Method for regulating and controlling thermal conductivity of nano semiconductor interface in contact and non-contact states

Abstract

The invention relates to a method for regulating and controlling thermal conductivity of a nanometer semiconductor interface in contact and non-contact states. The method comprises the following steps: (1) establishing a molecular dynamics thermal transport model consisting of a hot area A and a cold area B; (2) executing molecular dynamics simulation and data processing: comparing interface thermal conductance at different torsion angles in a contact state and a non-contact state so as to determine a dependency relationship of the interface thermal conductance on the torsion angles; in the contact state, comparing the overlapping areas of the phonon state densities at the contact interface under different torsion angles, and determining the influence of the overlapping areas of the phonon state densities on heat transport of different interface torsion angles; and in a non-contact state, comparing the force constants of the interface interaction potential and the LJ potential at different torsion angles, and determining the influence of the force constants on heat transport in different interface torsion angle states. By regulating and controlling the torsion angle, the normal load and the potential well depth, effective regulation and control of the ITC are realized, and an important basis is provided for thermal management of a nano device.

Description

Technical Field

[0001] The present invention relates to the technical field of molecular dynamics, and particularly relates to a method for regulating the interfacial thermal conductance of a nano-semiconductor under contact and non-contact states. Background Art

[0002] In high-power density devices and highly integrated chips, it is crucial to control and understand the thermal management of materials at the nanoscale. With the rapid development of high-power density devices and the further improvement of chip integration, a large amount of heat accumulates at the interface, and the chip heating power density increases linearly, which has become the main obstacle restricting the further improvement of semiconductor integration. Therefore, effectively solving the heat dissipation problem is crucial for the service life and reliability of semiconductor devices. In order to significantly improve the heat dissipation efficiency of semiconductor devices and achieve energy conservation and consumption reduction, regulating the interfacial thermal conductance (ITC) has become a key measure.

[0003] Researchers have proposed various strategies, including interlayer coupling strength, changing interface roughness, using interface nanostructures, introducing defects, changing interface mixing, and applying external strain, etc. Wang et al. studied the introduction of controlled concentrations of vacancy defects on the substrate surface of 2D-MoS2 / 3D-GaN to enhance the ITC of the 2D / 3D interface and the thermal conductivity of 2D materials. Kelayeh et al. regulated the interfacial thermal resistance of the Si / Ge heterojunction by changing the content of Si / Ge at the interface (mixed region). Gordiz et al. studied the phonon transport at the interface of crystalline silicon (Si) and germanium (Ge), especially the contribution of interface vibration modes to heat transport. Chen et al. studied the regulation of Kapitza thermal resistance in few-layer graphene (FLG) by strain engineering through molecular dynamics simulation, thus proving that the thermal resistance can be controlled by applying mechanical strain.

[0004] Interfacial heat transport can also be regulated by system size, temperature, and phonon coupling strength. Liu et al. deeply analyzed the influence of the number of graphene layers and temperature on the interfacial thermal conductance of the diamond / graphene heterostructure. The results show that the interfacial thermal conductance of the diamond / single-layer graphene heterostructure is significantly better than that of the diamond / multi-layer graphene structure, and is at least twice that of the latter; high temperature can also effectively promote interfacial heat transport. Liu et al. studied the influence of factors such as temperature, size, and material defects on the thermal conductivity of the graphene / SiC heterojunction interface through non-equilibrium molecular dynamics simulation, indicating the influence of phonon density of states and interfacial coupling strength on interfacial heat transfer. Ding et al. studied the influence of phonon coupling strength on the interfacial thermal conductance in the graphene / MoS2 heterostructure, indicating that the main channel of heat transport is the coupling between low-frequency out-of-plane phonons.

[0005] In the research on regulating interfacial thermal conductance using the lattice mismatch method, the twist angle has been proven to be one of the important means to adjust the thermal properties of materials. Specifically, the influence of the interlayer twist angle on phonon dispersion, such as the phonon modes of interlayer coupling and moiré patterns, was mainly discussed. Ren et al. studied the effect of interlayer twist on heat transfer in graphene / h-BN van der Waals heterostructures and found that rotation can generate moiré patterns, and this structural change can regulate the interlayer interaction potential and phonon modes, achieving effective control of phonon transport. Li et al. studied the effect of the twist angle on the ITC of bilayer MoS2, and the results showed that the twisted bilayer affects the interlayer vdW coupling interaction, which in turn leads to changes in the interfacial adhesion strength and phonon interfacial transport.

