矽鍺(100)2X1 表面矽甲烷和鍺甲烷分解吸附之DFT計算

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行政院國家科學委員會專題研究計畫成果報告

矽鍺(100)2X1 表面矽甲烷和鍺甲烷分解吸附之 DFT 計算研究成果報告(精簡版)

計畫類別：個別型

計畫編號： NSC 95-2221-E-011-157-

執行期間： 95 年 08 月 01 日至 96 年 07 月 31 日執行單位：國立臺灣科技大學化學工程系

計畫主持人：蔡大翔

計畫參與人員：博士班研究生-兼任助理：鄭家樑

碩士班研究生-兼任助理：沈明逸、梁嘉文

處理方式：本計畫可公開查詢

中華民國 96 年 07 月 19 日

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矽鍺(100)2×1 表面矽甲烷和鍺甲烷分解吸附之 DFT 計算

DFT calculation of silane and germane dissociative adsorption on SiGe(100)-2×1 計畫編號 NSC 95-2221-E011-157

執行期限: 95 年 08 月 01 日至 96 年 07 月 31 日主持人：蔡大翔執行單位:台灣科技大學化工系

參與人員：蔡大翔、鄭家樑、碩士班研究生

一、中文摘要

我們使用密度泛函數法 (density functional theory，DFT)用以計算分析矽甲烷(SiH₄)和鍺甲烷(GeH4)於矽鍺 (100)-2×1 表面上之分解吸附反應。由於鍺加入於矽(100)-2×1 表面不僅影響了二聚體(dimer)的傾斜與其表面的反應性(surface reactivity)，鍺的加入於反應能量學上發現矽甲烷和鍺甲烷與四種不同 dimer ： Si*-Si 、 Ge*-Si、Ge*-Ge 和 Si*-Ge。於半氫覆蓋表面，矽甲烷和鍺甲烷之吸附能障 (energy barrier)均相對於純淨(pristine) 表面來得高。且於相同 dimer 上矽甲烷的能障是高於鍺甲烷，對於速率常數(rate constant)之計算為使用過渡狀態理論(transition-state theory)加以計算，我們整理可得 SiGe 表面吸附反應之反應性與其 dimer 上之鍺存在之型式有關，若表面鍺之型式為 Ge*-Ge 時，表面之反應性隨著 Ge*-Ge 之含量上昇而下降；若於低鍺含量下表面之鍺是較傾向形成 Ge*-Si 之型式，則開始時表面反應性先上昇，然後由於 Ge*-Ge 的形成後再下降。鍺甲烷吸附反應之計算所得之速率常數於 Si*-Si 上對 Ge*-Ge 上於 650℃下為 2.1，此值相當符合鍺甲烷於 Si(100)相對於 Si(100) 覆蓋一層鍺之吸附機率 (adsorption probability)實驗比值，此值為 1.7 是經由超音速分子束技術。

由於理論計算與實驗結果相當吻合以支持於 Si(100)上之單層鍺存在有 Ge*-Ge 型式之 dimer。

二、英文摘要

SiH4 and GeH4 dissociative adsorptions on buckled SiGe(100)-2×1 surface have been analyzed using density functional theory (DFT) at the B3LYP level. The Ge alloying in Si(100)-2×1 surface affects the dimer buckling and its surface reactivity.

Systematic Ge influences on the reaction energetics are also found in SiH4 and GeH4 reactions with four dimers of Si*-Si, Ge*-Si, Ge*-Ge, and Si*-Ge (*

denotes the protruded atom). On the half H-covered surface, the energy barriers for silane and germane adsorption are higher than those on the pristine surface.

The energy barrier for silane adsorption is higher than the corresponding barrier for germane adsorption. Rate constants are also calculated using the transition-state theory. We conclude that the SiGe surface reactivity in adsorption reaction depends on the Ge presence in dimer form. If surface Ge is present in form of Ge*-Ge, the surface reactivity decreases as the Ge*-Ge content increases. If surface Ge prefers to be in

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form of Ge*-Si at low Ge content, the surface reactivity increases first, then decreases at high Ge surface content when Ge*-Ge prevails. The calculated rate constant ratio of GeH4 adsorption on Si*-Si over Ge*-Ge at 650°C is 2.1, which agrees with the experimental ratio of GeH4 adsorption probability on Si(100) over Si(100) covered by one monolayer Ge. The experimental ratio is 1.7 measured through supersonic molecular beam techniques. This consistency between calculation and experimental results supports that one monolayer of Ge on Si(100) exists in form of Ge*-Ge dimer.

三、計畫緣由與目地

本研究為一理論計算之計劃，由於晶片計算速率之提昇，促使近年來計算化學快速進步，許多實驗上困難之細節，可由理論計算提供較細部之了解，而化學氣相沉積之模擬計算已成風潮，引導研究走向分子和原子層面之了解。由文獻報導可知使用鍺甲烷作為前驅物用以沉積矽鍺薄膜時，

其膜成長速率較純矽來得快，有相當多研究認為是由於鍺元素存在於表面之故，使得成長過程中增強了表面氫分子之脫附，進而提供了更多的懸鏈鍵(dangling bond)使能夠沉積之位置增多。由已發表文獻可知於矽鍺(100) 2×1 表面上矽甲烷與鍺甲烷之吸附分解反應之反應機構的研究不是很多，

