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標題: | 奈米薄膜之晶格熱傳導係數分析 The analysis of lattice thermal conductivity in thin film |
作者: | Tai-Ming Chang 張泰鳴 |
指導教授: | 黃美嬌 |
關鍵字: | 薄膜,聲子波茲曼方程式,晶格熱傳導係數, Thin-film,Phonon Boltzmann transport equation,Lattice thermal conductivity, |
出版年 : | 2005 |
學位: | 碩士 |
摘要: | 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。本論文主要目標在於重建一個計算單層奈米薄膜平面方向晶格熱傳導係數之理論。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輸方程式,並且考慮(i)受尺寸影響而改變的聲子色散關係;(ii)因邊界散射而改變的聲子非平衡分佈;(iii)求取熱傳導係數時,保有聲子群速為頻率之函數,使整個理論更具一致性;以及(iv)以最大允許波向量配合聲子色散關係求德拜溫度。從分析中得知,因薄膜空間上的限制造成聲子群速變慢、德拜溫度下降,而邊界的粗糙度也改變了聲子在原來塊材下的非平衡分佈,還有因尺寸效應而造成聲子邊界散射率增強,這些因素都會導致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、邊界粗糙度以及厚度的敏感度來看,皆與前人的理論分析和實驗數據相當一致。 The lattice thermal conductivity of a thin film structure is a critical issue to improve the figure of merit of thermoelectric materials. The main purpose of this thesis is to re-establish a theory for calculating the in-plane lattice thermal conductivity of a thin film. The theory is constructed based on the particle-concept. The phonon Boltzmann transport equation with the relaxation time approximation is solved. For completeness and consistency, the proposed theory takes into account (i) the modification of the acoustic phonon dispersion relation due to spatial confinement, (ii) the change in the non-equilibrium phonon distribution due to partially diffuse boundary scattering, (iii) the frequency -dependence of the phonon group velocity, and (iv) the adoption of the maximum allowed wave vector in order to calculate the Debye temperature according to the modified phonon dispersion relation. From the calculations, we predict that the decrease of the phonon group velocity and the Debye temperature, the increase of the boundary roughness and the enhanced phonon scattering lead to a significant reduction of the lattice thermal conductivity. The sensitivities of the thermal conductivity on the temperature, the boundary roughness, and the film thickness agree well recent theoretical and experimental investigations. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/36853 |
全文授權: | 有償授權 |
顯示於系所單位: | 機械工程學系 |
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