在氧化鋅磊晶薄膜物理特性中晶體缺陷結構的角色

國 立 交 通 大 學

光電工程學系暨研究所

博 士 論 文

在氧化鋅磊晶薄膜物理特性中晶體缺陷結構的角色

The role of crystal defect structures in the physical

properties of ZnO epitaxial films

研 究 生：劉維仁

指 導 教 授：徐嘉鴻 教授

謝文峰 教授

在氧化鋅磊晶薄膜物理特性中晶體缺陷結構的角色

The role of crystal defect structures in the physical

properties of ZnO epitaxial films

研 究 生：劉 維 仁 Student：Wei-Rein Liu

指導教授：徐 嘉 鴻 教 授 Advisor : Dr. Chia-Huang Hsu

謝 文 峰 教 授 Dr. Wen-Feng Hsieh

國 立 交 通 大 學

光 電 工 程 研 究 所

博 士 論 文

A Dissertation

Submitted to Department of Photonics and Institute of Electro-Optical Engineering College of Electrical Engineering and Computer Science

National Chiao Tung University In Partial Fulfillment of the Requirements

for the Degree of Doctor of Philosophy

in

Electro-Optical Engineering

February 2009

Hsinchu, Taiwan, Republic of China

誌 謝

時間的流逝真是快速，轉眼間我即將離開這個具有充滿回憶的地方。回想過 去這幾年，在我腦海裡不斷的浮現出我所經歷的人事物，感覺到所有一切的事都 才剛剛發生而已，沒想到我即將要畢業了要進入我人生的另ㄧ段旅程了。 本論文得以順利完成，首先我要感謝指導教授徐嘉鴻老師(大媽)及謝文峰老 師，從碩士班到博士班這七年半來，老師對我的用心栽培與諄諄教誨，讓我的學 識和能力不斷提升；在為學及做人態度上，潛移默化亦使我受益良多。其次要感 謝口試委員們對論文的指正以及建議，使本論文更臻完善，也讓我對於未來研究 的方向以及需要補強的地方了然於胸。 同時也要感謝清華大學洪銘輝及郭瑞年 教授所提供高品質的成長於矽基板上氧化物緩衝層試片，使得實驗得以順利進行； 還有東海大學簡世森學長在SPM相關分析與實驗的協助；以及同步輻射的學長世 宏、永偉、志謨、同學恒睿、學弟碧軒對於XRD實驗儀器及真空技術所給予的協 助及幫忙。 再來我要謝謝雷射診測實驗室那些曾經陪伴我ㄧ起走過這些年的夥伴夥伴 們:阿政、裕奎及智章學長在實驗、課業、生活上的指導及協助，黃董、楊松及國 峰對實驗室公務的分擔以及生活經驗分享；救過我一命的吳俊毅，沒有你那天睡 在實驗室，我可能掛在9樓；此外還有實驗室內可愛的學弟妹們岳勳、宜錦、小 郭、志遠、小豪、盈璇、延垠等，使得我在這幾年內的生活多采多姿，真是太感 謝你們了。還有在廣鎵光電的蔡炯期學長，由於您的幫忙，使得laser MBE沒壞 在我手裡，另外曾經跟我一起準備博士資格考的介任、明芳、阿達，沒有你們的 陪伴，這一仗真的很難打。 我還要感謝的我的雙親給予我最大的支持與鼓勵。 在我的求學之路曾經跌倒 了數次。您們都用最大的包容力，無怨無悔地支持及陪伴我，讓我站起來繼續走 下去，希望我的表現沒有讓您們失望。也感謝我的另一半怡欣，在博士生生涯中， 辛苦地陪我走過來。而今而後，但願我在為人處世上能夠學得更加謙卑與風趣。 最後感謝國科會的經費支持及交通大學奈米中心、同步輻射中心設備支援， 才能讓本論文得以順利完成。