因此本計劃針對此議題使用密度泛函數理論法以模擬矽甲烷與鍺甲烷之吸附分解反應機構於矽鍺(100) 2×1 表面上。

四、模擬方法

於圖一中所示為經最適化之矽鍺 (100)2×1 之叢集模型，用以模擬矽甲烷與鍺甲烷之吸附分解反應之反應機構，此八種不同表面矽鍺排列方式代表不同之 dimer 對經重構 (reconstruction)之矽鍺(100)2×1 表面模型。

所有計算均以 DFT 方法、B3LYP 修正函數和基底函數 (basis set)為使用 6-311+G*所完成。分子結構之最適化過程均無任何之幾何束制。零點能 (zero-point energy)亦計算於相同之方法。過渡狀態結構為由延著擬反應座標(pseudoreaction coordinate)和一級鞍點(first-order saddle point)過程求得。所有計算結果均為使用 Gaussian 03 商用套裝軟體所完成。

五、結果與討論

當我們以 6-31G* 、 6-31G**

和 6-31+G*為 basis set 作計算，根據所得之總能量結果指出是 Si^*-GeSi1 3H1 8 模型比 Ge^*-SiSi1 3H1 8 來得低，亦即 Si^*-GeSi1 3H1 8 模型比 Ge^*-SiSi1 3H1 8 穩定，可是和文獻上，不論是理論或實驗研究之結果不合，於是使用 triple-zeta basis set 作計算，發現使用 6-311G* 、 6-311+G* 和 6-311++G**時，由零點能量結果指出是 Si^*-GeSi1 3H1 8 比 Ge^*-SiSi1 3H1 8 來得高，亦即 Ge^*-SiSi1 3H1 8 比 Si^*-GeSi1 3H1 8 來得穩定，其零點能量差之計算結果列於表一中。

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表二所列為 Si^*-SiSi1 3H1 8 、 Ge^*-SiSi1 3H1 8和 Ge^*-GeSi1 3H1 8分別代表 Si*-Si、Ge*-Si 和 Ge*-Ge dimer 的叢集模型計算所得之 dimer 鍵長 R 和 dimer 傾斜角 θ 與文獻中理論計算結果， dimer 鍵長 R 為 dimer 兩原子之距離， 傾斜角 θ 為 dimer 和表面平面之 夾角，由 6-311G*、 6-311+G*和 6-311++G** 之計算結果與文獻上實驗結果和其它理論計算結果較吻合，也比以較低 basis set(6-31G 系列 ) 計算結果來得準確，由此計算結果可以看出當使用 6-31G 系列之 basis set 的結果，不論是加入極化或擴散函數是不足以提供較佳之計算結果，且考慮計算資源和時間之故，於其後之計算工作上選擇用 6-311+G* 基底函數且方法為 B3LYP 為主。

於表三中所列為研究所使用所有叢集模型之 dimer 鍵長、傾斜角和電荷量 (charge) 之計算結果。對 Si_{1 5 - x}GexH1 8 (x=0-2)叢集模型而言，傾斜角隨著於 dimer 中 Ge 原子數目的增加而呈現穩定地增加，分別為 9.9^°(Si*-Si)，

14.5^°(Ge-Si*) ， 16.3^°(Ge*-Ge) 。相同的趨勢亦呈現在 dimer 鍵長上， 2.234 Å (Si*-Si) ， 2.347Å (Ge*-Si)，2.429Å(Ge*-Ge)。對於 Si1 5 - xGexH1 6 (x=0-2) 叢集模型為代表純淨表面，其 dimer 傾斜角可以看出是稍微大於 Si1 5 - xGexH1 8 系列叢集模型。其傾斜角亦是隨 Ge 原子數目的增加而增加，分別為 12.4^°(Si*-Si) ，

15.2^°(Ge*-Si) ， 16.5^°(Ge*-Ge) ， dimer 鍵長亦是相同之趨勢，不再贅述。

表四所列為 SiH₄ 和 GeH₄分解吸附於 Si_{1 5 - x}GexH1 8 系列叢集模型之活化能障 (activation energy barrier, EA) 和反應熱 (reaction energy, ΔERXN) 由結果可看出 SiH4於不同 dimer 對上吸附反應的反應熱作比較，隨著 dimer 的鍺原子數目的增加而增加。由鍵的形成和斷裂觀點可以瞭解此反應熱數據趨勢，由於 SiH₄ 中

Si-H( g )鍵須打斷以進行吸附反

應，且 Si-SiH_{3 ( a )}和 Si-H_{( a )}此兩個新的鍵結要形成，若當 dimer 對為 Ge*-Si 時，此新鍵結為 Ge-SiH3 ( a )和 Si-H_{( a )}，而當 dimer 對為 Ge-Ge 時，此新鍵結為 Ge -SiH3 ( a )和 Ge-H_{( a )}，由於 Ge-SiH_{3 ( a )} 的鍵強度 (bond strength) 比 Si-SiH3 ( a )來得弱，且 Ge-H_{( a )}的鍵強度比 Si-H_{( a )}亦來得弱，以致於當 dimer 鍺原子愈多其反應熱愈小。另一方面，若比較 SiH₄ 和 GeH4於相同之 dimer 上之反應熱來看，GeH₄ 之反應熱總是比 SiH₄ 來得更低，其原因為需打斷較弱的 Ge-H 鍵之故。相關之束縛能 (binding energy) ： 84[Ge-H( g )] 、 90[Si-H( g )] (kcal/ mol) 。 SiH4 和 GeH4 吸附於純淨表面之反應熱計算結果列於表五中。

