Method for regulating and controlling atomic scale silicon-silicon and aluminum-aluminum interface thermal conductance

Abstract

The invention relates to a method for regulating and controlling atomic scale silicon-silicon and aluminum-aluminum interface thermal conductance. The method comprises the following steps: (1) establishing a silicon-silicon and aluminum-aluminum molecular dynamics thermal transport model consisting of a hot area and a cold area; (2) executing molecular dynamics simulation and data processing: (1) determining a dependency relationship of interface thermal conductivity on a torsion angle; (2) determining the influence of the overlapping area of the phonon state density on heat transport in different interface contact states; (3) revealing the internal reason of the interface contact state influencing the interface thermal conductivity; (4) determining the dependency relationship of the system temperature on the interface thermal conductance; and (5) calculating the overlapping area of the phonon state density, the phonon number and the phonon participation rate at different temperatures to reveal the internal mechanism that the system temperature affects the interface thermal conductivity. According to the invention, research on silicon-silicon and aluminum-aluminum interface heat transport is carried out based on the torsion angle and temperature, and an important basis is provided for understanding an internal mechanism of heat transfer of solid materials with different contact interfaces and searching an effective method for controlling interface heat conduction.

Description

Technical Field

[0001] The present invention relates to the field of molecular dynamics technology, and in particular to a method for regulating thermal conductivity of silicon-silicon and aluminum-aluminum interfaces at atomic scale. Background Art

[0002] The design of micro-nano electromechanical systems usually uses semiconductor and metal devices, which have the characteristics of precision structure and high power density. However, these characteristics make heat dissipation one of the main factors limiting the performance of micro-nano electromechanical systems. The key to effective heat dissipation lies in the interfacial thermal conductivity (ITC) between materials. When two substances of different temperatures come into contact, heat energy flows from the high-temperature side to the low-temperature side, generating heat flux. ITC describes the amount of heat passing through the interface per unit time, per unit area, and per unit temperature drop. Therefore, regulating the ITC of semiconductor and metal materials is particularly important for the design and thermal management of micro-nano electromechanical systems.

[0003] It is well known that heat transfer at the contact interface is mainly affected by the scattering of hot carriers (phonons, electrons, etc.), and the heat transfer performance of the system usually depends on the regulation method of ITC. In recent years, computational methods such as equilibrium molecular dynamics (EMD), nonequilibrium molecular dynamics (NEMD), and atomic Green's function (AGF) have been widely used to study the interfacial heat transfer process. Researchers have tried to control the interfacial thermal conductivity by controlling lattice matching, interface coupling strength, interface roughness, interface defects, and pressure. Among them, regarding the effect of interface defects on interfacial thermal conductivity, Wang et al. studied the heat transfer at the h-BN / Cu and a-BN / Cu interfaces. The NEMD results showed that inelastic phonon scattering is the intrinsic mechanism for the enhancement of the thermal conductivity of the a-BN / Cu interface. Recently, Wu et al. used a combination of first-principles calculations and MD simulations to study the effect of carbon vacancies on diamond thermal conductivity and Cu / diamond ITC. The results showed that ITC was significantly improved in Cu and diamond heterostructures containing carbon vacancy defects. In addition, Liu et al. used non-equilibrium molecular dynamics simulation to study the effect of interface coupling strength on interfacial heat transport in graphene / MoS2 bilayer heterostructures. The results showed that enhancing the interface coupling strength can enhance the coupling degree of phonons, thereby improving ITC. This phenomenon also exists at the metal-semiconductor interface. Wu et al. used the diffusion mismatch model, acoustic mismatch model and non-equilibrium molecular dynamics method to calculate and analyze the thermal conductivity of C / Cu and Si / Cu interfaces, proving that ITC can be significantly improved by enhancing the interface coupling strength. In order to regulate the coupling degree of the interface, Giri et al. studied the effect of interface coupling strength on ITC through numerical simulation. By inserting a layer of CaTiO3 / SiTiO3 at the interface 0.5 Sr 0.5TiO3 layer was added to improve the coupling degree of the interface, and it was found that the phonon density of states (PDOS) at the interface achieved a perfect match, allowing long-wave phonons to be transmitted across the interface in a ballistic manner, thereby improving the ITC.

[0004] According to lattice dynamics theory, temperature can significantly affect the transport of phonons. As phonons are carriers of heat transport, it is necessary to explore the effect of temperature on ITC. The MD simulations performed by Landry and McGaughey predicted that the ITC at the Si / Ge interface would increase with temperatures above 500K, and they attributed this trend to inelastic phonon scattering. However, Feng et al. used NEMD simulations and Landauer analysis to show that ITC has a strong dependence on temperature even at room temperature. Xu et al. found that with increasing temperature, atomic diffusion at the Al / Cu interface intensified and the interfacial phonon thermal conductivity increased. Wu et al. studied the temperature dependence of ITC at the GaN / Ba heterostructure interface and found that the enhancement of interfacial inelastic phonon scattering caused the phonon transmission coefficient to increase with increasing temperature, thereby increasing ITC.

