Polymer composite TIM heterogeneous interface heat conduction multi-scale simulation method based on strain gradient response

Abstract

The invention discloses a polymer composite TIM heterogeneous interface heat conduction multi-scale simulation method based on strain gradient response, which adopts parameter transfer to realize cross-scale calculation, and sequentially comprises the following steps of: (1) calculating phonon properties and electric polarization properties of a polymer composite TIM heterogeneous interface on the basis of a first principle under a micro scale, obtaining a force constant matrix and phonon state density and polarization intensity of materials on two sides of an interface; (2) under a mesoscale, based on a machine learning potential function, performing unbalanced molecular dynamics simulation to obtain thermal conductivity, thermal boundary resistance and phonon work quantity spectral density of the polymer composite TIM heterogeneous surface; and (3) under the macroscale, establishing a finite element analysis model which comprises a heat source, a TIM and a cold source, and performing temperature field and heat flux density calculation on the finite element analysis model. Through a'parameter transfer 'strategy, the spanning from the quantum mechanics scale to the continuous medium scale is realized, the limitation of a single-scale method is overcome, and the calculation precision and the simulation scale are both considered.

Description

Technical Field

[0001] This invention relates to the field of computer simulation and thermal management materials technology, specifically to a multi-scale simulation method for thermal conduction at heterogeneous interfaces of polymer composite TIMs based on strain gradient response. Background Technology

[0002] Fourth-generation semiconductor materials (such as gallium nitride and gallium oxide) possess properties such as high breakdown electric field, high electron mobility, and excellent power density, showing broad application prospects in high-power devices and high-frequency electronics. However, these materials generally suffer from low thermal conductivity and high interfacial thermal resistance, leading to localized overheating during device operation and severely impacting their reliability and lifespan. Currently, a common thermal management approach is to introduce "thermally conductive interface materials (TIMs) with high thermal conductivity" to enhance heat transfer. However, due to factors such as lattice mismatch, poor chemical bonding, and phonon spectrum discontinuities at the interface, the heat transfer efficiency of traditional high thermal conductivity TIMs in semiconductor heterojunctions remains limited.

[0003] From the perspective of heat conduction mechanisms, heat conduction in solids mainly relies on the propagation and scattering of phonons. In solid-interface heat conduction, if the thermal interface material (TIM) and the substrate materials on both sides have good phonon spectrum matching, heat can propagate efficiently across the interface via phonons, resulting in low interfacial thermal resistance and excellent interfacial thermal conductivity. However, in practical heterogeneous interface systems, the spectral mismatch and limited transmission of phonons at the interface lead to a large interfacial thermal resistance. The materials on both sides of the interface undergo varying degrees of thermal expansion and contraction driven by temperature differences, thus forming a local strain gradient near the interface. If a polymer composite material with strain gradient response characteristics is used in the TIM, it will undergo spatially non-uniform thermal expansion and contraction driven by temperature differences, thereby forming a strain gradient and further exciting a local polarization field (i.e., flexoelectric polarization). Existing research indicates that in ferroelectric or flexoelectric composite systems, the polarization field can modulate the electrostatic potential distribution between interfacial atoms, change the force constant matrix, reconstruct the phonon dispersion relation, and especially enhance phonon mode matching in the mid-to-high frequency range, improving phonon transmittance and thus effectively enhancing interfacial thermal conductivity.

[0004] However, the composite structure of polymers and strain gradient-response materials is complex, posing significant challenges to experimental research. To elucidate its microscopic heat conduction mechanism and guide material design, it is urgent to establish a multi-scale simulation method for heat conduction at the interface of strain gradient-response polymer composite TIM heterostructures, enabling interface structure optimization and prediction of thermal management performance. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a multi-scale simulation method for thermal conduction at heterogeneous interfaces of polymer composite TIMs based on strain gradient response.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A multi-scale simulation method for thermal conduction at heterogeneous interfaces of polymer composite TIMs based on strain gradient response, which employs parameter transfer to achieve cross-scale calculations, includes the following steps: (1) At the microscale, based on first principles, the phonon properties and polarization properties of the polymer composite TIM heterostructure are calculated to obtain the force constant matrix, the phonon density of states and polarization intensity of the materials on both sides of the interface; (2) At the mesoscale, non-equilibrium molecular dynamics simulations are performed based on machine learning potential functions to obtain the thermal conductivity, thermal boundary resistance and phonon work spectral density of the polymer composite TIM heterostructure. (3) At the macroscopic scale, a finite element analysis model is established, which includes a heat source, a TIM (thermal induction generator), and a cold source, and its temperature field and heat flux density are calculated. In this step, the data obtained in step (1) is used as the input parameters or constraints in step (2); and the data obtained in step (2) is used as the input parameters or constitutive relations of the finite element analysis model in step (3).

