least two material layers and their interface locations. The contact interface is one or more of the following: ideal planar contact, rough contact surface, and surface with artificial microstructure. Set initial and boundary conditions, and apply the interface scattering boundary condition at the contact interface; The geometric model is meshed to obtain computational grid cells; The boundary conditions include at least one or more of the following: isothermal boundary, adiabatic boundary, heat flux boundary, and / or heat source boundary; the mesh type is a structured mesh and / or an unstructured mesh, used to statistically analyze the contribution of phonons to the temperature and heat flux of the local mesh region. The heat flux density at the heat source boundary satisfies in, For heat source power, The area of ​​the heat source.

7. The micro / nano-scale heat transfer simulation method for heterogeneous structures according to claim 6, characterized in that, Based on simulated phonon groups, equivalent total relaxation time, interface phonon transmission characteristic parameters, and computational grid cells, the phonon Boltzmann transport equation is solved, and the energy accumulation and heat transport contribution of phonons in each computational grid cell are statistically analyzed to obtain the local temperature distribution and heat flux density distribution of each computational grid cell. Specifically: Step 2.1: Based on the geometric model, boundary conditions and mesh generation results, import the material microscopic phonon characteristic parameters and equivalent total relaxation time; Step 2.2: Emit a single phonon particle from the isothermal boundary and / or heat source boundary, drive the phonon particle to fly within the computational domain, and determine and execute phonon-phonon scattering events based on the equivalent total relaxation time; simultaneously, determine and execute phonon-boundary scattering events based on boundary conditions, and determine and execute phonon-interface scattering events based on interface scattering boundary conditions; wherein, the determination is based on spatial position: if the entire flight process remains within the computational domain and does not encounter a boundary, phonon-phonon scattering occurs; if it encounters a boundary, phonon-boundary scattering occurs; if it encounters an interface, phonon-interface scattering occurs. Step 2.3: After a scattering event occurs, update the frequency, group velocity direction, and / or energy weight of the phonon particles, and accumulate the contribution of the phonon flight process to the local temperature and heat flux density of the grid cells. Step 2.4: Determine whether the phonon particle has reached the preset maximum scattering threshold and / or reached the isothermal boundary; if either condition is met, terminate the phonon particle tracking; otherwise, return to step 2.3 to continue tracking. Step 2.5: Determine whether the number of phonon particles that have been emitted and tracked has reached the maximum number of phonons set in the simulation; if not, return to step 2.2 to continue emitting new phonon particles; if the maximum number has been reached, output the temperature distribution and heat flux density distribution of each grid cell in the computational domain. The frequency, polarization branch, and initial flight direction of the phonon particles are determined based on the Bose-Einstein distribution and / or importance sampling. in, To reduce Planck's constant, Boltzmann's constant, For the boundary temperature, The frequency of the phonon; The flight time of phonons is sampled using an exponential distribution, specifically: in, A random number between 0 and 1; For the flight time of phonons; Let be the equivalent total relaxation time of the phonon.

8. The micro / nano-scale heat transfer simulation method for heterogeneous structures according to claim 7, characterized in that, The macroscopic heat transfer parameters of the heterostructure are calculated and output based on the local temperature distribution and heat flux density distribution, specifically as follows: Select statistical regions of preset thickness on both sides of the interface, calculate the average temperature on both sides of the interface, and obtain the interface temperature difference. ; Statistical analysis of steady-state heat flux density across the interface along the interface normal direction ; Based on interface temperature difference With steady-state heat flux density Calculate the thermal conductivity of the interface With interfacial thermal resistance ,satisfy Output the temperature distribution, heat flux density distribution, and / or equivalent thermal conductivity corresponding to the interface thermal conductivity and interface thermal resistance.

9. A micro / nano-scale heat transfer simulation system with a heterogeneous structure, characterized in that, include: The calculation module obtains the microscopic phonon characteristic parameters of each component material of the heterostructure to be simulated through first-principles calculations. A simulated phonon group for solving phonon transport problems is generated based on the material's microscopic phonon characteristic parameters. The construction module, for the material interface of the heterostructure, solves the transmittance and reflectance of phonons at the interface based on the microscopic phonon characteristic parameters, obtains the interface phonon transmission characteristic parameters, and establishes the corresponding interface scattering boundary conditions. The merging module addresses the defects present in the heterostructure by constructing a defect scattering model based on the Massen criterion, calculating the average relaxation time of defect scattering corresponding to different phonon modes, and merging them to obtain the equivalent total relaxation time. The partitioning module constructs a geometric structure file of the heterogeneous structure and performs spatial discretization. Then, it sets initial conditions and boundary conditions and performs mesh partitioning of the geometric structure to obtain computational mesh cells. The acquisition module, based on the simulated phonon group, equivalent total relaxation time, interface phonon transmission characteristic parameters, and computational grid cells, solves the phonon Boltzmann transport equation, statistically analyzes the energy accumulation and heat transport contribution of phonons in each computational grid cell, and obtains the local temperature distribution and heat flux density distribution of each computational grid cell. The output module calculates and outputs the macroscopic heat transfer parameters of the heterostructure based on the local temperature distribution and heat flux density distribution, thereby completing the micro-nano scale heat transfer simulation of the heterostructure.

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