[0006] The thermal management of electronic components involves both contact and non-contact states. From the existing research, certain progress has been made in the regulation of ITC, and it can be effectively regulated under various working conditions. However, for the contact and non-contact states, the internal mechanism of the twist angle on the thermal conductivity has not been thoroughly resolved and further research is still needed. Si and Ge, as typical semiconductor materials, have unique advantages in studying the lattice mismatch problem in the contact and non-contact states of the interface. They have exactly the same diamond cubic crystal structure and similar lattice constants. More importantly, the Si-Si and Ge-Ge systems provide an ideal platform for studying the influence of the twist angle and interfacial interaction on heat conduction. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a method for regulating the interfacial thermal conductance of nano-semiconductors in contact and non-contact states.

[0008] To solve the above problems, a method for regulating the interfacial thermal conductance of nano-semiconductors in contact and non-contact states according to the present invention includes the following steps:

[0009] ⑴ Establish a molecular dynamics heat transport model composed of a hot region A and a cold region B, where A and B represent silicon-silicon (Si-Si) and germanium-germanium (Ge-Ge) respectively, and the two materials have the same lattice structure;

[0010] The hot region A includes a silicon or germanium heat transfer atom region, a heat source, and a rigid body, and non-periodic boundary conditions are set in the x, y, and z directions;

[0011] The cold region B includes a silicon or germanium heat transfer atom region, a cold source, and a fixed layer;

[0012] The rigid body and the fixed layer are each composed of a single unit cell and are respectively arranged at both ends of the z direction of the model;

[0013] A heat transfer interface is formed between the hot region A and the cold region B;

[0014] Berendsen thermostats are respectively set at both ends of the model to control the temperature of the system;

[0015] ⑵ Perform molecular dynamics simulation and data processing:

[0016] ① In the contact state, the torsional angle range is taken as 5 - 45°, and the heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces are respectively set as 320K and 280K. Compare the interfacial thermal conductances at different torsional angles to determine the dependence of the interfacial thermal conductance on the torsional angle; and compare the overlapping areas of the phonon density of states at the contact interface at different torsional angles to determine the influence of the overlapping area of the phonon density of states on the heat transport at different interfacial torsional angles;

[0017] ② In the non-contact state, the torsional angle range is taken as 0 - 45°, and the heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces are respectively set as 320K and 280K. Compare the interfacial thermal conductances at different torsional angles to determine the dependence of the interfacial thermal conductance on the torsional angle; and compare the interfacial interaction potential and the force constant of the LJ (Lennard-Jones) potential at different torsional angles to determine the influence of the force constant on the heat transport in different interfacial torsional angle states, and further reveal the internal reason for the influence of different torsional angles on the interfacial heat transport in the non-contact state.

[0018] The molecular dynamics simulation and data processing in the step ⑵ also include: in the contact state, the torsional angle range is taken as 5 - 45°, and the heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces are respectively set as 320K and 280K. Compare the phonon participation rate and the interfacial distance of the contact interface at different torsional angles to further reveal the internal reason for the influence of the interfacial contact state on the interfacial thermal conductance.

[0019] The molecular dynamics simulation and data processing in the step ⑵ also include: in the non-contact state, the heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces are respectively set as 320K and 280K. Calculate the interfacial interaction potential and the force constant of the LJ (Lennard-Jones) potential under different normal loads or when changing the potential well depth, and reveal the internal mechanism of the influence of the system normal load and potential well depth on the interfacial thermal conductance.

[0020] The present invention has the following advantages compared with the prior art:

[0021] 1. In the present invention, atomic-level silicon-silicon and germanium-germanium are used as the research objects, and a corresponding heat transport system model is established to study the regulation mechanism of the torsional angle on the interfacial heat transport in the contact and non-contact states.

[0022] 2. The present invention determines the regulation mechanism of the torsional angle on the interfacial heat transport in the contact and non-contact states by calculating the interfacial thermal conductances at different torsional angles in the contact and non-contact states.

[0023] 3. In the contact state, the present invention reveals the internal reasons affecting the interfacial thermal conductance by combining the overlapping area of phonon density of states and the phonon participation ratio at different torsion angles.

[0024] 4. In the non-contact state, the present invention evaluates the dependence of ITC on the torsion angle from the perspectives of LJ potential, force constant, etc.

[0025] 5. In the non-contact state, by regulating the normal load and the depth of the potential well, the present invention systematically analyzes the changes in the interfacial interaction potential and the force constant of the LJ potential, and reveals the internal mechanism of the influence of the system normal load and the depth of the potential well on the interfacial thermal conductance.

[0026] 6. By changing the torsion angle, applying a normal load, and changing the depth of the potential well, the present invention realizes the effective regulation of ITC. This discovery provides an important basis for the effective thermal management of nanoscale devices, and thus provides theoretical guidance for the design of nanodevices with controllable interfacial thermal conductance. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The following further elaborates on the specific embodiments of the present invention with reference to the drawings.