[0007] In step (1), S1. Construct an atomic model of the polymer composite TIM heterostructure and form a continuous strain gradient by applying atomic displacement in the interface normal direction. To simulate the strain distribution of TIM under bending deformation; S2. Perform geometric optimization and ground-state energy calculation on the atomic model with strain gradient to obtain the electron density distribution of the system under strain gradient conditions, and calculate the polarization intensity based on the Berry phase method. and quantify strain gradient With polarization intensity Coupling relationship ,in The flexural conductivity of TIM; S3, the polarization intensity Characterized as potential disturbance caused by flexural polarization To obtain the total potential including the flexural effect , The total potential of the system; The intrinsic potential energy is unaffected by flexural polarization. This refers to the potential disturbance caused by flexural polarization. electric potential field The gradient; S4. Based on the total potential, calculate the interatomic force constant matrix using density functional perturbation theory. , ,in , Numbering the atoms within the unit cell; , For Cartesian coordinate components; The matrix of eigenforce constants when unaffected by polarization perturbation. This is the perturbation term caused by flexural polarization; S5, Based on the interatomic force constant matrix Construct and solve the dynamic matrix Obtain the phonon dispersion relation and the phonon state density of the materials on both sides of the interface; S6. Based on the phonon state density of the materials on both sides of the interface, calculate the phonon spectrum overlap factor S between different material components in the composite structure to quantitatively evaluate the interface phonon mode matching degree under strain gradient control.

[0008] Disturbance term caused by flexural polarization It is obtained by calculation using the following formula: ,in , Indicates the first , Atoms in direction , The displacement components.

[0009] In step (2), S1. Construct a dataset, which includes the force constant matrix obtained in step (1), the phonon state density, polarization intensity and phonon spectrum overlap factor of the materials on both sides of the interface; S2. Divide the dataset into training, validation, and test sets, and train the energy function using the NequIP framework. and force field function The machine learning potential function was determined, and Smooth L1 Loss was used to jointly optimize the energy, atomic force, and polarization response until the training error reached the target of energy < 5 meV / atom and atomic force < 0.05 eV / Å. S3. Embed the trained machine learning potential function into the LAMMPS platform, perform long-scale molecular dynamics simulation of the interface structure under NVT conditions, and collect the velocity time series of atoms in different regions. S4. Using the Green-Kubo method, the average kinetic energy relaxation behavior of phonon populations at different frequencies is characterized by the phonon velocity autocorrelation function, and the phonon power spectral density is obtained by performing a Fourier transform on the phonon velocity autocorrelation function characterization. S5. Based on local PDOS differences, PSD peak intensity, and interfacial force constant matrix perturbation, through... Obtain the effective phonon transmission coefficient ,in and These represent the frequency-dependent phonon impedances of materials 1 and 2, respectively. It is a polarization enhancement factor; S6. Based on the phonon effective transmission coefficient and phonon mode distribution, through Calculate the mode-selective phonon transport flux, where wave vector The corresponding phonon mode index; The transmittance is for single-mode phonons. exist The value is 1 for the time period and 0 for the rest, used for frequency filtering; S7. Solve for the interfacial thermal boundary resistance (TBR) based on the frequency-resolved heat flow model. , ,in The steady-state heat flux density at the interface, For temperature gradient, This represents the temperature difference between the materials on both sides.

[0010] The polarization enhancement factor through get.

