以分子動力學模擬研究矽鍺材料之介面熱阻及介面穿透率

Abstract

近年來因高介面密度材料的低熱傳導係數能改善熱電元件的效率，所以受到廣泛的研究，然而介面如何影響聲子傳輸之詳細機制迄今未明。因此本研究乃企圖利用分子動力學模擬工具來研究矽/鍺合金介面的熱傳性質。 在此研究中，矽及鍺原子間作用力是採用兼具二體及三體勢能的Stillnger-Weber勢能函數，介面參數的設定包括介面厚度及介面內鍺原子佔有的比例。研究發現，介面厚度為10UC時，介面熱阻隨鍺原子比例先增後減，於鍺原子比例為0.5時達到最大；當介面厚度為2UC時，熱阻變化卻呈現W字型，在鍺原子比例為0.5的兩側出現兩個比完美介面熱阻值還低的局部最小值。 本研究進一步設計縱波與橫波穿透率實驗來了解相關機制。研究結果顯示，縱波不論經過厚或薄介面，除了最長的縱波波包(k=0.1(2 /a))外，隨著鍺原子比例增加，穿透率皆呈V字型分布，在鍺原子比例為0.5時為最低；此與前述觀察到之介面厚度10UC時之熱阻變化趨勢一致，顯示在此介面厚度下矽鍺原子質量不匹配所造成的散射是造成熱阻的主因。此外，我們也觀察到當聲子經過合金介面時會發生極化之轉變與非彈性散射，使得較多橫波聲子得以穿透介面，因此合金介面熱阻值才有機會比完美介面還要低。而當鍺原子佔有比例增加時，前述效果卻不敵質量不匹配散射所帶來的影響，故而在2UC介面的熱阻計算中才出現了介面熱阻呈現W字型的結果。

In recent years, studies show materials embedded with high-density interfaces are potential candidates for thermoelectric devices due to their low thermal conductivities and acceptable power factors. Yet, the detailed mechanism of the phonon transmission through the interface is still unclear. This study aims at exploring the transport phenomena of phonons through the Si/Ge alloy interfaces in use of the molecular dynamics simulation. Also targeted are the involved thermal boundary resistance (TBR) and the effects of the interface thickness and composition on TBR. In this study, the Stillinger-Weber (SW) potential was used to describe the interaction among Si and Ge atoms. Two interface thicknesses, 10UC and 2UC, were attempted. The simulation results show that as the Ge atomic concentration ( ) increases, the TBR associated with the 10UC-interface increases first, peaks at =0.5, and decreases thereafter. On the other hand, the variation trend of the TBR associated with the 2UC-interface appears to be W-shaped; two local minimums, even below the TBR of the perfectly smooth interface, are observed at =0.1 and 0.9. For illumination, wave-packet numerical experiments were designed and performed. The investigation indicates that except the very long longitudinal wave, the variation trend of the transmissivity of the longitudinal waves against the Ge concentration is V-shaped, minimized at =0.5, consistent with the variation trend of the TRB associated with the 10UC-interface and implying the dominance of the mass difference scattering in determining the TBR. Furthermore, the polarization change and inelastic scattering were both observed as waves passed through the alloy interfaces, thereby allowing more phonons to transmit. When the mass difference scattering is weak (i.e. thin alloy interface and low mass difference), the above two mechanisms possibly lead to a TBR smaller than the TBR associated with the perfectly smooth interface. This explains the observed W-shaped variation trend of the TBR associated with the 2UC-interface against the Ge concentration.