在氧化鋅磊晶薄膜物理特性中晶體缺陷結構的角色

研究生：劉維仁 指導教授: 徐嘉鴻 教授

謝文峰 教授

國立交通大學光電工程學系暨研究所

摘要

我們利用雷射濺鍍法於不同的基板上成長高品質(0001) c 軸方向的氧化鋅 (ZnO)磊晶薄膜;使用的基板包括 c 軸方向的藍寶石(α-Al2O3)基板和使用奈米厚 的γ相氧化鋁(γ-Al2O3)或氧化釔(Y2O3)做為緩衝層的(111)方向的矽基板。針對氧 化鋅長在藍寶石基板的系統，X 光繞射結果指出相對於 c 軸方向藍寶石基板的晶 格，c 軸方向的氧化鋅其晶格沿著樣品表面法線方向旋轉 30 度，亦即兩者的橫 向磊晶關係式為[10 10]_sapphire &[1120]_ZnO 和 [1120]sapphire &[0110]ZnO。在沿著薄膜表

面法線及水平方向氧化鋅 X 光繞射峰寬度呈現巨大的差異，揭示出特定貫穿式 差排(threading dislocation)類型的幾何關係；從 X 光繞射及穿透式電子顯微鏡實 驗數據計算出的貫穿式差排密度顯示出大部分差排是刃(edge)差排類型。結合散 射及顯微術量測結果，證實貫穿式差排並非均勻分布在氧化鋅薄膜內，氧化鋅薄 膜是由柱狀的磊晶核芯周圍環繞高密度的貫穿式刃差排的磊晶晶粒所組成。藉由 掃描式電容顯微鏡及導電式原子力顯微鏡針對貫穿式差排聚集處做電性量測，發 現其平帶電壓平移及電位勢障提高，這歸因於高密度的貫穿式刃差排存在而造成 的界面捕獲電荷密度。另一方面，由於貫穿式螺旋(screw)差排密度遠小於貫穿 式刃差排，因此我們無法確認貫穿式螺旋差排的位置及其電性。 對 c 軸方向氧化鋅磊晶薄膜成長於使用超薄γ相氧化鋁為緩衝層的(111)矽基 I   

板的結構分析結果顯示(111)方向的γ相氧化鋁磊晶緩衝層在沿磊晶緩衝層水平 方向上存在兩個相互旋轉 60 度的晶畴，由此可以歸納三者的磊晶關係式為 2 3 2 3 {1010}_ZnO||{224}_{γ−Al O}or {422}_{γ−Al O} ||{224}_{Si。藉由X 光繞射及光激發光譜實驗對氧化} 鋅磊晶層的結晶品質及光學性質研究，明確地將能帶邊緣輻射與深層缺陷輻射的 強度比值與偏離垂直基板表面方向X 光繞射峰φ 掃描的訊號寬度聯繫起來; 並且 能帶邊緣輻射的寬度與氧化鋅(0002)繞射峰 θ−rocking curve 的寬度表現出很強 的相依性；這些現象證明，能帶邊緣輻射與深層缺陷輻射強度的比值主要受貫穿 式刃差排影響，而能帶邊緣輻射的寬度與貫穿式螺旋差排有關。 X 光繞射、光激發光譜及穿透式電子顯微鏡實驗證實，使用奈米厚、高介電 質(high-k)材料氧化釔為緩衝層的(111)矽基板上可以成長同時具有高品質結晶 及光學特性的氧化鋅磊晶薄膜。奈米厚氧化釔不僅可以提供成長完美氧化鋅磊晶 薄膜的緩衝層，更可以成為氧化鋅及矽基板間的絕緣層。藉由 X 光繞射及穿透 式 電 子 顯 微 鏡 量 測 ， 氧 化 鋅 與 氧 化 釔 間 的 磊 晶 關 係 式 遵 循 2 3 (0001) 2 1 10< >_ZnO|| (111) 10 1< >_{Y O} 關係。 氧化鋅晶格與氧化釔中的氧六方形次晶 格(sub-lattice)具同向排列，二者之間的界面結構可以妥善地用 7 或 8 倍氧化鋅 {1120}的面距匹配 6 或 7 倍氧化釔{440}的面距的晶畴匹配磊晶模型描述；如此 大的晶格不匹配可以藉由錯配差排(misfit dislocation)在界面上以 6 或 7 倍氧化釔 {440}面距週期性地排列做調節，使得殘留應力明顯降低。即使是厚度只有 0.21 μm 的氧化鋅薄膜也展現優秀的光激發輻射特性。我們的實驗結果證明了氧化釔 可以成為整合氧化鋅光電元件與以矽為主體的積體電路於一體的模板。 最後，從 X 光繞射、穿透式電子顯微鏡實驗數據，分別計算生長於上述三種 基板的氧化鋅磊晶薄膜的貫穿式差排密度，結果顯示刃差排型式都是主要的結構 缺陷；氧化鋅晶格總是與藍寶石基板，γ 相氧化鋁及氧化釔中氧的六方形次晶格 呈同向排列，其所對應的二維次晶格晶格常數分別為 2.75、2.8、3.75 Å，與氧 化鋅的晶格常數(3.249 Å)比較，預期沿水平方向的應力狀態對於氧化鋅成長於 c II   