[0005] In addition to the aforementioned methods that can effectively regulate the interfacial thermal conductivity coefficient, the interfacial contact state at different torsion angles can also have a significant impact on cross-interface heat transfer, but the intrinsic mechanism of interfacial heat transfer at different torsion angles has not yet been fully resolved. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a method for regulating thermal conductivity of silicon-silicon and aluminum-aluminum interfaces at atomic scale.

[0007] To solve the above problems, the present invention provides a method for regulating thermal conductivity of silicon-silicon and aluminum-aluminum interfaces at the atomic scale, comprising the following steps:

[0008] ⑴ Establish a molecular dynamics heat transport model of silicon-silicon and aluminum-aluminum consisting of hot and cold areas, directly change the contact state of the interface by twisting the hot area, and set Berendsen thermostats at both ends of the model to control the temperature of the system;

[0009] The heat region includes a heat transfer atomic region I, a heat source and a rigid body; non-periodic boundary conditions are set in the x, y and z directions;

[0010] The cold region includes a fixed wall, a cold source and a heat transfer atomic zone II;

[0011] A heat transfer interface is formed between the heat transfer atomic region I and the heat transfer atomic region II;

[0012] ⑵Perform molecular dynamics simulation and data processing:

[0013] ① Take the torsion angle range of 5 to 45°, set the heat source and cold source temperatures of the silicon-silicon interface to 320K and 280K respectively, and the heat source and cold source temperatures of the aluminum-aluminum interface to 120K and 80K respectively, and compare the interface thermal conductance at different torsion angles to determine the dependence of the interface thermal conductance on the torsion angle;

[0014] ② Taking the torsion angle range of 5-45°, the heat source and cold source temperatures of the silicon-silicon interface are set to 320K and 280K respectively, and the heat source and cold source temperatures of the aluminum-aluminum interface are set to 120K and 80K respectively, and comparing the overlapping area of ​​the phonon state density at the contact interface under different torsion angles to determine the influence of the overlapping area of ​​the phonon state density on the heat transport of different interface contact states;

[0015] ③ Taking the torsion angle range of 5-45°, the heat source and cold source temperatures of the silicon-silicon interface were set to 320K and 280K respectively, and the heat source and cold source temperatures of the aluminum-aluminum interface were set to 120K and 80K respectively. The phonon participation rate and interlayer distance of the contact interface at different torsion angles were compared to further reveal the intrinsic reason why the interface contact state affects the interface thermal conductivity;

[0016] ④ Take the temperature range of silicon-silicon system as 100K~550K, the temperature range of aluminum-aluminum system as 100K~300K, the temperature difference between the heat source and the cold source is always kept at 40K, compare the interface thermal conductance at different system temperatures, and then determine the dependence of system temperature on interface thermal conductance;

[0017] ⑤ Take the temperature range of silicon-silicon system as 100K~550K, the temperature range of aluminum-aluminum system as 100K~300K, the temperature difference between the heat source and the cold source is always maintained at 40K, calculate the overlapping area, number of phonons, and phonon participation rate of phonon state density at different temperatures to reveal the intrinsic mechanism of the system temperature affecting the interfacial thermal conductivity.

[0018] The molecular dynamics simulation and data processing in step (2) also include: taking the torsion angle as 5 to 45°, comparing the overlapping area, phonon participation rate, and interfacial layer spacing of the phonon state density under different interface contact states, and determining the intrinsic mechanism of the influence of different torsion angles on interfacial heat transport.

[0019] The step (2) of performing molecular dynamics simulation and processing data also includes: taking the temperature range of the silicon-silicon system as 100K~550K, and the temperature range of the aluminum-aluminum system as 100K~300K, comparing the overlapping area, number of phonons, and phonon participation rate of the phonon state density at different system temperatures, and determining the intrinsic mechanism of the influence of different system temperatures on the interface thermal conductivity.

