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研究生: 鄭家樑
Chia-Liang Cheng
論文名稱: 矽鍺(100)-2x1表面之矽/鍺甲烷二矽/鍺烷分解吸附與氫遷移脫附之DFT理論計算研究
DFT studies of SiH4,GeH4,Si2H6 and Ge2H6 dissociative adsorption and hydrogen migration/desorption on SiGe(100)-2x1
指導教授: 蔡大翔
Dah-Shyang Tsai
口試委員: 洪儒生
Lu-Sheng Hong
江志強
Jyh-Chiang Jiang
黃鶯聲
Ying-Sheng Huang
林聖賢
Sheng-Hsien Lin
周更生
Kan-Sen Chou
蔣孝澈
Anthony Shiaw-Tseh Chiang
學位類別: 博士
Doctor
系所名稱: 工程學院 - 化學工程系
Department of Chemical Engineering
論文出版年: 2007
畢業學年度: 95
語文別: 中文
論文頁數: 133
中文關鍵詞: 矽甲烷鍺甲烷二矽烷二鍺烷分解吸附遞移脫附密度泛函數理論矽鍺(100)-2x1
外文關鍵詞: SiGe(100)-2x1, silane, germane, disilane, digermane, dissociative adsorption, migration, desorption, density functional theory
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  • 我們使用密度泛函數(DFT)法研究SiH4, GeH4, Si2H6, and Ge2H6分解吸附與氫遷移和脫附於SiGe(100)-2x1表面。由於鍺加入於Si(100)-2x1表面內影響了dimer的傾斜和表面的反應性,SiH4, GeH4, Si2H6, and Ge2H6與Si*-Si, Ge*-Si, Ge*-Ge, and Si*-Ge(*代表上位原子)此四種不同dimer反應,經系統化分析於反應能量上之影響。於半氫覆蓋表面,SiH4, GeH4, Si2H6, and Ge2H6吸附能障是高於各反應物於潔淨表面之能障,而SiH4 之吸附能障是高於GeH4的,Si2H6之吸附能障亦是高於Ge2H6。由計算結果顯示Si2H6/Ge2H6分解路徑為經由Si-H/Ge-H鍵之斷裂比經由Si-Si/Ge-Ge鍵之斷裂來得容易。我們基於兩個理由認為吸附反應下SiGe表面的反應性和鍺存在於表面有關。有鍺存在時氫脫附是較容易進行的,且於Ge*-Si dimer存在時,更易使SiH4, GeH4, Si2H6, and Ge2H6進行分解吸附反應。研究中亦使用過渡狀態理論以計算速率常數,於650℃下計算所得GeH4於Si*-Si和Ge*-Ge dimer上之速率常數比為2.1,此值和文獻中GeH4吸附於Si(100)表面和具一單層鍺覆蓋之Si(100)之反應機率比相吻合,經超音速分子束實驗所得之實驗比值為1.7。雖然計算結果顯示Ge*-Si是表面上最具反應性之dimer,然實驗結果為於Si(100)-2x1上對鍺甲烷和二鍺烷反應機率是單調下降,此意味著使用鍺烷和二鍺烷於初期磊晶時僅伴隨著Si*-Si和Ge*-Ge此二dimer。
    對氫遷移和脫附而言,由於氫遷移之能障通常是低於氫脫附步驟之能障,我們認為氫分子再結合脫附為速率決定步驟。因氫由鍺位遷移至矽位之能障低於其相反方向之能障,使得氫傾向於留滯於矽位上。由於較弱之Ge-H鍵,使得於化學氣相反應下之SiGe-2x1表面是比Si(100)-2x1更具有反應性並提供了較多的懸鍵。


    Dissociative adsorptions of SiH4, GeH4, Si2H6, and Ge2H6 along with hydrogen migration and desorption on the buckled SiGe(100)-2x1 surface have been studied by using density functional theory (DFT) at the B3LYP level. The Ge alloying in the Si(100)-2x1 surface affects the dimer buckling and its surface reactivity. Systematic Ge influences on the reaction energetics are found in SiH4, GeH4, Si2H6, and Ge2H6 reactions with four dimers of Si*-Si, Ge*-Si, Ge*-Ge, and Si*-Ge (* denotes the protruded atom). On a half H-covered surface, the energy barriers for silane, germane, disilane, and digermane adsorption are higher than those on the pristine surface. The energy barrier for silane adsorption is higher than the corresponding barrier for germane adsorption. The energy barrier for disilane adsorption is higher than the corresponding barrier for digermane adsorption. The calculation results suggest that disilane/digermane dissociation path on SiGe(100) surface via Si-H/Ge-H bond scission is more favorable than via Si-Si/Ge-Ge bond scission. We conclude that the SiGe surface reactivity in adsorption reaction depends on the Ge presence on surface for two-fold reasons. The hydrogen desorption is easier on Ge, and the presence of Ge*-Si dimer facilitates the dissociative adsorption of SiH4, Si2H6, GeH4, Ge2H6. Rate constants are also calculated using the transition-state theory.
