薄膜內微觀熱傳導分析

Abstract

本文係以微觀角度來探討微小尺寸系統內之熱傳導現象。本研究採用聲子輻射熱傳模式分析薄膜熱傳問題，同時，亦分別應用傳利葉定律和熱波理論對此一問題作分析並比較三種模式之結果。在數值方法上，本研究採用雙熱通量模式（two-flux model）來求解聲子輻熱射熱傳方程式。本文首先對單層薄膜之熱傳導作一分析。比較三種模式所獲得結果之異同，並比較各物理參數所造成的影響。其中，聲子輻射熱傳模式在薄膜邊界上會有溫度落差產生。由研究結果顯示，影響聲子輻射熱傳模式最重要的參數是薄膜厚度與聲子平均自由路徑的比值。本研究之結果顯示，當薄膜厚度約100倍聲子平均自由路徑時，聲子輻射熱傳模式與傅利葉定律之結果吻合。在熱傳現象達到穩定狀態時，聲子輻射熱傳模式亦趨近於傅利葉定律之結果。對於雙層薄膜熱傅問題西方亦有所探討。同樣利用上述三種模式對雙層薄膜熱傳問題作一分析與比較。在不考慮界面熱阻的情形下，其與單層薄膜熱傳問題最大的不同是，熱波不但在邊界有反彈現象，而且在薄膜交界面處也有反彈波的生成。

This study discusses conductive heat transfer from microscopic point of view. Phonon radiative transfer model as well as Fourier's law and thermal wave theory are utilized to analyze heat conduction in thin films. Two-flux model is used to solve the equation of phonon radiative transfer. First, we analyze heat conduction in one layer thin film. Comparison of the results among the above three models has been done. Influence of physical properties on this problem is also the topic of the study. The solution of the equation of phonon radiative transfer produces temperature jumps at boundaries. The most important parameter in phonon radiative transfer model is the ratio of thin film thickness to phonon mean free path. The results show that phonon radiative transfer model approaches to Fourier's law when the film is getting thicker. In another way, phonon radiative transfer model also approaches to Fourier's law at steady state. Meanwhile, we also discuss heat conduction in two layer thin films. We use the above three models to analyze this problem. Under the assumption of no resistance exist at the interface, the most important difference from the one layer thin film is that, teermal wave not only bounded from the boundaries, but also from the interface.