[0028] Figure 1 It is a schematic diagram of the heat transfer model of the system and the atomic stacking states of the A-B interface at different torsion angles in the embodiment of the present invention. Among them: (a) is the heat transfer model, where A and B represent Si-Si and Ge-Ge respectively; (b) is the front view of the atomic stacking state of the A-B interface when the torsion angle is 0°; (c) is the front view of the atomic stacking state of the A-B interface when the torsion angle is 45°; (d) is the top view of the atomic stacking state of the A-B interface when the torsion angle is 0°; (e) is the top view of the atomic stacking state of the A-B interface when the torsion angle is 45°.

[0029] Figure 2 It is the ITC of the A-B interface at different system lengths and torsion angles in the embodiment of the present invention. Among them: (a) ITC of the Si-Si interface under different system sizes; (b) ITC of the Ge-Ge interface under different system sizes; (c) ITC and interfacial binding energy of Si-Si; (d) ITC and interfacial binding energy of Ge-Ge.

[0030] Figure 3 It is the overlapping area of phonon density of states of the A-B interface at different torsion angles in the embodiment of the present invention. The inset shows the phonon correlation factor at different torsion angles. Among them: (a) Si-Si interface; (b) Ge-Ge interface.

[0031] Figure 4Phonon participation rates at twist angles of 5°, 15°, 35°, and 45° in the embodiments of the present invention. Among them: (a) Si-Si interface; (b) Ge-Ge interface.

[0032] Figure 5 Graph of the change in the interface distance between the cold region and the hot region at different twist angles in the embodiments of the present invention. Among them: (a) Si-Si interface; (b) Ge-Ge interface.

[0033] Figure 6 ITC at different twist angles under the SW-LJ potential energy in the embodiments of the present invention. Among them: (a) Si-Si interface; (b) Ge-Ge interface.

[0034] Figure 7 Interface distance, LJ potential, and force constant of the A-B interface at different twist angles when the normal load applied in the z direction is 45 nN in the embodiments of the present invention. Among them: (a) Interface distance of the Si-Si interface at different twist angles; (b) Interface distance of the Ge-Ge interface at different twist angles; (c) LJ potential between the Si-Si interfaces at different twist angles; (d) LJ potential between the Ge-Ge interfaces at different twist angles; (e) Force constant between the Si-Si interfaces at different twist angles; (f) Force constant between the Ge-Ge interfaces at different twist angles.

[0035] Figure 8 Influence of different normal loads and interface potential well depths on the thermal conductivity of the Si-Si and Ge-Ge interfaces at twist angles of 0° and 45° in the embodiments of the present invention. Among them: (a) Case where the twist angle of the Si-Si interface is 0°; (b) Case where the twist angle of the Si-Si interface is 45°; (c) Case where the twist angle of the Ge-Ge interface is 0°; (d) Case where the twist angle of the Ge-Ge interface is 45°.

[0036] Figure 9 Influence of different normal loads on the interface thermal conductivity and influence of the interface potential well depth parameter and different normal loads on the interface distance in the embodiments of the present invention. Among them: (a) Influence of different normal loads on the interface thermal conductivity of Si-Si at twist angles of 0° and 45° with the same interface potential well depth; (b) Influence of different normal loads on the interface thermal conductivity of the Ge-Ge interface at twist angles of 0° and 45° with the same interface potential well depth; (c) Influence of the interface potential well depth parameter on the interface distance under normal loads of 45 nN and 65 nN and twist angles of 0° and 45°; (d) Influence of the interface potential well depth parameter on the interface distance under normal loads of 45 nN and 65 nN and twist angles of 0° and 45°.

[0037] Figure 10 For the Si-Si interface in the embodiments of the present invention, under the conditions of normal loads of 45 nN and 65 nN and torsion angles of 0° and 45°, the force constants (a-b) and LJ potentials (c-d) at different interface potential well depths are shown. The inset shows the LJ potential and force constant at a low interface potential well depth (5ε).

[0038] Figure 11 For the Ge-Ge interface in the embodiments of the present invention, under the conditions of normal loads of 45 nN and 65 nN and torsion angles of 0° and 45°, the force constants (a-b) and LJ potentials (c-d) at different interface potential well depths are shown. The inset shows the LJ potential and force constant at a low interface potential well depth (5ε). Detailed implementation manners

[0039] A method for regulating the thermal conductivity of a nano-semiconductor interface in contact and non-contact states includes the following steps:

[0040] ⑴ Establish a molecular dynamics heat transport model composed of a hot region A and a cold region B, where A and B represent silicon-silicon (Si-Si) and germanium-germanium (Ge-Ge) respectively, and the two materials have the same lattice structure.