    The calculated rate constant ratio of GeH4 adsorption on Si*-Si over Ge*-Ge at 650℃ is 2.1, which agrees with the experimental ratio of GeH4 adsorption probability on Si(100) surface over that on one monolayer Ge covered Si(100) surface. The experimental ratio is 1.7 measured by supersonic molecular beam techniques. Although the calculation results indicate Ge*-Si is the most active dimer on surface, the experimental results of a monotonic decrease in germane and digermane reaction probability on Si(100)-2x1 indicate only two dimers of Si*-Si and Ge*-Ge are involved in the initial epitaxial growth using GeH4 and Ge2H6.
    As for hydrogen migration and desorption, the H2 recombinative desorption is the rate-determining step on SiGe(100) surface, since the energy barriers of H-atom migration steps are generally lower than those of H2 desorption. The chemisorbed H trends to stay on the Si-site, since the barrier for H-migration from the Ge-site to the Si-site is lower that in the opposite dirction. The SiGe(100)-2x1 surface in chemical vapor deposition is more reactive and provides more dangling bonds than the Si(100)-2x1 because of weaker Ge-H bond.

    中文摘要.......................................................I 英文摘要.....................................................III 目錄...........................................................V 圖目錄......................................................VIII 表目錄......................................................XIII 第一章 緒論....................................................1 1-1 前言.......................................................1 1-2 矽鍺與砷化鎵之比較.........................................2 1-3 文獻回顧...................................................4 第二章 理論計算方法...........................................13 2-1 量子力學基本概念..........................................13 2-2 波恩-歐朋罕默近似 (Born-Oppenheimer Approximation)........18 2-3 計算化學的方法............................................21 2-3-1 分子力學法..............................................22 2-3-2 半經驗法................................................23 2-3-3 全初始法 (ab initio)....................................24 2-3-4 密度泛函數理論法.......................................25 2-3-5 基底函數組(basis set)...................................29 2-4 過渡狀態理論(Transition-state theory, TST)................33 2-5 本論文使用計算方法........................................36 第三章 結果與討論............................................38 3-1 SiH4/GeH4於SiGe(100)-2×1表面分解吸附之DFT理論計算.........38 3-1-1 叢集模型(cluster model)的選擇...........................38 3-1-2 基準點計算(benchmark calculation).......................42 3-1-3 傾斜二聚體之表面(surface of buckled dimers).............45 3-1-4 矽烷和鍺烷之分解吸附(dissociative adsoption of SiH4 and GeH4)...................................................48 3-1-5 速率常數(rate constant).................................54 3-1-6 小結....................................................59 3-2 Si2H6/Ge2H6於SiGe(100)-2×1表面分解吸附之DFT理論計算.......69 3-2-1 二矽烷和二鍺烷經由Si-Si/Ge-Ge鍵斷裂之分解吸附(dissociative adsorption of Si2H6 and Ge2H6 via Si-Si /Ge-Ge secession)..71 3-2-2 二矽烷和二鍺烷經由Si-H/Ge-H鍵斷裂之分解吸附(dissociative