界面熱阻對非平板薄膜系統熱傳導效應之分析

Abstract

本文主要在探討微觀尺寸下圓柱形及球形多層薄膜內(Multi-layer thin film)界面熱阻對熱傳導現象的影響。在極微小尺寸下，當薄膜尺寸小至與材料的平均自由路徑相同級數時，熱傳導的行為已非巨觀下連續的概念所能描述。本文中自行推導出圓柱座標及球座標下的聲子輻射熱傳模式，探討微小尺寸下薄膜熱物理性質的改變。在界面處以非彈性散異理論模式來分析界面熱阻的影響。由研究結果發現，薄膜尺寸愈小，造成邊界上的溫度落差愈大，聲子的穿透現象(Ballistic transport)愈明顯，薄膜的熱傳導係數也隨著薄膜尺寸的縮小而愈小。此時薄膜內的聲子處於高度不平衡狀態，降低了能量傳遞的能力，與實驗結果比較亦相當符合。曲率的改變對薄膜熱傳導係數亦有明顯的影響，曲率愈大造成薄膜內聲子的碰撞機率增加，使得熱傳導係數愈大，其中又以球形薄膜受曲率的影響最大。在界面處以非彈性散異理模式來分析界面熱阻的影響。由研究結果得知，以非彈性散異理論模式所得到的界面熱阻可視為一定值，曲率及尺寸的改變對熱阻大小所造成的影響並不明顯。

This study deals with the effects of interface thermal resistance on the heat transfer for a non- planar thin film system based on the microscopic heat transport theory. In the acoustic thin limit, where the film thickness is much less than the phonon mean free path, macroscopic heat transport theory can’t be applied. The equation of phonon radiative transfer is applied to analyze the effects of curvature and film thickness on the thermal conductivity of thin film system, including interfacial effects. The results showed a significant reduction of effective thermal conductivity when the film thickness is getting thinner. Phonon heat conduction is in high non-equilibrium state inside the film and boundary scattering effect is dominant here. The agreements between the present predictions of the thermal conductivity and the experimental data are achieved. Furthermore, curvature also has significant effect on the thermal conductivity. Larger curvature would enhance energy transport inside the thin film. Regarding for inelastic diffuse mismatch model, thermal resistances can be treated as a constant. Both size and curvature effects can’t be evident to see.