尺寸效應與界面熱阻對超晶格奈米線熱傳導之影響

Abstract

本文應用二維圓柱座標聲子輻射熱傳方程式，搭配修正後的聲子平均自由徑，模擬奈米線內部的熱傳問題；且進一步應用非彈性散異理論模式的假設，模擬界面熱阻對超晶格奈米線熱傳之影響。本文主要在探討溫度、幾何尺寸、界面熱阻及材料組成比率對超晶格奈米線等效熱傳導係數之影響，以提供作為未來發展熱電材料的依據。本文研究發現利用本文修正後的聲子平均自由徑，超晶格奈米線的等效熱傳導係數降低了約三分之一到二分之一左右。且超晶格奈米線的等效傳導係數受到徑向及軸向尺寸效應的雙重影響，隨著週期厚度及直徑的縮小而降低。當超晶格奈米線週期厚度小於直徑時，界面熱阻在總熱阻中所扮演的角色隨著週期厚度的縮小，越來越重要，此為「超晶格結構」的特徵；反之，當週期厚度大於直徑時，界面熱阻隨著週期厚度的增加而急遽下降，此時超晶格奈米線內部的熱傳行為趨近於「奈米線結構」，其等效熱傳導係數隨著低熱傳導係數含量的減少而降低。

The size effects on thermal conductivity of superlattice nanowires with circular cross-section are investigated. The effective thermal conductivity of superlattice nanowires is predicted by using equation of phonon radiative transfer. The inelastic mismatch model (DMM) is applied to simulate the interface thermal resistance. The effective thermal conductivity of superlattice nanowires is dependent on temperature, the diameter, the periodic length and the volumetric fraction of the constituent materials. The results show that the effective thermal conductivity of Si/Si0.9Ge0.1 superlattice nanowire is reduced by a factor of 3 or 2 by correcting phonon mean free path. As the result of radial and axial size effects, the effective thermal conductivity of superlattice nanowires decreases with reduction of the diameter and the periodic length. When the periodic length is smaller than the diameter, the interface thermal resistance plays an important role on heat conduction of superlattice nanowires, however, as the periodic length increases, the dominative degree of interface thermal resistance gets more and more slight. When the periodic length is smaller than the diameter, the heat conduction of the superlattice nanowire is analogy to of the nanowire. In this regime, the lower the atomic percentage of low thermal conductivity material is, the lower the effective thermal conductivity of superlattice nanowires. The results of this study can be used to develop high efficiency thermoelectric materials.