Method for regulating thermal conductivity of nanometer semiconductor interface in contact and non-contact state

Abstract

The application relates to a method for regulating the thermal conductivity of a nanometer semiconductor interface in contact and non-contact states, which comprises the following steps: (1) establishing a molecular dynamics thermal transport model composed of a hot region A and a cold region B; (2) performing molecular dynamics simulation and data processing: comparing the interface thermal conductivities under different twist angles in the contact state and the non-contact state to determine the dependence of the interface thermal conductivity on the twist angle; in the contact state, comparing the overlapping areas of the phonon state density at the contact interface under different twist angles to determine the influence of the overlapping area of the phonon state density on the thermal transport of different interface twist angles; in the non-contact state, comparing the force constants of the interface interaction potential and the LJ potential under different twist angles to determine the influence of the force constant on the thermal transport of different interface twist angles. The application realizes effective regulation of the ITC by regulating the twist angle, the normal load and the potential well depth, and provides an important basis for the thermal management of nanometer devices.

Description

Technical Field

[0001] This invention relates to the field of molecular dynamics technology, and in particular to a method for controlling the thermal conductivity of nano-semiconductor interfaces under contact and non-contact conditions. Background Technology

[0002] In high-power-density devices and highly integrated chips, controlling and understanding the thermal management of materials at the nanoscale is crucial. With the rapid development of high-power-density devices and further increases in chip integration, a large amount of heat accumulates at the interface, and the chip's heat dissipation power density increases linearly, making it a major obstacle to further increases in semiconductor integration. Therefore, effectively solving the heat dissipation problem is essential for the lifespan and reliability of semiconductor devices. To significantly improve the heat dissipation efficiency of semiconductor devices and achieve energy saving and consumption reduction, adjusting interfacial thermal conductivity (ITC) has become a key measure.

[0003] Researchers have proposed various strategies, including interlayer coupling strength, altering interface roughness, using interfacial nanostructures, introducing defects, modifying interfacial mixing, and applying external strain. Wang et al. investigated how to enhance the ITC of the 2D / 3D interface and the thermal conductivity of the 2D material by introducing controlled concentrations of vacancy defects on the substrate surface of 2D-MoS2 / 3D-GaN. Kelayeh et al. modulated the interfacial thermal resistance of Si / Ge heterojunctions by changing the Si / Ge content at the interface (mixing region). Gordiz et al. studied phonon transport at the interface between crystalline silicon (Si) and germanium (Ge), particularly the contribution of interfacial vibrational modes to thermal transport. Chen et al. used molecular dynamics simulations to study the effect of strain engineering on the Kapitza thermal resistance in few-layer graphene (FLG), demonstrating that thermal resistance can be controlled by applying mechanical strain.

[0004] Interfacial thermal transport can also be modulated by system size, temperature, and phonon coupling strength. Liu et al. analyzed in detail the effects of graphene layer number and temperature on the interfacial thermal conductivity of diamond / graphene heterostructures. The results showed that the interfacial thermal conductivity of diamond-monolayer graphene heterostructures was significantly better than that of diamond-multilayer graphene structures, reaching at least twice the latter; high temperature also effectively promoted interfacial thermal transport. Liu et al. used nonequilibrium molecular dynamics simulations to study the effects of temperature, size, and material defects on the interfacial thermal conductivity of graphene / SiC heterojunctions, demonstrating the influence of phonon density of states and interfacial coupling strength on interfacial thermal transfer. Ding et al. studied the effect of phonon coupling strength on the interfacial thermal conductivity in graphene / MoS2 heterostructures, indicating that the main channel for heat transport is the coupling between low-frequency out-of-plane phonons.

[0005] In studies utilizing lattice mismatch methods to modulate interfacial thermal conductivity, torsion angle has proven to be a crucial means of adjusting material thermal properties. Specifically, the influence of interlayer torsion angle on phonon dispersion, such as interlayer coupled phonon modes and moiré patterns, has been discussed. Ren et al. investigated the effect of interlayer torsion on heat transport in graphene / hexagonal boron nitride van der Waals heterostructures, finding that rotation can generate moiré patterns. This structural change can modulate interlayer interaction potentials and phonon modes, achieving effective control over phonon transport. Li et al. studied the effect of torsion angle on the interlayer thermal conductivity (ITC) of bilayer MoS2, showing that torsion of the bilayer affects interlayer vdW coupling interactions, leading to changes in interfacial adhesion strength and phonon interfacial transport.