[0011] In step (3), S1. Construct a three-layer physical structure model representing the actual application using software. The three layers are as follows: The first layer represents the heat source, the second layer represents the TIM, and the third layer represents the cold source; S2. Define the thermal conductivity of the second layer material using the simulation results from step 2. The thermal boundary resistance (TBR) of the interface is calculated and imported as an input parameter into the physical structure model. S3: Apply boundary conditions and loads to the physical structure model, including: applying constant heat flux boundary conditions to the upper surface or interior of the first layer to simulate device heating; setting isothermal boundary conditions to the lower surface or designated area of ​​the third layer to simulate a cold source; and setting natural convection boundary conditions on the outer surface of the model excluding the loading surface. S4: Perform finite element analysis on the physical structural model with assigned material properties, boundary conditions, and loads to obtain the steady-state temperature field; S5: Based on the solution results of the steady-state temperature field, output thermal management performance indicators including regional temperature distribution cloud map, heat flux density vector distribution map, total thermal resistance of the system and thermal response time.

[0012] Thermal conductivity in step S2 The interfacial thermal boundary resistance (TBR) is determined by the following function:

[0013]

[0014] in, For normalized weighted functions; The intrinsic interfacial thermal resistance under non-flexible polarization control; The flexural polarization enhancement coefficient; It reflects the degree to which unit polarization intensity contributes to the improvement of phonon transmittance; This represents the frequency-dependent polarization intensity calculated based on the Berry phase method.

[0015] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable by the processor, wherein the processor, when executing the program, implements the above-described multi-scale simulation method for thermal conduction at polymer composite TIM heterostructure interfaces based on strain gradient response.

[0016] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described multi-scale simulation method for thermal conduction at polymer composite TIM heterostructure interfaces based on strain gradient response.

[0017] The beneficial effects of this invention are: for the first time, a complete physical chain of strain gradient → flexural polarization → force constant perturbation → phonon spectrum modulation → interfacial thermal conduction is coupled in the simulation, which can reveal the deep mechanism of bending deformation affecting TIM thermal conduction from the microscopic, mesoscopic and macroscopic levels.

[0018] By employing a "parameter transfer" strategy, a leap from the quantum mechanical scale to the continuous medium scale is achieved, overcoming the limitations of single-scale methods and balancing computational accuracy with simulation scale.

[0019] It can serve as an efficient "computational experiment" platform to selectively screen and optimize TIM formulations and structures that perform well in complex thermal conduction environments, thereby shortening the R&D cycle and reducing experimental costs. Attached Figure Description

[0020] Figure 1 This diagram illustrates the placement relationship between the heat source, TIM, and cold source, and the principle of enhancing thermal conduction through a polymer composite TIM heterogeneous interface based on strain gradient response.

[0021] Figure 2 This is a schematic diagram of the multi-scale simulation principle.

[0022] Figure 3 The results show the PDOS calculations before and after polarization at different frequencies at the microscale.

[0023] Figure 4 The results show the calculated overlap factor of the phonon spectrum before and after microscale polarization.

[0024] Figure 5 This represents the change in phonon transmittance before and after mesoscale polarization.

[0025] Figure 6 The mesoscale PSD(ω) varies with frequency.

[0026] Figure 7 A comparison of thermal conductivity before and after macroscopic polarization.

[0027] Figure 8 A comparison of the temperature distribution along the cross-sectional direction of the three-layer structure before and after polarization. Detailed Implementation

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only used to illustrate the present invention and are not intended to limit the scope of protection of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] like Figure 1 and Figure 2 As shown, this invention discloses a multi-scale simulation method for heat conduction at a polymer composite TIM heterointerface based on strain gradient response. It employs parameter transfer to achieve cross-scale calculations. The placement relationship of the heat source, TIM, and cold source in the simulation, and the schematic diagram of the principle of enhanced heat conduction at the polymer composite TIM heterointerface based on strain gradient response are shown below. Figure 1 As shown in the diagram. At the microscale, phonon dispersion and density of states are calculated based on first-principles calculations to obtain the force constant matrix, phonon density of states (PDOS) on both sides of the interface, and polarization intensity. At the mesoscale, machine learning is used, employing non-equilibrium molecular dynamics (NEMD) methods and training an MLP using the NequIP framework to obtain thermal conductivity, heat flow rate (TBR), and work spectral density. At the macroscale, temperature field and heat flux density are calculated based on finite element analysis. The multi-scale simulation principle diagram is shown below. Figure 2 As shown.