III    軸方向的藍寶石、γ 相氧化鋁應為壓縮應力；相反地，成長於氧化釔上的氧化鋅 應為拉伸應力。然而，僅有成長在藍寶石上的氧化鋅被觀察到其沿水平方向呈壓 縮應力；成長在γ 相氧化鋁及氧化釔上的氧化鋅都是受到拉伸應力；事實上，對 氧化鋅成長於使用其他氧化物為緩衝層的(111)矽基板上，包含氧化釓(Gd2O3)

和參雜氧化釔的氧化鉿(Y2O3-doped HfO2)等系統，所有氧化鋅磊晶薄膜都在水

平方向受到拉伸應力；此外，存在於氧化鋅及氧化物緩衝層界面上的高密度錯配 差排，調節了絕大部分晶格匹配所造成的應力。由於氧化鋅的熱膨脹係數 (α~4-6.5 × 10-6 _K-1_{)小於藍寶石基板(8 × 10}-6 _K-1_{)，但大於矽基板的(8 × 10}-6 _K-1₎ 熱膨脹係數，這個趨勢與我們所觀察的氧化鋅成長於藍寶石基板及矽基板上的應 力態相符，顯示氧化鋅磊晶層的應力態主要是由成長完成後冷卻過程中因磊晶薄 膜與基板間熱膨脹係數差所導致的熱應力所支配；因為使用的氧化物緩衝層厚度 為只有數奈米厚，因此在這些使用的氧化物緩衝層案例中，來自緩衝層熱應力的 影響是可以忽略的。

The role of crystal defect structures in the physical

properties of ZnO epitaxial films

Student: Wei-Rein Liu Advisor: Prof. Chia-Hung Hsu

Prof. Wen-Feng Hsieh

Department of Photonics & Institute of Electro-Optical Engineering

National Chiao Tung University

Abstract

High-quality c-oriented ZnO film has been epiaxially grown by utilizing PLD on the sapphire (0001), and Si (111) substrates with a nano-thick γ-Al2O3 or Y2O3 buffer

layer, respectively. XRD results show a 30° offset between the {2020} reflections

of ZnO and sapphire verifies the in-plane epitaxial relationship of [10 10] sapphire ||

[1120] ZnO and [1120]sapphire || [0110]ZnO; the great disparity of X-ray diffraction line

widths between the normal and in-plane reflections reveals the specific threading dislocation (TD) geometry of ZnO. The calculated TDs densities from XRD and TEM indicate most TDs are pure edge dislocations. From a combination of scattering and microscopic results, it is found that the TDs are not uniformly distributed in the ZnO films, but the ZnO films consist of columnar epitaxial cores

IV   

surrounded by annular regions of edge threading dislocations at a large density. The shift of flatband voltage and the raise of potential barrier at the aggregation of TDs observed by scanning capacitance microscope and conduction atomic force microscope were attributed to the interface trap densities caused by the existence of high-density edge threading dislocations. On the other hand, because the distribution of the screw TDs is much less than that of the edge TDs, we cannot identify the location of the screw TDs and their electrical properties.

The structural analysis of c-oriented ZnO epitaxial films on Si(111) substrates with a thin γ-Al2O3 buffer layer erveals that epitaxial γ-Al2O3 buffer layer consists of

two (111) oriented domains rotated 60° from each other against the surface normal and the in-plane epitaxial relationship among ZnO layer, γ-Al2O3 buffer and Si buffer

follows . Studies on the crystalline quality and optical properties of ZnO epi-layers by XRD and PL measurements clearly indicate the intensity ratio of deep-level emission (DLE) to near-band edge emission (NBE) of ZnO films correlates with the width of φ−scan across off-normal reflection and the NBE linewidth is strongly dependent on the width of ZnO (0002) rocking curve. These observations manifest that the (IDLE/INBE) ratio is dominantly

affected by edge TDs and the line width of NBE emission is mainly related to screw TDs.