[0041] The hot region A includes a silicon or germanium heat transfer atom region, a heat source, and a rigid body, and non-periodic boundary conditions are set in the x, y, and z directions.

[0042] The cold region B includes a silicon or germanium heat transfer atom region, a cold source, and a fixed layer.

[0043] The rigid body and the fixed layer are each composed of a single unit cell (UC) and are respectively arranged at both ends of the z direction of the model;

[0044] A heat transfer interface is formed between the hot region A and the cold region B to study the regulation mechanism of the torsion angle on the interface heat transport in contact and non-contact states.

[0045] Berendsen thermostats are respectively arranged at both ends of the model to regulate the temperature of the system.

[0046] ⑵ Perform molecular dynamics simulation and data processing:

[0047] ① In the contact state, take the torsion angle range of 5 - 45°, set the heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces to 320 K and 280 K respectively, compare the interface thermal conductivities at different torsion angles to determine the dependence of the interface thermal conductivity on the torsion angle; and compare the overlapping areas of the phonon state densities at the contact interface at different torsion angles to determine the influence of the overlapping area of the phonon state densities on the heat transport at different interface torsion angles;

[0048] ② In the non-contact state, the range of the torsion angle is taken as 0 - 45°, the heat source and cold source temperatures of the Si-Si and Ge-Ge interfaces are set to 320 K and 280 K respectively, and the interfacial thermal conductances at different torsion angles are compared to determine the dependence of the interfacial thermal conductance on the torsion angle; and the interfacial interaction potential and the force constant of the LJ (Lennard-Jones) potential at different torsion angles are compared to determine the influence of the force constant on the heat transport in different interfacial torsion angle states, further revealing the internal reason for the influence of different torsion angles on the interfacial heat transport in the non-contact state.

[0049] The execution of molecular dynamics simulation and data processing in the present invention further includes:

[0050] In the contact state, the range of the torsion angle is taken as 5 - 45°, the heat source and cold source temperatures of the Si-Si and Ge-Ge interfaces are set to 320 K and 280 K respectively, and the phonon participation rate and the interfacial distance of the contact interface at different torsion angles are compared to further reveal the internal reason for the influence of the interfacial contact state on the interfacial thermal conductance.

[0051] In the non-contact state, the heat source and cold source temperatures of the Si-Si and Ge-Ge interfaces are set to 320 K and 280 K respectively, and the interfacial interaction potential and the force constant of the LJ (Lennard-Jones) potential under different normal loads applied or the well depth changed are calculated to reveal the internal mechanism of the influence of the system normal load and the well depth on the interfacial thermal conductance.

[0052] Embodiment

[0053] The present invention takes the atomic-level Si-Si and Ge-Ge systems as the research objects and explores the dependence of the interfacial thermal conductance on the torsion angle in the contact state and the non-contact state. The specific process is as follows:

[0054] (1) Establish a molecular dynamics model.

[0055] As Figure 1 (a) shows, an interfacial heat transfer system composed of a hot region A and a cold region B (A - B represent Si - Si and Ge - Ge respectively) is constructed, and the heat transfer behavior at different torsion angles under this stacked structure is studied. d represents the distance between the hot region A and the cold region B defined when the torsion angle is 0, that is, when there is no lattice mismatch, and is used to judge the contact state of the model. The interfacial interaction is the SW potential energy, and a firm bond is formed between the interfacial atoms, resulting in an interface that fits very closely. At this time It is defined as the contact state. In the non-contact state, the interfacial interaction is the LJ potential, and the interaction between interfacial atoms is the non-bonding van der Waals interaction. The LJ potential only describes the weak attraction / repulsion between atoms and maintains the interaction at the equilibrium distance with the minimum potential energy. Therefore, after the relaxation of the MD simulation is completed, the distance between the interfaces is the equilibrium distance with the minimum potential energy, at which time is defined as the non-contact state.

[0056] During the simulation, on the premise of ensuring energy conservation, the direction of heat flux transfer in the z direction is as shown by the arrow in the figure, and unit cells (UCs) are set at both ends as fixed layers and rigid bodies. The two UCs adjacent to the rigid body are designated as temperature control source domains, called the heat source and the cold source respectively, and the Berendsen thermostat is used to adjust the temperature. The Si and Ge interfaces have 90° symmetry, so the twist angle is selected in the range of 0° to 45° to study the interfacial heat transfer behavior at different twist angles.

[0057] To meet the original intention of having a complete primitive cell in the x and y directions of the substrate and studying at any angle, the present invention designs the size of the hot region to be much larger than that of the cold region. After the hot region is twisted, it is trimmed according to the size of the cold region so that the interfacial contact area of the model is almost the same after rotating different angles.