SiH4 和 GeH₄ 之吸附反應速率常數是以傳統過渡狀態理論 (conventional transition-state theory) 作計算，其穿遂效應 (tunneling effect)使用 Wigner 近

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似法加以計算。理論計算所得之 SiH4 和 GeH₄ 於純淨表面吸附反應之速率常數繪製於圖二中，其選擇之溫度範圍為氫脫附足夠快的溫度，650~800℃。通常具有較低能障之 SiH₄和 GeH₄之速率常數是較高的。僅有一例外為 SiH₄ 於 Ge^*-GeSi1 3H1 6 叢集模型上之

速率常數是較於 Si^*-SiSi1 3H1 6 上來得高的。此例外亦隱含著當能障較小時，分布函數 (partition function) 的效應是決定速率常數的重要因素。 GeH₄ 於 Si*-Si 和 Ge*-Ge 之速率常數比插入於圖二中，可看出其比率隨成長溫度上昇而降低。

六、結論

我們理論分析了鍺原子於 dimer 幾何結構的影響和 SiH4/GeH4 分解吸附於 SiGe(100)-2×1 表面上，此計算結果是完成於無氫覆蓋 dimer 和半氫覆蓋 dimer 二種不同 two-dimer 系列叢集模型上。隨著 dimer 上鍺原子數目增加使得 dimer 結構更為傾斜，且純淨表面之 dimer 傾斜角較半氫覆蓋表面來得大。同時反應熱亦隨 dimer 鍺原子數目增加而增加。若不考慮較不穩定 Si*-Ge dimer， SiH₄ 和 GeH₄ 吸附於 Ge*-Si 的能量障礙是最低的，而在 Ge*-Ge 則是最高的。對於 Si*-Ge 之反應熱和能量障礙仍列出作比較參考。計算所得速率常數之趨勢通常是和能量障礙之趨勢相符合。此計算結果不僅和超音速分子束技術實驗結果相吻合且提供了更詳細的了解。

七、參考文獻

1. Chia-Liang Cheng, Dah-Shyang Tsai and Jyh-Chiang Jiang, Surf.

Sci., 600, 3194(2006)

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八、附圖與附表

圖一經最適化後 SiGe(100)-2×1 結構

0.95 1.00 1.05 1.10

10000 100000 1000000 1E 7 1E 8 1E 9 1E 10 1E 11

G eH₄ rate constant Si*-S iS i₁₃H₁₆ G e*-S iS i₁₃H₁₆ Si*-G eS i₁₃H₁₆ G e*-G eS i₁₃H₁₆

S iH₄ rate constant S i*-S iS i₁₃H₁₆ G e*-S iS i₁₃H₁₆ S i*-G eS i₁₃H₁₆ G e*-G eS i₁₃H₁₆

600 700 800

1.5 2.0 2.5

Ratio of reaction constant

Temperature (^oC) GeH4 adsorption reaction constant ratio of Si*-Si/Ge*-Ge

k (s-1 )

1000/T K

圖二 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。

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表一 Si*-GeSi₁₃H18 和 Ge*-SiSi₁₃H18叢集模型零點能差 ΔE 比較表 Zero-point energy (hartree)

method/basis set Si*-GeSi₁₃H₁₈ Ge*-SiSi₁₃H₁₈ ΔE (kcal/mol) B3LYP/6-31G* -6138.694626 -6138.690882 -2.35 B3LYP/6-31G** -6138.715418 -6138.711612 -2.39 B3LYP/6-31+G* -6138.724014 -6138.721354 -1.67 B3LYP/6-311G* -6140.991354 -6140.993953 1.63 B3LYP/6-311+G* -6140.995512 -6140.998195 1.68 B3LYP/6-311++G** -6141.024512 -6141.027217 1.70 ΔE＝E(Si*-GeSi13H18)－E(Ge*-SiSi13H18 )

表二 Si^*-SiSi1 3H1 8、Ge^*-SiSi1 3H1 8 和 Ge^*-GeSi1 3H1 8之計算所得 dimer 鍵長 R 和傾斜角 θ 與文獻中理論計算結果

Si*-SiSi13H18 Ge*-SiSi13H18 Ge*-GeSi13H18

Basis set R (Å)

θ

(^o) R (Å)

θ

(^o) R (Å)

θ

(^o) 6-31G* 2.240 10.1 2.296 13.9 2.349 14.2 6-31G** 2.240 10.8 2.296 14.1 2.349 14.5 6-31+G* 2.237 10.3 2.307 10.9 2.384 15.3 6-311G* 2.240 9.8 2.347 14.0 2.430 15.6 6-311+G* 2.234 9.9 2.347 14.5 2.429 16.3 6-311++G** 2.233 9.9 2.347 14.5 2.429 16.2 表三於 B3LYP/6-311+G*下 Si1 5 - xGexH1 8(x=0-2)和 Si1 5 - xGexH1 6 (x=0-2)

叢集模型之 dimer 鍵長 R 和 dimer 傾斜角 θ 比較表

Cluster R (Å)

θ

(^o) Charge(NBO) Δcharge Si*-SiSi₁₃H₁₈ 2.234 9.9 -0.157(Si*) 0.077(Si) 0.234 Ge*-SiSi₁₃H₁₈ 2.347 14.5 -0.139(Ge*) 0.192(Si) 0.331 Ge*-GeSi₁₃H₁₈ 2.429 16.3 -0.107(Ge*) 0.237(Ge) 0.344 (Si*-GeSi₁₃H₁₈) 2.313 9.8 -0.164(Si*) 0.154(Ge) 0.318