2 3 2 3

(1010)_ZnO || {224}_{γ−Al O} or {422}_{γ−Al O} || {224}_Si

V   

Both high-quality structural and optical properties of ZnO epi-film on Si (111) substrates using a nano-thick high-k oxide Y2O3 buffer layer was verified by XRD,

TEM, and PL measurements. The nano-thick Y2O3 epi-layer serves not only as a

buffer layer to ensure the growth of ZnO epi-film of high structural perfection but also as an insulator layer between ZnO and Si. Determined by XRD and TEM the epitaxial relationship between ZnO and Y2O3 follows

3 2 1 10 ) 111 ( || 0 1 1 2 ) 0001

( < >ZnO < >YO . ZnO lattice aligns with the hexagonal

oxygen (O) sub-lattice in Y2O3 and the interfacial structure can be well described by

domain matching epitaxy with 7 or 8 ZnO {1120} planes matching 6 or 7 {440} planes of Y2O3; the large lattice mismatch is thus accommodated by the misfit

dislocations (MDs) localized at the interface with a periodicity of 6(7) times of

3 2 ) 0 4 4

( YO inter-planar spacing, leading to a significant reduction of residual strain.

Superior photoluminescence were obtained even for ZnO-films as thin as 0.21 μm. Our results demonstrate that the Y2O3 layer well serves as a template for integrating

ZnO based optoelectronic devices with Si substrate.

Finally, the calculated TDs densities from XRD and TEM indicate most TDs are pure edge dislocations for ZnO epi-films on sapphire (0001), γ-Al2O3/Si(111), or Y2O3

/Si(111) substrates. The lattice of ZnO is always aligned with the hexagonal O sub-lattice in the oxide layer underneath. The lattice constant ao of 2D hexagonal

VI   

VII   

oxygen sub-lattice are 2.75, 2.80, 3.75 Å for sapphire, γ-Al2O3and Y2O3, respectively.

As compared with the lattice constant a of ZnO (3.249 Å), compressive strain along in-plane direction is expected for ZnO epi-film grown on sapphire (0001) and γ−Al2O3(111). In contrast, the expected lateral strain is tensive for ZnO epi-film on

Y2O3(111). However, compressive lateral strain is only observed for ZnO epi-layers

grown on sapphire. On both γ-Al2O3 and Y2O3 buffer layers, ZnO epi-films bear

tensile strain. In fact, for ZnO epi-film grown on Si(111) using other oxide buffer layers, including Gd2O3, and Y2O3 doped HfO2, all ZnO epi-film suffers tensile strain

along in-plane direction. Moreover, high density of MDs at ZnO/oxide-buffer interface should accommodate most of the strain caused by lattice mismatch. It is noted that the thermal expansion coefficient of ZnO (α ~4-6.5 × 10-6 _K-1_{) is less than}

that of sapphire (8 × 10-6 _K-1_{) but larger than that of Si (2.6-3.6 × 10}-6 _K-1_{). The}

trend agrees with the observed strain state of ZnO layer grown on sapphire and Si. This observation strongly suggests that the strain of the ZnO-epi layers is dictated by the thermal stress built up during the post-growth cooling. Because of the nano-thickness of the employed buffer layers, the influence coming from the buffer is negligible in these cases.

VIII    Contents Abstract in Chinese ... I Abstract in English ... IV  Contents ... VIII List of Figures ... XIII List of Tables ... XVIII