[0006] Thermal management of electronic components involves both contact and non-contact states. Existing research shows that significant progress has been made in controlling interfacial thermal conductivity (ITC), which can be effectively regulated under various operating conditions. However, the intrinsic mechanism by which the torsion angle affects thermal conductivity in both contact and non-contact states has not been fully resolved and requires further investigation. Si and Ge, as typical semiconductor materials, possess unique advantages in studying lattice mismatch issues in contact and non-contact states. Both have identical diamond cubic crystal structures and similar lattice constants. More importantly, Si-Si and Ge-Ge systems provide ideal platforms for studying the influence of torsion angle and interfacial interactions on heat conduction. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a method for controlling the thermal conductivity of nano-semiconductor interfaces under contact and non-contact conditions.

[0008] To address the above problems, the present invention provides a method for controlling the thermal conductivity of a nano-semiconductor interface under contact and non-contact states, comprising the following steps:

[0009] (1) Establish a molecular dynamics thermal transport model consisting 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 crystal structure;

[0010] The thermal region A includes a silicon or germanium heat transfer atomic 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 atomic region, a cold source, and a fixing layer;

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

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

[0014] Berendsen thermostats were installed at both ends of the model to regulate the system temperature.

[0015] (2) Performing molecular dynamics simulations and data processing:

[0016] ① Under contact conditions, the torsion angle range is taken as 5 to 45°. The heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces are set to 320K and 280K, respectively. The interfacial thermal conductivity under different torsion angles is compared to determine the dependence of interfacial thermal conductivity on torsion angle. The overlapping area of ​​phonon state density at the contact interface under different torsion angles is also compared to determine the influence of the overlapping area of ​​phonon state density on thermal transport at different interfacial torsion angles.

[0017] ② In the non-contact state, the torsion angle range is taken as 0 to 45°, and the heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces are set to 320K and 280K, respectively. The interfacial thermal conductivity under different torsion angles is compared to determine the dependence of interfacial thermal conductivity on the torsion angle. The force constants of the interfacial interaction potential and the LJ (Lennard-Jones) potential under different torsion angles are compared to determine the influence of the force constants on the thermal transport under different interfacial torsion angles, and further reveal the intrinsic reasons for the influence of different torsion angles on interfacial thermal transport under the non-contact state.

[0018] The molecular dynamics simulation and data processing in step (2) further includes: in the contact state, taking the torsion angle range of 5 to 45°, setting the heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces to 320K and 280K respectively, comparing the phonon participation rate and interface distance of the contact interface under different torsion angles, and further revealing the intrinsic reasons why the interface contact state affects the interface thermal conductivity.

[0019] Step (2) of performing molecular dynamics simulation and data processing also includes: in a non-contact state, setting the heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces to 320K and 280K respectively, calculating the force constants of the interfacial interaction potential and LJ (Lennard-Jones) potential under different normal loads or changes in the potential well depth, and revealing the intrinsic mechanism of the influence of the system's normal load and potential well depth on the interfacial thermal conductivity.

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

[0021] 1. In this invention, atomic-level silicon-silicon and germanium-germanium are taken as research objects, and corresponding heat transport system models are established to study the regulation mechanism of the torsion angle on the interface heat transport under contact and non-contact states.

[0022] 2. This invention determines the control mechanism of the torsion angle on the interfacial heat transport under different torsion angles in contact and non-contact states by calculating the interfacial thermal conductivity under different torsion angles in contact and non-contact states.

[0023] 3. In the contact state, this invention, by combining the overlapping area of ​​phonon states density and phonon participation rate under different torsion angles, reveals the intrinsic reasons affecting interfacial thermal conductivity.

[0024] 4. This invention evaluates the dependence of ITC on the torsion angle by combining LJ potential and force constant in a non-contact state.

[0025] 5. This invention systematically analyzes the changes in the force constants of the interface interaction potential and the LJ potential by adjusting the normal load and potential well depth in a non-contact state, revealing the intrinsic mechanism of the influence of the system's normal load and potential well depth on the interface thermal conductivity.

