A micro-nano structure heat conduction numerical simulation method based on multi-source information fusion
By combining multi-source information fusion with first-principles calculations and experimental measurement data, the intrinsic and extrinsic phonon scattering characteristics are decoupled and determined, and a numerical simulation method for thermal conduction in micro-nanostructures is developed. This solves the problem of insufficient simulation accuracy in existing technologies and enables more accurate thermal design of semiconductor devices.
Patent Information
- Application Number
- CN202510972043.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-15
- Publication Date
- 2025-10-21
- Estimated Expiration
- 2045-07-15
AI Technical Summary
Existing thermal simulation software for semiconductor devices lacks accuracy in simulating the heat conduction process of micro-nanostructures, especially in the decoupling simulation of intrinsic and extrinsic phonon scattering characteristics, resulting in inaccurate thermal simulation results.
By adopting the multi-source information fusion method, combining first-principles calculations and experimental measurement data, the intrinsic and extrinsic phonon scattering characteristics are decoupled and determined through the phonon Monte Carlo simulation method, and the scattering model parameters are optimized using genetic algorithms to perform numerical simulations of heat conduction in micro-nanostructures.
It improves the accuracy of thermal design of semiconductor devices, can more accurately simulate the heat conduction process of micro-nanostructures, and improves the simulation accuracy of temperature distribution and heat flux density.
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Figure CN120493576B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the field of numerical simulation of heat conduction in micro-nano structures, and in particular relates to a numerical simulation method of heat conduction in micro-nano structures based on multi-source information fusion. Background Art
[0002] The thermal characteristics of semiconductor devices severely limit their performance and service life. To optimize semiconductor device thermal characteristics and effectively control junction temperature and temperature distribution, thermal design is essential during the design and manufacturing process. Thermal simulation is a key method for semiconductor device thermal design.
[0003] Among existing thermal simulation methods for semiconductor devices, existing thermal simulation software such as Comsol, Fluent, ICEPAK, and FloTHERM all perform numerical simulations based on the macroscopic heat conduction equation. The miniaturization of semiconductor devices has resulted in the internal structural dimensions of most semiconductor devices being in the micro-nano range, and the heat conduction process within the micro-nanostructure no longer follows the macroscopic heat conduction equation. Therefore, thermal simulation software based on the macroscopic heat conduction equation has poor accuracy in the thermal design of semiconductor devices. Furthermore, while numerical simulation methods based on the phonon Boltzmann transport equation can describe the heat conduction process within the micro-nanostructure range, they lack the ability to decouple and accurately quantify the intrinsic and extrinsic phonon scattering characteristics of actual materials, resulting in low accuracy in thermal simulation results. Summary of the Invention
[0004] The purpose of the present invention is to propose a numerical simulation method for heat conduction in micro-nano structures based on multi-source information fusion.
[0005] The technical solution to achieve the purpose of the present invention is: a numerical simulation method of heat conduction in micro-nanostructures based on multi-source information fusion, comprising the following steps:
[0006] Step 1: For the target material used in the micro-nanostructure, collect the phonon dispersion relation of the target material and generate the simulated phonon group required for numerical simulation;
[0007] Step 2: For the target material, collect the intrinsic thermal conductivity data calculated by first principles, and extract preliminary intrinsic phonon scattering characteristics from the intrinsic thermal conductivity data based on the intrinsic scattering model and genetic algorithm optimization;
[0008] Step 3: Based on the preliminary intrinsic scattering characteristics and the simulated phonon group, the intrinsic thermal conductivity is numerically simulated using the phonon Monte Carlo simulation method to obtain the numerical simulation results of the intrinsic thermal conductivity;
[0009] Step 4: Compare the numerical simulation results of the intrinsic thermal conductivity with the first-principles calculation results, optimize the intrinsic scattering model parameters, and determine the intrinsic phonon scattering characteristics;
[0010] Step 5: For the experimental sample of the target material, collect the geometric dimension data of the experimental sample and the experimentally measured thermal conductivity data of the experimental sample, and extract preliminary extrinsic phonon scattering characteristics from the thermal conductivity data of the experimental sample based on the extrinsic scattering model;
[0011] Step 6: Based on the intrinsic phonon scattering characteristics, preliminary extrinsic phonon scattering characteristics, and simulated phonon groups, a phonon Monte Carlo simulation method is used to perform numerical simulation on the thermal conductivity of the experimental sample to obtain a numerical simulation result of the thermal conductivity of the experimental sample;
[0012] Step 7: Compare the numerical simulation results and experimental measurement results of the thermal conductivity of the experimental sample, optimize the extrinsic scattering model parameters, and determine the extrinsic phonon scattering characteristics;
[0013] Step 8: Based on the intrinsic phonon scattering characteristics and extrinsic phonon scattering characteristics and the simulated phonon group, a thermal conduction numerical simulation is performed on the micro-nanostructure of the target material to obtain the steady-state temperature distribution, steady-state heat flux density distribution and thermal conductivity of the micro-nanostructure.
[0014] A micro-nanostructure heat conduction numerical simulation system based on multi-source information fusion implements the micro-nanostructure heat conduction numerical simulation method based on multi-source information fusion to achieve micro-nanostructure heat conduction numerical simulation based on multi-source information fusion, and is divided into eight modules to respectively perform steps 1 to 8.
[0015] Compared with the existing technology, the present invention has the following significant advantages: 1) By integrating multi-source data from first-principles calculations and experimental measurements, the present invention can decouple and determine the intrinsic and extrinsic phonon scattering characteristics in actual materials; 2) Based on the phonon Monte Carlo simulation method, the present invention decouples and simulates intrinsic phonon scattering and extrinsic boundary scattering and impurity scattering, and can more accurately simulate the heat conduction process of actual material micro-nanostructures; 3) The present invention is applicable to the numerical simulation calculation of heat conduction in arbitrarily complex micro-nanostructures of semiconductor materials, which helps to improve the accuracy of thermal design of semiconductor devices. BRIEF DESCRIPTION OF THE DRAWINGS
[0016] Figure 1 This is a flow chart of the numerical simulation method for heat conduction in micro-nano structures based on multi-source information fusion of the present invention.
[0017] Figure 2 The figures show the intrinsic thermal conductivity of GaN and the thermal conductivity data of the experimental sample, as well as the numerical simulation results corresponding to the data observation points.
[0018] Figure 3 These are the numerical simulation results of the directional thermal conductivity of GaN films with different thicknesses at 300K in this embodiment. DETAILED DESCRIPTION
[0019] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.
[0020] like Figure 1 As shown, the present invention provides a numerical simulation method for heat conduction of micro-nano structures based on multi-source information fusion, comprising the following steps:
[0021] Step 1: For the target material used in the micro-nanostructure, collect the phonon dispersion relation of the target material and generate the simulated phonon group required for numerical simulation, specifically:
[0022] Step 1.1: For the target material used in the micro-nanostructure, collect the phonon dispersion relation of the target material. The phonon dispersion relation is expressed as ω(p,k), where ω is the frequency, k is the wave vector, and p represents the dispersion branch, which is divided into LA, TA1, and TA2 dispersion branches;
[0023] Step 1.2: Generate the simulated phonon group required for numerical simulation based on the phonon dispersion relation and the number of simulated phonons in a single spatial unit, where:
[0024] The generation rules for each simulated phonon are as follows:
[0025] 1) Calculate the energy of a single simulated phonon using the expression:
[0026] ;
[0027] Where: e is the energy of the simulated phonon, V is the volume of a single space unit, N is the number of simulated phonons in a single space unit, is the reduced Planck constant, f eq is the Bose-Einstein distribution function, T is the temperature of the space unit, T eq is the reference temperature, N b is the frequency discrete equal parts, △ω is the frequency width of each discrete interval, and D is the phonon state density;
[0028] 2) Calculate the frequency of simulated phonons;
[0029] Calculate the phonon number-frequency cumulative distribution function g i (T), the expression is:
[0030] ;
[0031] Where ω i For the midpoint frequency of the ith frequency interval, generate a [0,1] uniformly distributed random number R1. If g i-1 < R1≤ g i, determine that the frequency of the simulated phonon is in the i-th frequency interval, and generate another [0,1] uniformly distributed random number R2 to determine the frequency ω of the simulated phonon:
[0032] ;
[0033] 3) Calculate and simulate the dispersion branches of phonons;
[0034] The proportion of different dispersion branch phonons in the frequency range of the simulated phonon frequency is calculated as follows:
[0035] ;
[0036] Where Y LA is the proportion of LA phonons, Y LA+TA1 For the ratio of LA and TA1 phonons, generate a random number R3 uniformly distributed between [0,1]. If R3 ≤ Y LA , then the simulated phonon belongs to the LA dispersion branch. If Y LA < R3 ≤ Y LA+TA1 , then the simulated phonon belongs to the TA1 dispersion branch. If R3 > Y LA+TA1 , then the simulated phonon belongs to the TA2 dispersion branch;
[0037] 4) Calculate the velocity and direction of the simulated phonons;
[0038] Calculate the velocity of the simulated phonon using the formula:
[0039] ;
[0040] v is the velocity of the simulated phonon;
[0041] Calculate the velocity direction of the simulated phonon, specifically:
[0042] ;
[0043] Where θ and φ are the polar angle and azimuthal angle of the simulated phonon velocity direction, R4 and R5 are two random numbers uniformly distributed between [0,1];
[0044] 5) Calculate the spatial position of simulated phonons;
[0045] Generate three random numbers R6, R7 and R8 uniformly distributed between [0,1] and calculate the spatial position r of the simulated phonon, specifically:
[0046] ;
[0047] Where r0 represents the coordinate origin of the space unit, l x 、l y and l zare the length, width and height of the spatial unit respectively, 、 and is the unit vector in the direction of the three coordinate axes of the Cartesian coordinate system.