Si*-SiSi13H16 2.261 12.4 -0.185(Si*) 0.176(Si) 0.361 Ge*-SiSi13H16 2.373 15.2 -0.131(Ge*) 0.245(Si) 0.376 Ge*-GeSi13H16 2.454 16.5 -0.105(Ge*) 0.285(Ge) 0.390 (Si*-GeSi13H16) 2.342 12.5 -0.172(Si*) 0.234(Ge) 0.406

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表四 SiH4 和 GeH4 分解吸附於 Si1 - xGexSi1 3H1 8 叢集模型之活化能障 E_A和反應熱 ΔE_{R X N} 之比較表

Precursor/cluster EA (kcal/mol) ΔERXN (kcal/mol)

SiH₄/Si*-SiSi₁₃H₁₈ 13.8 -48.9 SiH₄/Ge*-SiSi₁₃H₁₈ 12.6 -44.8 SiH4/Ge*-GeSi13H18 18.1 -38.0 (SiH4/Si*-GeSi13H18) 17.4 -43.4

GeH₄/Si*-SiSi₁₃H₁₈ 12.0 -52.4 GeH₄/Ge*-SiSi₁₃H₁₈ 10.5 -47.7

GeH4/Ge-GeSi13H18 14.0 -41.4 (GeH₄/Si*-GeSi₁₃H₁₈) 15.7 -46.7 (Si*-GeSi₁₃H₁₈)是較 Ge*-SiSi₁₃H₁₈叢集模型不穩定

表五 SiH4 和 GeH4 分解吸附於 Si1 - xGexSi1 3H1 6 叢集模型之活化能障 EA和反應熱 ΔER X N 之比較表

Precursor/cluster EA (kcal/mol) ΔERXN (kcal/mol)

SiH4/Si*-SiSi13H16 11.8 -48.5 SiH₄/Ge*-SiSi₁₃H₁₆ 11.3 -42.7 SiH₄/Ge*-GeSi₁₃H₁₆ 17.4 -36.1 (SiH4/Si*-GeSi13H16) 15.8 -42.4

GeH4/Si*-SiSi13H16 10.7 -51.1 GeH₄/Ge*-SiSi₁₃H₁₆ 8.0 -47.3 GeH₄/Ge*-GeSi₁₃H₁₆ 13.3 -39.1 (GeH4/Si*-GeSi13H16) 14.6 -45.3 (Si*-GeSi13H18)是較 Ge*-SiSi13H18叢集模型不穩定

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DFT study on dissociative adsorption of SiH

₄

and GeH

₄

on SiGe(1 0 0)-2 · 1 surface

Chia-Liang Cheng, Dah-Shyang Tsai

^*

, Jyh-Chiang Jiang

Department of Chemical Engineering, National Taiwan University of Science and Technology 43, Keelung Road, Section 4, Taipei 106, Taiwan Received 7 December 2005; accepted for publication 7 June 2006

Available online 30 June 2006

Abstract

SiH4and GeH4dissociative adsorptions on a buckled SiGe(1 0 0)-2· 1 surface have been analyzed using density functional theory (DFT) at the B3LYP level. The Ge alloying in the Si(1 0 0)-2· 1 surface affects the dimer buckling and its surface reactivity. Systematic Ge influences on the reaction energetics are found in SiH4and GeH4reactions 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 and germane adsorption are higher than those on the pristine surface. The energy barrier for silane adsorption is higher than the corresponding barrier for germane adsorption. Rate constants are also calculated using the transition-state theory. We conclude that the SiGe surface reactivity in adsorption reaction depends on the Ge presence in dimer form. If the surface Ge is present in form of Ge^*–Ge, the surface reactivity decreases as the Ge^*–Ge content increases. If the surface Ge prefers to be in form of Ge^*–Si at low Ge contents, the surface reactivity increases first, then decreases at high Ge surface contents when Ge^*–Ge prevails. The calculated rate constant ratio of GeH₄adsorption on Si^*–Si over Ge^*– Ge at 650C is 2.1, which agrees with the experimental ratio of GeH4adsorption probability on Si(1 0 0) over Si(1 0 0) covered by one monolayer Ge. The experimental ratio is 1.7 measured through supersonic molecular beam techniques. This consistency between calculation and experimental results supports that one monolayer of Ge on Si(1 0 0) exists in form of Ge^*–Ge dimer.

Keywords: Density functional calculations; Surface chemical reaction; Adsorption kinetics; Silane; Germane

1. Introduction

The growth kinetics of SiGe heteroepitaxial thin ﬁlm is of importance in the semiconductor industry since SiGe/

Si(1 0 0) heterostructures allow band-gap engineering on high-speed devices in conjunction with the established silicon technology. The SiGe epitaxial growth is generally car- ried out using either gas-source molecular beam epitaxy or ultrahigh vacuum chemical vapor deposition[1–4]. These techniques typically employ conditions of high vacuum and low precursor pressure, hence gas-phase reactions are hardly involved in the growth kinetics. Major surface reaction paths consist of direct interactions between the precursors and the growing SiGe alloy surface. Silane SiH4and

germane GeH4 are two common precursors used in the SiGe heteroepitaxy, and their dissociative adsorptions are the starting points of surface reaction paths.