[0026] 6. This invention achieves effective control of ITC by changing the torsion angle, applying a normal load, and altering the potential well depth. This discovery provides an important foundation for effective thermal management of nanoscale devices, thus offering theoretical guidance for designing nanodevices with controllable interface thermal conductivity. Attached Figure Description

[0027] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

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

[0029] Figure 2 The ITC of the AB interface in this embodiment of the invention is shown under different system lengths and torsion angles. Among them: (a) ITC of Si-Si interface under different system sizes; (b) ITC of Ge-Ge interface under different system sizes; (c) ITC and interface bonding energy of Si-Si; (d) ITC and interface bonding energy of Ge-Ge.

[0030] Figure 3 The figure shows the overlap area of ​​the phonon density of states at different torsion angles at the AB interface in the embodiments of the present invention. The inset shows the phonon correlation factor at different torsion angles. Wherein: (a) Si-Si interface; (b) Ge-Ge interface.

[0031] Figure 4The phonon participation rates in the embodiments of the present invention are 5°, 15°, 35° and 45°. Wherein: (a) Si-Si interface; (b) Ge-Ge interface.

[0032] Figure 5 This diagram illustrates the variation of the interface distance between the cold and hot zones under different torsion angles in an embodiment of the present invention. Wherein: (a) Si-Si interface; (b) Ge-Ge interface.

[0033] Figure 6 These are the ITC values ​​under different torsional angles under the SW-LJ potential energy in this embodiment of the invention. Wherein: (a) Si-Si interface; (b) Ge-Ge interface.

[0034] Figure 7 This invention relates to an embodiment where, when the normal load applied in the z-direction is 45 nN, the interface distance, LJ potential, and force constant of the AB interface are measured under different torsion angles. Specifically: (a) the interface distance between the Si-Si interfaces under different torsion angles; (b) the interface distance between the Ge-Ge interfaces under different torsion angles; (c) the LJ potential between the Si-Si interfaces under different torsion angles; (d) the LJ potential between the Ge-Ge interfaces under different torsion angles; (e) the force constant between the Si-Si interfaces under different torsion angles; and (f) the force constant between the Ge-Ge interfaces under different torsion angles.

[0035] Figure 8 This invention illustrates the effects of different normal loads and interface potential well depths on the thermal conductivity of Si-Si and Ge-Ge interfaces at torsion angles of 0° and 45°. Specifically: (a) at a Si-Si interface torsion angle of 0°; (b) at a Si-Si interface torsion angle of 45°; (c) at a Ge-Ge interface torsion angle of 0°; and (d) at a Ge-Ge interface torsion angle of 45°.

[0036] Figure 9 This invention illustrates the effects of different normal loads on interfacial thermal conductivity and the effects of interfacial well depth parameters and different normal loads on interfacial distance in embodiments of the present invention. Specifically: (a) the effect of different normal loads on interfacial thermal conductivity of Si-Si at the same interfacial well depth and with torsion angles of 0° and 45°; (b) the effect of different normal loads on interfacial thermal conductivity of Ge-Ge at the same interfacial well depth and with torsion angles of 0° and 45°; (c) the effect of the interfacial well depth parameter on interfacial distance when the normal loads are 45nN and 65nN and the torsion angles are 0° and 45°; and (d) the effect of the interfacial well depth parameter on interfacial distance when the normal loads are 45nN and 65nN and the torsion angles are 0° and 45°.

[0037] Figure 10 In this embodiment of the invention, the force constant (ab) and LJ potential (cd) at different interface well depths are shown for the Si-Si interface under normal loads of 45nN and 65nN and torsional angles of 0° and 45°. The inset shows the LJ potential and force constant at a low interface well depth (5ε).

[0038] Figure 11 In this embodiment of the invention, for the Ge-Ge interface, the force constant (ab) and LJ potential (cd) at different interface potential well depths are shown under normal loads of 45 nN and 65 nN and torsional angles of 0° and 45°. The inset shows the LJ potential and force constant at a low interface potential well depth (5ε). Detailed Implementation

[0039] A method for controlling the thermal conductivity of nano-semiconductor interfaces under contact and non-contact conditions includes the following steps:

[0040] (1) Establish a molecular dynamics thermal transport model consisting 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 crystal lattice structure.

[0041] Thermal region A contains silicon or germanium heat transfer atomic regions, a heat source, and a rigid body, and non-periodic boundary conditions are set in the x, y, and z directions.