[0048] Step 2: For the target material, collect the intrinsic thermal conductivity data calculated by first principles, and extract preliminary intrinsic phonon scattering characteristics from the intrinsic thermal conductivity data based on the intrinsic scattering model and genetic algorithm optimization. Specifically:
[0049] Step 2.1: For the target material, collect the intrinsic thermal conductivity data calculated by first principles and select the observation points of the intrinsic thermal conductivity data evenly according to the temperature range;
[0050] Step 2.2, extracting preliminary intrinsic phonon scattering characteristics from the intrinsic thermal conductivity data observation points through the intrinsic scattering model and genetic algorithm optimization;
[0051] First, the relaxation time model in the intrinsic scattering model is constructed, and the expression is as follows:
[0052] ;
[0053] In the formula is the relaxation time of intrinsic scattering, (a1, a2, a3, b1, b2, b3) are the relaxation time model parameters;
[0054] According to the intrinsic thermal conductivity data observation points, the fitness function fit of the genetic algorithm is constructed as follows:
[0055] ;
[0056] Where: κ j is the thermal conductivity value of the jth intrinsic thermal conductivity data observation point, T j is the temperature value corresponding to the jth intrinsic thermal conductivity data observation point, n is the number of intrinsic thermal conductivity data observation points, k B is the Boltzmann constant, and the optimal parameters of the relaxation time model are obtained by genetic algorithm;
[0057] Then the normal scattering ratio model in the intrinsic scattering model is constructed as:
[0058] ;
[0059] Where η N is the normal scattering ratio, ω c is the phonon cutoff frequency of the first Brillouin zone, c and d are the normal scattering scale model parameters;
[0060] The parameter values of c and d in the normal scattering proportional model are preset to extract the preliminary intrinsic scattering characteristics.
[0061] Step 3: Based on the preliminary intrinsic scattering characteristics and simulated phonon groups, the intrinsic thermal conductivity is numerically simulated using the phonon Monte Carlo simulation method to obtain the numerical simulation results of the intrinsic thermal conductivity, specifically:
[0062] Step 3.1, set the one-dimensional heat conduction process, numerical simulation space, spatial unit, time unit step, boundary conditions and initial conditions required for the numerical simulation of intrinsic thermal conductivity, specifically:
[0063] The one-dimensional heat conduction direction is defined as the z-axis direction of the Cartesian coordinate system, and the numerical simulation space, space unit, number of space units and unit time step △t0 are set. The two surfaces perpendicular to the one-dimensional heat conduction direction are set as isothermal boundaries, and the temperatures are set to T h0 and T c0 , set the four surfaces parallel to the one-dimensional heat conduction direction as adiabatic boundaries, set the initial temperature T0 and reference temperature T of all space units eq0 ;
[0064] Step 3.2, based on the simulated phonon group generated in step 1, initialize the simulated phonon group for all spatial units;
[0065] Step 3.3: simulate the motion evolution of all simulated phonons within a unit time step, including the emission, translation, boundary scattering, intrinsic scattering, and statistical calculation of simulated phonons. Specifically:
[0066] 1) Use a simulated phonon group to emit simulated phonons from the isothermal boundary and calculate the number, velocity direction and spatial coordinates of the emitted simulated phonons, specifically;
[0067] Calculate the number of simulated phonons emitted, specifically:
[0068] ;
[0069] Where A0 represents the area of the isothermal boundary, N h0 and N c0 The temperature is T h0 and T c0 The number of simulated phonons emitted per unit time step by the isothermal boundary of ;
[0070] Calculate the direction of the emitted simulated phonon velocity, specifically:
[0071] ;
[0072] Where θ 00 and φ 00 are the polar and azimuthal angles of the emitted simulated phonon velocity directions, R9 and R 10are two random numbers uniformly distributed between [0,1];
[0073] Calculate the spatial coordinates of the emitted simulated phonons, specifically:
[0074] ;
[0075] Where r 00 is the spatial coordinate of the emitted simulated phonon, z b0 is the z-axis coordinate value corresponding to the isothermal boundary, l x0 、l y0 and l z0 is the length, width and height of the space unit, R 11 and R 12 are two random numbers uniformly distributed between [0,1];
[0076] 2) Perform translational motion and boundary scattering on all simulated phonons;
[0077] The translation motion calculation process is:
[0078] ;
[0079] Where v0 is the velocity vector of the simulated phonon, r b0 is the spatial coordinate before simulating the translational motion of the phonon, r a0 is the spatial coordinate after simulating the translational motion of the phonon;
[0080] When the simulated phonon moves to the adiabatic boundary, boundary scattering occurs, which is of the nature of specular scattering and is expressed as:
[0081] ;
[0082] Where v a0 is the velocity vector of the simulated phonon after boundary scattering, is the unit normal vector of the adiabatic boundary pointing to the interior of the numerical simulation space;
[0083] 3) Based on the preliminary intrinsic scattering characteristics, determine whether all simulated phonons have undergone intrinsic scattering, and update the frequency, dispersion branch and velocity of the simulated phonons that have undergone intrinsic scattering. Specifically:
[0084] i) Based on the preliminary eigenscattering characteristics, determine whether the simulated phonons undergo eigenscattering;
[0085] Calculate the intrinsic scattering probability P of each simulated phonon per unit time step 10 , the expression is:
[0086] ;
[0087] Generate a random number R uniformly distributed between [0,1]13 , if R 13 ≤ P 10 When , the simulated phonon undergoes intrinsic scattering, otherwise, the simulated phonon does not undergo intrinsic scattering;
[0088] ii) For the simulated phonons that undergo intrinsic scattering, first update the frequency of the simulated phonons;
[0089] Calculate the phonon number-frequency cumulative distribution function G during intrinsic scattering i (T), the expression is:
[0090] ;
[0091] Generate a random number R uniformly distributed between [0,1] 14 , if G i-1 < R 14 ≤ G i , then the updated frequency is in the i-th frequency interval, and another [0,1] uniformly distributed random number R is generated 15 To determine the frequency:
[0092] ;
[0093] Where ω 10 is the frequency of the simulated phonon after eigenscattering;
[0094] Then, the dispersion branch of the simulated phonons is updated;
[0095] After calculating the intrinsic scattering, the proportion of different dispersion branch phonons in the frequency range of the simulated phonon frequency is:
[0096] ;
[0097] Where Q 10 is the proportion of LA phonons, Q 20 Generate a random number R uniformly distributed between [0,1] for the ratio of LA and TA1 phonons 16 , if R 16 ≤ Q 10 , then the updated dispersion branch is LA, if Q 10 < R 16 ≤ Q 20 , then the updated dispersion branch is TA1, if R 16 > Q 20 , then the updated dispersion branch is TA2;
[0098] Finally, the velocity of the simulated phonons is updated;
[0099] Update the simulated phonon velocity to:
[0100] ;
[0101] v 10 is the velocity of the simulated phonon after intrinsic scattering;
[0102] Generate a random number R uniformly distributed between [0,1] 17 , R 17 The normal scattering ratio η of the simulated phonon N Compare, if R 17 ≤ η N , then keep the velocity direction of the simulated phonon unchanged, if R 17 > η N , and then generate two random numbers R uniformly distributed between [0,1] 18 and R 19 , update the velocity direction of the simulated phonon to:
[0103] ;
[0104] Where θ 10 and φ 10 is the polar angle and azimuthal angle of the simulated phonon velocity direction after intrinsic scattering;
[0105] 4) Statistically calculate the temperature distribution and heat flux density distribution at the current moment;
[0106] After completing the emission, translation, boundary scattering, and intrinsic scattering motion evolution of all simulated phonons within a unit step, the energy density in each spatial unit is counted, and the temperature of each spatial unit at the current moment is calculated through Newton iteration. The calculation formula is as follows:
[0107] ;
[0108] Where T a0 The temperature at the current moment is used to statistically calculate the heat flux density q0 of each spatial unit. The calculation formula is:
[0109] ;
[0110] in is the unit vector pointing to the direction of one-dimensional heat conduction, v 0i Simulate the velocity vector of the phonon at the current moment;
[0111] Step 3.4, determine whether the one-dimensional heat conduction system has reached thermal stability and calculate the numerical simulation results of intrinsic thermal conductivity;
[0112] Repeat step 3.3 and calculate the time-averaged heat flux density of each spatial unit every 200 time steps. If the coefficient of variation of the heat flux density of each spatial unit is less than 3%, the one-dimensional heat conduction system is considered to have reached a steady state.
[0113] After the one-dimensional heat conduction system reaches steady state, the temperature distribution and heat flux density distribution are taken for 200 consecutive moments, and the time average calculation is performed on each spatial unit to obtain the steady-state temperature distribution and steady-state heat flux density distribution. The numerical simulation results of the intrinsic thermal conductivity are as follows:
[0114] ;
[0115] Where κ0 is the numerical simulation result of intrinsic thermal conductivity, △z0 is the spatial distance in the one-dimensional heat conduction direction, △T0 is the steady-state temperature difference between the distances △z0, and q ave0 is the average steady-state heat flux density within the distance △z0.
