超晶格薄膜平面方向晶格熱傳導係數之分析

Abstract

當熱電元件尺寸縮小時，其晶格熱傳導係數會因尺寸效應而降低，致冷效率因而提升。其中超晶格薄膜是由不同材質之薄膜週期性堆疊而構成，內部存在多層介面，使得熱傳導係數可更顯著地降低。本論文主要研究目標在重建一個計算超晶格薄膜平面方向晶格熱傳導係數之理論，其次再探討溫度記憶效應所造成之影響。整個分析的理論基礎是以粒子說觀念來處理聲子，以鬆弛時間近似法來求解聲子波茲曼傳遞方程式，得到受邊界影響而改變的非平衡聲子分佈，再配合適當之聲子色散關係及鬆弛時間模型以求出熱傳導係數。從分析中得知，由於聲子接觸到超晶格薄膜之介面時會產生反射或穿透之情形，在經過無數次與介面作用後會使聲子熱流量降低，並且當薄膜厚度降低時，與邊界作用之次數會更加頻繁故上述之效應會愈趨明顯，這些因素都會導致超晶格薄膜平面方向之晶格熱傳導係數驟降。從預測出的熱傳導係數與溫度、厚度的關係來看，皆與前人之實驗數據相當一致。並且發現在適當的厚度比下，可將熱傳導係數降到最低。而在分析溫度記憶效果後，可推論在室溫附近可忽略其所造成之影響。

It is known that the thermal conductivity of a thin-film superlattices semiconductor has a larger figure-of-merit, mainly because its thermal conductivity is significantly reduced by the size effects. The goal of this study is to re-establish a theory for calculating/predicting the in-plane lattice thermal conductivity of a thin-film superlattices semiconductor. The theory is particle-based for the thickness of each layer still being larger than the phonon coherent length scale. The phonon Boltzmann transport equation is thus solved under the single relaxation-time approximation and proper boundary conditions. From the calculation results of the present model, it is found that the phonon heat flow rate is largely decreased due to the infinitely many interactions between phonons and the partially specular and partially diffuse interfaces through reflections and refractions. Moreover, the thinner each layer, the stronger the interface scattering effect is. An optimum thickness ratio resulting in a minimum lattice thermal conductivity is also found due to a balance between the difference of the intrinsic thermal conductivities and the boundary scattering effect. It is also shown that the predicted thermal conductivities also agree well with the experimental measurements. Finally, the temperature-memory effect on the lattice thermal conductivity is found to be negligible at room temperature.