[0020] Compared with the prior art, the present invention has the following advantages:

[0021] 1. The present invention takes silicon-silicon and aluminum-aluminum as research objects, first establishes a molecular dynamics heat transfer model, and then runs the model at different torsion angles and temperatures. By calculating the interface thermal conductivity at different torsion angles and temperatures and processing and analyzing, the dependence of silicon-silicon and aluminum-aluminum interface thermal conductivity on the interface contact state and temperature is determined: in the process of twisting from a small angle to a large angle, the interface atoms are deformed, and the lattice vibration state changes, resulting in a gradual decrease in the overlapping area of ​​the phonon state density, a decrease in the coupling degree of the interface phonons, and a shift of the phonon participation rate in the local direction. Some phonons are trapped inside the lattice, hindering the transmission of interface phonons. At the same time, as the degree of interface mismatch increases, the interlayer distance gradually increases, resulting in a decrease in ITC. In addition, high temperature can also significantly increase the thermal conductivity of the interface, because high temperature will excite more low-frequency phonons with high transmission efficiency to carry energy across the interface for heat transfer. At the same time, the thermal expansion effect of the lattice causes the interface phonon state density to be reconstructed. At the contact interface, the reconstruction of the phonon state density will lead to an increase in the overlapping area of ​​the phonon state density, resulting in additional energy transfer channels. Finally, the increase in phonon participation with increasing temperature indicates that the phonon energy moves toward the nonlocalized modes, contributing more to the interfacial heat transfer, thereby improving the interfacial thermal conductivity.

[0022] 2. The present invention determines the dependence of the interface thermal conductivity on the interface contact state by calculating the interface thermal conductivity at different torsion angles.

[0023] 3. The present invention reveals the intrinsic reason why the interface contact state affects the interface thermal conductivity by statistically analyzing the overlapping area, phonon participation rate and inter-layer distance of the phonon state density at different torsion angles.

[0024] 4. The present invention displays the changing relationship curve between the interface thermal conductivity and the system temperature at different torsion angles by characterizing the interface temperature difference, heat flow and interface thermal conductivity at different torsion angles and system temperatures.

[0025] 5. The present invention reveals the intrinsic mechanism of how system temperature affects interfacial thermal conductivity by extracting the overlapping area, number of phonons, and phonon participation rate of phonon state density at different system temperatures.

[0026] 6. The present invention regulates interfacial heat transport by changing the interfacial contact state and temperature, which provides an important basis for understanding the internal mechanism of heat transfer of solid materials with different contact interfaces and finding effective methods to control interfacial thermal conductivity. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The specific implementation modes of the present invention are further described in detail below in conjunction with the accompanying drawings.

[0028] Figure 1: Molecular dynamics model of silicon-silicon and aluminum-aluminum interface heat transfer system in the embodiment of the present invention. Wherein: a represents the heat transfer model of silicon-silicon system; b represents the heat transfer model of aluminum-aluminum system.

[0029] Figure 2 Schematic diagram of the enlarged interface of 0° and 45° in the embodiment of the present invention. Among them: a and b are the front views of the interface of 0° and 45° of the silicon-silicon system respectively; c and d are the top views of the interface of 0° and 45° of the silicon-silicon system respectively; e and f are the front views of the interface of 0° and 45° of the aluminum-aluminum system respectively; g and h are the top views of the interface of 0° and 45° of the aluminum-aluminum system respectively.

[0030] Figure 3 The dependence of the interface thermal conductivity on the torsion angle in the embodiment of the present invention is shown in Figure 1. Wherein: a is the dependence of the interface thermal conductivity on the torsion angle in the silicon-silicon system; b is the dependence of the interface thermal conductivity on the torsion angle in the aluminum-aluminum system.

[0031] Figure 4 The calculation process of extracting the interface temperature difference between the hot area and the cold area in the embodiment of the present invention is shown in FIG. 1 , where a is the fitting process of the interface temperature difference in the silicon-silicon system; and b is the fitting process of the interface temperature difference in the aluminum-aluminum system.

[0032] Figure 5 1 is the functional relationship between the overlapping area of ​​phonon state density (a) in the silicon-silicon system and the overlapping area of ​​phonon state density (b) in the aluminum-aluminum system and the torsion angle in the embodiment of the present invention.

[0033] Figure 6 1 is the relationship between the phonon participation rate (a) in the silicon-silicon system and the phonon participation rate (b) in the aluminum-aluminum system and the torsion angle in the embodiment of the present invention.

[0034] Figure 7 1 is the relationship between the interfacial layer distance and the torsion angle in the silicon-silicon and aluminum-aluminum systems in the embodiments of the present invention.

[0035] Figure 8 The dependence of different temperatures on the interface thermal conductivity at different torsion angles in the silicon-silicon system (a) and the dependence of different temperatures on the interface thermal conductivity at different torsion angles in the aluminum-aluminum system (b) in the embodiment of the present invention.

