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研究生:傅薈如
研究生(外文):Huei-Ru Fuh
論文名稱:利用第一原理計算研究應變下[110]矽奈米線的電子結構
論文名稱(外文):Ab inito study of electronic properties of strained [110] Si nanowires
指導教授:郭光宇郭光宇引用關係
指導教授(外文):Guang-Yu Guo
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:物理研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:英文
論文頁數:48
中文關鍵詞:第一原理應變矽奈米線電子結構有效質量
外文關鍵詞:first principlestrainsilicon nanowireelectronic band structureeffective mass
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近十年來,矽是被用於製造大量電子元件的材料。由於在電子元件介面上不可避免的晶格不匹配,使得應變效應普遍存在於半導體的電子元件中。此應變效應在奈米尺度下對電子結構及其電學性質有顯著的影響。
  利用應變效應可以用來有效操控半導體奈米線的物理性質。本篇論文主要透過第一原理計算了解並改變[110]矽奈米線在應變效應下電子結構及電子態性質。本文使用OpenMX (Open source package for Material eXplorer) 計算軟體,這套軟體是建構在密度泛函理論(DFT)之下,所使用的模守恆贗勢(NCPPs),並使價電子區域波函數局域化,使得在計算過程中達到電腦計算時間與原子數呈線性關係[O(N)]。
  計算結果顯示出[110]矽奈米線在未加應變效應下有直接能隙,當直徑越大能隙會越小。在外加足夠的張應變與壓應變下會使得能隙從直接能隙變成間接能隙。電子的有效質量會隨著壓應變而變大,隨著張應變趨近一定值(0.15m0);電洞的有效質量隨著壓應變而變小,隨著張應變而變大。電子和電洞在能帶邊緣(CBM、VBM)的電荷密度分布,在應變效應下並無顯著的影響,電荷主要分布在奈米線的中心位置。
For decades, silicon has been the material of choice for mass fabrication of electronics. Strains always exist in semiconductor electronic devices. Due to unavoidable lattice mismatches at interfaces, effects of strains on the electronic, electrical properties would be particularly significant at nanometer scales.

Strain effect can be used to manipulate the physical properties of semiconductor nanowires. Here, we can make use of the strains to enhance the electronic properties through ab initio calculations of strained [110] silicon nanowires.

The electronic structure of strained [110] silicon nanowires have been studied with the density functional theory (DFT) using the norm-conserving pseudopotentials (NCPPs). The electronic states are found by O(N) Krylov-subspace method, as implemented by OpenMX (Open source package for Material eXplorer) code. The calculation results show that the band structure of silicon nanowires tends to have an indirect band gap under compressive and tensile strain. Under tensile strain, the electron effective mass remains almost unchangd (∼0.15m0) while the hole effective mass increases slightly. Under compressive strain, the electron effective mass increases significantly, while the hole effective mass decreases slightly. The valance band maximum (VBM) state and conduction band minimum (CBM) state charge density are always distributed inside the silicon nanowires structure with applied strain.
1 Introduction ...6
2 Density functional theory ...7
2.1 Density functional theory ...7
2.1.1 The Hohenberg-Kohn theorems...7
2.1.2 The Kohn-Sham equations ...9
3 Electronic structure computational methods ...12
3.1 Calculation method ...12
3.1.1 About OpenMX ...12
3.2 Norm-conserving pseudopotentials (NCPPs) ...13
3.3 Pseudo-atomic localized basis functions ...14
3.3.1 Localized atom-centered orbitals ...14
3.3.2 Total energy term in OpenMX ...15
3.3.3 Two-center integrals ...17
3.4 Locality and linear scaling O(N) methods ...19
4 The electronic properties of bulk Si ...22
4.1 The bulk Si band structure ...22
4.2 The strained bulk Si ...24
5 The quantum confinement theory ...27
5.1 The Si nanowires confinement theory ...27
6 Atomic and electronic structures of strained [110] Si nanowires ...33
6.1 The [110] silicon nanowires structure ...33
6.2 The conduction band strucutre ...36
6.3 The valence band strucutre ...37
6.4 The band gap properties ...38
6.5 Effective mass ...41
6.6 Nature of the band-edge orbitals ...44
7 Summary ...46
Bibliography ...47
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