利用晶格波茲曼法之奈米尺度聲子熱傳模擬

Abstract

近年來隨著製程技術的迅速發展，半導體產業、光電產業及微機電系統的需求，使微型化成爲趨勢，其中材料的熱物理性質也隨著尺度的縮小而與傳統尺度的物理現象有所不同，用於研究巨觀熱傳現象的傅立葉熱傳導定率(Fourier Law of Heat Conduction)將不適用。其中原因爲在巨觀下，分子可視爲連續體，對於連續介質現象，利用傳統的連續、動量及能量方程，即可求得系統的巨觀變量；然而在微尺度中，分子碰撞減少，只可利用分子動力學方法經過適當的積分後，導出連續方程，由微觀推導出巨觀公式。 本研究採用晶格Boltzmann法(Lattice Boltzmann Method, LBM)模擬微尺度熱傳問題，此方法於近十年間，逐漸受到廣泛的使用。本文利用週期性邊界條件取出週期性單元作爲模擬區域，於材料邊界使用非彈性擴散失諧理論模式。由研究結果可發現，矽(Si)薄膜、鍺矽(Ge-Si)薄膜及孔洞材料不僅有尺寸效應，於微尺度下材料界面產生的界面散射將使熱傳導係數下降及溫度分布產生滑移。

Current microfabrication technologies have allowed the semiconductor industry, photovoltaic industry and microelectromechanical system to produce smaller devices. Microscopic heat transfer differs from macroscopic. Micro-scale heat transfer no longer follows the Fourier law. In macroscopic scale, substance is considered as continuum, and the transport phenomena can be described by macroscopic governing equations. As the size shrinks, heat carriers become rarefied when characteristic length of the thin film is comparable with the molecule mean free path. Because the frequency of the carriers collision decreases, we need to consider motions and interactions of the individual molecules. This article uses Lattice Boltzmann Method to solve phonon Boltzmann-BGK equation and simulate heat transfer in the thin film with different material arrangement. Several geometries are studied including: Si thin film, Ge-Si embedded supper lattice, Ge-Pore embedded supper lattice and Ge-Si compacted supper lattice. This research uses periodic boundary and IDMM interface boundary. Results suggest that reducing feature size will decrease the thermal conductivity, and temperature will become non-continuum distributions in the interface. And the effective thermal conductivity changes not only with the length of the thin film, but also with the boundary thermal resistance.