臺灣博碩士論文加值系統

一維奈米結構由於其材料特性優異，而被用於半導體產業，例如半導體奈米線方面，而當材料尺寸縮小至奈米等級時，就無法以傳統力學的分析方法來加以研究，所以本論文將用分子模擬方法，來研究一維奈米線的機械性質。
本論文將會使用不同分子模擬方法，對於奈米材料的機械性質做一系統的比較，例如:楊氏係數、波松比和降伏應力會有何不同，藉以釐清是否有些現象只是因為所採用的分子模擬方法而造成的，而非材料本身的特性所致。另外，希望經由分子模擬結果，來解釋彈性常數於不同晶格方向，為何會變軟與變韌，並更進ㄧ步地探討其發生原因。
模擬結果中發現，不同主胞室長度的奈米線在分子靜力學法中，不適合用於分析塑性行為，其降伏點會隨著主胞室長度而有所不同，而不同晶格方向奈米線其彈性常數，和其表面應力與內部應力間的消長有關，[100]和[111]奈米線其彈性常數會隨著線寬變小而變軟，110]
奈米線則隨著線寬變小而變韌。

One dimensional nanostructures (i.e., nanowires) have been widely used in semiconductor industry due to their unique material characteristics. It is known that the properties of nanomaterials could not be realized by traditional mechanics. Our research systematically adopts
both molecular statics and dynamics simulation to study the mechanical properties (i.e., Young’s modulus, Poisson’s ratio, yield stress, etc) of nanowires in order to clarify the size dependence of mechanical properties for nanowires. The underlying mechanisms for the size effect are also examined.
It is shown from both molecular methods that the mechanical properties of nanowires depend on the lateral size of nanowires and the trend of size dependence is significantly influenced by the crystal orientations It is found that molecular statics method may not be a good way to analyze the plastic behavior of nanowires since the yield stress would be altered due to the periodic size length.

目錄
中文摘要………………………………………………………………I
英文摘要…………………………………………………………… II
誌謝………………………………………………………………… III
目錄……………………………………………………………………IV
圖目錄………………………………………………………………VIII
表目錄………………………………………………………………XIV
符號說明………………………………………………………………XV
第一章 緒論..............................................................................................1
1.1 前言...............................................................................................1
1.2 文獻回顧.......................................................................................2
1.2.1 分子靜力學文獻回顧.........................................................3
1.2.2 分子動力學文獻回顧.........................................................3
1.2.3 以分子動力學研究奈米線機械性質之文獻回顧............4
1.2.4 尺寸效應機制文獻回顧.....................................................7
1.3 研究動機.......................................................................................8
1.4 本文架構.......................................................................................9
第二章 分子靜力學與分子動力學原理................................................10
2.1 分子靜力學.................................................................................10
2.1.1 最速下降法[25] ................................................................10
2.1.2 共軛梯度法.......................................................................12
2.2 分子動力學.................................................................................13
2.2.1 分子動力學之基本假設...................................................13
2.2.2 勢能函數...........................................................................14
2.2.3 邊界條件與最小映像法則...............................................16
2.2.4 截斷半徑...........................................................................17
(a) Verlet 表列法..................................................................18
(b) Cell link 表列法.............................................................18
2.2.5 運動方程式.......................................................................21
2.2.6 Gear's 五階預測修正法....................................................21
2.2.7 系統速度、溫度修正.......................................................25
2.2.8 原子應力...........................................................................25
第三章 分子靜力學模擬方法與結果....................................................27
3.1 原子模型.....................................................................................27
3.2 程式模擬流程.............................................................................28
3.3 程式驗證.....................................................................................29
3.4 模擬規劃.....................................................................................31

3.5 模擬方法.....................................................................................34
3.6 模擬結果.....................................................................................35
3.6.1 晶格間距...........................................................................35
3.6.2 彈性常數...........................................................................36
3.6.3 表面應力...........................................................................37
3.6.4 截面形狀...........................................................................38
3.6.5 塑性行為...........................................................................39
第四章 分子動力學模擬方法與結果....................................................64
4.1 程式模擬流程圖.........................................................................64
4.2 程式驗證.....................................................................................66
4.3 模擬規劃.....................................................................................67
4.4 模擬方法.....................................................................................68
4.5 模擬結果.....................................................................................69
4.5.1 晶格間距...........................................................................69
4.5.2 楊氏係數...........................................................................69
4.5.3 降伏應力...........................................................................69
第五章 結論與未來展望........................................................................78
5.1 結論.............................................................................................78
5.2 未來展望.....................................................................................79
參考文獻......................................................82
附錄A.........................................................84

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