奈米尺度聲子熱傳之介面效應分析

Abstract

在宏觀的尺度下，物質可視為連續體，並可由宏觀的方程式主導。當物質尺度越來越小時，特徵尺寸到達粒子間的距離，此時，連續體的假設不再適用，宏觀方程式不能準確預測物體的行為。波茲曼方程式以粒子的觀點出發，以平均的概念求得物體的行為，因此得以用來主導微觀尺度之下物體的行為。 在微觀尺度下，物質內部碰撞的次數大為減少，於是介面的反應機制更為重要。本文使用波茲曼聲子熱輻射方程式以有限差分法解一維及二維熱傳問題。探討在散射介面與鏡射介面反應機制之下，對於聲子的熱傳性質的影響。 在尺度越來越小時，兩種介面機制的熱傳係數皆減小。散射介面所得到的熱傳係數較鏡射介面為大，但是都比塊材的熱傳係數小。介面的分佈方向也影響著熱傳係數，介面的方向與熱傳方向呈垂直時，所形成的熱阻較大，熱傳係數也就越小。

In the past decades, thermal conductivities of nanostructures have attracted considerable attention with the increased importance of nanodevices. Experimental results showed that the thermal conductivities of nanostructures are often smaller than those of their corresponding bulk material. The causes of the reduction of thermal conductivity include the micro-structural difference and the boundary and interface effects. There are two groups to model the thermal conductivities in nanostructures. One group is wave models, which assumes that phonons form superlattice bands and calculates the modified phonon dispersion using lattice dynamics. The other group is particle models, which assumes that the major reason for reduction of the thermal conduction is the scattering of phonons at interfaces. This thesis focus on the particle models in one-dimension and two-dimension nanostructures for studying the thermal conductivities. As the size becomes smaller, the larger temperature drop at the interfaces occurs which is resulted from the ballistic transport and the effect of interface. There are many theories for treating the reaction of phonons striking onto the interface, such as acoustic mismatch model(AMM), diffuse mismatch model(DMM), and inelastic mismatch model(IDMM). The results of simulation shows that the temperature jump at the interface of acoustic model is larger than diffuse model. The thermal conductivities of all models are decreased as the decreasing of thickness. And as the films thick, the thermal conductivity approaches the value of bulk.