[0116] Step 4: Compare the numerical simulation results of the intrinsic thermal conductivity with the first-principles calculation results, optimize the intrinsic scattering model parameters, and determine the intrinsic phonon scattering characteristics, specifically:
[0117] Calculate the numerical simulation results of the intrinsic thermal conductivity at the temperature corresponding to all the intrinsic thermal conductivity data observation points calculated by the first principles; compare the numerical simulation results of all the intrinsic thermal conductivity data observation points with the first principles calculation results. If the relative error between the two intrinsic thermal conductivity data observation points is greater than 5%, continue to optimize the model parameters c and d in the intrinsic scattering model, and recalculate the numerical simulation results of the intrinsic thermal conductivity at the temperature corresponding to all the intrinsic thermal conductivity data observation points; if the relative error between the two intrinsic thermal conductivity data observation points is less than 5%, determine the model parameters c and d in the intrinsic scattering model, that is, determine the intrinsic phonon scattering characteristics.
[0118] Step 5: For the experimental samples of the target material, collect the geometric dimension data of the experimental samples and the experimentally measured thermal conductivity data of the experimental samples, and extract preliminary extrinsic phonon scattering characteristics from the thermal conductivity data of the experimental samples based on the extrinsic scattering model, specifically:
[0119] Step 5.1, for the experimental sample of the target material, collect the geometric dimension data of the experimental sample and the experimentally measured thermal conductivity data of the experimental sample, and evenly select the observation points of the thermal conductivity data of the experimental sample according to the temperature range;
[0120] Step 5.2: Construct an extrinsic scattering model and extract preliminary extrinsic phonon scattering characteristics from the thermal conductivity data of the experimental sample;
[0121] Construct the boundary scattering model in the extrinsic scattering model, and the expression is as follows:
[0122] ;
[0123] Where sp represents the boundary scattering property, 0 represents diffuse scattering, 1 represents specular scattering, and Lc is the characteristic size of the experimental sample, α is the boundary scattering model parameter;
[0124] Construct the defect scattering model in the extrinsic scattering model, and the expression is as follows:
[0125] ;
[0126] Where τ D is the relaxation time of defect scattering, B and β are the boundary scattering model parameters;
[0127] The values of α, B and β are preset to extract preliminary extrinsic scattering characteristics.
[0128] Step 6: Based on the intrinsic phonon scattering characteristics, preliminary extrinsic phonon scattering characteristics, and simulated phonon groups, the thermal conductivity of the experimental sample is numerically simulated using the phonon Monte Carlo simulation method to obtain the numerical simulation results of the thermal conductivity of the experimental sample, specifically:
[0129] Step 6.1, set the one-dimensional heat conduction process, numerical simulation space, spatial unit, time unit step, boundary conditions and initial conditions required for the numerical simulation of thermal conductivity of the experimental sample;
[0130] Step 6.2, based on the simulated phonon group generated in step 1, initialize the simulated phonon group for all spatial units;
[0131] Step 6.3: Simulate the motion evolution of all simulated phonons within a unit time step, including the emission, translation, boundary scattering, intrinsic scattering, defect scattering, and statistical calculation of simulated phonons. The specific method is as follows:
[0132] 1) Use a simulated phonon group to emit simulated phonons from the isothermal boundary and calculate the number, velocity direction and spatial coordinates of the emitted simulated phonons, specifically;
[0133] Calculate the number of simulated phonons emitted, specifically:
[0134] ;
[0135] Where A1 represents the area of the isothermal boundary, T eq1 Indicates the set reference temperature, N h1 and N c1 The temperature is T h1 and T c1 The number of simulated phonons emitted by the isothermal boundary within the unit time step △t1;
[0136] Calculate the direction of the emitted simulated phonon velocity, specifically:
[0137] ;
[0138] Where θ 01 and φ 01 is the polar angle and azimuthal angle of the emitted simulated phonon velocity direction, R 20 and R 21 are two random numbers uniformly distributed between [0,1];
[0139] Calculate the spatial coordinates of the emitted simulated phonons, specifically:
[0140] ;
[0141] Where r 01 is the spatial coordinate of the emitted simulated phonon, z b1 is the z-axis coordinate value corresponding to the isothermal boundary, l x1 、l y1 and l z1 is the length, width and height of the space unit, R 22 and R 23 are two random numbers uniformly distributed between [0,1];
[0142] 2) Perform translational motion and boundary scattering on all simulated phonons;
[0143] The translation motion calculation process is:
[0144] ;
[0145] Where v1 is the velocity vector of the simulated phonon, r b1 is the spatial coordinate before simulating the translational motion of the phonon, r a1 is the spatial coordinate after simulating the translational motion of the phonon;
[0146] When the simulated phonons move to the adiabatic boundary, the nature of the boundary scattering is determined based on the preliminary extrinsic phonon scattering characteristics, and the boundary scattering simulation is performed;
[0147] If the boundary scattering property of the simulated phonon sp is 1, the boundary scattering with the property of mirror scattering is performed, which is expressed as:
[0148] ;
[0149] Where v a1 is the velocity vector of the simulated phonon after specular scattering, is the unit normal vector of the adiabatic boundary pointing to the interior of the numerical simulation space;
[0150] If the boundary scattering property of the simulated phonon sp is 0, the boundary scattering with diffuse scattering property is performed to generate two random numbers R uniformly distributed between [0,1]. 24 and R 25 , the velocity direction of the simulated phonon after diffuse scattering is:
[0151] ;
[0152] Where φ n is the azimuth angle of the adiabatic boundary normal vector pointing to the interior of the numerical simulation space, θ 21 and φ 21 are the polar angle and azimuth angle of the velocity direction after diffuse scattering;
[0153] 3) Based on the intrinsic scattering characteristics, determine whether all simulated phonons undergo intrinsic scattering, and update the frequency, dispersion branch, and velocity of the simulated phonons that undergo intrinsic scattering. Specifically:
[0154] i) Based on the intrinsic scattering characteristics, determine whether the simulated phonon undergoes intrinsic scattering;
[0155] Calculate the intrinsic scattering probability P of each simulated phonon per unit time step 11 , the expression is:
[0156] ;
[0157] Generate a random number R uniformly distributed between [0,1] 26 , if R 26 ≤ P 11 When , the simulated phonon undergoes intrinsic scattering, otherwise, the simulated phonon does not undergo intrinsic scattering;
[0158] ii) For the simulated phonons that undergo intrinsic scattering, first update the frequency of the simulated phonons;
[0159] Calculate the phonon number-frequency cumulative distribution function H in the intrinsic scattering process i (T), the expression is:
[0160] ;
[0161] Generate a random number R uniformly distributed between [0,1] 27 , if H i-1 < R 27 ≤ H i , then the updated simulated phonon frequency is located in the i-th frequency interval, and another [0,1] uniformly distributed random number R is generated 28 To determine the frequency:
[0162] ;
[0163] Where ω 11 is the frequency of the simulated phonon after eigenscattering;
[0164] Then, the dispersion branch of the simulated phonons is updated;
[0165] After calculating the intrinsic scattering, the proportion of different dispersion branch phonons in the frequency range of the simulated phonon frequency is:
[0166] ;
[0167] Where Q 11 is the proportion of LA phonons, Q 21 Generate a random number R uniformly distributed between [0,1] for the ratio of LA and TA1 phonons 29 , if R 29 ≤ Q 11 , then the updated dispersion branch is LA, if Q 11 < R 29 ≤ Q 21 , then the updated dispersion branch is TA1, if R 29 > Q 21 , then the updated dispersion branch is TA2;
[0168] Finally, the velocity of the simulated phonons is updated;
[0169] Update the simulated phonon velocity to:
[0170] ;
[0171] v 11 is the velocity of the simulated phonon after intrinsic scattering;
[0172] Generate a random number R uniformly distributed between [0,1] 30 , R 30 The normal scattering ratio η of the simulated phonon N Compare, if R 30 ≤ η N , then keep the velocity direction of the simulated phonon unchanged, if R 30 > η N , and then generate two random numbers R uniformly distributed between [0,1] 31 and R 32 , update the velocity direction of the simulated phonon to:
[0173] ;
[0174] Where θ 11 and φ 11 is the polar angle and azimuthal angle of the simulated phonon velocity direction after intrinsic scattering;
[0175] 4) Based on the preliminary extrinsic phonon scattering characteristics, determine whether all simulated phonons undergo defect scattering, and update the velocity direction of simulated phonons that undergo defect scattering, specifically:
[0176] Calculate the defect scattering probability P of each simulated phonon per unit time step 21 , the expression is:
[0177] ;
[0178] Generate a random number R uniformly distributed between [0,1] 33 , if R 33 ≤ P 21 When , the simulated phonon undergoes defect scattering, otherwise, the simulated phonon does not undergo defect scattering;
[0179] Generate two random numbers R uniformly distributed between [0,1] 34 and R 35 , the velocity direction of the simulated phonon after defect scattering is updated as:
[0180] ;
[0181] Where θ 21 and φ 21 The polar and azimuthal angles of the simulated phonon velocity direction after defect scattering;
[0182] 5) Statistically calculate the temperature distribution and heat flux density distribution at the current moment;
[0183] After completing the simulation of phonon emission, translation, boundary scattering, intrinsic scattering, and defect scattering within a unit step, the energy density in each spatial unit is counted, and the temperature of each spatial unit at the current moment is calculated through Newton iteration. The calculation formula is as follows:
[0184] ;
[0185] Where T a1 is the temperature at the current moment, and the heat flux density q1 of each spatial unit is calculated as follows:
[0186] ;
[0187] in is the unit vector pointing to the direction of one-dimensional heat conduction, v 1i Simulate the velocity vector of the phonon at the current moment;
[0188] Step 6.4: Determine whether the one-dimensional heat conduction system has reached thermal stability and calculate the numerical simulation results of the thermal conductivity of the experimental sample;
[0189] Repeat step 6.3 and calculate the time-averaged heat flux density of each spatial unit every 200 time steps. If the coefficient of variation of the heat flux density of each spatial unit is less than 3%, the one-dimensional heat conduction system is considered to have reached a steady state.