[0030] The steps are as follows: (1) At the microscale, based on first principles, the phonon properties and polarization properties of the polymer composite TIM heterostructure are calculated to obtain the force constant matrix, the phonon density of states and polarization intensity of the materials on both sides of the interface; At the microscale, an atomic model was constructed using Material Studio software, and a continuous strain gradient was formed by adjusting the interface geometry (applying atomic displacements in the interface normal direction). To simulate the strain distribution of the composite TIM layer under bending deformation.

[0031] The atomic model of the composite TIM layer was geometrically optimized and its ground-state energy was calculated using Quantum ESPRESSO software, yielding the electron density distribution of the system under strain gradient conditions. Polarization intensity was calculated based on the Berry phase method. Quantitative strain gradient With polarization intensity Coupling relationship:

[0032] in, Let TIM be the flexural polarization coefficient. Treating flexural polarization as a type of electrostatic potential energy gradient perturbation, the total potential of the system is expressed as:

[0033]

[0034] in, The total potential of the system; This represents the intrinsic potential energy unaffected by flexural polarization. The potential disturbance caused by flexural polarization; electric potential field The gradient.

[0035] After the potential energy surface is modulated by the polarization field, the force constant matrix changes, causing a blue shift or mode redistribution in the high-frequency region of phonon dispersion, thereby improving the phonon spectrum matching across the interface. After obtaining the polarization-induced potential, the interatomic force constant matrix is ​​calculated based on the density functional perturbation theory (DFPT) module, and the interatomic force constant matrix is ​​extracted. :

[0036] in, , Numbering the atoms within the unit cell; , For Cartesian coordinate components; The matrix of eigenforce constants when unaffected by polarization perturbation. The perturbation term caused by flexural polarization:

[0037] in, , Indicates the first , Atoms in direction , The displacement components.

[0038] The dynamic matrix is ​​established by calling the above force constant matrix using the Phonopy software. :

[0039] in, , This represents the mass of the corresponding atom; It is a lattice vector; Let be the wave vector. For each By finding the frequencies of all modes at a point (along a highly symmetric path), the phonon dispersion relation can be obtained. Calculate PDOS:

[0040] in, for The total number; Assign modal numbers; In the calculation, the Gaussian function is used instead of smoothing. A phonon spectrum overlap factor is introduced. (overlap factor) as an indicator of modality fit:

[0041] in, and The two types of PDOS are shown respectively. At the mesoscale, PDOS can be used as spectral embeddings of atomic local environments to construct additional features in MLP training data.

[0042] (2) At the mesoscale, non-equilibrium molecular dynamics simulations are performed based on machine learning potential functions to obtain the thermal conductivity, thermal boundary resistance and phonon work spectral density of the polymer composite TIM heterostructure. The force constant matrix obtained from microscale calculations PDOS, polarization intensity phonon spectrum overlap factor The dataset was brought in at the mesoscale and trained using the NequIP framework, including the energy function. and force field function Smooth L1 Loss was used to optimize the energy, atomic force, and polarization response simultaneously. The dataset was divided into training, validation, and test sets in an 8:1:1 ratio. The training objective error was set as follows: energy < 5 meV / atom, atomic force < 0.05 eV / Å.

[0043] At the mesoscale, after obtaining the machine learning potential function (MLP), it was embedded into the LAMMPS platform to perform long-scale molecular dynamics simulations of the interface structure under NVT conditions, collecting phonon velocity time series from different regions. The Green-Kubo method was used to characterize the average kinetic relaxation behavior of phonon populations at different frequencies using the phonon velocity autocorrelation function (VACF).

[0044] The phonon power spectral density (PSD) is obtained by performing a Fourier transform on the VCF:

[0045] PSD reflects the ability of phonons at different frequencies to participate in energy transport. Its peak position and amplitude can be directly compared with PDOS obtained at the microscale to verify the consistency of cross-scale parameters.