[0036] Fig. 9 Figure 3 is the relationship between the number of phonons with a torsion angle of 15° in a silicon-silicon system (a), the number of phonons with a torsion angle of 45° in a silicon-silicon system (c), the number of phonons with a torsion angle of 15° in an aluminum-aluminum system (b), the number of phonons with a torsion angle of 45° in an aluminum-aluminum system (d) and the system temperature in an embodiment of the present invention.

[0037] Fig.101 is the functional relationship between the overlapping area of ​​phonon state density (a) in the silicon-silicon system and the overlapping area of ​​phonon state density (b) in the aluminum-aluminum system and the system temperature in the embodiment of the present invention.

[0038] Fig.11 1 is the relationship between the phonon participation rate (a) in the silicon-silicon system, the phonon participation rate (b) in the aluminum-aluminum system and the system temperature in the embodiment of the present invention. DETAILED DESCRIPTION

[0039] A method for regulating thermal conductivity of silicon-silicon and aluminum-aluminum interfaces at the atomic scale, comprising the following steps:

[0040] ⑴ Establish a molecular dynamics heat transport model of silicon-silicon and aluminum-aluminum consisting of hot and cold areas, directly change the contact state of the interface by twisting the hot area, and set Berendsen thermostats at both ends of the model to control the temperature of the system;

[0041] Among them: the hot region includes the heat transfer atomic zone I, the heat source and the rigid body; non-periodic boundary conditions are set in the x, y and z directions;

[0042] The cold region includes fixed walls, cold sources, and heat transfer atomic zone II;

[0043] A heat transfer interface is formed between the heat transfer atomic region I and the heat transfer atomic region II.

[0044] ⑵Perform molecular dynamics simulation and data processing:

[0045] ① Take the torsion angle range of 5 to 45°, set the heat source and cold source temperatures of the silicon-silicon interface to 320K and 280K respectively, and the heat source and cold source temperatures of the aluminum-aluminum interface to 120K and 80K respectively, and compare the interface thermal conductance at different torsion angles to determine the dependence of the interface thermal conductance on the torsion angle;

[0046] ② Taking the torsion angle range of 5-45°, the heat source and cold source temperatures of the silicon-silicon interface are set to 320K and 280K respectively, and the heat source and cold source temperatures of the aluminum-aluminum interface are set to 120K and 80K respectively, and comparing the overlapping area of ​​the phonon state density at the contact interface under different torsion angles to determine the influence of the overlapping area of ​​the phonon state density on the heat transport of different interface contact states;

[0047] ③ Taking the torsion angle range of 5-45°, the heat source and cold source temperatures of the silicon-silicon interface were set to 320K and 280K respectively, and the heat source and cold source temperatures of the aluminum-aluminum interface were set to 120K and 80K respectively. The phonon participation rate and interlayer distance of the contact interface at different torsion angles were compared to further reveal the intrinsic reason why the interface contact state affects the interface thermal conductivity;

[0048] ④ Take the temperature range of silicon-silicon system as 100K~550K, the temperature range of aluminum-aluminum system as 100K~300K, the temperature difference between the heat source and the cold source is always kept at 40K, compare the interface thermal conductance at different system temperatures, and then determine the dependence of system temperature on interface thermal conductance;

[0049] ⑤ Take the temperature range of silicon-silicon system as 100K~550K, the temperature range of aluminum-aluminum system as 100K~300K, the temperature difference between the heat source and the cold source is always maintained at 40K, calculate the overlapping area, number of phonons, and phonon participation rate of phonon state density at different temperatures to reveal the intrinsic mechanism of the system temperature affecting the interfacial thermal conductivity.

[0050] The present invention further includes performing molecular dynamics simulation and processing data:

[0051] The twist angle is 5 to 45°, and the overlapping area, phonon participation rate, and interfacial layer spacing of the phonon state density under different interface contact states are compared to determine the intrinsic mechanism of the influence of different twist angles on interfacial heat transport.

[0052] The temperature range of the silicon-silicon system is 100K~550K, and the temperature range of the aluminum-aluminum system is 100K~300K. The overlapping area, number of phonons, and phonon participation rate of the phonon state density at different system temperatures are compared to determine the intrinsic mechanism of the influence of different system temperatures on the interface thermal conductivity.

[0053] Example

[0054] This invention takes silicon-silicon and aluminum-aluminum systems as research objects, and explores the research methods of interface contact state and temperature-controlled interface heat transport mechanism.

[0055] The specific process is as follows:

[0056] (1) Establishment of molecular dynamics model

[0057] like Figure 1 As shown, an interfacial heat transport and heat transfer system consisting of a hot area and a cold area is established to explore the intrinsic mechanism of heat transport at the silicon-silicon and aluminum-aluminum interfaces.