It is known that GeH4inclusion in the precursor source changes the silicon hydride deposition kinetics. For in- stance, an addition of 10% GeH₄was reported to accelerate the SiH4growth rate on Si(1 0 0) by a factor of 25 at 550C [5]. The acceleration eﬀect at low growth temperatures (6600C) originates from the Ge assistance in surface hydrogen desorption, which is the rate-determining step [6–8]. At high growth temperature (P650C), desorption of hydrogen is suﬃciently fast, opening up most sites of dangling bonds for dissociative adsorption which becomes a critical step. The dependence of growth rate on the GeH4

content is not monotonic under high temperatures, the growth rate increases with the GeH4 content in the low concentration range, reaches a maximum, and decreases

doi:10.1016/j.susc.2006.06.011

*Corresponding author. Tel.: +886 2 27376618; fax: +886 2 27376644.

E-mail address:[email protected](D.-S. Tsai).

www.elsevier.com/locate/susc Surface Science 600 (2006) 3194–3201

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at a higher GeH4content. Kim et al. reported a maximum growth rate between 0.8 and 2.6% GeH4content in the high temperature range[9]; Racanelli and Greve reported that a maximum was between 0.8 and 1.25% GeH4 content at 665C[10]. Since the dissociative adsorption is considered to be a critical step at high temperatures, the reactivity of strained SiGe surface in hydride adsorption has been a cen- tral issue. Engstrom et al. showed that the Si(1 0 0) surface was more reactive than the Ge(1 0 0) surface in the GeH4

dissociative adsorption, and the reactivity of a strained Ge surface was in between[11,12].

To precisely control the composition of epitaxial layer, a detailed understanding on chemisorption of both SiH4and GeH4 is necessary. Based on adsorption experiments, Gates et al. argued that SiH4dissociation should be most favorable at the adjacent dangling bonds of a single dimer on Si(1 0 0)-2· 1 [13–15]. Kang and Musgrave conﬁrmed that the energy barrier of SiH₄adsorption on a single dimer was lower than that across two dimers based on the density functional theory (DFT) results [16]. Miyamoto et al.

formulated a model that assumed chemisorption on two dangling bonds (two-site) below 600C and switched to four-site chemisorption above 600C [17]. More speciﬁ- cally, the ﬁrst step in SiH4 chemisorption was scission of one of the four Si–H bonds across a dimer pair of dangling

bonds on Si(1 0 0)-2· 1. The following step could be SiH3

desorption or stabilization of SiH3with two more dangling bonds [18–20]. This was the so-called two-site two-step model. The GeH4 chemisorption is expected to follow a similar path consisting of lower energy barriers. Lin and Chou studied the GeH4 adsorption on Si(1 0 0)-2· 2 and Ge(1 0 0)-2· 2 surface using the supercell model [21]. Lin and Lee calculated the energetics of SiH4 and GeH4

adsorptions on the Si(1 0 0)-2· 2 surface based on DFT with generalized gradient approximation and pseudopoten- tial approximation [22]. In the literature, few theoretical articles estimated the kinetic diﬀerences in SiH4 and GeH4adsorption on dimers of the mixed SiGe surface.

In this work, we investigate SiH4and GeH4dissociative adsorption reaction on the SiGe(001)-2· 1 surfaces with and without hydrogen coverage using the DFT method.

Discussion is focused on inﬂuences of the Ge surface alloying on energetics and rate constants of the SiH₄and GeH₄ adsorptions.

2. Methodology

Clusters of Si_15xGexH18 and Si_15xGexH16 (x = 1, 2) with one or two Ge atoms among four surface atoms are used to represent a two-dimer surface. Other clusters with

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more than two Ge surface atoms are also used in calculation, but the results are supplementary since the diﬀerences are small. The surface of Si_15xGe_xH₁₈ cluster has one dimer with two dangling bonds and the other dimer passiv- ated with hydrogen, while that of Si_15xGexH16cluster is a pristine surface with two dimers of four dangling bonds.

Only the dimer of dangling bonds is considered in SiH4

and GeH4 adsorption reaction. The truncated bulk Si–Si bonds are terminated with 16 Si–H bonds to preserve the sp³hybridization of the subsurface Si atoms.

When the importance of dimer reactant needs to be emphasized, the ﬁrst two elements of cluster notation denote the dimer on which SiH4or GeH4is adsorbed. Since a dimer of dangling bonds is buckled (or tilted), a star sign is used to denote the protruded atom of the buckled dimer involved in adsorption. For example, Ge^*-SiSi13H18 has a buckled Ge^*–Si dimer and the Ge atom is a protruded atom. Ge^*–GeSi₁₃H₁₆cluster has a buckled Ge^*–Ge dimer, the Ge^*–Ge dimer is involved in adsorption and the other Si–Si dimer of dangling bonds is not involved in adsorption. This paper mainly discusses eight surface clusters, which are Si^*–SiSi13H18, Ge^*–SiSi13H18, Si^*–GeSi13H18, Ge^*–GeSi13H18, Si^*–SiSi13H16, Ge^*–SiSi13H16, Si^*–Ge- Si13H16, and Ge^*–GeSi13H16. Structures of four optimized clusters are illustrated inFig. 1.

Geometry optimizations of the clusters were performed without artiﬁcial symmetric or geometric constraints. The B3LYP three-parameter hybrid exchange-correlation functional was employed for all the DFT calculations[23–25].

Unscaled zero-point energies were also evaluated at the same level. Si^*–SiSi13H16 was the first cluster being optimized by removing four surface hydrogen atoms from an optimized structure of Si₁₅H₂₀. Other clusters were subse- quently optimized after substituting surface Si with Ge, or adding surface hydrogen to Si^*–SiSi13H16. One SiH4or GeH4 molecule was placed on top of a dimer, and the geometry of reactant adduct was optimized again. The transition state (TS) structure was obtained by following a pseudo-reaction coordinate, and the first-order saddle point was located using the Berny transition-state algo- rithm. All calculations were performed using the Gaussian 03 suite of programs[26]. The definitions of activation energy barrier EAand reaction energy DERXNare illustrated inFig. 2.

