As one simple metamaterial, nanopatterns are often fabricated across a thin film so that the thermal transport can be manipulated. The etched sidewalls for these nanostructures are usually rough due to surface defects introduced during the nanofabrication, whereas the top and bottom film surfaces are smoother. In existing analytical models, the contrast between these surfaces has not been addressed and all boundaries are assumed to be diffusive for phonon reflection. In this paper, a new two-step approach to address this issue is proposed for phonon transport modeling of general thin-film-based structures. In this approach, the effective in-plane phonon mean free paths ({\Lambda}_Film) are first modified from the bulk phonon MFPs to account for the influence of the top/bottom film surfaces, with possibly enhanced probability of specular phonon reflection at cryogenic temperatures. This {\Lambda}_Film is further modified to include the scattering by etched sidewalls with almost completely diffusive phonon scattering. Such a two-step phonon mean free path modification yields almost identical results as frequency-dependent phonon Monte Carlo simulations for etched nanowires and representative nanoporous thin films. This simple yet accurate analytical model can be applied to general thin-film-based nanostructures to combine the phonon size effects along orthogonal directions.

中文翻译：

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用于薄膜纳米结构热导率预测的声子平均自由程的两步修正

作为一种简单的超材料，纳米图案通常在薄膜上制造，以便可以操纵热传输。由于在纳米制造过程中引入的表面缺陷，这些纳米结构的蚀刻侧壁通常很粗糙，而顶部和底部薄膜表面则更光滑。在现有的分析模型中，尚未解决这些表面之间的对比度问题，并且假设所有边界对于声子反射都是漫射的。在本文中，提出了一种新的两步方法来解决这个问题，用于一般薄膜结构的声子传输建模。在这种方法中，有效的面内声子平均自由程（{\Lambda}_Film）首先从体声子 MFP 中修改，以考虑顶部/底部薄膜表面的影响，在低温下可能增加镜面声子反射的可能性。该 {\Lambda}_Film 进一步修改为包括蚀刻侧壁的散射，几乎完全是散射声子散射。这种两步声子平均自由程修改产生与蚀刻纳米线和代表性纳米多孔薄膜的频率相关声子蒙特卡罗模拟几乎相同的结果。这种简单而准确的分析模型可以应用于一般的基于薄膜的纳米结构，以结合沿正交方向的声子尺寸效应。这种两步声子平均自由程修改产生与蚀刻纳米线和代表性纳米多孔薄膜的频率相关声子蒙特卡罗模拟几乎相同的结果。这种简单而准确的分析模型可以应用于一般的基于薄膜的纳米结构，以结合沿正交方向的声子尺寸效应。这种两步声子平均自由程修改产生与蚀刻纳米线和代表性纳米多孔薄膜的频率相关声子蒙特卡罗模拟几乎相同的结果。这种简单而准确的分析模型可以应用于一般的基于薄膜的纳米结构，以结合沿正交方向的声子尺寸效应。