[0042] Cold region B contains silicon or germanium heat transfer atomic regions, a cold source, and a fixing layer.

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

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

[0045] Berendsen thermostats were installed at both ends of the model to regulate the system temperature.

[0046] (2) Performing molecular dynamics simulations and data processing:

[0047] ① Under contact conditions, the torsion angle range is taken as 5 to 45°. The heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces are set to 320K and 280K, respectively. The interfacial thermal conductivity under different torsion angles is compared to determine the dependence of interfacial thermal conductivity on torsion angle. The overlapping area of ​​phonon state density at the contact interface under different torsion angles is also compared to determine the influence of the overlapping area of ​​phonon state density on thermal transport at different interfacial torsion angles.

[0048] ② In the non-contact state, the torsion angle range is taken as 0 to 45°, and the heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces are set to 320K and 280K, respectively. The interfacial thermal conductivity under different torsion angles is compared to determine the dependence of interfacial thermal conductivity on the torsion angle. The force constants of the interfacial interaction potential and the LJ (Lennard-Jones) potential under different torsion angles are compared to determine the influence of the force constants on the thermal transport under different interfacial torsion angles, and further reveal the intrinsic reasons for the influence of different torsion angles on interfacial thermal transport under the non-contact state.

[0049] The molecular dynamics simulation and data processing in this invention also include:

[0050] Under contact conditions, the torsion angle range was set to 5–45°, and the heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces were set to 320K and 280K, respectively. The phonon participation rate and interfacial distance of the contact interface were compared under different torsion angles to further reveal the intrinsic reasons why the interfacial contact state affects the interfacial thermal conductivity.

[0051] In a non-contact state, the heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces were set to 320K and 280K, respectively. The force constants of the interfacial interaction potential and LJ (Lennard-Jones) potential under different normal loads or changes in the potential well depth were calculated, revealing the intrinsic mechanism of the influence of the system's normal load and potential well depth on the interfacial thermal conductivity.

[0052] Example

[0053] This invention focuses on atomic-level silicon-silicon and germanium-germanium systems, investigating the dependence of interfacial thermal conductivity on torsion angle in both contact and non-contact states. The specific process is as follows:

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

[0055] like Figure 1 As shown in (a), an interfacial heat transport system consisting of a hot region A and a cold region B (AB representing Si-Si and Ge-Ge, respectively) was constructed, and the heat transfer behavior under different torsion angles in this stacked structure was studied. d represents the distance between the hot region A and the cold region B when the torsion angle is 0, i.e., when lattice mismatch has not occurred, and is used to determine the contact state of the model. The interfacial interaction is the SW potential energy, and a stable bond is formed between the interfacial atoms, resulting in a very tightly bonded interface. Defined as a contact state. In the non-contact state, the interface interaction is an LJ potential, and the interactions between interface atoms are non-bonding van der Waals interactions. The LJ potential only describes the weak attraction / repulsion between atoms, and the interaction is maintained at the equilibrium distance where the minimum potential energy is reached. Therefore, after the MD simulation relaxation is completed, the distance between the interfaces is the equilibrium distance where the minimum potential energy is reached. Defined as a non-contact state.

[0056] During the simulation, while ensuring energy conservation, the heat flow direction in the z-axis is as shown by the arrows in the figure. Unit cells (UCs) are set at both ends as a fixed layer and a rigid body, respectively. The two UCs adjacent to the rigid body are designated as temperature-controlled source domains, referred to as the heat source and cold source, and the temperature is regulated using a Berendsen thermostat. The Si-Ge interface exhibits 90° symmetry; therefore, the torsion angle is selected within the range of 0° to 45° to study the interfacial heat transfer behavior at different torsion angles.

[0057] To meet the initial goal of having complete unit cells in the x and y directions of the base and studying at arbitrary angles, this invention designs the hot region to be much larger than the cold region. After the hot region is twisted, it is trimmed according to the size of the cold region, so that the contact area of ​​the model interface is almost the same after rotating at different angles.

[0058] Since boundary effects affect ITC at all torsion angles, this invention primarily explores the impact of different torsion angles on ITC under the same conditions. Therefore, it ultimately does not affect the overall trend of ITC variation with torsion angle. Furthermore, considering computational resource limitations, the length of the nanoribbon system at different torsion angles is fixed at 19 × 19 × 30 UCs. Aperiodic boundary conditions are applied along the x, y, and z directions. The system requires a 100 ps relaxation in a canonical ensemble (NVT) with a time step of 0.5 fs to reach a stable temperature state, thereby eliminating the influence of initial conditions on the simulation results.