[0058] Since the boundary effect will affect the ITC at all twist angles, but in the present invention, the influence of different twist angles on the ITC under the same influence conditions is mainly explored. Therefore, it will not ultimately affect the overall trend of the change of ITC with the twist angle. In addition, considering the limitation of computing resources, the length of the nanoribbon system at different twist angles is fixed at 19×19×30 UCs. The system adopts non-periodic boundary conditions in the x, y, and z directions. The system needs to be relaxed for 100 ps in the canonical ensemble (NVT) with a time step of 0.5 fs to reach a stable temperature state, so as to eliminate the influence of the initial conditions on the simulation results.

[0059] Figure 1 (b - e) illustrate the atomic stacking states of the A - B interface at different twist angles. The simulation is transferred to the microcanonical ensemble (NVE), and the temperature adjustment regions of the A - B interface are both set to 320 K and 280 K. After the system reaches complete equilibrium, the simulation runs for 500 ps to obtain stable temperature distribution and heat flux data, so as to calculate the ITC.

[0060] All molecular dynamics simulations are carried out using the LAMMPS software package.

[0061] (2) Determine the dependence of the heat transport of the Si - Si and Ge - Ge interfaces in the contact state and the non-contact state on different twist angles.

[0062] The heat flux can be obtained from the heat absorbed by the Berendsen thermostat after equilibration over a period of time. Based on the least squares method, a fitting method is established, where the slope represents the heat flux curve. The heat flux (J) refers to the amount of heat transferred per unit area per unit time, and the heat flux flowing through the interface can be expressed as

[0063]

[0064] where: Q represents the heat absorbed or removed by the thermostat, unit: eV; A is the area of the interface, unit: m 2 ; t represents the simulation time, unit: s. The contact area of the A - B interface is 106.480 nm 2 .

[0065] ITC reflects the heat flux under a unit temperature change at the interface. The temperature difference at the interface (denoted by the symbol ΔT) can be determined by linearly fitting the temperature position curve. The hot region A and the cold region B each consist of six layers, and the temperature of each layer is calculated based on the atomic velocity. Then, the average temperature of each region is obtained, and further the temperature change at the interface is determined: ΔT = T A –T B ; T A is the average temperature of the hot region A; T B is the average temperature of the cold region B. According to the interface formula of Fourier's law, the ITC at the A - B interface can be expressed by the following formula:

[0066]

[0067] where: G represents the interfacial thermal conductance, unit: MW / m 2 K; ΔT is the temperature difference between the hot region A and the cold region B, unit: K.

[0068] Contact state:

[0069] ① The dependence of the interfacial heat transport of Si - Si and Ge - Ge on different twist angles under the contact state.

[0070] Under the contact state, the distance The interfacial interaction potential is strong, and the Stillinger - Weber (SW) interfacial interaction potential with strong covalent bond ability is adopted. The lattice constants of silicon and germanium can be obtained from the original parameters of the potential function. When the twist angle is 0° under the contact state, the model is a bulk crystal without a contact interface and the interface distance is 0. To avoid the special case of the bulk crystal structure, the twist angle range of the contact state is set from 5° to 45°.

[0071] As the twist angle increases, the system always remains in the contact state At this time, the contact range does not change, only the commensurability of the contact changes. In non-equilibrium molecular dynamics (NEMD) simulations, the boundary effects caused by the system size are obvious, thus affecting the interfacial heat transfer. As Figure 2 (a-b) shows the ITC of Si-Si and Ge-Ge at a twist angle of 5° under different system sizes. As the system length increases, the ITC of both materials increases. This is attributed to the reduction of the boundary scattering effect with the increase of the system length, thus enhancing the ITC. As Figure 2 (c-d) shows the influence of different twist angles on the ITC and the binding energy. The results show that the ITC and the interfacial binding energy gradually decrease with the increase of the twist angle. At a temperature of 300K and an angle of 5°, the ITC value of the Si-Si interface calculated by SW is 5148.6 MW / m 2 K; when the twist angle is 45°, the ITC value drops to about 850.697 MW / m 2 K. The ITC value of the Ge-Ge interface calculated by the SW interaction potential is 5066.9 MW / m 2 K; when the twist angle is 45°, the ITC value drops to about 538.7 MW / m 2 K.

[0072] Therefore, the interfacial heat transfer characteristics are closely related to the binding energy. At small angles, the interfacial binding energy is large, indicating that the system is more stable at this time, the interfacial heat transfer ability is stronger, and the ITC is correspondingly larger.

[0073] ② Determine the influence of different twist angles on the interfacial thermal conductivity by combining the overlapping area of phonon density of states, phonon participation rate, and interfacial distance.