adsorption of Si2H6 and Ge2H6 via Si-Si / Ge-Ge secession).75 3-2-3 速率常數(rate constant).................................81 3-2-4 小結....................................................85 3-3氫於SiGe(100)-2×1表面上之遷移和脫附反應路徑之DFT理論計算.102 3-3-1 計算方法.............................................103 3-3-2 H2再結合脫附(recombinative desorption)..............106 3-3-3 氫遷移(migration)...................................109 3-3-4 脫附和遷移之路徑組合................................112 3-3-5 intradimer和interdimer間之結構......................117 3-3-6 小結................................................126 第四章 結論..................................................127 參考文獻.....................................................129 圖 目 錄 頁次 圖1-1 氣相源中GeH4/SiH4比和磊晶膜中Ge/Si比之關係圖.............9 圖1-2 於570至700℃間不同Ge量下之成長速率圖.....................9 圖3-1 Si(100)-2×1表面的結構...................................39 圖3-2 經最適化後之SiGe(100)-2×1結構...........................40 圖3-3 典型吸附分解反應(GeH4+Ge*-SiSi13H18)和TS結構之位能圖 (potential energy diagram)..............................42 圖3-4 SiH4(空心)和GeH4(實心)吸附於pristine SiGe(100)表面之速率常 數。GeH4於Si*-Si和Ge*-Ge dimer上之速率常數比圖插入於圖上56 圖3-5 GeH4於四種不同表面,分別為clean Si(100)、Si1-xGex磊晶層 於Si(100)、1ML純Ge於Si(100)和clean Ge(100)之反應機率...57 圖3-6 SiH4(空心)和GeH4(實心)吸附於half H-covered SiGe (100) 表面之速率常數..........................................58 圖3-7 SiH4和GeH4於Si*-SiSi13H18叢集模型之位能曲線圖...........61 圖3-8 SiH4和GeH4於Ge*-SiSi13H18叢集模型之位能曲線圖...........62 圖3-9 SiH4和GeH4於Ge*-GeSi13H18叢集模型之位能曲線圖...........63 圖3-10 SiH4和GeH4於Si*-GeSi13H18叢集模型之位能曲線圖..........64 圖3-11 SiH4和GeH4於Si*-SiSi13H16叢集模型之位能曲線圖..........65 圖3-12 SiH4和GeH4於Ge*-SiSi13H16叢集模型之位能曲線圖..........66 圖3-13 SiH4和GeH4於Ge*-GeSi13H16叢集模型之位能曲線圖..........67 圖3-14 SiH4和GeH4於Si*-GeSi13H16叢集模型之位能曲線圖..........68 圖3-15 典型經Si-Si鍵斷裂吸附分解反應(Si2H6+Ge*-SiSi13H16)和TS結 構之位能圖(potential energy diagram)...................71 圖3-16 典型經Si-H鍵斷裂吸附分解反應(Si2H6+Ge*-SiSi13H16)和TS結 構之位能圖(potential energy diagram)...................75 圖3-17 不同基材溫度下Ge2H6於Si(100)表面不同Ge覆蓋量時之反應機 率.....................................................80 圖3-18 不同基材溫度下GeH4於Si(100)表面不同Ge覆蓋量時之反應機 率 ...................................................80 圖3-19 Si2H6和Ge2H6經Si-H/Ge-H鍵斷裂吸附於pristine SiGe(100) 之速率常數.............................................82 圖3-20 於700℃不同入射能量下GeH4、Ge2H6、SiH4和Si2H6於Si(100) 表面上之初始反應機率...................................83 圖3-21 Si2H6和Ge2H6經Si-H/Ge-H鍵斷裂吸附於H-half pristine SiGe(100)之速率常數....................................84 圖3-22 Si2H6/Ge2H6於Si*-SiSi13H18經Si-Si/Ge-Ge鍵斷裂吸附分解 反應和TS結構之位能曲線圖(potential energy diagram).....86 圖3-23 Si2H6/Ge2H6於Ge*-SiSi13H18經Si-Si/Ge-Ge鍵斷裂吸附分解 反應和TS結構之位能曲線圖(potential energy diagram).....87 圖3-24 Si2H6/Ge2H6於Ge*-GeSi13H18經Si-Si/Ge-Ge鍵斷裂吸附分解 反應和TS結構之位能曲線圖(potential energy diagram).....88 圖3-25 Si2H6/Ge2H6於Si*-GeSi13H18經Si-Si/Ge-Ge鍵斷裂吸附分解 反應和TS結構之位能曲線圖(potential energy diagram).....89 圖3-26 Si2H6/Ge2H6於Si*-SiSi13H16經Si-Si/Ge-Ge鍵斷裂吸附分解 反應和TS結構之位能曲線圖(potential energy diagram).....90 圖3-27 Si2H6/Ge2H6於Ge*-SiSi13H16經Si-Si/Ge-Ge鍵斷裂吸附分解 反應和TS結構之位能曲線圖(potential energy diagram).....91 圖3-28 Si2H6/Ge2H6於Ge*-GeSi13H16經Si-Si/Ge-Ge鍵斷裂吸附分解 反應和TS結構之位能曲線圖(potential energy