尺寸效應和界面熱阻對熱電致冷器性能之影響

Abstract

本文用聲子輻射熱傳方程式來處理在微尺度下材料內部的熱傳導現象，分析超晶格(superlattice)中薄膜內部一維的熱傳問題，並用非彈性散異理論處理薄膜間所造成的界面熱阻問題。本文主要在探討超晶格結構之熱電材料中，層數多寡和薄膜厚度變化對其等效熱傳導係數的影響，並討論對熱電材料之熱電優值(figure-of-merit)的影響。本文研究發現超晶格結構下每一層薄膜的厚度就會決定其等效熱傳導係數的大小，在每一層薄膜厚度固定下，並不會因為層數增加而改變超晶格的熱傳導係數，對熱電優值當然也是一樣。當每一層薄膜厚度和材料之聲子平均自由路徑相當時，尺寸效應造成熱傳導係數降低的現象最為顯著。界面熱阻不會隨超晶格厚度的改變而有所變化，僅和層數多寡有關，且厚度越小，界面熱阻在超晶格的總熱阻中所扮演的角色越重要。對於使用Bi2Te3/Sb2Te3的超晶格作為熱電材料來說，不論超晶格總厚度的大小，單層薄膜的厚度越小對熱電優值的提升越有幫助。

This study discusses the problem of one dimensional thermal transport inside the superlattice structure. Equation of phonon radiative transfer and inelastic diffusive mismatch model were used to analyze small scale heat transfer and interface thermal resistance respectively. This study focuses on the effects of variations of periods and thickness on the effective thermal conductivity and figure-of-merit of superlattice used for thermoelectric materials. When the thickness of each thin is fixed, the effective thermal conductivity and figure-of-merit would not change with periods. It is noticed that when the thickness of each film is comparable to phonon mean free path, the effect of size on decrease of thermal conductivity is significant. Otherwise, interface thermal resistance changes with only periods but thickness of superlattice, and it plays an important role as thickness of superlattice decreases. If Bi2Te3/Sb2Te3 superlattice is used for thermoelectric material, no matter how thick superlattice is, it is helpful to increase figure-of-merit when the thickness of each film is thinner.