Chapter 1 Introduction ... 1

1.1 Basic properties of ZnO, overview of ZnO thin film growth and related Problems . ... 1

1.1.1 Basic properties of ZnO and itspotential applications ... 1

1.1.2 Current status of epitaxial ZnO thin film growth and problems ... 5

1.2 Motivation ... 7

1.3 Organization of the dissertation ... 8

References ... 10

Chapter 2 Theoretical background and characterization techniques ... 12

2.1 Epitaxy ... 12

IX   

2.1.2 Domain mismatch epitaxy (DME) ... 13

2 .2 Structural defect in epitaxy ... 15

2.2.1 Dislocations ... 16

2.2.1.1 The theory of dislocation ... 16

2.2.1.2 The influence of dislocation on electrical and optical properties .... 20

2.3 Characterization techniques ... 21

2.3.1 X-ray diffraction (XRD) ... 21

2.3.1.1 The equivalence of Bragg law and reciprocal lattice ... 21

2.3.1.2 XRD technique ... 27

2.3.1.3 Threading dislocation distortion for XRD analysis ... 31

2.3.1.4 XRD line width analysis ... 35

2.3.2 Transmission electron microscope (TEM) ... 36

2.3.2.1 Selected area electron diffraction (SAED) ... 36

2.3.2.2 Threading dislocation density analysis ... 37

2.3.3 Scanning probe microscopy (SPM) ... 38

2.3.3.1 Theory of SCM ... 39

2.3.3.2 Theory of CAFM ... 42

2.3.4 Photoluminescence characterization ... 43

2.3.4.1 General concepts ... 44

X    2.3.4.3 Bound excitons ... 49 2.3.4.4 Two-electron satellites ... 51 2.3.4.5 LO-phonon replicas ... 53 2.3.4.6 Defect emission... 55 References ... 58

Chapter 3 Experimental setups and procedures ... 62

3.1 Epitaxial growth of ZnO film ... 62

3.1.1 Preparation of substrate and buffer layer ... 62

3.1.2 Preparation of ZnO films ... 64

3.2 Structural characterization ... 66

3.2.1 X-ray Diffraction ... 66

3.2.2 Transmission Electron Microscopy ... 67

3.3 Electrical characterization ... 68

3.4 Optical characterization ... 68

3.4.1 Photoluminescence ... 68

XI   

Chapter 4 Epitaxial ZnO films on c-plane sapphire ... 71

4.1. Introduction ……….. 71

4.2 Structural properties and analysis of defect structures ... 72

4.3 Correlation between defect structures and morphology ... ………. 82

4.4 Correlation between defect structures and electrical properties ... 85

4.5 Summary ... 89

References ... ……….… 93

Chapter 5 Epitaxial ZnO films on Si (111) using a γ-Al2O3 buffer Layer ... 96

5.1 Introduction ... 96

5.2 Structural properties ... 97

5.3 Analysis of defect structures ... 102

5.4 Optical properties ... 103

5.5 Correlated crystal structure with Optical properties ... 105

5.6 Summary ... 110

References ... 111

Chapter 6 Epitaxial ZnO on Si (111) using a Y2O3 buffer Layer ... 114

XII   

6.2 Crystal structure ... 115

6.3 Domain matching and interface engineering ... 118

6.4 Photoluminescence ... 122

6.5 Summary ... 124

References ... 126

Chapter 7 Conclusions and Prospects ... ………….. 128

7.1 Conclusions ………128

7.2 Prospects ... 133

List of Figures

Fig. 1-1 Atomic arrangement of wurtzite ZnO. ... 1  Fig. 1-2 The room temperature PL spectrum of ZnO epi-film grown on c-plane

sapphire. ... 4  Fig. 1-3 Electroluminescence spectrum from a p–i–n junction and PL spectrum of a

p-type ZnO film measured at 300 K ... 4 

Fig. 2-1 High-resolution TEM cross section image with(0110) foil plane of sapphire and (2110) plane of ZnO showing domain epitaxy in ZnO/apphire system .. 15  Fig. 2-2 The typical structural defect in epitaxy ... 16  Fig. 2-3 Three types of dislocation are screw, edge, and mixed types, respectively. ... 19  Fig. 2-4 The stress and strain associated with screw and edge dislocation. ... 19  Fig. 2-5 The construction of a 2D crystal structure from ‘lattice+basis”... 22  Fig. 2-6 The equivalence of Bragg’s Law and the Laue condition for a 2D square

lattice ... 25  Fig. 2-7 The diagram of direct and the reciprocal lattice of a cubic symmetric crystal.