diagram).....92 圖3-29 Si2H6/Ge2H6於Si*-GeSi13H16經Si-Si/Ge-Ge鍵斷裂吸附分解 反應和TS結構之位能曲線圖(potential energy diagram).....93 圖3-30 Si2H6/Ge2H6於Si*-SiSi13H18經Si-H/Ge-H鍵斷裂吸附分解反 應和TS結構之位能曲線圖(potential energy diagram).......94 圖3-31 Si2H6/Ge2H6於Ge*-SiSi13H18經Si-H/Ge-H鍵斷裂吸附分解反 應和TS結構之位能曲線圖(potential energy diagram).......95 圖3-32 Si2H6/Ge2H6於Ge*-GeSi13H18經Si-H/Ge-H鍵斷裂吸附分解反 應和TS結構之位能曲線圖(potential energy diagram).......96 圖3-33 Si2H6/Ge2H6於Si*-GeSi13H18經Si-H/Ge-H鍵斷裂吸附分解反 應和TS結構之位能曲線圖(potential energy diagram).......97 圖3-34 Si2H6/Ge2H6於Si*-SiSi13H16經Si-H/Ge-H鍵斷裂吸附分解反 應和TS結構之位能曲線圖(potential energy diagram).......98 圖3-35 Si2H6/Ge2H6於Ge*-SiSi13H16經Si-H/Ge-H鍵斷裂吸附分解反 應和TS結構之位能曲線圖(potential energy diagram).......99 圖3-36 Si2H6/Ge2H6於Ge*-GeSi13H16經Si-H/Ge-H鍵斷裂吸附分解反 應和TS結構之位能曲線圖(potential energy diagram)......100 圖3-37 Si2H6/Ge2H6於Si*-GeSi13H16經Si-H/Ge-H鍵斷裂吸附分解反 應和TS結構之位能曲線圖(potential energy diagram)......101 圖3-38 (a)Si14GeH19 (b)Si13Ge2H19(I) (c)Si13Ge2H19(II) (d) Si13Ge2H19(III)叢集模型。藍色為鍺;灰色為矽;白色為 氫....................................................104 圖3-39 三種可能氫遷移路徑示意圖。氫原子經(a)遷移至dimer上之 另一原子;(b)遷移至同列另一dimer上;(c)遷移至相鄰列之 另一dimer上。大圓代表矽或鍺原子,小圓代表為氫原子.....105 圖3-40 於Si14GeH19叢集模型氫遷移和脫附可能路徑之位能圖.......112 圖3-41 於Si13Ge2H19(I)叢集模型氫遷移和脫附可能路徑之位能圖...114 圖3-42 於Si13Ge2H19(II)叢集模型氫遷移和脫附可能路徑之位能圖..116 圖3-43 於Si13Ge2H19(III)叢集模型氫遷移和脫附可能路徑之位能圖.116 圖3-44 氫遷移於(a)intradimer和(b)interdimer間之TS結構之關鍵 參數示意圖............................................118 圖3-45 氫脫附於(a)intradimer和(b)interdimer間之TS結構之關鍵 參數示意圖............................................119 表 目 錄 頁次 表1-1 矽、鍺與砷化鎵半導體材料特性比較.........................4 表3-1 Si*-GeSi13H18 和Ge*-SiSi13H18叢集模型零點能差ΔE比較表...43 表3-2 Si*-SiSi13H18、Ge*-SiSi13H18和Ge*-GeSi13H18之計算所得 dimer鍵長R和傾斜角θ與文獻中理論和實驗結果之比較表.......44 表3-3 於B3LYP/6-311+G*下Si15-xGexH18(x=0-2)和Si15-xGexH16 (x=0-2)叢集模型之dimer鍵長R和傾斜角θ比較表..............46 表3-4 SiH4和GeH4分解吸附於Si1-xGexSi13H18叢集模型之活化能障 EA和反應熱ΔERXN之比較表.................................49 表3-5 SiH4和GeH4分解吸附於Si1-xGexSi13H16叢集模型之活化能障 EA和反應熱ΔERXN之比較表.................................51 表3-6 SiH4和GeH4分解吸附於D1D2Si11H18叢集模型之活化能障EA和 反應熱ΔERXN之比較表。D1為參與吸附反應之dimer,D2為相鄰 有氫覆蓋之dimer.........................................54 表3-7 最快和最慢速率常數於純淨表面和半氫覆蓋表面之修正後頻率 因和活化能之數據........................................59 表3-8 Si2H6和Ge2H6經Si-Si/Ge-Ge鍵斷裂分解吸附於Si1-xGexSi13H18 叢集模型之活化能障EA和反應熱ΔERXN之比較表...............73 表3-9 Si2H6和Ge2H6經Si-Si/Ge-Ge鍵斷裂分解吸附於Si1-xGexSi13H16 叢集模型之活化能障EA和反應熱ΔERXN之比較表...............74 表3-10 Si2H6和Ge2H6經Si-H/Ge-H鍵斷裂分解吸附於Si1-xGexSi13H18 叢集模型之活化能障EA和反應熱ΔERXN之比較表..............76 表3-11 Si2H6和Ge2H6經Si-H/Ge-H鍵斷裂分解吸附於Si1-xGexSi13H16 叢集模型之活化能障EA和反應熱ΔERXN之比較表..............77 表3-12 於不同叢集模型上之intradimer和interdimer間脫附能障Ed和 脫附反應熱Erxn........................................108 表3-13 於不同叢集模型上之intradimer和interdimer氫遷移能障 EGe→Si、ESi→Ge、ESi→Si、EGe→Ge和能量差E (kcal/mol) 於Si-Ge對上之正向和反向...............................111 表3-14 於intradimer和interdimer間氫遷移中LM、TS和產物之關 鍵參數值..............................................122 表3-15於interdimer間氫脫附中LM、TS和產物之關鍵參數值.........124 表3-16於intradimer間氫脫附中LM、TS和產物之關鍵參數值.........125

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