臺灣博碩士論文加值系統

　　近年來由於半導體製程技術持續精進使得電晶體尺寸不斷微縮，同時短通道效應也成了電晶體尺寸微縮面對到的一大瓶頸，增加閘極對通道的控制或抑制汲極端的電壓對通道的影響，可以抑制短通道效應，像是鰭式電晶體，另外一個用來抑制短通道效應的方法就是直接把通道中較易受到汲極端電場影響的區域摘除，隨著尺寸微縮，當通道層厚度低到極致時就是單一原子層：二維材料的崛起。矽稀（Silicene），和第一個二維材料石墨稀相比，不僅具有與傳統矽基電晶體具有高度兼容性的潛在優勢，而且還保持了與石墨稀一樣的超高載子遷移率，使其備受矚目，而在2015年，矽稀電晶體的原型已被證明是可行的。
　　我們利用密度泛函來計算矽稀並模擬其與氧化層二氧化矽的接面性質，由於未加上應力的矽稀具有無能隙的的Dirac-cone，我們首先單獨計算矽稀加上應便力後的電子結構，並觀察其所打開的能隙可以做為應便力的函數，我們使用很廣泛的交換相關近似來進行運算，不僅包含了標準的局域密度近似以及廣義梯度近似，還包括了雜化泛函HSE06、PBE0和BE3LYP，甚至進一步考慮了超越密度泛涵理論，在計算材料的能隙方面上優於上述交換近似的GW理論，我們將矽稀放置在二氧化矽基板上並期許二氧化矽基板可以使矽稀造成應力打開能隙，為了避免再介面處兩層接面系統產生化學鍵，讓矽稀保留π鍵而維持Dirac-cone的高載子遷移率，我們需要仔細在二氧化矽接面處選擇適當的原子，並在接面處加入額外的鈍化元素，在我們的研究的所有情況中，發現矽截止面再加上氫原子鈍化的二氧化矽基板能提供矽烯高載子遷移率以及維持矽烯材料的完整性，更進一步的調查接面的鍵結，我們發現上述表面的最佳性質是由於鈍化原子解決了二氧化矽接面處懸鍵的關係，這個部分指示我們在矽烯放在二氧化矽的實驗製程中，可以進一步考慮使用氫、鹵素或單懸鍵功能離子(如氫氧根離子)的鈍化處理，我們同時也計算沒加上應力、加上應力的單獨矽烯，計算出的結果沒加上應力的矽烯及加上應力的矽烯其載子遷移率大約都在同一個數量級範圍，仍舊維持很高的載子遷移率，而放在二氧化矽基板上的矽烯所估算出來的載子遷移率大約小了沒加上應力的矽烯一個數量級的大小，希望所有我們的計算結果都可以為開發基於二維材料的電晶體在工業生產線可行性評估提供有用指標性參考。

The tremendous advances of modern semiconductor technology has brought forth extraordinarily scaling down of transistors, while in the meantime it is approaching the bottleneck caused by the short-channel effect. One possible solution in overcoming this is to increase the gate-to-channel control or suppress the drain-side-voltage effect, such as the Fin Field-Effect Transistor. Another way to suppress the short-channel effect is to eliminate the region dominated by the drain-side electric field (v.s that from the gate), e.g. to fabricate a thinner channel, and the thinnest that can possibly be made is a single layer of atoms, the so-called two-dimensional materials. Silicene, compared to the first two-dimensional material graphene, not only has a potential advantage of being highly compatible with traditional silicon-based transistor, but also preserve the super high mobility as graphene. In fact, in 2015, a prototype of the first silicene transistor has been demonstrated to be feasible
We perform density-functional calculations of both a stand-alone silicene and the interface with the silicon dioxide. Since a strain less silicene has a gapless Dirac cone, we first calculate the electronic structures of the stand-alone strained silicene, and observe its band gap opened as a function of the applied strains. We perform such calculations using a wide range of exchange-correlation functionals, including not only the standard local-density and generalized-gradient approximations but also hybrid functionals HSE06, PBE0, and B3LYP, and further go beyond density-functional theory using the GW approximation to justify which of the above exchange-correlation functionals outperforms the rest in determining the band gap. Then we place the silicene on a silicon dioxide substrate, expecting the mismatch strain to open a band gap. To avoid chemical bonding at the interface so that the silicene π-bonds and in turn the Dirac-cone high mobility are preserved, we need to carefully choose an appropriate termination atomic layer of the silicon dioxide and introduce additional passivation atoms at the interface. We find the Si-terminated silicon dioxide surface passivated by the hydrogen atoms serves as the optimal substrate to obtain a high-mobility semiconducting silicene on top of it, among all the cases in this study. Further investigation into the interface bonding reveals that the optimal property of the above surface likely results from one bond per passviated atom. This suggest that further experiments in fabricating silicene on a silicon dioxide surface may consider passivation treatments using hydrogen, halogens, or single-dangling-bond functional groups like hydroxides. Direct calculations of the mobility of the strain-free, strained but stand-alone, and on-substrate silicenes show that the strained one preserves the same order of magnitude for the mobility, and that of the on-substrate is estimated to be lowered by one order. All our computational findings can provide helpful preliminary guidance in developing transistor based on two-dimensional materials that is feasible in the industrial product lines.

摘要 i
Abstract iii
致謝 v
目錄 vii
表目錄 xi
圖目錄 xiii
中英對照表 xix
Chapter 1 1
前言及研究動機 1
章節架構 7
Chapter 2 8
2.1多電子系統理論 8
2.1.1 Born-oppenheimer approximation 9
2.1.2 Hartree-Fock approximation 10
2.2密度泛函理論 12
2.2.1 Thomas-Fermi Theory 12
2.2.2 Hohenberg-Kohn Theory 13
2.2.3 Kohn-Sham equation 17
2.2.4局域密度近似法 21
2.2.5廣義梯度近似法 23
2.2.6雜化泛函法 25
2.3 GW Theory 27
2.3.1 Quasiparticles 29
2.3.2 Green’s Function 30
2.3.3 Hedin’s Equations 35
2.3.4 Dielectric Function and Screened Coulomb Potential 38
2.3.5 The procedure of GW calculation 42
2.3.6不同近似的比較 44
2.4 Mobility 46
2.4.1 Boltzmann transport theory 46
2.4.2 Deformation potential theory 48
2.4.3 Effective mass approximation 50
Chapter 3 51
3.1塊材計算 51
3.1.1 Silicene 52
3.1.2 Silicene Mobility 61
3.1.3 SiO2 67
3.2結構計算 74
3.2.1轉換表面晶胞 74
3.2.2晶格匹配 76
3.2.3截止層及植入元素 79
3.2.4橫向平移 83
3.2.5結構優化 86
3.2.6電子結構計算 89
3.3 GW計算 92
Chapter 4 95
附錄 98
附錄1計算表格及數據 98
附錄2 GW 104
附錄3 VASP操作技巧 106
附錄2-1 一般計算K-POINTS檔 107
附錄2-2 能帶圖KPOINTS檔 108
參考文獻 110

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