[0058] The present invention constructs a Si-Si and Al-Al vertical stacking structure consisting of a heat source and a cold source, with a torsion angle of 45°. The torsion angle is defined as the angle at which the hot zone rotates relative to the cold zone along the z-axis. In order to ensure that the contact area between models with different torsion angles is consistent, the hot zone is designed to be much larger than the cold zone during the modeling process. After applying the required torsion to the hot zone, it is trimmed according to the size of the cold zone so that the hot zone is the same size as the cold zone. The dimensions of the Si-Si interface model along the x, y, and z directions are 21×21×15 regular unit cells (UC); the dimensions of the Al-Al interface model along the x, y, and z directions are 25×25×15 regular UCs. The system transfers heat along the z-axis, and a UC is set at both ends as a fixed wall. The two UCs adjacent to the fixed wall are designated as temperature control zones, which are called heat sources and heat sinks, respectively. The system adopts non-periodic boundary conditions along the x, y, and z directions.

[0059] The system was initially relaxed in the canonical ensemble (NVT) for 100 ps with a time step of 0.5 fs. Subsequently, the simulation was transferred to the microcanonical ensemble (NVE) and the temperatures of the heat source and heat sink were regulated using a Berendsen thermostat. The temperature regulation regions for the Si-Si interface were set to 320 K and 280 K, respectively, while the temperature regulation regions for the Al-Al interface were set to 120 K and 80 K, respectively. After the system was fully equilibrated, the simulation was run for 500 ps to obtain stable temperature distribution and heat flow data, which were used to calculate the ITC.

[0060] The present invention adopts the Stillinger-Weber (SW) potential of Vink et al. to describe the interaction between silicon atoms. The SW potential is also applicable to the interaction between interfaces. The embedded atom method (EAM) potential of Ercolessi et al. is applicable to simulate the interaction between silicon atoms and is used to describe the interaction between Al atoms and the effect between interfaces.

[0061] All molecular dynamics simulations were performed using the LAMMPS software package.

[0062] (2) Determine the effect of different torsion angles on heat transport at Si-Si and Al-Al interfaces

[0063] The Si-Si and Al-Al interface heat transfer models are used to study the heat transfer behavior of the interface under different torsion angles. The torsion angle is selected in the range of 5-45°, the heat source and cold source temperatures of the Si-Si interface are set to 320K and 280K, respectively, and the heat source and cold source temperatures of the Al-Al interface are set to 120K and 80K, respectively. The interface thermal conductance under different torsion angles is compared to determine the dependence of the interface thermal conductance on the torsion angle.

[0064] The temperature difference at the interface, represented by the symbol ΔT, is determined by the temperature position curve, such as Figure 4a and 4b. The system is divided into hot and cold zones along the z axis, each zone containing six plate layers. The temperature of each plate layer is calculated based on the atomic velocity. The average temperature of each section is then calculated, and the temperature T of the hot zone is determined using a linear fitting method. h and the temperature of the cold zone T c . It can be seen that the temperature difference at the interface is given by the following formula: ΔT = T h -T c .wen

[0065] The Berendsen thermostat is designed to adjust the heat source and heat sink area to achieve the desired temperature, so that the system can generate heat flux in the z direction. After the system relaxes and equilibrates, the heat flux can be obtained by plotting the thermal energy absorbed by the Berendsen thermostat versus time. The least squares method is used to linearly fit the curve, where the slope represents the heat flux. Therefore, the heat flux J can be expressed as Where: Q represents the heat absorbed or removed by the thermostat, unit: eV; A represents the area of ​​the contact interface, unit: m 2 ; t represents simulation time, unit: s.

[0066] The interfacial thermal conductivity of Si-Si and Al-Al interfaces is described by the interface form of Fourier's law. The interfacial thermal conductivity is expressed as Where G represents the interfacial thermal conductivity, unit: MW / m 2 K; ΔT represents the temperature difference between the hot area and the cold area, unit: K.

[0067] Figure 3 Figures 3a and 3b show the effect of twist angle on ITC of Si-Si and Al-Al interfaces at different temperatures. The results show that with the increase of twist angle, ITC gradually decreases, and at a smaller angle, the ITC value reaches the maximum. At 300K, the ITC of Si-Si interface and Al-Al interface are 6400MW / m 2 K and 11000MW / m 2 At 100K, the ITCs of Si-Si interface and Al-Al interface are 3800MW / m 2 K and 7100MW / m 2 K; when the twist angle reaches 45°, the ITC of the Si-Si interface decreases to about 650MW / m 2 K and 830MW / m 2 K; the ITC of Al-Al interface at 100K and 300K is reduced to about 2030MW / m 2 K and 1795MW / m 2 K.