 ... 25  Fig. 2-8 The diagram of direct and the reciprocal lattice for a hexagonal symmetric

crystal. ... 26  Fig. 2-9 The diagram shows the radial scan along surface normal of XRD and

corresponding variation of q vector in reciprocal space. ... 28 

XIII   

Fig. 2-10 The diagram show the reciprocal lattice for c-oriented ZnO and the radial scans along surface-normal, in-plane and off- normal direction, respectively.  ... 29  Fig. 2-11 The diagrams show the orientation distribution of subgrains of a typical

mosaic crystal and the rocking curve of XRD and corresponding variation of

q vector ... 30 

Fig. 2-12 The diagram show azimuthal scan across the off-normal ZnO(1014)peak. . 31 

Fig. 2-13 The picture illustrates imaging conditions for dislocations with the maximum and minimum of gb product. ... 38  Fig. 2-14 Scanning capacitance microscopy block diagram. ... 40  Fig. 2-15 Change from accumulation to depletion due to alternating electric field of

SCM. ... 40  Fig. 2-16 Capacitance versus applied AC voltage (C-V) curves for n-type

semiconductor with different carrier concentration. ... 42  Fug. 2-17 Conductive AFM block diagram. ... 43  Fig. 2-18 The exciton dispersion in a two-particle (electron-hole) excitation diagram

of the entire crystal ... 46  Fig. 2-19 Details of the band structure of hexagonal semiconductors around the Γ point. ... 47 

XIV   

Fig. 2-20 Free excitonic fine structure region of the 10 K PL spectrum of a ZnO single

crystal. ... 49 

Fig. 2-21 Bound excitonic region of the 10 K PL spectrum of a ZnO single crystal. . 51 

Fig. 2-22 10K PL spectrum in the TES region of the main bound exctions line. ... 53 

Fig. 2-23 10K PL spectrum in the region where DAP transition and LO-phonon replicas are expected to appear. ... 54 

Fig. 3-1 Layout of the PLD growth system ... 65 

Fig. 3-2 The picture and schematic of a four-circle diffractomter ... 66 

Fig. 3-3 Layout of the PL system ... 69 

Fig. 4-1 PL spectrum measured at room temperature ... 73 

Fig. 4-2 Azimuthal scans of ZnO {2022} and sapphire{2022} peaks ... 76 

Fig. 4-3 Superimposed radial and symmetric _{ω scans of ZnO (0002) and (1010)} reflections... 76 

Fig. 4-4 Williamson-Hall plots for a ZnO layer of radial scans and ω-rocking curves ... 72 

Fig. 4-5 The profile of a radial scan across ZnO (1014) reflection measured in an asymmetric geometry. ... 80 

Fig. 4-6 Two-beam bright-field cross-sectional electron micrographs of a ZnO thin film with g = (0002), (1120) , and (1122)  ... 84 

XV   

Fig. 4-7 AFM topography and SCM differential capacitance (dC/dV) image of a ZnO film of area 1×1 μm2 _{acquired at V}

tip = 2 V ... 85 

Fig. 4-8 AFM topography and SCM differential capacitance (dC/dV) image acquired at Vtip = 0.664 V in ZnO film. ... 91 

Fig. 4-9 AFM topography and C-AFM current image of ZnO film with area of 0.4×0.4 μm2 _{acquired at V}

tip = 3 V. ... 92 

Fig. 5-1 XRD radical scan along surface normal of a 0.3μm thick ZnO layer grown on the γ−Al2O3/Si(111) composite substrate. ... 99 

Fig. 5-2 The profiles of φ-scans across ZnO{1011} , γ-Al2O3{440}, and Si{220}

reflections... 99  Fig. 5-3 The diagram of the reciprocal lattice of c-oriented ZnO film on Si(111) using γ-Al2O3 buffer layer. ... 100 

Fig. 5-4 Two-beam bright-field cross-sectional TEM micrographs of the ZnO film with g = (0002)ZnO. ... 103 

Fig. 5-5 Typically PL spectra measured at 15K for ZnO epi-layers deposited on γ-Al2O3/Si(111) at 200oC and 300oC ... 105 

Fig. 5-6 The ratio (IDLE/INBE) and net carrier concentration dependence of Δφ of ZnO

diffracted peak. ... 109  (1011)

Fig. 5-7 The ratio (IDLE/INBE) and net carrier concentration dependence of edge TDs

XVI   

density for pile-up model calculation ... 109  Fig. 5-8 After exchanging abscissa of Fig. 5-7 (a) with (b) ... 110  Fig. 6-1 XRD radical scan along surface normal. ... 116  Fig. 6-2 φ-scan profiles across {1011}_ZnO , , and {220}Si off-normal

reflections... 116  3 2 } 440 { _YO

Fig. 6-3 Schematic of atomic arrangement of O sub-lattice in Y2O3 (111) planes.. .. 119 

Fig. 6-4 Cross-sectional TEM micrograph recorded along [112]_Si projection.. ... 121 Fig. 6-5 PL spectra of the ZnO film on Y2O3/Si (111) measured at 300 K and 13 K.