[0046] To characterize the transmaterial transport capability of phonons at the interface, a frequency-dependent effective phonon transport coefficient is defined. Based on local PDOS differences, PSD peak intensity, and perturbation of the interface force constant matrix, this method adopts the following expression:

[0047] Among them, and These represent the frequency-dependent phonon impedances of materials 1 and 2, respectively. The polarization enhancement factor takes into account the enhanced interface coupling under flexural polarization, reflecting the "on" effect of the flexural polarization field on the phonon transmission path in a specific frequency range, and can be fitted as follows:

[0048] To further characterize the contribution of high-frequency phonons at the interface, the "mode-selective phonon transport flux" is defined:

[0049] in, wave vector The corresponding phonon mode index; The transmittance is for single-mode phonons. exist The value is 1 for time intervals and 0 for all other intervals, used for frequency filtering. The modal-selective propagation channel number, taking into account both PDOS distribution and interface coupling strength, can reveal the microscopic mechanism by which enhanced modal coupling and propagation channel expansion are achieved in the mid-to-high frequency bands under flexural polarization modulation.

[0050] Once the phonon mode distribution and effective transmission coefficient are obtained, the interfacial thermal boundary resistance (TBR) can be solved based on the frequency-resolved heat flow model.

[0051]

[0052] in, The steady-state heat flux density at the interface, For temperature gradient, This represents the temperature difference between the materials on both sides.

[0053] (3) At the macroscopic scale, a finite element analysis model is established, which includes a heat source, a TIM (thermal induction generator), and a cold source, and its temperature field and heat flux density are calculated. At a macroscopic scale, using the Heat Transfer in Solids module of COMSOL Multiphysics software, a three-layer structure representing a real-world application is constructed: First layer: High heat flux density source region (simulated heat source); Second layer: Adjustable flexible thermal interface material (simulated TIM); The third layer: thermally conductive substrate (simulating a cold source).

[0054] Among them, the thermal conductivity of the second layer TIM material Both the interfacial thermal resistance (TBR) and the input from the mesoscale simulation results are:

[0055]

[0056] in, For normalized weighted functions; The intrinsic interfacial thermal resistance under non-flexible polarization control; The flexural polarization enhancement coefficient; It reflects the degree to which unit polarization intensity contributes to the improvement of phonon transmittance; This represents the frequency-dependent polarization intensity calculated based on the Berry phase method.

[0057] During the simulation, a constant heat flux boundary condition is applied to the upper surface or interior of the first layer to simulate device heating; an isothermal boundary condition is set on the lower surface or a designated area of ​​the third layer to simulate a cold source; and natural convection boundary conditions are set on the outer surface of the model, excluding the loading surface. The steady-state temperature field is obtained through finite element analysis, and key thermal management performance indicators such as regional temperature distribution, heat flux density vector distribution, total thermal resistance, and thermal response time are output. Specific Implementation This embodiment employs the following three-layer structure to verify the feasibility of the method of the present invention: Upper layer (heat source): Simulates β-Ga2O3 semiconductor substrate (high heat flux density region), with a thickness of 10 micrometers; Intermediate (TIM): Simulates a polymer composite TIM with strain gradient response, with a thickness of 1 micrometer; Lower layer (cold source): simulated Al2O3 heat sink substrate, with a thickness of 10 micrometers.

[0059] Multi-scale computation executes three steps sequentially: microscopic → mesoscopic → macroscopic, and is coupled through parameter passing. At the microscopic scale, the PDOS calculation results before and after polarization at different frequencies are as follows: Figure 3 As shown, comparing the spectral lines before and after polarization, the phonon spectrum shift is significant. The calculated results of the phonon spectrum overlap factor before and after polarization are as follows: Figure 4 As shown, the phonon spectrum overlap factor is significantly increased after polarization. At the mesoscale, the changes in phonon transmittance before and after polarization are as follows: Figure 5 As shown in the figure, flexural polarization significantly enhances high-frequency transmission. PSD(ω) is as follows... Figure 6 As shown, this illustrates the frequency range variation that dominates heat dissipation in the TIM. On a macroscopic scale, the thermal conductivity before and after polarization is compared to... Figure 7 As shown in the figure, the thermal conductivity κ increases by more than 20% after polarization. Figure 8 The figure shows the temperature distribution along the cross-sectional direction of the three-layer structure before and after polarization. As can be seen from the figure, the interface resistance is effectively reduced and the heat conduction effect is improved.

[0060] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable by the processor, wherein the processor executes the program to implement the above-described multi-scale simulation method for thermal conduction at polymer composite TIM heterostructure interfaces based on strain gradient response.