[0190] After the one-dimensional heat conduction system reaches a steady state, the temperature distribution and heat flux density distribution are taken for 200 consecutive moments, and the time average calculation is performed on each spatial unit to obtain the steady-state temperature distribution and steady-state heat flux density distribution. The numerical simulation results of the thermal conductivity of the experimental sample are calculated as follows:
[0191] ;
[0192] Where κ1 is the numerical simulation result of thermal conductivity of the experimental sample, △z1 is the spatial distance in the one-dimensional heat conduction direction, △T1 is the steady-state temperature difference within the △z1 distance, and q ave1 is the average steady-state heat flux density within the distance △z1.
[0193] Step 7: Compare the numerical simulation results and experimental measurement results of the thermal conductivity of the experimental sample, optimize the extrinsic scattering model parameters, and determine the extrinsic phonon scattering characteristics, specifically:
[0194] Calculate the numerical simulation results of the thermal conductivity of the experimental samples at the temperatures corresponding to the observation points of the thermal conductivity data of all experimental samples; compare the numerical simulation results and experimental measurement results of the thermal conductivity data observation points of all experimental samples; if the relative error between the two observation points of the thermal conductivity data of the experimental samples is greater than 10%, continue to optimize the model parameters α, B and β in the extrinsic scattering model, and recalculate the numerical simulation results of the thermal conductivity of the experimental samples at the temperatures corresponding to the observation points of the thermal conductivity data of all experimental samples; if the relative error between the two observation points of the thermal conductivity data of all experimental samples is less than or equal to 10%, determine the model parameters α, B and β of the extrinsic scattering model, that is, determine the extrinsic phonon scattering characteristics.
[0195] Step 8: Based on the intrinsic phonon scattering characteristics and extrinsic phonon scattering characteristics and the simulated phonon group, a thermal conduction numerical simulation is performed on the micro-nanostructure of the target material. The numerical simulation results include: the steady-state temperature distribution, steady-state heat flux density distribution and thermal conductivity of the micro-nanostructure, specifically:
[0196] Step 8.1: Set the heat conduction process, numerical simulation space, spatial unit, time unit step, boundary conditions, and initial conditions required for numerical simulation based on the micro-nanostructure of the target material.
[0197] Step 8.2, based on the simulated phonon group generated in step 1, initialize the simulated phonon group for all spatial units;
[0198] Step 8.3: Simulate the motion evolution of all simulated phonons within a unit time step, including the emission, translation, boundary scattering, intrinsic scattering, defect scattering, and statistical calculation of simulated phonons. The specific method is as follows:
[0199] 1) Use a simulated phonon group to emit simulated phonons from the isothermal boundary and calculate the number, velocity direction and spatial coordinates of the emitted simulated phonons, specifically;
[0200] Calculate the number of simulated phonons emitted, specifically:
[0201] ;
[0202] Where A2 represents the area of the isothermal boundary, T eq2 Indicates the set reference temperature, N h2 and N c2 The temperature is T h2 and T c2 The number of simulated phonons emitted by the isothermal boundary within the unit time step △t2;
[0203] Calculate the direction of the emitted simulated phonon velocity, specifically:
[0204] ;
[0205] Where θ 02 and φ 02 is the polar angle and azimuthal angle of the emitted simulated phonon velocity direction, R 36 and R 37 are two random numbers uniformly distributed between [0,1];
[0206] Calculate the spatial coordinates of the emitted simulated phonons, specifically:
[0207] ;
[0208] Where r 02 is the spatial coordinate of the emitted simulated phonon, z b2 is the z-axis coordinate value corresponding to the isothermal boundary, l x2 、l y2 and l z2 is the length, width and height of the space unit, R 38 and R 39 are two random numbers uniformly distributed between [0,1];
[0209] 2) Perform translational motion and boundary scattering on all simulated phonons;
[0210] The translation motion calculation process is:
[0211] ;
[0212] Where v2 is the velocity vector of the simulated phonon, r b2 is the spatial coordinate before simulating the translational motion of the phonon, r a2 is the spatial coordinate after simulating the translational motion of the phonon;
[0213] When the simulated phonons move to the adiabatic boundary, the nature of the boundary scattering is determined based on the extrinsic phonon scattering characteristics, and the boundary scattering simulation is performed;
[0214] If the boundary scattering property of the simulated phonon sp is 1, the boundary scattering with the property of mirror scattering is performed, which is expressed as:
[0215] ;
[0216] Where v a2 is the velocity vector of the simulated phonon after specular scattering, is the unit normal vector of the adiabatic boundary pointing to the interior of the numerical simulation space;
[0217] If the boundary scattering property of the simulated phonon sp is 0, the boundary scattering with diffuse scattering property is performed to generate two random numbers R uniformly distributed between [0,1]. 40 and R 41 , the velocity direction of the simulated phonon after diffuse scattering is:
[0218] ;
[0219] Where φ n is the azimuth angle of the adiabatic boundary normal vector pointing to the interior of the numerical simulation space, θ 22 and φ 22 are the polar angle and azimuth angle of the velocity direction after diffuse scattering;
[0220] 3) Based on the intrinsic scattering characteristics, determine whether all simulated phonons undergo intrinsic scattering, and update the frequency, dispersion branch, and velocity of the simulated phonons that undergo intrinsic scattering. Specifically:
[0221] i) Based on the intrinsic scattering characteristics, determine whether the simulated phonon undergoes intrinsic scattering;
[0222] Calculate the intrinsic scattering probability P of each simulated phonon per unit time step 12 , the expression is:
[0223] ;
[0224] Generate a random number R uniformly distributed between [0,1] 42 , if R 42 ≤ P 12 When , the simulated phonon undergoes intrinsic scattering, otherwise, the simulated phonon does not undergo intrinsic scattering;
[0225] ii) For the simulated phonons that undergo intrinsic scattering, first update the frequency of the simulated phonons;
[0226] Calculate the phonon number-frequency cumulative distribution function F during intrinsic scattering i(T), the expression is:
[0227] ;
[0228] Generate a random number R uniformly distributed between [0,1] 43 , if F i-1 < R 43 ≤ F i , then the updated simulated phonon frequency is located in the i-th frequency interval, and another [0,1] uniformly distributed random number R is generated 44 To determine the frequency:
[0229] ;
[0230] Where ω 12 is the frequency of the simulated phonon after eigenscattering;
[0231] Then, the dispersion branch of the simulated phonons is updated;
[0232] After calculating the intrinsic scattering, the proportion of different dispersion branch phonons in the frequency range of the simulated phonon frequency is:
[0233] ;
[0234] Where Q 12 is the proportion of LA phonons, Q 22 Generate a random number R uniformly distributed between [0,1] for the ratio of LA and TA1 phonons 45 , if R 45 ≤ Q 12 , then the updated dispersion branch is LA, if Q 12 < R 45 ≤ Q 22 , then the updated dispersion branch is TA1, if R 45 > Q 22 , then the updated dispersion branch is TA2;
[0235] Finally, the velocity of the simulated phonons is updated;
[0236] Update the simulated phonon velocity to:
[0237] ;
[0238] v 12 is the velocity of the simulated phonon after intrinsic scattering;
[0239] Generate a random number R uniformly distributed between [0,1] 46 , R 46 The normal scattering ratio η of the simulated phonon N Compare, if R46 ≤ η N , then keep the velocity direction of the simulated phonon unchanged, if R 46 > η N , and then generate two random numbers R uniformly distributed between [0,1] 47 and R 48 , update the velocity direction of the simulated phonon to:
[0240] ;
[0241] Where θ 12 and φ 12 is the polar angle and azimuthal angle of the simulated phonon velocity direction after intrinsic scattering;
[0242] 4) Based on the extrinsic phonon scattering characteristics, determine whether all simulated phonons undergo defect scattering, and update the velocity direction of simulated phonons that undergo defect scattering, specifically:
[0243] Calculate the defect scattering probability P of each simulated phonon per unit time step 22 , the expression is:
[0244] ;
[0245] Generate a random number R uniformly distributed between [0,1] 49 , if R 49 ≤ P 22 , then the simulated phonon undergoes defect scattering, otherwise, the simulated phonon does not undergo defect scattering;
[0246] Generate two random numbers R uniformly distributed between [0,1] 50 and R 51 , the velocity direction of the simulated phonon after defect scattering is updated as:
[0247] ;
[0248] Where θ 22 and φ 22 The polar and azimuthal angles of the simulated phonon velocity direction after defect scattering;
[0249] 5) Statistically calculate the temperature distribution and heat flux density distribution at the current moment;
[0250] After completing the emission, translation, boundary scattering, intrinsic scattering, and defect scattering motion evolution of all simulated phonons within a unit step, the energy density in each spatial unit is counted, and the temperature of each spatial unit at the current moment is calculated through Newton iteration. The calculation formula is as follows:
[0251] ;
[0252] Where T a2 is the temperature at the current moment, and the heat flux density q2 of each spatial unit is calculated as follows:
[0253] ;
[0254] in is the unit vector pointing to the direction of one-dimensional heat conduction, v 2i Simulate the velocity vector of the phonon at the current moment;
[0255] Step 8.4, determining whether the heat conduction system of the micro-nanostructure has reached a thermal steady state, and calculating the numerical simulation results of the heat conduction of the micro-nanostructure;
[0256] Repeat step 8.3, calculating the time-averaged heat flux density of each spatial unit every 200 time steps. If the relative deviation of the time-averaged heat flux density of each spatial unit in the two statistics is less than 3%, the heat conduction system is considered to have reached a steady state.