3. Benchmark calculation

Equilibrium geometries of Si^*–GeSi₁₃H₁₈ and Ge^*– SiSi13H18 were optimized at the B3LYP level using 6-31G*, 6-31G**, 6-31+G*, 6-311G*, 6-311+G*, and 6- 311++G** Pople basis sets as benchmark study. Table 1 compares values of the energy diﬀerence DE between optimized isomers of Si^*–GeSi13H18 and Ge^*–SiSi13H18. Results using the basis sets of 6-31G*, 6-31G**, and 6- 31+G* indicate Si^*–GeSi13H18 is a more stable isomer.

On the contrary, results using the higher level basis sets of 6-311G*, 6-311+G*, and 6-311++G** show that Ge^*–

SiSi13H18 is more stable. Jenkins and Srivastava [27], and Miwa[28]calculated the total energy of mixed Si–Ge dimer surface using the so-called supercell methods and found that the conﬁguration with a Ge atom in the up position was energetically favorable compared with the Si-up con- ﬁguration. They also showed that energy of the Si–Ge dimer was lower than those of Si–Si and Ge–Ge dimers.

These theoretical results are consistent with the high reso- lution photoemission spectra results of Patthey and his coworkers[29,30].

Dimer bond lengths and buckle angles of Si^*–SiSi13H18, Ge^*–SiSi13H18, Ge^*–GeSi13H18of this work, along with the reported values in the literature[27–35], are listed inTable 2. The dimer bond length is the distance between two dimer atoms. The buckle angle is the angle between the dimer and the nominal surface plane, which is deﬁned by the second Si layer in a cluster. Again, our results of Si^*–Si, Ge^*–Si, Ge^*–Ge bond lengths and tilt angles using 6-311G*, 6- 311+G*, and 6-311++G** are generally in line with the experimental results and other theoretical results, much better than those results using the low level basis sets.

Therefore we conclude that using a basis set higher than the Pople triple-zeta basis (6-311G) is crucial in the DFT calculation of SiGe cluster at the B3LYP level. Basis sets lower than 6-311G, either with polarization functions or

Fig. 2. Potential energy diagram of a typical adsorption reaction (GeH4+ Ge^*–SiSi13H18) and its TS geometry.

Table 1

Zero point energies of Si^*–GeSi13H18 and Ge^*–SiSi13H18 optimized clusters, and the diﬀerence between two clusters DE in a benchmark study Method/basis set Zero-point energy (hartree) DE(kcal/mol)

Si^*–GeSi13H18 Ge^*–SiSi13H18

B3LYP/6-31G^* 6138.694626 6138.690882 2.35 B3LYP/6-31G^** 6138.715418 6138.711612 2.39 B3LYP/6-31+G^* 6138.724014 6138.721354 1.67 B3LYP/6-311G^* 6140.991354 6140.993953 1.63 B3LYP/6-311+G^* 6140.995512 6140.998195 1.68 B3LYP/6-311++G^** 6141.024512 6141.027217 1.70 DE= E(Si^*–GeSi13H18) E(Ge^*–SiSi13H18).

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with diﬀuse functions, are insuﬃcient to generate accurate results. To ensure accurate results in not only optimization but also TS calculation, we employ the 6-311+G* basis set throughout this work.

4. Results and discussion 4.1. Surface of buckled dimers

A number of experimental and theoretical studies have demonstrated that the Si(1 0 0), Ge(1 0 0), mixed SiGe(1 0 0) pristine surfaces are composed of the buckled dimers. The geometries of all optimized clusters in this study also show that those dimers with dangling bonds are buckled and those H-covered dimers are lying in the nominal surface plane. Values of the dimer bond length and the buckle angle of two representative surface clusters are listed inTable 3. For Si_15xGe_xH₁₈ (x = 0–2) clusters, the buckle angle steadily increases with the number of Ge atoms in dimer, 9.9 (Si^*–Si), 14.5 (Ge^*–Si), and 16.3 (Ge^*–Ge). The dimer bond length also increases, 2.234 (Si^*–Si), 2.347 (Ge^*–Si), and 2.429 A˚ (Ge^*–Ge). The dimer buckle angle of Si_15xGexH16 (x = 0–2) clusters, representing a pristine surface, is slightly larger than that of Si_15xGexH18, repre-

increases as the number of Ge atoms, 12.4 (Si^*–Si), 15.2

(Ge^*–Si), 16.5 (Ge^*–Ge), so does the bond length. In short, as the number of Ge atoms increases, the dimer becomes longer and further buckled.

Also listed in Table 3 are the parameters of Si^*-Ge- Si13H18 cluster, which is an isomer of Ge^*–SiSi13H18. Although, the configuration with the Ge atom in the up position is more stable than the configuration with Si in the up position, both configurations are considered in the dissociative adsorption reactions. The zero-point energy difference between Ge^*–SiSi13H18and Si^*–GeSi13H18is only 1.68 kcal/mol, shown inTable 1. The Boltzmann probability (P) ratio of these two isomers can be estimated as follows, P(Si^*–GeSi13H18)/P(Ge^*–SiSi13H18)ffi exp(DE/RT).