[0068] It is worth noting that the use of stronger SW and EAM potentials at the contact interface leads to a higher degree of interface coupling. Therefore, the interface thermal conductivity calculated by MD simulation is higher than the experimental value, but this does not affect the variation trend of the interface thermal conductivity at different torsion angles.

[0069] (3) Determine the influence of overlapping area of ​​phonon state density, phonon participation rate, and interfacial layer distance on interfacial thermal conductivity

[0070] In order to further reveal the intrinsic mechanism of the torsion angle affecting interfacial thermal conductivity, the present invention extracted the overlapping area of ​​phonon state density, phonon participation rate, and interfacial layer distance, and determined the dependence of interfacial thermal conductivity on the torsion angle.

[0071] Since the energy is carried by phonons, in order to further analyze the evolution mechanism of cross-interface heat transfer at different torsion angles, the present invention extracts the phonon state density at the contact interface to monitor the contribution of phonons to heat transport. The calculation formula is:

[0072]

[0073] Where: PDOS(ω) represents the phonon state density, unit: au; ω represents the vibration frequency, unit: Thz; t represents the time, unit: s; τ represents the total vibration time, unit: s; i represents the atomic number from which the phonon state density is extracted;<v(t)v(0)> represents the velocity autocorrelation function.

[0074] From the perspective of lattice dynamics, the interfacial phonon heat transport between two materials depends largely on the overlap of their phonon state densities. The present invention introduces the concept of phonon state density overlap area to further quantitatively compare the differences in lattice vibration matching at the interface, which can be calculated as:

[0075]

[0076] Where: PDOS overlap represents the overlapping area of ​​phonon state density; ω represents the vibration frequency, unit: Thz; DOS c Represents the phonon state density in the cold region, unit: au; DOS h Represents the phonon state density in the thermal region, in units of au.

[0077] The larger the overlapping area of ​​phonon state density, the greater the degree of phonon vibration matching, which is conducive to more efficient energy transfer between the two. Based on the calculation results of phonon state density, the area of ​​phonon state density overlap is obtained by integrating the overlapping parts of the hot zone and cold zone phonon spectra. The overlapping area of ​​phonon state density at Si-Si and Al-Al interfaces decreases with the increase of torsion angle, such as Figure 5a and 5b. The smaller overlapping area of ​​the phonon state density means that the phonon coupling is weak and the band structure does not match. The mismatch of the interface band structure makes it impossible to establish an effective energy transfer channel on the interface, the number of channels for phonons to transfer heat through the contact interface is reduced, the heat transfer efficiency of the interface is reduced, and the interface thermal conductivity decreases with the increase of the torsion angle.

[0078] In order to elucidate the mechanism of phonon localization within the structure, the phonon participation rate (PPR) at the interface was calculated:

[0079]

[0080] Where: PPR(ω) represents the phonon participation rate; N represents the total number of atoms in the calculation of the phonon participation rate; PDOS i (ω) represents the phonon state density of the ith atom, unit: au.

[0081] PPR can be used as an indicator to evaluate the degree of phonon localization and its effect on interfacial thermal conductivity. According to the results of previous studies, a PPR exceeding 0.4 indicates the presence of non-localized modes, which has a beneficial effect on thermal energy transfer. Figure 6 As shown in Figures 6a and 6b, at relatively small angles, the PPR of phonons is greater than 0.4, indicating that the phonons at these angles are in non-local modes and contribute more to heat transfer. At larger torsion angles, the PPR shifts toward local modes, and the PPR value of optical phonon modes in the high-frequency region decreases significantly, thereby limiting its contribution to heat transfer. The PPR results show that as the torsion angle increases, the PPR gradually shifts toward local modes, and the phonon energy is more confined inside the lattice. This leads to reduced phonon transmission, which contributes little to cross-interface heat transport, and ultimately leads to a decrease in interfacial thermal conductivity.

[0082] contrast Figure 5 a and Figure 2 a. Figure 5 b and Figure 2 b found that although the overlapping area of ​​phonon state density gradually decreases with the increase of torsion angle, the decrease is relatively small and inconsistent with the change trend of interface thermal conductivity under different torsion angles. Therefore, it is believed that other factors affect the change of interface thermal conductivity. Previous studies have shown that the change of interlayer distance can significantly affect the thermal transport of the interface. The definition of interlayer distance in this invention is as follows Figure 7 As shown in the middle illustration. Subsequently, the interlayer distances at different twist angles were extracted. As the twist angle increases, the interlayer distance of the interface gradually increases, as shown in Figure 7As shown. When the contact interface is twisted, the stacking state of atoms at the interface changes from AA stacking to AB stacking, and the atomic structure at the interface becomes mismatched, resulting in a change in the distance between the interface layers. As the interlayer spacing increases, the potential energy interaction at the contact interface weakens, the interface coupling weakens, and the number of heat conduction channels decreases, resulting in a decrease in the interface heat transfer efficiency. In addition, the irregular arrangement of atoms at the interface increases the scattering of phonons and reduces the transmission of phonons at the interface, resulting in a decrease in the thermal conductivity of the interface. Current studies have shown that the change in interface thermal conductivity at different torsion angles is mainly the result of the combined effect of the coupling strength of the phonon state density at the contact interface and the change in interlayer spacing. These two factors jointly affect the characteristics of the interface thermal conductivity.

