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通过建立声子散射概率函数描述声子在输运过程中的散射,提出了一种模拟声子弹道扩散导热的蒙特卡罗方法,并将其应用于硅纳米薄膜中的稳态和瞬态弹道扩散导热过程的研究.提出的蒙特卡罗方法对边界发射的声子束进行跟踪,根据散射概率函数模拟声子束在传播区域内经历的散射过程,并通过统计声子束的分布得到温度分布.稳态导热过程的模拟发现,尺寸效应会引起边界温度跳跃,其值随着Knudsen数的增大而增大;计算的硅纳米薄膜的热导率随着厚度的增大而增大,与文献中的实验数据和理论模型相符.通过瞬态导热过程的模拟得到了纳米薄膜内的温度分布随时间的变化,发现瞬态导热过程中的热波现象与空间尺度相关,材料尺寸越小,弹道输运越强,薄膜中的热波现象也越显著.
A phonon-based Monte Carlo method is proposed to simulate the propagation of phonons through the establishment of phonon scattering probability function. The proposed method is applied to the steady-state and transient trajectories of silicon nanofilms The research on the diffusion and thermal conduction process. The proposed Monte Carlo method tracks the phonon beam emitted from the boundary and simulates the scattering process of the phonon beam in the propagation area according to the scattering probability function. The temperature distribution is obtained through the distribution of the statistical phonon beam Simulations of steady-state thermal conduction show that the size effect causes a jump in the boundary temperature and increases with Knudsen’s number. The thermal conductivity of the calculated silicon nanofilms increases with increasing thickness, The experimental data in the literature are consistent with the theoretical model.The temperature distribution in the nanofilm over time is obtained through the simulation of the transient thermal conduction process and it is found that the thermal wave phenomenon in the transient thermal conduction is related to the spatial scale and the smaller the material size, The stronger the ballistic transport, the more pronounced the thermal wave in the film.