以分子動力學模擬研究矽鍺材料在奈米尺度下之熱傳相關性質

Abstract

本論文採用平衡分子動力學數值工具來研究矽/鍺塊材、薄膜、奈米線以及超晶格薄膜之聲子色散關係及態密度，並使用非平衡分子動力學研究矽薄膜平面方向與矽奈米線軸向之熱傳現象。模擬中，原子作用力採用兼具有二體及三體勢能的Stillinger-Weber勢能函數。 在聲子色散關係研究中發現，薄膜/奈米線等結構之色散曲線與塊材最大的不同在於離散模式的產生，超晶格薄膜在平行薄膜平面方向也是，但在垂直薄膜平面方向則是產生了迷你布里淵區。在態密度方面，薄膜與奈米線隨尺寸變化的趨勢相同，但奈米線之變化較劇烈，都是尺寸愈小，分佈愈往低頻移動。超晶格薄膜之週期厚度對其態密度的影響不大，且矽鍺層之態密度與其本身材料之塊材相似，但多出許多峰值，對應色散曲線中之菱形結構。 在熱傳導係數的模擬中我們以奈米結構之態密度做量子修正，並以外插法消除數值的尺寸效應。薄膜與奈米線隨著溫度的增加，熱傳導係數先因聲子被激發的模式增多而增加，之後因為倒逆散射的機制增強而漸漸減小；尺寸愈大時，上述趨勢形成之峰值愈明顯。在薄膜量子修正方面，發現應以奈米結構下的聲子態密度進行量子修正為佳，其熱傳導係數隨溫度的變化趨勢與理論在固定鏡射率下的計算曲線相符。最後本論文亦嘗試以調整表面位能來控制薄膜表面粗糙度，但由於統計誤差的影響，在模擬的表面粗糙度範圍內並沒有觀測出熱傳導係數隨表面粗糙度增加而降低的趨勢。

This thesis employs the equilibrium molecular dynamics (EMD) simulation to calculate the phonon dispersion relations and density of states of Si/Ge bulk materials, thin films, nanowires as well as superlattice thin films. It also applies the non-equilibrium molecular dynamics (NEMD) simulation to a calculation of the in-plane thermal conductivity of silicon thin films and the axial thermal conductivity of silicon nanowires. In the simulations, the Stillinger-Weber (SW) potential, including both the two-body and the three-body interactions, is adopted. As far as the dispersion relations are concerned, remarkable differences between bulk materials and thin films/nanowires are observed. In particular, the latter possesses many discrete vibration modes. These modes are also observed in the in-plane spectrum of the superlattice thin films; mini-Brillouin zones are generated in the cross-plane spectrum on the other hand. As the film/wire thickness decreases, the phonon DOS tends to shift to the lower frequencies. The lower dimension, the more the shift is. The superlattice period shows little effect on the DOS of superlattice thin films and the DOS of each layer is similar to its bulk counterpart, in spite of numerous additional peaks corresponding to the rhombus structures appearing in the cross-plane spectrum. In obtaining the thermal conductivity, both the quantum correction based on the measured DOS of the associated nanostructure and the elimination of the finite-size error by an extrapolation technique are performed. It is found as the temperature increases, the thermal conductivities of thin films and nanowires increase first because of the increased excited phonon modes and then decrease due to the enhanced Umklapp scattering. A peak value is thus observed at some temperature. Finally, an attempt is made to control the surface roughness of thin films by adjusting the model parameters associated with the surface potential. However, the computed thermal conductivity does not as expected decrease with the increasing surface roughness, which is attributed to the non-negligible statistic error.