The probability ratio is 0.10 (100C), 0.38 (600 C), 0.49 (900C). The estimated probability ratios clearly indicate that Si^*–GeSi13H18 is less important, but should not be ignored completely in the growth temperature range. As for the pristine surface isomers of Ge^*–SiSi₁₃H₁₆and Si^*– GeSi13H16, the zero-point energy diﬀerence is also small, 2.01 kcal/mol. In general, the less stable isomer has a shorter dimer length and a smaller buckle angle,Table 3.

Owing to a 4.2% lattice mismatch between Si and Ge, Si_1xGex/Si(1 0 0) heteroepitaxy is a strained layer epitaxy.

The strain not only increases the degree of dimer buckling but also alters the electronic nature of dimer bond. One important feature of the bonding in a pristine Si(1 0 0) dimer is that it involves a strong r-bond and a weaker p-bond. The 4.2% mismatch causes the Ge atom to displace from the Si surface. The displacement is associated with an electron density shift from the dangling bond of the down atom to that of the up atom. The electron density shift renders certain ionic character to the dimer and decreases the p-bond character because of reduced overlap in the dangling bond. The consequence is that the dimer bond length increases with the number of Ge atoms, and the charge diﬀerence between the up atom and the down atom also increases. The charge diﬀerences between dimer atoms are evaluated using natural bond orbital (NBO)

Table 2

Calculated structure parameters (dimer bond length R and tilt angle h) for Si^*–SiSi13H18, Ge^*–SiSi13H18and Ge^*–GeSi13H18clusters and a compar- ison with other theoretical and experimental results

Basis set Si^*–SiSi13H18 Ge^*–SiSi13H18 Ge^*–GeSi13H18

R(A˚ ) h () R(A˚ ) h() R(A˚ ) h()

6-31G^* 2.240 10.1 2.296 13.9 2.349 14.2

6-31G^** 2.240 10.8 2.296 14.1 2.349 14.5

6-31 + G^* 2.237 10.3 2.307 10.9 2.384 15.3

6-311G^* 2.240 9.8 2.347 14.0 2.430 15.6

6-311 + G^* 2.234 9.9 2.347 14.5 2.429 16.3

6-311 ++ G^** 2.233 9.9 2.347 14.5 2.429 16.2 Jenkins and

Srivastava[27]

(ab initio)

2.25 16.1

Takahasi et al.[31]

(exp)

2.37 20.0

Bullock et al.[32]

(exp)

2.25 19.0

Jenkins and Srivastava[27]

(ab initio)

2.34 19.3

Miwa[28]

(ab initio)

2.41 21.1

Chen et al.[30]

(exp)

2.43 ± 0.1

31 ± 2

Cho and Kang[33]

(ab initio)

2.39 16.3

Oyanagi et al.[34]

(ab initio)

2.40 ± 0.08

N.A

Frontes et al.[35]

(exp)

2.55 ± 0.04

12.4

Table 3

Dimer bond length R and tilt angle h of Si15xGexH18 (x = 0–2) and Si15xGexH16 (x = 0–2) clusters optimized at the B3LYP level using 6 311 + G^*basic set

Cluster R(A˚ ) h() Charge (NBO) Dcharge

Si^*–SiSi13H18 2.234 9.9 0.157(Si^*) 0.077(Si) 0.234 Ge^*–SiSi13H18 2.347 14.5 0.139(Ge^*) 0.192(Si) 0.331 Ge^*–GeSi13H18 2.429 16.3 0.107(Ge^*) 0.237(Ge) 0.344 (Si^*–GeSi13H18) 2.313 9.8 0.164(Si^*) 0.154(Ge) 0.318 Si^*–SiSi13H16 2.261 12.4 0.185(Si^*) 0.176(Si) 0.361 Ge^*–SiSi13H16 2.373 15.2 0.131(Ge^*) 0.245(Si) 0.376 Ge^*–GeSi13H16 2.454 16.5 0.105(Ge^*) 0.285(Ge) 0.390 (Si^*–GeSi13H16) 2.342 12.5 0.172(Si^*) 0.234(Ge) 0.406 The structure parameters of Si^*–GeSi13H18and Si^*–GeSi13H16clusters are parenthesized since the isomers are less stable than Ge^*–SiSi13H18 and Ge^*–SiSi13H16. Also listed are the charge diﬀerences between dimer atoms.

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charge diﬀerence is 0.234 (Si^*–Si) < 0.331 (Ge^*–Si) < 0.344 (Ge^*–Ge). For Si15xGexH16, the charge diﬀerence is higher, 0.361 (Si^*–Si) < 0.376 (Ge^*–Si) < 0.390 (Ge^*–Ge). Both increase with the number of Ge atoms.

4.2. Dissociative adsorption of SiH4and GeH4

As an example,Fig. 2illustrates the TS geometry of dissociative adsorption GeH4on the cluster Ge^*–SiSi13H18via scission of a Ge–H bond. The optimized TS geometry shows that the H atom of GeH4is abstracted by a positive down Si atom, simultaneously the Ge atom of GeH4 is interacting with a negative up Ge atom in dimer. The reaction mechanism was investigated by Brown and Doren[19]

on SiH4 adsorption on the Si(1 0 0)-2· 1 pristine surface.