[0074] To deeply understand the phonon transport mechanism in Si-Si and Ge-Ge structures and evaluate the influence of system vibration on the interlayer heat transfer of materials, a systematic study of the vibration spectrum was carried out, and the phonon density of states (PDOS) at the interface was calculated. The calculation was based on the unit cell atoms in the hot region A and cold region B of the contact interface:

[0075]

[0076] In the formula: PDOS(ω) represents the phonon density of states, 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 for extracting the phonon density of states; <v(t)v(0)> represents the velocity autocorrelation function; <v(0)v(0)> represents the time average of the square of the initial velocity; <> represents the time average of the unit cell atoms in the single hot region A and cold region B in the system.

[0077] From the perspective of lattice dynamics, the interfacial coupling has a significant impact on whether an effective energy dissipation channel can be established at the interface. The overlapping area of the phonon spectra of the two materials can be used as a qualitative measure of phonon coupling, and the matching degree of phonon mode overlap is analyzed by calculating the area of the overlapping region of the PDOS. In the present invention, the overlapping part of the phonon spectra of the hot region A and the cold region B is calculated, and the area of the overlapping region of the phonon density of states within the cut-off frequency range is integrated:

[0078]

[0079] where: PDOS overlap is the overlapping area of the phonon spectra; ω represents the vibration frequency, unit: THz; DOS A is the phonon density of states of the hot region A, unit: au; DOS B is the phonon density of states of the cold region B, unit: au.

[0080] The PDOS overlapping regions of the Si-Si interface and the Ge-Ge interface at 10° and 45° twist angles are respectively as Figure 3 (a-b) shown. The results show that as the twist angle increases, the PDOS overlapping regions of the Si-Si and Ge-Ge interfaces both decrease. A low degree of phonon coupling means that there are fewer effective energy transfer channels established by phonon heat transfer, and the efficiency of interfacial heat transfer is reduced, resulting in a decrease in ITC. The present invention also calculates the phonon correlation factor to describe the phonon-phonon coupling strength of the phonon spectra. As shown in the inset: as the rotation angle increases, the phonon correlation factors of the Si / Si and Ge / Ge interfaces decrease accordingly, which is the same as the result that the overlapping area of the PDOS of the present invention decreases with the increase of the twist angle, thus proving the reliability of using the overlapping area of the PDOS to evaluate the phonon coupling strength in the present invention.

[0081] In order to measure the proportion of atoms participating in a certain intrinsic vibration and describe the localization of phonon modes, a dimensionless parameter between 0 and 1, the participation ratio (PPR), is introduced. Its calculation method is as follows:

[0082]

[0083] where: PPR(ω) represents the phonon participation ratio; N represents the total number of atoms for calculating the phonon participation ratio; PDOS i (ω) represents the phonon density of states of the i-th atom, unit: au.

[0084] It is generally considered that when the phonon vibration mode PPR is below 0.2, it is called a localized phonon mode; in this mode, phonons basically lose their ability as heat energy carriers, and the localization of all phonons in Si and Ge will have a significant impact on heat transport. As Figure 4As shown in (a - b), at a relatively small twist angle, the phonon participation ratio (PPR) exceeds 0.2, and phonons are in a non - local mode. When the twist angle increases, the PPR decreases, leading to phonon localization; this localization confines phonon energy within the lattice, thereby suppressing the phonon's heat transport ability. The results show that the phonon mode tends to localize as the twist angle increases, weakening the ability of phonons as heat carriers and ultimately resulting in a decrease in the interfacial thermal conductance (ITC).

[0085] As can be seen from Figure 2 (c - d) and Figure 3 (a - b), the variation trend of the partial density of states (PDOS) overlap area with the twist angle is different from that of the interfacial thermal conductance, indicating that there are other factors affecting the ITC. When the twist angle changes, the contact range does not change, but only the commensurability of the contact changes. In the present invention, the definition of the interfacial distance d in both the contact and non - contact states is that as the twist angle increases, the change in commensurability causes lattice mismatch, which leads to an increase in the surface distance of the interface relative to the commensurate state, and the interfacial heat transport changes significantly with the change of this interfacial distance. At this time, d reflects the weakening of the nesting degree between the cold region and the hot region, and the larger d is, the weaker the nesting degree is. Therefore Figure 5 (a - b) studied the interfacial distance of the Si - Si and Ge - Ge interfaces relative to the commensurate state at different twist angles. When the twist angle increases, the interfacial atomic structure changes from AA stacking to AB stacking, and this transformation further increases the interfacial distance, thus causing significant changes in the interfacial heat transport characteristics. Comparing Figure 2 (c) and Figure 2 (d), Figure 5 (a) and Figure 5 (b), it can be seen that the variation trend of the interfacial binding energy with the twist angle is opposite to that of the interfacial distance; the binding energy gradually weakens as the interfacial distance increases, which is consistent with the previous research results. This weakening reduces the interfacial coupling degree and decreases the probability of phonons carrying energy for cross - interfacial heat transfer, resulting in a decrease in the ITC. The current research reveals that the variation of the ITC with the twist angle is essentially the result of the combined action of the PDOS overlap area and the interfacial distance on the interface.