[0059] Figure 1 (be) illustrates the atomic stacking state of the AB interface under different torsion angles. The simulation was transferred to the microcanonical ensemble (NVE), and the temperature regulation regions of the AB interface were set to 320K and 280K. After the system reached complete equilibrium, the simulation was run for 500 ps to obtain stable temperature distribution and heat flux data, thereby calculating the ITC.

[0060] All molecular dynamics simulations were performed using the LAMMPS software package.

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

[0062] Heat flux can be obtained by measuring the heat absorbed by the Berendsen thermostat after a period of equilibrium. A fitting method is established based on the least squares approach, where the slope represents the heat flux curve. Heat flux (J) refers to the amount of heat transferred per unit area per unit time; the heat flux across an interface can be expressed as…

[0063]

[0064] Where: Q represents the heat absorbed or removed by the thermostat, in eV; A is the area of ​​the interface, in m². 2 t represents the simulation time, in seconds. The contact area of ​​the AB interface is 106.480 nm. 2 .

[0065] ITC reflects the heat flux per unit temperature change at the interface. The temperature difference at the interface (denoted by ΔT) can be determined by linearly fitting a temperature location curve. Hot region A and cold region B each consist of six layers. The temperature of each layer is calculated based on atomic velocities, and then the average temperature of each region is obtained, thus determining the temperature change at the interface: ΔT = T A –T B ;T A T is the average temperature of thermal region A; B This is the average temperature of cold region B. According to Fourier's law and the interface formula, the ITC at the AB interface can be expressed as follows:

[0066]

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

[0068] Contact status:

[0069] ① The dependence of heat transport at Si-Si and Ge-Ge interfaces under contact conditions on different torsion angles.

[0070] In contact state, distance The interfacial interaction potential energy is relatively strong, employing the Stillinger-Weber (SW) interfacial interaction potential energy, which possesses strong covalent bonding capabilities. The lattice constants of silicon and germanium can be obtained from the original parameters of the potential function. In the contact state with a torsion angle of 0°, the model represents a bulk crystal with no contact interface and an interface distance of 0. To avoid the special case of a bulk crystal structure, the torsion angle range in the contact state is set to 5° to 45°.

[0071] As the torsion angle increases, the system maintains contact. At this point, the contact domain remains unchanged; only the commensurability of the contact changes. In nonequilibrium molecular dynamics (NEMD) simulations, boundary effects caused by system size are significant, thus affecting interfacial heat transfer. For example... Figure 2 (ab) shows the ITC of Si-Si and Ge-Ge at different system sizes with a twist angle of 5°. The ITC of both materials increases with increasing system length. This is attributed to the reduction of boundary scattering effects with increasing system length, thus enhancing the ITC. Figure 2 (cd) illustrates the effect of different torsion angles on ITC and bonding energy. The results show that ITC and interfacial bonding energy gradually decrease with increasing torsion angle. At a temperature of 300 K 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 torsion angle is 45°, the ITC value decreases to approximately 850.697 MW / m. 2 K. The ITC value of the Ge-Ge interface calculated from the SW interaction potential is 5066.9 MW / m. 2 K; When the torsion angle is 45°, the ITC value decreases to approximately 538.7 MW / m. 2 K.

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

[0073] ②The effect of different torsion angles on interfacial thermal conductivity is determined by combining the overlap area of ​​phonon density of states, phonon participation rate, and interfacial distance.

[0074] To gain a deeper understanding of the phonon transport mechanism in Si-Si and Ge-Ge structures and to evaluate the impact of system vibrations on interlayer thermal transport, a systematic study of the vibrational spectrum was conducted, and the phonon density of states (PDOS) at the interface was calculated. The calculations were based on the unit cell atoms in the hot region A and the cold region B at the contact interface.

[0075]

[0076] In the formula: PDOS(ω) represents the phonon density of states, in units of au; ω represents the vibrational frequency, in units of Thz; t represents time, in units of s; τ represents the total vibration time, in units of s; i represents the atomic number from which the phonon density of states is extracted;<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 atoms in a single hot region A and cold region B of the system.

