矽、鍺不同晶格面的熱傳導之分子動力學模擬

Thermal Conductivities of Si and Ge at Different Index Planes by Molecular Dynamics Simulation

張偉庭(Wei-Ting Chang)

指導教授 ： 楊照彥

國立臺灣大學/工學院/應用力學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.00306

摘要

近年來在奈米碳管,奈米線,和微奈米尺度的超合金等問題上有廣泛被加以討論及模擬研究,本論文主要是在模擬研究奈米尺度下四價元素矽,鍺在不同晶格面的熱傳導量之比較,而所用方法為分子動力學法,其所運用到的運動方程式為古典力學中的牛頓力學,和漢彌爾頓方程式。分子初始位置是由鑽石結構單位晶包週期性排列,以有限的塊材來表示無限邊界的晶格排列,分子初始速度是由統計力學中麥克斯威爾分佈來加以給定。因為四價元素的鍵結主要為共價鍵屬於三體勢能且需要考慮到分子間的鍵角角度問題,所以選用Tersoff位勢能函數可以來計算共價鍵元素之間作用力和分子加速度,再由Velocity-Verlet積分方法可以得到每個分子新的位置和新的速度,因此在平衡狀態之下求得x,y,z三個方向的熱通量,經過不同時間的熱通量再來計算自我相關函數,最後再由Green-Kubo關係式得到熱傳導量。

關鍵字

分子動力學 ； 漢彌爾頓方程式 ； Tersoff位勢能函數 ； 自我相關函數 ； Green-Kubo關係式

並列摘要

In recent years, many researches on nanotube, nanowire, and superlattices have been carried out. In this thesis, we study the thermal conductivities of silicon and germanium at different index planes in the nanoscale. The simulation method used molecular dynamics simulation, and the governing equation is Hamiltonian equations of motion in classical Newtonian mechanics. The molecular initial position of a diamond unit cell structure is used for periodic boundary condition and expresses the infinite boundary crystal lattice arrangement by the limited bulk material. The molecular initial velocity is determined by Maxwell-Boltzmann distribution. Because silicon and germanium mainly belongs to three body potential for the covalent bonding and also the needs to consider the intermolecular bonding angle, we choose Tersoff potential to calculate covalent bonding intermolecular force and molecular acceleration. We obtain each molecular new position and the new velocity by the Velocity-Verlet integration method, and obtain the heat flux under the state of equilibrium. Through the different time evolution, we calculate the autocorrelation function from heat flux. Finally, we calculate the thermal conductivity by Green-Kubo formalism. We compare the thermal conductivities of silicon and germanium at different index planes.

並列關鍵字

molecular dynamics simulation ； Hamiltonian equations of motion ； Tersoff potential ； autocorrelation function ； Green-Kubo formalism

參考文獻

23. “單壁奈米碳管儲氫性能之分子動力學模擬”黃怡翔撰 民93[2004]

24. “單壁奈米碳管機械性質之分子動力學模擬”吳明彥撰 民95[2006]

25. “單壁奈米碳管彈力性質之分子動力學模擬”謝志明撰 民94[2005]

2. Bird, G. A., Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon Press .Oxford(1994)

4. S. Iijima, Helical Microtubles of Graphitic Carbon, Nature, Vol. 354, pp.56 (1991)