[0086] Non - contact state:

[0087] ① The dependence of the interfacial heat transport of the Si - Si and Ge - Ge interfaces in the non - contact state on different twist angles.

[0088] In the non - contact state, the distance The interfacial interaction potential energy is weak. Using the Lennard - Jones (LJ) interfacial interaction potential energy will result in a large layer spacing at the end of relaxation. A weak van der Waals (vdW) interaction is applied between the hot region A and the cold region B, with the parameter ε = 0.01744 eV and the equilibrium constant The present invention adjusts 2.6σ As the cut-off distance in the LJ interaction, beyond which the atomic interaction between atoms will be ignored.

[0089] As Figure 6 (a-b) shows the influence of different twist angles on the ITC when the interface interaction potential between Si-Si and Ge-Ge is the SW-LJ potential energy. The results show that the ITC gradually decreases with the increase of the twist angle, and at small angles, the ITC value reaches the maximum. At a temperature of 300K and an angle of 5°, the ITC value of the Si-Si interface is 116.9 MW / m 2 K; when the twist angle is 45°, the ITC value drops to about 105.1 MW / m 2 K; the calculated ITC value of the Ge-Ge interface is 76.5 MW / m 2 K; when the twist angle is 45°, the ITC value drops to about 62.6 MW / m 2 K. It should be emphasized that by comparing Figure 6 (a) with Figure 2 (c), Figure 6 (b) with Figure 2 (d), it can be found that: under both the SW and SW-LJ interface interaction potentials, the ITC decreases with the increase of the twist angle. And it is worth noting that the ITC values calculated by the SW-LJ interface interaction potential are generally lower than the results of the SW potential, and its downward trend is relatively gentle, which may be due to the weaker van der Waals interaction of the LJ potential.

[0090] ② Combine the force constants of the interface interaction potential and the LJ potential to determine the influence of the force constants on the thermal transport in different interface twist angle states, and further reveal the internal reason for the influence of the interface non-contact state on the interface thermal conductivity.

[0091] As Figure 7 (a-b) shows, the interface distances at different twist angles are calculated. As the twist angle increases, the interface distance also increases, and the interface distance is affected by the interface potential. To deeply study the influence mechanism of different twist angles on the phonon thermal transport at the interface, the interface LJ potential and force constants at different twist angles are further calculated, and the results are shown in Figure 7 (c-f) respectively. As the twist angle increases, the interface LJ potential and force constants at small twist angles are significantly greater than those at large twist angles. This indicates that as the twist angle increases, the increase in the interface distance leads to a weakening of the potential energy interaction on the contact surface. The interface interaction potential is closely related to the force constant. Therefore, the harmonic force constant in the LJ potential decreases, making the interface interaction weaker. The decreasing force constant reduces the phonon frequency, resulting in a decrease in the ITC, as shown in Figure 7(as shown in (a-b). Current research shows that the essence of the change in ITC under non-contact conditions with the twist angle is the result of the change in the harmonic force constant in the LJ potential.)

[0092] ③ Calculate the interface interaction potential and the force constant of the LJ potential under different normal loads or by changing the depth of the potential well to reveal the internal mechanism by which the system normal load and the depth of the potential well affect the interface thermal conductivity.)