[0257] After the heat conduction system reaches a steady state, the temperature distribution and heat flux density distribution are taken for 200 consecutive moments, and the time average calculation is performed on each spatial unit to obtain the numerical simulation results of the steady-state temperature distribution and steady-state heat flux density distribution of the target material micro-nanostructure;
[0258] The numerical simulation results of the thermal conductivity of the target material micro-nanostructure are as follows:
[0259] ;
[0260] Where κ2 is the numerical simulation result of the thermal conductivity of the target material micro-nanostructure, △r is the spatial distance of the main heat flow direction, △T2 is the steady-state temperature difference within the △r distance, and q ave2 is the average heat flux density within the △r distance.
[0261] The present invention also proposes a micro-nanostructure heat conduction numerical simulation system based on multi-source information fusion, implements the micro-nanostructure heat conduction numerical simulation method based on multi-source information fusion, realizes the micro-nanostructure heat conduction numerical simulation based on multi-source information fusion, and performs steps 1 to 8 respectively in eight modules.
[0262] In summary, the present invention can integrate multi-source data from first-principles calculations and experimental measurements, decouple and determine the intrinsic and extrinsic phonon scattering characteristics in actual materials, accurately simulate the heat conduction process of micro-nanostructures of actual materials, and help improve the accuracy of thermal design of semiconductor devices.
[0263] Example
[0264] In order to verify the effectiveness of the solution of the present invention, the following numerical simulation experiment design was carried out.
[0265] In this embodiment, a micro-nano thin film structure of gallium nitride material is selected to perform numerical simulation of heat conduction of the micro-nano structure based on multi-source information fusion.
[0266] For gallium nitride materials, the phonon dispersion relation of gallium nitride is collected as follows:
[0267] ;
[0268] Collect the intrinsic thermal conductivity data of GaN calculated by first principles, with a temperature range of 100-400K, such as Figure 2 As shown, 7 intrinsic thermal conductivity data observation points are selected, from which the relaxation time model of the intrinsic phonon scattering model is extracted as follows:
[0269] ;
[0270] By optimizing the intrinsic scattering model parameters through numerical simulation, the normal scattering ratio model parameters c = 0.991, d = 1.3565 in the intrinsic scattering model are determined. The numerical simulation results of the intrinsic thermal conductivity of GaN corresponding to the intrinsic thermal conductivity data observation point are as follows: Figure 2 As shown in the figure, the relative errors compared with the first-principles calculation results are less than or equal to 3.8%;
[0271] The geometric size of the GaN experimental sample collected is 1.38 mm × 3.24 mm × 6.50 mm, and the characteristic size L is calculated. c = 2.39 mm, collect the experimentally measured thermal conductivity data of the experimental samples in the temperature range of 10-400K, such as Figure 2 As shown, 15 observation points of thermal conductivity data of experimental samples were selected;
[0272] The parameters of the extrinsic scattering model are optimized by numerical simulation, and the boundary scattering model parameter α is determined to be 0.1, and the defect scattering model parameter B is determined to be 6.02×10 -33 , β = -1.0, the numerical simulation results of the thermal conductivity of the GaN experimental sample corresponding to the observation point of the thermal conductivity data of the experimental sample are as follows Figure 2 As shown, the relative errors with the experimental measurement results are less than or equal to 8.9%;
[0273] Based on the intrinsic and extrinsic phonon scattering characteristics, a numerical simulation of the directional heat conduction of micro-nano films based on gallium nitride materials was conducted. The results showed that: as the thickness of the micro-nano film decreases, the boundary temperature jump of the steady-state temperature distribution continues to increase, and the steady-state heat flux density continues to decrease, which is consistent with the influence mechanism of the size effect. In addition, the thermal conductivity also continues to decrease. The directional thermal conductivity of a 10-nanometer-thick film is less than one-tenth of that of a 10-micron-thick film. Figure 3 shown.
[0274] The above examples demonstrate that the method proposed in the present invention can decouple and determine the intrinsic and extrinsic phonon scattering properties in actual GaN materials through multi-source data from first-principles calculations and experimental measurements, thereby enabling numerical simulation of heat conduction in GaN micro- and nano-thin film structures of varying thicknesses. This means that the present invention is suitable for thermal simulation of semiconductor devices and helps improve the accuracy of their thermal design.
[0275] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0276] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be determined by the appended claims.
Claims
1. A numerical simulation method for heat conduction in micro-nanostructures based on multi-source information fusion, characterized in that: The steps include: Step 1: For the target material used in the micro-nanostructure, collect the phonon dispersion relation of the target material and generate the simulated phonon group required for numerical simulation; Step 2: For the target material, collect the intrinsic thermal conductivity data calculated by first principles, and extract preliminary intrinsic phonon scattering characteristics from the intrinsic thermal conductivity data based on the intrinsic scattering model and genetic algorithm optimization; Step 3: Based on the preliminary intrinsic scattering characteristics and the simulated phonon group, the intrinsic thermal conductivity is numerically simulated using the phonon Monte Carlo simulation method to obtain the numerical simulation results of the intrinsic thermal conductivity; Step 4: Compare the numerical simulation results of the intrinsic thermal conductivity with the first-principles calculation results, optimize the intrinsic scattering model parameters, and determine the intrinsic phonon scattering characteristics; Step 5: For the experimental sample of the target material, collect the geometric dimension data of the experimental sample and the experimentally measured thermal conductivity data of the experimental sample, and extract preliminary extrinsic phonon scattering characteristics from the thermal conductivity data of the experimental sample based on the extrinsic scattering model; Step 6: Based on the intrinsic phonon scattering characteristics, preliminary extrinsic phonon scattering characteristics, and simulated phonon groups, a phonon Monte Carlo simulation method is used to perform numerical simulation on the thermal conductivity of the experimental sample to obtain a numerical simulation result of the thermal conductivity of the experimental sample; Step 7: Compare the numerical simulation results and experimental measurement results of the thermal conductivity of the experimental sample, optimize the extrinsic scattering model parameters, and determine the extrinsic phonon scattering characteristics; Step 8: Based on the intrinsic phonon scattering characteristics and extrinsic phonon scattering characteristics and the simulated phonon group, a thermal conduction numerical simulation is performed on the micro-nanostructure of the target material to obtain the steady-state temperature distribution, steady-state heat flux density distribution and thermal conductivity of the micro-nanostructure.
2. The method for numerical simulation of heat conduction in micro-nanostructures based on multi-source information fusion according to claim 1, characterized in that: In step 1, for the target material used in the micro-nanostructure, the phonon dispersion relation of the target material is collected to generate the simulated phonon group required for numerical simulation, specifically: Step 1.1: For the target material used in the micro-nanostructure, collect the phonon dispersion relation of the target material. The phonon dispersion relation is expressed as ω(p,k), where ω is the frequency, k is the wave vector, and p represents the dispersion branch, which is divided into LA, TA1, and TA2 dispersion branches; Step 1.2: Generate the simulated phonon group required for numerical simulation based on the phonon dispersion relation and the number of simulated phonons in a single spatial unit, where: The generation rules for each simulated phonon are as follows: 1) Calculate the energy of a single simulated phonon using the expression: ; Where: e is the energy of the simulated phonon, V is the volume of a single space unit, N is the number of simulated phonons in a single space unit, is the reduced Planck constant, f eq is the Bose-Einstein distribution function, T is the temperature of the space unit, T eq is the reference temperature, N b is the frequency discrete equal parts, △ω is the frequency width of each discrete interval, and D is the phonon state density; 2) Calculate the frequency of simulated phonons; Calculate the phonon number-frequency cumulative distribution function g i (T), the expression is: ; Where ω i For the midpoint frequency of the ith frequency interval, generate a [0,1] uniformly distributed random number R1. If g i-1 <R1≤ g i , determine that the frequency of the simulated phonon is in the i-th frequency interval, and generate another [0,1] uniformly distributed random number R2 to determine the frequency ω of the simulated phonon: ; 3) Calculate and simulate the dispersion branches of phonons; The proportion of different dispersion branch phonons in the frequency range of the simulated phonon frequency is calculated as follows: ; Where Y LA is the proportion of LA phonons, Y LA+TA1 For the ratio of LA and TA1 phonons, generate a random number R3 uniformly distributed between [0,1]. If R3 ≤ Y LA , then the simulated phonon belongs to the LA dispersion branch. If Y LA < R3 ≤ Y LA+TA1 , then the simulated phonon belongs to the TA1 dispersion branch. If R3 > Y LA+TA1 , then the simulated phonon belongs to the TA2 dispersion branch; 4) Calculate the velocity and direction of the simulated phonons; Calculate the speed of the simulated phonon, specifically: ; v is the velocity of the simulated phonon; Calculate the velocity direction of the simulated phonon, specifically: ; Where θ and φ are the polar angle and azimuthal angle of the simulated phonon velocity direction, R4 and R5 are two random numbers uniformly distributed between [0,1]; 5) Calculate the spatial position of simulated phonons; Generate three random numbers R6, R7 and R8 uniformly distributed between [0,1] and calculate the spatial position r of the simulated phonon, specifically: ; Where r0 represents the coordinate origin of the space unit, l x 、l y and l z are the length, width and height of the spatial unit respectively, 、 and is the unit vector in the direction of the three coordinate axes of the Cartesian coordinate system.