[0083] (4) Determine the effect of temperature on heat transport at Si-Si and Al-Al interfaces

[0084] Temperature is also important for interfacial heat transport. Additional calculations were performed to gain insight into the effect of temperature on ITC at different twist angles, such as Figure 8 a and 8b. The Berendsen thermostat is still used to adjust the temperature to achieve different target temperatures. After reaching a steady state, the variation trend of the thermal conductivity of the Si-Si interface between the average temperature of 100K and 550K, and the variation trend of the thermal conductivity of the Al-Al interface between 100K and 300K are calculated. The interface thermal conductivity of the Si-Si and Al-Al interfaces at different torsion angles and different temperatures is extracted, and the results are shown in Figure 8 a and 8b. In the whole temperature range, the interface thermal conductivity of Si-Si and Al-Al contact interfaces with a twist angle of 15° is always lower than that of 45°, and the ITC of Si-Si and Al-Al interfaces increases with increasing temperature. This is similar to the previous research results on the interface thermal resistance of double-layer films at different temperatures.

[0085] (5) Determine the effect of temperature on the overlap area, number of phonons, and phonon participation rate of phonon state density

[0086] Phonons are the medium of interfacial heat transfer. The heat transfer at the interface can be quantified by the number of phonons excited at the contact interface, which can be calculated as:

[0087]

[0088] Where: N(ω) represents the number of phonons; N v It represents the number of atoms per unit volume; m represents the atomic mass, unit: amu; ω represents the vibration frequency, unit: Thz; is the reduced Planck constant; K B is the Boltzmann constant; t represents time, unit: s;<v(t)v(0)> represents the velocity autocorrelation function.

[0089] Fig. 9 The figure shows the change in the number of phonons at the Si-Si and Al-Al interfaces at different temperatures. As the temperature increases, the number of interface phonons at the Si-Si and Al-Al interfaces with different torsion angles continues to increase, and the number of low-frequency phonons increases significantly. The relationship between the number of phonons and temperature can be explained by the lattice dynamics theory. Temperature is a manifestation of atomic vibration in the crystal structure. At high temperatures, the atomic vibrations in the lattice are more intense, which will cause more atoms to be in an excited state, thereby exciting more phonons. This phenomenon is called the thermal excitation effect. According to the Planck hypothesis theory, the energy of phonons is proportional to the frequency. Low-frequency phonons have lower energy and smaller energy barriers, making it easier to pass through the interface. Therefore, as the temperature increases, more low-frequency phonons with high transmission efficiency are excited to carry energy for cross-interface heat transfer, which is beneficial to enhancing the thermal conductivity of the interface.

[0090] In addition, the test results of the overlapping area of ​​phonon state density of Si-Si and Al-Al interfaces at different temperatures and torsion angles are as follows: Fig.10 As shown in Figures 10a and 10b, it is found that the overlapping area of ​​the phonon state density gradually increases with increasing temperature and decreases with increasing torsion angle. The main reason for the increase in the overlapping area of ​​the phonon state density and the phonon state density with increasing temperature is that with increasing temperature, the thermal vibration energy of atoms increases, and the lattice undergoes thermal expansion, which is manifested as an increase in the lattice constant and an increase in the average distance between atoms in the lattice, resulting in an increase in thermal stress with increasing temperature. As the temperature increases, the thermal expansion gradually increases. Due to the presence of strong covalent bonds and metallic bonds at the interface, the tensile effect of the interatomic bonds increases, which in turn causes the stress of atoms at the interface to increase with increasing temperature. Thermal expansion causes changes in the lattice structure, and the change in the lattice vibration state leads to the reconstruction of the phonon state density at the interface, which in turn affects the coupling degree of the phonon spectrum at the interface. The increase in the overlapping area of ​​the phonon state density strongly proves that the coupling strength of phonons at the contact interface is enhanced, an effective energy transfer channel is formed at the interface, and the number of channels for phonons to transfer heat through the contact interface increases, thereby improving the efficiency of phonons transferring heat across the interface, resulting in an increase in the thermal conductivity of the interface.