[0093] To deeply explore the influence of different loads and interface potential well depths on ITC, the present invention has conducted a detailed study, and the results are as Figure 8 (as shown in (a-d). The study found that at the twist angles of 0° and 45°, for both Si-Si and Ge-Ge interfaces, the interface thermal conductivity under a larger normal load is significantly higher than that under a smaller normal load. In addition, as the depth of the interface potential well increases, ITC also shows an increasing trend. This indicates that by increasing the normal load and the depth of the interface potential well, the interface thermal conductivity can be effectively improved, thereby achieving effective regulation of the interface thermal conductivity. At the same potential well depth, regardless of whether the twist angle is 0° or 45°, the ITC of Si-Si and Ge-Ge interfaces increases with the increase of the normal load. The specific results are as Figure 9 (as shown in (a-b). In addition, regardless of how the load changes, the ITC at 0° is always greater than that at 45°. For the convenience of further exploration, the present invention selects the parameters under two loads of 45 nN and 65 nN, specifically as Figure 9 (as shown in (c-d). At the twist angles of 0° and 45°, as the normal load increases or the depth of the potential well deepens, the interface distance will increase. To understand more deeply the influence of interface interaction on ITC, the present invention calculates the interface LJ potential energy and the force constant. As Figure 10 (as shown in (a-d) and Figure 11 (as shown in (a-d), as the interface distance decreases, the interface LJ potential energy gradually increases, which in turn leads to a continuous increase in the force constant. By comparing Figure 10 (a) with Figure 10 (c), Figure 10 (b) with Figure 10 (d), and Figure 11 (a) with Figure 11 (c), Figure 11 (b) with Figure 11(d), it can be found that when the torsion angle is 0°, the increase in the LJ potential energy and force constant of the Si-Si and Ge-Ge interfaces is significantly greater than that at 45°. This indicates that at a torsion angle of 0°, the increase in the interfacial thermal conductance is significantly higher than that at a torsion angle of 45°. In the absence of a normal load and the interfacial potential well depth, the system energy is the lowest. Increasing the normal load and strengthening the interfacial potential well depth can easily pull the system away from the lowest energy point, and the interfacial distance will decrease, resulting in an enhanced potential energy interaction at the interface, further increasing the force constant, increasing the probability of phonons carrying energy for cross-interfacial heat transfer, and leading to an increase in ITC. Therefore, the current research of the present invention shows that increasing the potential well depth and increasing the normal load have similar influence mechanisms on the interfacial thermal conductance, and both methods can effectively control the interfacial heat transport.

[0094] In summary, the present invention realizes the effective regulation of ITC by controlling the torsion angle, normal load, and potential well depth, providing an important basis for the thermal management of nanodevices. More importantly, the proposed framework can be used in cooperation with existing methods, providing theoretical guidance for the design of nanodevices with controllable interfacial thermal conductance.

[0095] The above embodiments have elaborated on the principle and implementation manner of the present invention, and their explanations are only used to help understand the method and its core idea of the present invention more deeply. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A method for regulating the thermal conductivity of a nano-semiconductor interface in contact and non-contact states, comprising the following steps: ⑴ Establish a molecular dynamics heat transport model composed of a hot region A and a cold region B, where A and B represent silicon-silicon and germanium-germanium respectively, and the two materials have the same lattice structure; The hot region A includes a silicon or germanium heat transfer atomic region, a heat source, and a rigid body, and sets non-periodic boundary conditions in the x , y , z direction. The cold region B includes a silicon or germanium heat transfer atom region, a cold source, and a fixed layer; The rigid body and the fixed layer are each composed of a single unit cell and are respectively arranged at both ends in the z direction; A heat transfer interface is formed between the hot region A and the cold region B; Berendsen thermostats are respectively arranged at both ends of the model to regulate the temperature of the system; ⑵ Perform molecular dynamics simulation and data processing: ① In the contact state, take the torsion angle range of 5~45°, set the heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces to 320 K and 280 K respectively, compare the interface thermal conductivities at different torsion angles to determine the dependence of the interface thermal conductivity on the torsion angle; and compare the overlapping areas of the phonon state densities at the contact interface at different torsion angles to determine the influence of the overlapping area of the phonon state densities on the heat transport at different interface torsion angles; ② In the non-contact state, take the torsion angle range of 0~45°, set the heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces to 320 K and 280 K respectively, compare the interface thermal conductivities at different torsion angles to determine the dependence of the interface thermal conductivity on the torsion angle; and compare the interface interaction potential and the force constant of the LJ potential at different torsion angles to determine the influence of the force constant on the heat transport in different interface torsion angle states, and further reveal the internal reason for the influence of different torsion angles on the interface heat transport in the non-contact state.

2. The method for regulating the interfacial thermal conductivity of a nano-semiconductor in contact and non-contact states according to claim 1, wherein: The molecular dynamics simulation and data processing performed in the step ⑵ further include: in the contact state, take the torsion angle range of 5~45°, set the heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces to 320 K and 280 K respectively, compare the phonon participation rate and the interface distance at the contact interface at different torsion angles, and further reveal the internal reason for the influence of the interface contact state on the interface thermal conductivity.

3. The method for regulating the interfacial thermal conductance of a nano-semiconductor in contact and non-contact states as claimed in claim 1, wherein: The molecular dynamics simulation and data processing performed in the step ⑵ further include: in the non-contact state, set the heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces to 320 K and 280 K respectively, calculate the interface interaction potential and the force constant of the LJ potential under different normal loads or when changing the potential well depth, and reveal the internal mechanism of the influence of the system normal load and the potential well depth on the interface thermal conductivity.

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