3. The method for numerical simulation of heat conduction in micro-nanostructures based on multi-source information fusion according to claim 2, characterized in that: In step 2, for the target material, the intrinsic thermal conductivity data calculated by first principles is collected, and preliminary intrinsic phonon scattering characteristics are extracted from the intrinsic thermal conductivity data based on the intrinsic scattering model and genetic algorithm optimization. Specifically: Step 2.1: For the target material, collect the intrinsic thermal conductivity data calculated by first principles and select the observation points of the intrinsic thermal conductivity data evenly according to the temperature range; Step 2.2, extracting preliminary intrinsic phonon scattering characteristics from the intrinsic thermal conductivity data observation points through the intrinsic scattering model and genetic algorithm optimization; First, the relaxation time model in the intrinsic scattering model is constructed, and the expression is as follows: ; In the formula is the relaxation time of intrinsic scattering, (a1, a2, a3, b1, b2, b3) are the relaxation time model parameters; According to the intrinsic thermal conductivity data observation points, the fitness function fit of the genetic algorithm is constructed as follows: ; Where: κ j is the thermal conductivity value of the jth intrinsic thermal conductivity data observation point, T j is the temperature value corresponding to the jth intrinsic thermal conductivity data observation point, n is the number of intrinsic thermal conductivity data observation points, k B is the Boltzmann constant, and the optimal parameters of the relaxation time model are obtained by genetic algorithm; Then construct the normal scattering ratio model in the intrinsic scattering model, the expression is as follows: ; Where η N is the normal scattering ratio, ω c is the phonon cutoff frequency of the first Brillouin zone, c and d are the normal scattering scale model parameters; The parameter values of c and d in the normal scattering proportional model are preset to extract the preliminary intrinsic scattering characteristics.
4. The method for numerical simulation of heat conduction in micro-nanostructures based on multi-source information fusion according to claim 3, characterized in that: In step 3, based on the preliminary intrinsic scattering characteristics and the simulated phonon group, the intrinsic thermal conductivity is numerically simulated using the phonon Monte Carlo simulation method to obtain the numerical simulation results of the intrinsic thermal conductivity, specifically: Step 3.1, set the one-dimensional heat conduction process, numerical simulation space, spatial unit, time unit step, boundary conditions and initial conditions required for the numerical simulation of intrinsic thermal conductivity, specifically: The one-dimensional heat conduction direction is defined as the z-axis direction of the Cartesian coordinate system, and the numerical simulation space, space unit, number of space units and unit time step △t0 are set. The two surfaces perpendicular to the one-dimensional heat conduction direction are set as isothermal boundaries, and the temperatures are set to T h0 and T c0 , set the four surfaces parallel to the one-dimensional heat conduction direction as adiabatic boundaries, set the initial temperature T0 and reference temperature T of all space units eq0 ; Step 3.2, based on the simulated phonon group generated in step 1, initialize the simulated phonon group for all spatial units; Step 3.3: simulate the motion evolution of all simulated phonons within a unit time step, including the emission, translation, boundary scattering, intrinsic scattering, and statistical calculation of simulated phonons. Specifically: 1) Use a simulated phonon group to emit simulated phonons from the isothermal boundary and calculate the number, velocity direction and spatial coordinates of the emitted simulated phonons, specifically; Calculate the number of simulated phonons emitted, specifically: ; Where A0 represents the area of the isothermal boundary, N h0 and N c0 The temperature is T h0 and T c0 The number of simulated phonons emitted per unit time step by the isothermal boundary of ; Calculate the direction of the emitted simulated phonon velocity, specifically: ; Where θ 00 and φ 00 are the polar and azimuthal angles of the emitted simulated phonon velocity directions, R9 and R 10 are two random numbers uniformly distributed between [0,1]; Calculate the spatial coordinates of the emitted simulated phonons, specifically: ; Where r 00 is the spatial coordinate of the emitted simulated phonon, z b0 is the z-axis coordinate value corresponding to the isothermal boundary, l x0 、l y0 and l z0 is the length, width and height of the space unit, R 11 and R 12 are two random numbers uniformly distributed between [0,1]; 2) Perform translational motion and boundary scattering on all simulated phonons; The translation motion calculation process is: ; Where v0 is the velocity vector of the simulated phonon, r b0 is the spatial coordinate before simulating the translational motion of the phonon, r a0 is the spatial coordinate after simulating the translational motion of the phonon; When the simulated phonon moves to the adiabatic boundary, boundary scattering occurs, which is of the nature of specular scattering and is expressed as: ; Where v a0 is the velocity vector of the simulated phonon after boundary scattering, is the unit normal vector of the adiabatic boundary pointing to the interior of the numerical simulation space; 3) Based on the preliminary intrinsic scattering characteristics, determine whether all simulated phonons undergo intrinsic scattering, and update the frequency, dispersion branch, and velocity of the simulated phonons that undergo intrinsic scattering. Specifically: i) Based on the preliminary eigenscattering characteristics, determine whether the simulated phonons undergo eigenscattering; Calculate the intrinsic scattering probability P of each simulated phonon per unit time step 10 , the expression is: ; Generate a random number R uniformly distributed between [0,1] 13 , if R 13 ≤ P 10 When , the simulated phonon undergoes intrinsic scattering, otherwise, the simulated phonon does not undergo intrinsic scattering; ii) For the simulated phonons that undergo intrinsic scattering, first update the frequency of the simulated phonons; Calculate the phonon number-frequency cumulative distribution function G during intrinsic scattering i (T), the expression is: ; Generate a random number R uniformly distributed between [0,1] 14 , if G i-1 < R 14 ≤ G i , then the updated frequency is in the i-th frequency interval, and another [0,1] uniformly distributed random number R is generated 15 To determine the frequency: ; Where ω 10 is the frequency of the simulated phonon after eigenscattering; Then, the dispersion branch of the simulated phonons is updated; After calculating the intrinsic scattering, the proportion of different dispersion branch phonons in the frequency range of the simulated phonon frequency is: ; Where Q 10 is the proportion of LA phonons, Q 20 Generate a random number R uniformly distributed between [0,1] for the ratio of LA and TA1 phonons 16 , if R 16 ≤ Q 10 , then the updated dispersion branch is LA, if Q 10 < R 16 ≤ Q 20 , then the updated dispersion branch is TA1, if R 16 >Q 20 , then the updated dispersion branch is TA2; Finally, the velocity of the simulated phonons is updated; Update the simulated phonon velocity to: ; v 10 is the velocity of the simulated phonon after intrinsic scattering; Generate a random number R uniformly distributed between [0,1] 17 , R 17 The normal scattering ratio η of the simulated phonon N Compare, if R 17 ≤ η N , then keep the velocity direction of the simulated phonon unchanged, if R 17 > η N , and then generate two random numbers R uniformly distributed between [0,1] 18 and R 19 , update the velocity direction of the simulated phonon to: ; Where θ 10 and φ 10 is the polar angle and azimuthal angle of the simulated phonon velocity direction after intrinsic scattering; 4) Statistically calculate the temperature distribution and heat flux density distribution at the current moment; After completing the emission, translation, boundary scattering, and intrinsic scattering motion evolution of all simulated phonons within a unit step, the energy density in each spatial unit is counted, and the temperature of each spatial unit at the current moment is calculated through Newton iteration. The calculation formula is as follows: ; Where T a0 The temperature at the current moment is used to statistically calculate the heat flux density q0 of each spatial unit. The calculation formula is: ; in is the unit vector pointing to the direction of one-dimensional heat conduction, v 0i Simulate the velocity vector of the phonon at the current moment; Step 3.4, determine whether the one-dimensional heat conduction system has reached thermal stability and calculate the numerical simulation results of intrinsic thermal conductivity; Repeat step 3.3 and calculate the time-averaged heat flux density of each spatial unit every 200 time steps. If the coefficient of variation of the heat flux density of each spatial unit is less than 3%, the one-dimensional heat conduction system is considered to have reached a steady state. After the one-dimensional heat conduction system reaches steady state, the temperature distribution and heat flux density distribution are taken for 200 consecutive moments, and the time average calculation is performed on each spatial unit to obtain the steady-state temperature distribution and steady-state heat flux density distribution. The numerical simulation results of the intrinsic thermal conductivity are as follows: ; Where κ0 is the numerical simulation result of intrinsic thermal conductivity, △z0 is the spatial distance in the one-dimensional heat conduction direction, △T0 is the steady-state temperature difference between the distances △z0, and q ave0 is the average steady-state heat flux density within the distance △z0.
5. The method for numerical simulation of heat conduction in micro-nanostructures based on multi-source information fusion according to claim 4, characterized in that: In step 4, the numerical simulation results of the intrinsic thermal conductivity are compared with the first-principles calculation results, the intrinsic scattering model parameters are optimized, and the intrinsic phonon scattering characteristics are determined. Specifically: Calculate the numerical simulation results of the intrinsic thermal conductivity at the temperature corresponding to all the intrinsic thermal conductivity data observation points calculated by the first principles; compare the numerical simulation results of all the intrinsic thermal conductivity data observation points with the first principles calculation results. If the relative error between the two intrinsic thermal conductivity data observation points is greater than 5%, continue to optimize the model parameters c and d in the intrinsic scattering model, and recalculate the numerical simulation results of the intrinsic thermal conductivity at the temperature corresponding to all the intrinsic thermal conductivity data observation points; if the relative error between the two intrinsic thermal conductivity data observation points is less than 5%, determine the model parameters c and d in the intrinsic scattering model, that is, determine the intrinsic phonon scattering characteristics.