[0061] The electronic device can also communicate with one or more external devices (e.g., keyboards, pointing devices, Bluetooth devices, etc.), one or more devices that enable a user to interact with the electronic device, and / or any device that enables the electronic device to communicate with one or more other computing devices (e.g., routers, modems, etc.). This communication can be performed via input / output (I / O) interfaces. Furthermore, the electronic device can communicate with one or more networks (e.g., local area networks (LANs), wide area networks (WANs), and / or public networks, such as the Internet) via a network adapter. The network adapter communicates with other modules of the electronic device via a bus. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with the electronic device, including but not limited to: microcode, device drivers, redundant processors, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0062] From the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, terminal device, or network device, etc.) to execute the methods according to the embodiments of this disclosure.

[0063] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described multi-scale simulation method for thermal conduction at polymer composite TIM heterostructure interfaces based on strain gradient response.

[0064] The readable storage medium may include a readable medium in the form of volatile memory, such as random access memory (RAM) and / or cache memory, and may further include read-only memory (ROM). Program code is stored thereon, which is executed by a processor to cause the processor to perform the steps of the embodiments described in this specification.

[0065] The memory may also include programs / utilities having a set (at least one) of program modules, including but not limited to: an operating system, one or more application programs, other program modules, and program data, each or some combination of these examples may include an implementation of a network environment.

[0066] A bus can represent one or more of several types of bus structures, including a memory bus or memory controller, a peripheral bus, a graphics acceleration port, a processor, or a local bus that uses any of the various bus structures.

[0067] The embodiments should not be regarded as limitations on the present invention, but any improvements made based on the spirit of the present invention should be within the protection scope of the present invention.

Claims

1. A multi-scale simulation method for thermal conduction at polymer composite TIM heterostructure interfaces based on strain gradient response, characterized in that, It employs parameter passing to achieve cross-scale computation, and includes the following steps in sequence: (1) At the microscale, based on first principles, the phonon properties and polarization properties of the polymer composite TIM heterostructure are calculated to obtain the force constant matrix, the phonon density of states and polarization intensity of the materials on both sides of the interface; (2) At the mesoscale, non-equilibrium molecular dynamics simulations are performed based on machine learning potential functions to obtain the thermal conductivity, thermal boundary resistance and phonon work spectral density of the polymer composite TIM heterostructure. (3) At the macroscopic scale, a finite element analysis model is established, which includes a heat source, a TIM (thermal induction generator), and a cold source, and its temperature field and heat flux density are calculated. In this step, the data obtained in step (1) is used as the input parameters or constraints in step (2); and the data obtained in step (2) is used as the input parameters or constitutive relations of the finite element analysis model in step (3).

2. The method for multi-scale simulation of thermal conduction at polymer composite TIM heterostructure interfaces based on strain gradient response according to claim 1, characterized in that: In step (1), S1. Construct an atomic model of the polymer composite TIM heterostructure and form a continuous strain gradient by applying atomic displacement in the interface normal direction. To simulate the strain distribution of TIM under bending deformation; S2. Perform geometric optimization and ground-state energy calculation on the atomic model with strain gradient to obtain the electron density distribution of the system under strain gradient conditions, and calculate the polarization intensity based on the Berry phase method. and quantify strain gradient With polarization intensity Coupling relationship ,in The flexural conductivity of TIM; S3, the polarization intensity Characterized as potential disturbance caused by flexural polarization To obtain the total potential including the flexural effect , This represents the total potential of the system. The intrinsic potential energy is unaffected by flexural polarization. This refers to the potential disturbance caused by flexural polarization. electric potential field The gradient; S4. Based on the total potential, calculate the interatomic force constant matrix using density functional perturbation theory. , ,in , Numbering the atoms within the unit cell; , For Cartesian coordinate components; The matrix of eigenforce constants when unaffected by polarization perturbation. This is the perturbation term caused by flexural polarization; S5, Based on the interatomic force constant matrix Construct and solve the dynamic matrix Obtain the phonon dispersion relation and the phonon state density of the materials on both sides of the interface; S6. Based on the phonon state density of the materials on both sides of the interface, calculate the phonon spectrum overlap factor S between different material components in the composite structure to quantitatively evaluate the interface phonon mode matching degree under strain gradient control.