They predicted an energy barrier of 12–14 kcal/mol, depending on details of the theoretical model. This four- center TS was also the vital geometry in studying chloro- silane adsorption on the Si(1 0 0)-2· 1 pristine surface via scission of one Si–Cl bond[36]. In this study, TS of SiH4

and GeH4 adsorbed on the Si_1xGex clusters have been searched at diﬀerent dimers. For all cases being calculated, the only negative frequency of TS falls in the range of 330–

450 cm¹. Inspection of the normal mode corresponding to the negative eigenvalue shows that the reaction coordinate involves a concerted motion of the H atom away from the Ge atom in GeH4with motion of the Ge atom towards the another dimer atom.

Since the surface dimer is essentially charged, consisting of an electrophilic down atom and a nucleophilic up atom, the H-abstraction reaction is bound to occur between the down atom and the H atom. If we force the H atom of Si–H or Ge–H bond to approach the up atom during a saddle point search, the up atom of dimer sinks as the down atom rises like a seesaw.Table 4lists the activation energy barrier EA and the reaction energy DERXN of SiH4 and GeH4dissociative adsorption on Si_15xGexH18. When the reaction energies of SiH4 adsorption on diﬀerent dimers are compared, the DERXNvalue increases with the increasing Ge atom in the dimer. The sequence in DERXN value

can be understood in view of bond breaking and bond for- mation. The Si–H(g) is the bond being cleaved in SiH4

adsorption. Two new bonds Si–SiH_3(a) and Si–H_(a) are formed on the Si^*–Si dimer. When the dimer is Ge^*–Si, two new bonds are Ge–SiH3(a) and Si–H(a). When the dimer is Ge^*–Ge, two newly formed bonds are Ge–SiH3(a)

and Ge–H(a). Since the bond strength of Ge–SiH3(a)bond is less than that of Si–SiH3(a)bond, and that of Ge–H(a)bond is less than that of Si–H(a) bond, the value of reaction energy decreases with more Ge in the dimer. On the other hand, if the reaction energy of SiH4and that of GeH4on the same dimer are compared, the DERXN value of GeH4

adsorption is always less because less energy is required to break the Ge–H(g) bond. The binding energy of Ge–

H(g) bond has been estimated 84 kcal/mole, less than 90 kcal/mol of Si–H(g)bond in SiH4[37]. Reaction energies of SiH4and GeH4adsorption on the pristine surface are listed in Table 5. Adsorption reaction energy on the pristine surface follows the same trend in Table 4, but its DERXN value is slightly higher.

The EAvalues, listed inTables 4 and 5, do not follow the trend of reaction energy because of the complexity in dimers discussed earlier. The energy barrier for SiH4 or GeH4 adsorption on the Ge^*–Ge dimer is generally the highest among three dimers on the cluster surface with either two or four dangling bonds. The second lowest energy barrier is on Si^*–Si dimer, and the lowest barrier is on Ge^*–Si dimer. This interesting result has insightful implication in the growth kinetics and the grown SiGe layer composition. Engstrom and his coworkers measured the reaction probability of GeH4using supersonic molecular beam techniques. They reported the reaction probability of GeH₄ on the zero H-coverage Si(1 0 0) was 2–5 times that of GeH4on the zero-coverage Ge(1 0 0) surface [11]. In another experiment, at substrate temperature 650C when the surface hydrogen coverage could be ne- glected, as the surface Ge content on Si(1 0 0) increased from Ge zero coverage, the GeH4reaction probability steadily decreased with the increasing Ge surface content. The highest barrier of GeH4on a Ge^*–Ge dimer inTables 4 and 5 is generally in line with Engstrom’s conclusions.

Engstrom also measured the inﬂuence of strain on Si_1xGex overlayer in the dissociative adsorption of

Table 4

Activation barriers EAand reaction energy DERXNfor SiH4 and GeH4

dissociative adsorption on Si_1xGexSi13H18(x = 0 2) clusters Precursor/cluster EA(kcal/mol) DERXN(kcal/mol) SiH4/Si^*–SiSi13H18a 13.8 48.9

SiH4/Ge^*–SiSi13H18 12.6 44.8 SiH4/Ge^*–GeSi13H18 18.1 38.0 (SiH4/Si^*–GeSi13H18) (17.4) (43.4) GeH4/Si^*–SiSi13H18 12.0 52.4 GeH4/Ge^*–SiSi13H18 10.5 47.7 GeH4/Ge^*–GeSi13H18 14.0 41.4 (GeH4/Si^*–GeSi13H18) (15.7) (46.7) The parenthesized Si^*GeSi13H18is less stable than Ge^*–SiSi13H18.

aThe activation energy ﬁtted to RRKM model was 13.4 kcal/mol by Xia et al. (J. Vac. Sci. Technol. A, 1995) on SiH4dissociative adsorption on Si(1 0 0).

Table 5

Activation barriers EA and reaction energy DERXNfor SiH4and GeH4

dissociative adsorption on Si1xGexSi13H16(x = 0–2)

Precursor/cluster EA(kcal/mol) DERXN(kcal/mol) SiH4/Si^*–SiSi13H16 11.8 48.5

SiH4/Ge^*–SiSi13H16 11.3 42.7 SiH4/Ge^*–GeSi13H16 17.4 36.1 (SiH4/Si^*–GeSi13H16) (15.8) (42.4) GeH4/Si^*–SiSi13H16 10.7 51.1

GeH4/Ge^*–SiSi13H16 8.0 47.3

GeH4/Ge^*–GeSi13H16 13.3 39.1 (GeH4/Si^*–GeSi13H16) (14.6) (45.3) The parenthesized Si^*GeSi13H16is less stable than Ge^*–SiSi13H16.

3198 C.-L. Cheng et al. / Surface Science 600 (2006) 3194–3201