[0077] From a lattice dynamics perspective, interface coupling significantly influences whether an effective energy dissipation channel can be established at the interface. The overlap area of ​​the phonon spectra of two materials can be used as a qualitative measure of phonon coupling, and the degree of phonon mode overlap can be analyzed by calculating the PDOS overlap area. This invention calculates the overlap portion of the phonon spectra of hot region A and cold region B, and integrates the area of ​​the phonon density of states overlap region within the cutoff frequency range:

[0078]

[0079] Where: PDOS overlap It represents the area of ​​overlap of the phonon spectrum; ω represents the vibrational frequency, in Thz; DOS A This is the phonon density of states in thermal region A, in units of au; DOS B This is the phonon states density in cold region B, in units of au.

[0080] The PDOS overlap regions of the Si-Si and Ge-Ge interfaces at torsion angles of 10° and 45° are respectively shown in the figures below. Figure 3 As shown in (ab), the results indicate that the PDOS overlap area at both Si-Si and Ge-Ge interfaces decreases with increasing torsion angle. Low phonon coupling means fewer effective energy transfer channels established by phonon heat transfer, leading to reduced interface heat transfer efficiency and consequently, a decrease in ITC. This invention also calculates the phonon correlation factor to describe the phonon-phonon coupling strength of the phonon spectrum, as shown in the inset: with increasing rotation angle, the phonon correlation factor at both Si / Si and Ge / Ge interfaces decreases, consistent with the result that the PDOS overlap area decreases with increasing torsion angle, thus demonstrating the reliability of using the PDOS overlap area to evaluate phonon coupling strength in this invention.

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

[0082]

[0083] In the formula: PPR(ω) represents the phonon participation rate; N represents the total number of atoms used to calculate the phonon participation rate; PDOS i (ω) represents the phonon state density of the i-th atom, in units of au.

[0084] Phonon vibrational modes with a PPR below 0.2 are generally considered to be localized phonon modes; in this mode, phonons essentially lose their ability to act as heat carriers, and the localization of all phonons in Si and Ge has a significant impact on heat transport. For example... Figure 4As shown in (ab), at smaller torsion angles, the PPR exceeds 0.2, and phonons are in a nonlocal mode. As the torsion angle increases, the PPR decreases, leading to phonon localization. This localization confines phonon energy within the crystal lattice, thus suppressing the phonon's thermal transport capability. The results show that phonon modes tend to localize with increasing torsion angle, weakening the phonon's ability to act as a thermal energy carrier, ultimately leading to a decrease in ITC.

[0085] Depend on Figure 2 (cd)with Figure 3 (ab) shows that the trend of PDOS overlap area changing with the torsion angle differs from that of interfacial thermal conductivity, indicating that other factors also affect ITC. When the torsion angle changes, the contact range remains unchanged; only the commensurability of the contact changes. In this invention, the definition of the interfacial distance d in both contact and non-contact states is that as the torsion angle increases, the change in commensurability causes lattice mismatch, leading to an increase in the distance between the interface and the commensurable surface. Interfacial thermal transport changes significantly with this change in interfacial distance. In this case, d reflects the weakening of the nesting degree between the cold and hot regions; a larger d indicates a weaker nesting degree. Therefore… Figure 5 (ab) The interfacial distances of Si-Si and Ge-Ge interfaces relative to their commensurate states under different torsion angles were investigated. As the torsion angle increases, the interfacial atomic structure changes from AA stacking to AB stacking. This transformation further increases the interfacial distance, leading to a significant alteration in the interfacial thermal transport properties. (Comparison) Figure 2 (c) and Figure 2 (d) Figure 5 (a) and Figure 5 (b) It is evident that the trend of interfacial binding energy with changing torsion angle is opposite to that with changing interfacial distance; the binding energy gradually weakens as the interfacial distance increases, which is consistent with previous findings. This weakening reduces the degree of interfacial coupling, decreases the probability of phonon-carried energy being transported across the interface, and leads to a decrease in ITC. Current research reveals that the change in ITC with torsion angle is essentially the result of the combined effect of the overlap area of ​​PDOS on the interface and the interfacial distance.

[0086] Non-contact state:

[0087] ① Dependence of heat transport at Si-Si and Ge-Ge interfaces on different torsion angles under non-contact conditions.