3. The multi-scale simulation method for thermal conduction at polymer composite TIM heterostructure interfaces based on strain gradient response according to claim 2, characterized in that: Disturbance term caused by flexural polarization It is obtained by calculation using the following formula: ,in , Indicates the first , Atoms in direction , The displacement components.

4. The method for multi-scale simulation of thermal conduction at polymer composite TIM heterostructure interfaces based on strain gradient response according to claim 1, 2, or 3, characterized in that: In step (2), S1. Construct a dataset, which includes the force constant matrix obtained in step (1), the phonon state density, polarization intensity and phonon spectrum overlap factor of the materials on both sides of the interface; S2. Divide the dataset into training, validation, and test sets, and train the energy function using the NequIP framework. and force field function The machine learning potential function was determined, and Smooth L1 Loss was used to jointly optimize the energy, atomic force, and polarization response until the training error reached the target of energy < 5 meV / atom and atomic force < 0.05 eV / Å. S3. Embed the trained machine learning potential function into the LAMMPS platform, perform long-scale molecular dynamics simulation of the interface structure under NVT conditions, and collect the velocity time series of atoms in different regions. S4. Using the Green-Kubo method, the average kinetic energy relaxation behavior of phonon populations at different frequencies is characterized by the phonon velocity autocorrelation function, and the phonon power spectral density is obtained by performing a Fourier transform on the phonon velocity autocorrelation function characterization. S5. Based on local PDOS differences, PSD peak intensity, and interfacial force constant matrix perturbation, through... Obtain the effective phonon transmission coefficient ,in and These represent the frequency-dependent phonon impedances of materials 1 and 2, respectively. It is a polarization enhancement factor; S6. Based on the phonon effective transmission coefficient and phonon mode distribution, through Calculate the mode-selective phonon transport flux, where wave vector The corresponding phonon mode index; The transmittance is for single-mode phonons. exist The value is 1 for the time period and 0 for the rest, used for frequency filtering; S7. Solve for the interfacial thermal boundary resistance (TBR) based on the frequency-resolved heat flow model. , ,in The steady-state heat flux density at the interface, For temperature gradient, This represents the temperature difference between the materials on both sides.

5. The multi-scale simulation method for thermal conduction at polymer composite TIM heterostructure interfaces based on strain gradient response according to claim 4, characterized in that: The polarization enhancement factor through get.

6. The multi-scale simulation method for thermal conduction at polymer composite TIM heterostructure interfaces based on strain gradient response according to claim 4, characterized in that: In step (3), S1. Construct a three-layer physical structure model representing the actual application using software. The three layers are as follows: The first layer represents the heat source, the second layer represents the TIM, and the third layer represents the cold source; S2. Define the thermal conductivity of the second layer material using the simulation results from step 2. The thermal boundary resistance (TBR) of the interface is calculated and imported as an input parameter into the physical structure model. S3: Apply boundary conditions and loads to the physical structure model, including: applying constant heat flux boundary conditions to the upper surface or interior of the first layer to simulate device heating. Set isothermal boundary conditions on the lower surface or designated area of ​​the third layer to simulate a cold source; set natural convection boundary conditions on the outer surface of the model, excluding the loading surface. S4: Perform finite element analysis on the physical structural model with assigned material properties, boundary conditions, and loads to obtain the steady-state temperature field; S5: Based on the solution results of the steady-state temperature field, output thermal management performance indicators including regional temperature distribution cloud map, heat flux density vector distribution map, total thermal resistance of the system and thermal response time.

7. The method for multi-scale simulation of thermal conduction at polymer composite TIM heterostructure interfaces based on strain gradient response according to claim 6, characterized in that: Thermal conductivity in step S2 The interfacial thermal boundary resistance (TBR) is determined by the following function: in, For normalized weighted functions; The intrinsic interfacial thermal resistance under non-flexible polarization control; The flexural polarization enhancement coefficient; It reflects the degree to which unit polarization intensity contributes to the improvement of phonon transmittance; This represents the frequency-dependent polarization intensity calculated using the Berryphase method.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable by the processor, characterized in that, When the processor executes the program, it implements the multi-scale simulation method for thermal conduction at heterogeneous interfaces of polymer composite TIMs based on strain gradient response as described in any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the multi-scale simulation method for thermal conduction at polymer composite TIM heterostructure interfaces based on strain gradient response as described in any one of claims 1 to 7.

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