6. The method for numerical simulation of heat conduction in micro-nanostructures based on multi-source information fusion according to claim 5, characterized in that: In step 5, for the experimental sample of the target material, the geometric dimension data of the experimental sample and the experimentally measured thermal conductivity data of the experimental sample are collected, and preliminary extrinsic phonon scattering characteristics are extracted from the thermal conductivity data of the experimental sample based on the extrinsic scattering model, specifically: Step 5.1, for the experimental sample of the target material, collect the geometric dimension data of the experimental sample and the experimentally measured thermal conductivity data of the experimental sample, and evenly select the observation points of the thermal conductivity data of the experimental sample according to the temperature range; Step 5.2: Construct an extrinsic scattering model and extract preliminary extrinsic phonon scattering characteristics from the thermal conductivity data of the experimental sample; Construct the boundary scattering model in the extrinsic scattering model, and the expression is as follows: ; Where sp represents the boundary scattering property, 0 represents diffuse scattering, 1 represents specular scattering, and L c is the characteristic size of the experimental sample, α is the boundary scattering model parameter; Construct the defect scattering model in the extrinsic scattering model, and the expression is as follows: ; Where τ D is the relaxation time of defect scattering, B and β are the boundary scattering model parameters; The values of α, B and β are preset to extract preliminary extrinsic scattering characteristics.
7. The method for numerical simulation of heat conduction in micro-nanostructures based on multi-source information fusion according to claim 6, characterized in that: In step 6, based on the intrinsic phonon scattering characteristics and preliminary extrinsic phonon scattering characteristics and the simulated phonon group, the thermal conductivity of the experimental sample is numerically simulated using the phonon Monte Carlo simulation method to obtain the numerical simulation results of the thermal conductivity of the experimental sample, specifically: Step 6.1, set the one-dimensional heat conduction process, numerical simulation space, spatial unit, time unit step, boundary conditions and initial conditions required for the numerical simulation of thermal conductivity of the experimental sample; Step 6.2, based on the simulated phonon group generated in step 1, initialize the simulated phonon group for all spatial units; Step 6.3: Simulate the motion evolution of all simulated phonons within a unit time step, including the emission, translation, boundary scattering, intrinsic scattering, defect scattering, and statistical calculation of simulated phonons. The specific method is as follows: 1) Use a simulated phonon group to emit simulated phonons from the isothermal boundary and calculate the number, velocity direction and spatial coordinates of the emitted simulated phonons, specifically; Calculate the number of simulated phonons emitted, specifically: ; Where A1 represents the area of the isothermal boundary, T eq1 Indicates the set reference temperature, N h1 and N c1 The temperature is T h1 and T c1 The number of simulated phonons emitted by the isothermal boundary within the unit time step △t1; Calculate the direction of the emitted simulated phonon velocity, specifically: ; Where θ 01 and φ 01 is the polar angle and azimuthal angle of the emitted simulated phonon velocity direction, R 20 and R 21 are two random numbers uniformly distributed between [0,1]; Calculate the spatial coordinates of the emitted simulated phonons, specifically: ; Where r 01 is the spatial coordinate of the emitted simulated phonon, z b1 is the z-axis coordinate value corresponding to the isothermal boundary, l x1 、l y1 and l z1 is the length, width and height of the space unit, R 22 and R 23 are two random numbers uniformly distributed between [0,1]; 2) Perform translational motion and boundary scattering on all simulated phonons; The translation motion calculation process is: ; Where v1 is the velocity vector of the simulated phonon, r b1 is the spatial coordinate before simulating the translational motion of the phonon, r a1 is the spatial coordinate after simulating the translational motion of the phonon; When the simulated phonons move to the adiabatic boundary, the nature of the boundary scattering is determined based on the preliminary extrinsic phonon scattering characteristics, and the boundary scattering simulation is performed; If the boundary scattering property of the simulated phonon sp is 1, the boundary scattering with the property of mirror scattering is performed, which is expressed as: ; Where v a1 is the velocity vector of the simulated phonon after specular scattering, is the unit normal vector of the adiabatic boundary pointing to the interior of the numerical simulation space; If the boundary scattering property of the simulated phonon sp is 0, the boundary scattering with diffuse scattering property is performed to generate two random numbers R uniformly distributed between [0,1]. 24 and R 25 , the velocity direction of the simulated phonon after diffuse scattering is: ; Where φ n is the azimuth angle of the adiabatic boundary normal vector pointing to the interior of the numerical simulation space, θ 21 and φ 21 are the polar angle and azimuth angle of the velocity direction after diffuse scattering; 3) Based on the intrinsic scattering characteristics, determine whether all simulated phonons undergo intrinsic scattering, and update the frequency, dispersion branch, and velocity of the simulated phonons that undergo intrinsic scattering. Specifically: i) Based on the intrinsic scattering characteristics, determine whether the simulated phonon undergoes intrinsic scattering; Calculate the intrinsic scattering probability P of each simulated phonon per unit time step 11 , the expression is: ; Generate a random number R uniformly distributed between [0,1] 26 , if R 26 ≤ P 11 When , the simulated phonon undergoes intrinsic scattering, otherwise, the simulated phonon does not undergo intrinsic scattering; ii) For the simulated phonons that undergo intrinsic scattering, first update the frequency of the simulated phonons; Calculate the phonon number-frequency cumulative distribution function H in the intrinsic scattering process i (T), the expression is: ; Generate a random number R uniformly distributed between [0,1] 27 , if H i-1 < R 27 ≤ H i , then the updated simulated phonon frequency is located in the i-th frequency interval, and another [0,1] uniformly distributed random number R is generated 28 To determine the frequency: ; Where ω 11 is the frequency of the simulated phonon after eigenscattering; Then, the dispersion branch of the simulated phonons is updated; After calculating the intrinsic scattering, the proportion of different dispersion branch phonons in the frequency range of the simulated phonon frequency is: ; Where Q 11 is the proportion of LA phonons, Q 21 Generate a random number R uniformly distributed between [0,1] for the ratio of LA and TA1 phonons 29 , if R 29 ≤ Q 11 , then the updated dispersion branch is LA, if Q 11 < R 29 ≤ Q 21 , then the updated dispersion branch is TA1, if R 29 >Q 21 , then the updated dispersion branch is TA2; Finally, the velocity of the simulated phonons is updated; Update the simulated phonon velocity to: ; v 11 is the velocity of the simulated phonon after intrinsic scattering; Generate a random number R uniformly distributed between [0,1] 30 , R 30 The normal scattering ratio η of the simulated phonon N Compare, if R 30 ≤ η N , then keep the velocity direction of the simulated phonon unchanged, if R 30 > η N , and then generate two random numbers R uniformly distributed between [0,1] 31 and R 32 , update the velocity direction of the simulated phonon to: ; Where θ 11 and φ 11 is the polar angle and azimuthal angle of the simulated phonon velocity direction after intrinsic scattering; 4) Based on the preliminary extrinsic phonon scattering characteristics, determine whether all simulated phonons undergo defect scattering, and update the velocity direction of simulated phonons that undergo defect scattering, specifically: Calculate the defect scattering probability P of each simulated phonon per unit time step 21 , the expression is: ; Generate a random number R uniformly distributed between [0,1] 33 , if R 33 ≤ P 21 When , the simulated phonon undergoes defect scattering, otherwise, the simulated phonon does not undergo defect scattering; Generate two random numbers R uniformly distributed between [0,1] 34 and R 35 , the velocity direction of the simulated phonon after defect scattering is updated as: ; Where θ 21 and φ 21 The polar and azimuthal angles of the simulated phonon velocity direction after defect scattering; 5) Statistically calculate the temperature distribution and heat flux density distribution at the current moment; After completing the simulation of phonon emission, translation, boundary scattering, intrinsic scattering, and defect scattering within a unit step, the energy density in each spatial unit is counted, and the temperature of each spatial unit at the current moment is calculated through Newton iteration. The calculation formula is as follows: ; Where T a1 is the temperature at the current moment, and the heat flux density q1 of each spatial unit is calculated as follows: ; in is the unit vector pointing to the direction of one-dimensional heat conduction, v 1i Simulate the velocity vector of the phonon at the current moment; Step 6.4: Determine whether the one-dimensional heat conduction system has reached thermal stability and calculate the numerical simulation results of the thermal conductivity of the experimental sample; Repeat step 6.3 and calculate the time-averaged heat flux density of each spatial unit every 200 time steps. If the coefficient of variation of the heat flux density of each spatial unit is less than 3%, the one-dimensional heat conduction system is considered to have reached a steady state. After the one-dimensional heat conduction system reaches a steady state, the temperature distribution and heat flux density distribution are taken for 200 consecutive moments, and the time average calculation is performed on each spatial unit to obtain the steady-state temperature distribution and steady-state heat flux density distribution. The numerical simulation results of the thermal conductivity of the experimental sample are calculated as follows: ; Where κ1 is the numerical simulation result of thermal conductivity of the experimental sample, △z1 is the spatial distance in the one-dimensional heat conduction direction, △T1 is the steady-state temperature difference within the △z1 distance, and q ave1 is the average steady-state heat flux density within the distance △z1.