[0088] In non-contact mode, distance The interfacial interaction potential is relatively weak. Using the LJ interfacial interaction potential, a large interlayer spacing will be generated after relaxation. A weak van der Waals interaction (vdW) with parameters ε = 0.01744 eV and equilibrium constant is applied between hot region A and cold region B. This invention adjusts 2.6σ This serves as the cutoff distance in LJ interactions; beyond this distance, atomic interactions between atoms will be ignored.

[0089] like Figure 6 (ab) illustrates the effect of different torsion angles on the interfacial interaction potential (ITC) of Si-Si and Ge-Ge interfaces at the SW-LJ potential energy. The results show that the ITC gradually decreases with increasing torsion angle, reaching its maximum at small angles. At a temperature of 300 K and an angle of 5°, the ITC value of the Si-Si interface is 116.9 MW / m². 2 K; When the torsion angle is 45°, the ITC value decreases to approximately 105.1 MW / m. 2 The calculated ITC value for the K-Ge interface is 76.5 MW / m². 2 K; When the torsion angle is 45°, the ITC value decreases to approximately 62.6 MW / m. 2 K. It should be emphasized that the comparison Figure 6 (a) and Figure 2 (c) Figure 6 (b) and Figure 2 (d) It can be observed that under both the SW and SW-LJ interface interaction potentials, the ITC decreases with increasing torsion angle. It is also worth noting that the ITC value calculated from the SW-LJ interface interaction potential is generally lower than that of the SW potential, and its decreasing trend is relatively gentle. This may be due to the weaker van der Waals interaction of the LJ potential.

[0090] ② By combining the force constants of the interfacial interaction potential and the LJ potential, the influence of the force constants on thermal transport under different interfacial torsional angles is determined, further revealing the intrinsic reasons why the non-contact state of the interface affects the interfacial thermal conductivity.

[0091] like Figure 7 As shown in (ab), the interfacial distance under different torsion angles was calculated. The interfacial distance increases with increasing torsion angle and is influenced by the interfacial potential. To further investigate the influence mechanism of different torsion angles on interfacial phonon thermal transport, the interfacial LJ potential and force constant under different torsion angles were calculated, and the results are shown in (ab). Figure 7 As shown in (cf), with increasing torsion angle, the interfacial LJ potential and force constant at small torsion angles are significantly greater than those at large torsion angles. This indicates that with increasing torsion angle, the increased interfacial distance leads to a weakening of potential energy interaction at the contact surface. The interfacial interaction potential is closely related to the force constant; therefore, the decrease in the harmonic force constant in the LJ potential makes the interfacial interaction even weaker. The reduced force constant lowers the phonon frequency, thus leading to a decrease in ITC, such as... Figure 7As shown in (ab). Current research indicates that the variation of ITC with torsional angle in the non-contact state is essentially a result of the change in the harmonic force constant in the LJ potential.

[0092] ③ Calculate the force constants of the interfacial interaction potential and LJ potential under different normal loads or changes in the potential well depth, in order to reveal the intrinsic mechanism by which the system's normal load and potential well depth affect the interfacial thermal conductivity.

[0093] To further investigate the effects of different loads and interface potential well depths on ITC, this invention conducted a detailed study, the results of which are as follows: Figure 8 As shown in (ad). The study found that at torsion angles of 0° and 45°, the interfacial thermal conductivity (ITC) under a larger normal load was significantly higher than that under a smaller normal load for both Si-Si and Ge-Ge interfaces. Furthermore, the ITC also showed an increasing trend with increasing interfacial well depth. This indicates that increasing the normal load and the interfacial well depth can effectively improve the interfacial thermal conductivity, thereby achieving effective control over the interfacial thermal conductivity. At the same well depth, regardless of whether the torsion angle was 0° or 45°, the ITC of both Si-Si and Ge-Ge interfaces increased with increasing normal load, as shown in the specific results. Figure 9 As shown in (ab). Furthermore, regardless of load variations, the ITC at 0° is always greater than the ITC at 45°. For further investigation, this invention selected parameters under two loads: 45nN and 65nN, as detailed below. Figure 9 As shown in (cd). At torsional angles of 0° and 45°, the interfacial distance increases with increasing normal load or potential well depth. To gain a deeper understanding of the influence of interfacial interactions on ITC, this invention calculates the interfacial LJ potential energy and force constant. Figure 10 (ad) and Figure 11 As shown in (ad), as the interface distance decreases, the interface LJ potential energy gradually increases, leading to a continuous increase in the force constant. Through comparison... Figure 10 (a) and Figure 10 (c) Figure 10 (b) and Figure 10 (d) and Figure 11 (a) and Figure 11 (c) Figure 11 (b) and Figure 11(d) It can be observed that when the torsion angle is 0°, the increase in LJ potential energy and force constant at the Si-Si and Ge-Ge interfaces is significantly greater than that at 45°. This indicates that the increase in interfacial thermal conductivity is significantly higher at a torsion angle of 0° than at 45°. Without normal load and interfacial well depth, the system energy is at its lowest. Increasing the normal load and strengthening the interfacial well depth easily pulls the system away from the lowest energy point, reducing the interfacial distance and enhancing potential energy interaction at the interface. This further increases the force constant, increasing the probability of phonons carrying energy for cross-interfacial heat transport, leading to an increase in ITC. Therefore, the current research in this invention shows that increasing the well depth and increasing the normal load have similar effects on interfacial thermal conductivity, and both methods can effectively control interfacial heat transport.