[0091] Finally, the phonon participation rates of Si-Si and Al-Al interfaces at different temperatures were calculated, as Fig.11 As shown in the figure, the phonon participation rate gradually increases with increasing temperature, which is consistent with the observed trend of the PDOS overlap area at the interface. A high participation rate indicates that the phonon energy is non-local and contributes more to heat transfer, indicating that increasing temperature will excite more phonon modes to participate in heat transfer between interfaces, thereby increasing the thermal conductivity of the interface.

[0092] In summary, the present invention provides an important basis for understanding the internal mechanism of heat transfer in solid materials with different contact interfaces and for finding effective methods to control interface thermal conductivity based on the study of the effect of torsion angle and temperature on heat transport at Si-Si and Al-Al interfaces.

[0093] The technical solution provided by the present invention is described in detail above. The principle and implementation mode of the present invention are described in detail using specific embodiments herein, and the explanation of the above embodiments is only used to help to deeply understand the method and core idea of ​​the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made to the present invention without departing from the principle of the present invention, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A method for regulating thermal conductivity of silicon-silicon and aluminum-aluminum interfaces at the atomic scale, comprising the following steps: ⑴ Establish a molecular dynamics heat transport model of silicon-silicon and aluminum-aluminum consisting of hot and cold areas, directly change the contact state of the interface by twisting the hot area, and set Berendsen thermostats at both ends of the model to control the temperature of the system; The heat region comprises a heat transfer atomic zone I, a heat source and a rigid body; x , y , z Set non-periodic boundary conditions in the direction; The cold region includes a fixed wall, a cold source and a heat transfer atomic zone II; A heat transfer interface is formed between the heat transfer atomic region I and the heat transfer atomic region II; ⑵Perform molecular dynamics simulation and data processing: ① Taking the torsion angle range of 5~45°, the heat source and cold source temperatures of the silicon-silicon interface are set to 320 K and 280 K respectively, and the heat source and cold source temperatures of the aluminum-aluminum interface are set to 120 K and 80 K respectively, and comparing the interface thermal conductance at different torsion angles to determine the dependence of the interface thermal conductance on the torsion angle; ② Taking the torsion angle range of 5~45°, the heat source and cold source temperatures of the silicon-silicon interface are set to 320 K and 280 K, respectively, and the heat source and cold source temperatures of the aluminum-aluminum interface are set to 120 K and 80 K, respectively. Compare the overlapping area of ​​the phonon state density at the contact interface under different torsion angles to determine the influence of the overlapping area of ​​the phonon state density on the heat transport of different interface contact states; ③ Taking the torsion angle range of 5~45°, the heat source and cold source temperatures of the silicon-silicon interface were set to 320 K and 280 K, respectively, and the heat source and cold source temperatures of the aluminum-aluminum interface were set to 120 K and 80 K, respectively. The phonon participation rate and interlayer distance of the contact interface at different torsion angles were compared to further reveal the intrinsic reason why the interface contact state affects the interface thermal conductivity; ④ Take the temperature range of silicon-silicon system as 100 K~550 K, the temperature range of aluminum-aluminum system as 100 K~300 K, the temperature difference between the heat source and the cold source is always kept at 40 K, compare the interface thermal conductance at different system temperatures, and then determine the dependence of system temperature on interface thermal conductance; ⑤ The temperature range of the silicon-silicon system is 100 K~550 K, and the temperature range of the aluminum-aluminum system is 100 K~300 K. The temperature difference between the heat source and the cold source is always maintained at 40 K. The overlapping area, number of phonons, and phonon participation rate of the phonon state density at different temperatures are calculated to reveal the intrinsic mechanism by which the system temperature affects the interfacial thermal conductivity.

2. A method for regulating thermal conductivity of silicon-silicon and aluminum-aluminum interfaces at atomic scale according to claim 1, characterized in that: The molecular dynamics simulation and data processing in step (2) also include: taking the torsion angle of 5 to 45°, comparing the overlapping area, phonon participation rate, and interfacial layer spacing of the phonon state density under different interface contact states, and determining the intrinsic mechanism of the influence of different torsion angles on interfacial heat transport.

3. A method for regulating thermal conductivity of silicon-silicon and aluminum-aluminum interfaces at atomic scale according to claim 1, characterized in that: The step (2) of performing molecular dynamics simulation and processing data also includes: taking the temperature range of the silicon-silicon system as 100 K~550K, and the temperature range of the aluminum-aluminum system as 100 K~300 K, comparing the overlapping area, number of phonons, and phonon participation rate of the phonon state density at different system temperatures, and determining the intrinsic mechanism of the influence of different system temperatures on the interface thermal conductivity.

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