8. The method for numerical simulation of heat conduction in micro-nanostructures based on multi-source information fusion according to claim 7, characterized in that: In step 7, the numerical simulation results and experimental measurement results of the thermal conductivity of the experimental sample are compared to optimize the extrinsic scattering model parameters and determine the extrinsic phonon scattering characteristics, specifically: Calculate the numerical simulation results of the thermal conductivity of the experimental samples at the temperatures corresponding to the observation points of the thermal conductivity data of all experimental samples; compare the numerical simulation results and experimental measurement results of the thermal conductivity data observation points of all experimental samples; if the relative error between the two observation points of the thermal conductivity data of the experimental samples is greater than 10%, continue to optimize the model parameters α, B and β in the extrinsic scattering model, and recalculate the numerical simulation results of the thermal conductivity of the experimental samples at the temperatures corresponding to the observation points of the thermal conductivity data of all experimental samples; if the relative error between the two observation points of the thermal conductivity data of all experimental samples is less than or equal to 10%, determine the model parameters α, B and β of the extrinsic scattering model, that is, determine the extrinsic phonon scattering characteristics.
9. The method for numerical simulation of heat conduction in micro-nanostructures based on multi-source information fusion according to claim 8, characterized in that: In step 8, based on the intrinsic phonon scattering characteristics and extrinsic phonon scattering characteristics and the simulated phonon group, a thermal conduction numerical simulation is performed on the micro-nanostructure of the target material to obtain the steady-state temperature distribution, steady-state heat flux density distribution and thermal conductivity of the micro-nanostructure, specifically: Step 8.1: Set the heat conduction process, numerical simulation space, spatial unit, time unit step, boundary conditions, and initial conditions required for numerical simulation based on the micro-nanostructure of the target material. Step 8.2, based on the simulated phonon group generated in step 1, initialize the simulated phonon group for all spatial units; Step 8.3: Simulate the motion evolution of all simulated phonons within a unit time step, including the emission, translation, boundary scattering, intrinsic scattering, defect scattering, and statistical calculation of simulated phonons. The specific method is as follows: 1) Use a simulated phonon group to emit simulated phonons from the isothermal boundary and calculate the number, velocity direction and spatial coordinates of the emitted simulated phonons, specifically; Calculate the number of simulated phonons emitted, specifically: ; Where A2 represents the area of the isothermal boundary, T eq2 Indicates the set reference temperature, N h2 and N c2 The temperature is T h2 and T c2 The number of simulated phonons emitted by the isothermal boundary within the unit time step △t2; Calculate the direction of the emitted simulated phonon velocity, specifically: ; Where θ 02 and φ 02 is the polar angle and azimuthal angle of the emitted simulated phonon velocity direction, R 36 and R 37 are two random numbers uniformly distributed between [0,1]; Calculate the spatial coordinates of the emitted simulated phonons, specifically: ; Where r 02 is the spatial coordinate of the emitted simulated phonon, z b2 is the z-axis coordinate value corresponding to the isothermal boundary, l x2 、l y2 and l z2 is the length, width and height of the space unit, R 38 and R 39 are two random numbers uniformly distributed between [0,1]; 2) Perform translational motion and boundary scattering on all simulated phonons; The translation motion calculation process is: ; Where v2 is the velocity vector of the simulated phonon, r b2 is the spatial coordinate before simulating the translational motion of the phonon, r a2 is the spatial coordinate after simulating the translational motion of the phonon; When the simulated phonons move to the adiabatic boundary, the nature of the boundary scattering is determined based on the extrinsic phonon scattering characteristics, and the boundary scattering simulation is performed; If the boundary scattering property of the simulated phonon sp is 1, the boundary scattering with the property of mirror scattering is performed, which is expressed as: ; Where v a2 is the velocity vector of the simulated phonon after specular scattering, is the unit normal vector of the adiabatic boundary pointing to the interior of the numerical simulation space; If the boundary scattering property of the simulated phonon sp is 0, the boundary scattering with diffuse scattering property is performed to generate two random numbers R uniformly distributed between [0,1]. 40 and R 41 , the velocity direction of the simulated phonon after diffuse scattering is: ; Where φ n is the azimuth angle of the adiabatic boundary normal vector pointing to the interior of the numerical simulation space, θ 22 and φ 22 are the polar angle and azimuth angle of the velocity direction after diffuse scattering; 3) Based on the intrinsic scattering characteristics, determine whether all simulated phonons undergo intrinsic scattering, and update the frequency, dispersion branch, and velocity of the simulated phonons that undergo intrinsic scattering. Specifically: i) Based on the intrinsic scattering characteristics, determine whether the simulated phonon undergoes intrinsic scattering; Calculate the intrinsic scattering probability P of each simulated phonon per unit time step 12 , the expression is: ; Generate a random number R uniformly distributed between [0,1] 42 , if R 42 ≤ P 12 When , the simulated phonon undergoes intrinsic scattering, otherwise, the simulated phonon does not undergo intrinsic scattering; ii) For the simulated phonons that undergo intrinsic scattering, first update the frequency of the simulated phonons; Calculate the phonon number-frequency cumulative distribution function F during intrinsic scattering i (T), the expression is: ; Generate a random number R uniformly distributed between [0,1] 43 , if F i-1 < R 43 ≤ F i , then the updated simulated phonon frequency is located in the i-th frequency interval, and another [0,1] uniformly distributed random number R is generated 44 To determine the frequency: ; Where ω 12 is the frequency of the simulated phonon after eigenscattering; Then, the dispersion branch of the simulated phonons is updated; After calculating the intrinsic scattering, the proportion of different dispersion branch phonons in the frequency range of the simulated phonon frequency is: ; Where Q 12 is the proportion of LA phonons, Q 22 Generate a random number R uniformly distributed between [0,1] for the ratio of LA and TA1 phonons 45 , if R 45 ≤ Q 12 , then the updated dispersion branch is LA, if Q 12 < R 45 ≤ Q 22 , then the updated dispersion branch is TA1, if R 45 >Q 22 , then the updated dispersion branch is TA2; Finally, the velocity of the simulated phonons is updated; Update the simulated phonon velocity to: ; v 12 is the velocity of the simulated phonon after intrinsic scattering; Generate a random number R uniformly distributed between [0,1] 46 , R 46 The normal scattering ratio η of the simulated phonon N Compare, if R 46 ≤ η N , then keep the velocity direction of the simulated phonon unchanged, if R 46 > η N , and then generate two random numbers R uniformly distributed between [0,1] 47 and R 48 , update the velocity direction of the simulated phonon to: ; Where θ 12 and φ 12 is the polar angle and azimuthal angle of the simulated phonon velocity direction after intrinsic scattering; 4) Based on the extrinsic phonon scattering characteristics, determine whether all simulated phonons undergo defect scattering, and update the velocity direction of simulated phonons that undergo defect scattering, specifically: Calculate the defect scattering probability P of each simulated phonon per unit time step 22 , the expression is: ; Generate a random number R uniformly distributed between [0,1] 49 , if R 49 ≤ P 22 , then the simulated phonon undergoes defect scattering, otherwise, the simulated phonon does not undergo defect scattering; Generate two random numbers R uniformly distributed between [0,1] 50 and R 51 , the velocity direction of the simulated phonon after defect scattering is updated as: ; Where θ 22 and φ 22 The polar and azimuthal angles of the simulated phonon velocity direction after defect scattering; 5) Statistically calculate the temperature distribution and heat flux density distribution at the current moment; After completing the emission, translation, boundary scattering, intrinsic scattering, and defect scattering motion evolution of all simulated phonons within a unit step, the energy density in each spatial unit is counted, and the temperature of each spatial unit at the current moment is calculated through Newton iteration. The calculation formula is as follows: ; Where T a2 is the temperature at the current moment, and the heat flux density q2 of each spatial unit is calculated as follows: ; in is the unit vector pointing to the direction of one-dimensional heat conduction, v 2i Simulate the velocity vector of the phonon at the current moment; Step 8.4, determining whether the heat conduction system of the micro-nanostructure has reached a thermal steady state, and calculating the numerical simulation results of the heat conduction of the micro-nanostructure; Repeat step 8.3, calculating the time-averaged heat flux density of each spatial unit every 200 time steps. If the relative deviation of the time-averaged heat flux density of each spatial unit in the two statistics is less than 3%, the heat conduction system is considered to have reached a steady state. After the heat conduction system reaches a steady state, the temperature distribution and heat flux density distribution are taken for 200 consecutive moments, and the time average calculation is performed on each spatial unit to obtain the numerical simulation results of the steady-state temperature distribution and steady-state heat flux density distribution of the target material micro-nanostructure; The numerical simulation results of the thermal conductivity of the target material micro-nanostructure are as follows: ; Where κ2 is the numerical simulation result of the thermal conductivity of the target material micro-nanostructure, △r is the spatial distance of the main heat flow direction, △T2 is the steady-state temperature difference within the △r distance, and q ave2 is the average heat flux density within the △r distance.
10. A numerical simulation system for heat conduction in micro-nanostructures based on multi-source information fusion, characterized in that: Implement the numerical simulation method of heat conduction in micro-nano structures based on multi-source information fusion as described in any one of claims 1-9 to realize the numerical simulation of heat conduction in micro-nano structures based on multi-source information fusion, and perform steps 1-8 respectively in eight modules.
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