[0094] In summary, this invention achieves effective control of ITC by adjusting the torsion angle, normal load, and potential well depth, providing an important foundation for thermal management of nanodevices. More importantly, the proposed framework can be used in conjunction with existing methods, providing theoretical guidance for designing nanodevices with controllable interfacial thermal conductivity.

[0095] The above embodiments illustrate the principles and implementation methods of the present invention. These explanations are merely for the purpose of helping to deepen the understanding of the method and core ideas of the present invention. It should be noted that those skilled in the art can make various improvements and modifications to the present invention without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A method for controlling the thermal conductivity of a nano-semiconductor interface under contact and non-contact conditions, comprising the following steps: (1) Establish a molecular dynamics thermal transport model consisting 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 crystal structure. The thermal region A comprises silicon or germanium heat-transfer atomic regions, a heat source, and a rigid body, and in... x , y , z Set non-periodic boundary conditions in the direction; The cold region B includes a silicon or germanium heat transfer atomic region, a cold source, and a fixing layer; The rigid body and the fixed layer are each composed of a single unit cell and are respectively set in the model. z The two ends of a direction; A heat transfer interface is formed between the hot region A and the cold region B; Berendsen thermostats were installed at both ends of the model to regulate the system temperature. (2) Performing molecular dynamics simulations and data processing: ① Under contact conditions, the torsion angle range is taken as 5~45°, and the heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces are set to 320 K and 280 K, respectively. The interfacial thermal conductivity under different torsion angles is compared to determine the dependence of interfacial thermal conductivity on torsion angle. The overlapping area of ​​phonon state density at the contact interface under different torsion angles is also compared to determine the influence of the overlapping area of ​​phonon state density on thermal transport at different interfacial torsion angles. ② In the non-contact state, the torsion angle range is taken as 0~45°, and the heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces are set to 320 K and 280 K, respectively. The interfacial thermal conductivity under different torsion angles is compared to determine the dependence of interfacial thermal conductivity on torsion angle. The force constants of the interfacial interaction potential and LJ potential under different torsion angles are also compared to determine the influence of the force constants on the thermal transport under different interfacial torsion angles, further revealing the intrinsic reasons for the influence of different torsion angles on interfacial thermal transport under the non-contact state.

2. The method for controlling the thermal conductivity of a nano-semiconductor interface under contact and non-contact states as described in claim 1, characterized in that: The molecular dynamics simulation and data processing in step (2) further includes: in the contact state, taking the torsion angle range of 5~45°, and setting the heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces to 320 K and 280 K respectively, comparing the phonon participation rate and interface distance of the contact interface under different torsion angles, and further revealing the intrinsic reasons why the interface contact state affects the interface thermal conductivity.

3. The method for controlling the thermal conductivity of a nano-semiconductor interface under contact and non-contact states as described in claim 1, characterized in that: Step (2) of performing molecular dynamics simulation and data processing also includes: in a non-contact state, setting the heat source and cold source temperatures of the silicon-silicon and germanium-germanium interfaces to 320 K and 280 K respectively, calculating the force constants of the interfacial interaction potential and LJ potential under different normal loads or changes in the potential well depth, and revealing the intrinsic mechanism of the influence of the system normal load and potential well depth on the interfacial thermal conductivity.

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