 ... 123 

XVII   

List of Tables

Table 1-1 Physical properties of wurtzite ZnO ... 3 Table 2-1 The influence of TDs on electrical and optical properties of GaN epitaxial film. ... 20 Table 2-2 The values of ᇞ, ΨE, and f (ᇞ, ΨE) for the three edge dislocation systems in

ZnO with 1 1120 3

E

b = < > and slip planes {1100}for (1014) reflection. ... 35 Table 3-1 List the parameters of growth for ZnO epi-films on different substrates. ... 65 Table 7-1 The influence of TDs on electrical and optical properties of ZnO epitaxial film. ... 132  

XVIII   

Chapter 1 Introduction

1.1 Basic properties of ZnO, overview of ZnO thin film growth and related

problems

1.1.1 Basic properties of ZnO and its potential applications

ZnO is an ideal material for applications in UV light emitters, varistors, transparent high power electronics, surface acoustic wave devices, piezoelectric transducers, and chemical as well as gas sensing. ZnO is a II-VI compound semiconductor with ionicity between covalent and ionic compounds. At ambient conditions, the thermodynamically stable form of ZnO has a hexagonal wurtzite structure belonging to space group _{(Schoenflies type symbol) or equivalently} (Hermann-Mauguin type symbol) (SG number186) with two formula units per primitive cell, as schematically shown in Fig. 1-1. Its lattice constants are a = 3.249 Å and c = 5.2063 Å. 4 6v C 3 P6 mc

Fig.1-1 Atomic arrangement of wurtzite ZnO

2

The basic properties of ZnO are summarized in Table 1-1 [1]. ZnO is a direct band-gap semiconductor with energy gap Eg = 3.37 eV at room temperature (RT).

An attractive feature of ZnO is its large exciton binding energy, 60 meV, which is about three times larger than that of GaN or ZnSe [2, 3]. ZnO thus has great thermal stability for excitons and offers a great application prospect for lasers with small thresholds even at high temperatures. The band gap of ZnO can be tailored by divalent substitution at the cation site to achieve band gap engineering. For example, Cd substitution leads to a reduction of band gap to ~3.0 eV [4]. Substituting Zn by Mg in epitaxial films can increase the band gap to approximately 4.0 eV while still maintaining the wurtzite structure [5].

Electron doping in nominally undoped ZnO has been attributed to Zn interstitials, oxygen vacancies, or hydrogen [6-11]. The intrinsic defect levels that lead to n-type doping lie approximately 0.01–0.05 eV below the conduction band. The photoluminescence (PL) spectrum of undoped ZnO measured at RT is shown in Fig. 1-2. The strong near-band-edge (NBE) UV emissions at ~3.28 eV are attributed to exciton states; the features in visible region around 2.3 eV are ascribed to the deep-level defect states. In 2005, Tsukazaki et al. demonstrated the first blue light-emitting diode (LED) of homostructural p-i-n junction based on ZnO [12]. The dominant feature in electroluminescence spectrum, as shown in Fig. 1-3, does not

originate from the recombination from near band edge but from deep level emission. This provides strong evidence that defects play a crucial role in the performance of ZnO-based photoelectronic devices.

Table 1-1 Physical properties of wurtzite ZnO. [1]

2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6

NBE

PL intensity (a.u.)

Photon energy (eV) PL @ RT

DLE

Fig.1-2 The room temperature PL spectrum of ZnO epi-film grown on c-plane sapphire.

Fig. 1-3 Electroluminescence spectrum from a p–i–n junction (blue) and PL spectrum of a p-type ZnO film measured at 300 K. The p–i–n junction was operated by feeding in a direct current of 20 mA. [12]

1.1.2 Current status of epitaxial ZnO thin film growth and problems

Sapphire has been used most frequently for epitaxial growth partly because high quality, large-size single crystal wafers are easily available. In the case of ZnO heteroepitaxial growth, sapphire (α-Al2O3), primarily with the (0001)-plane normal

(c-plane) and in some cases with the (1120)-plane normal (a-plane), is the most commonly used substrate. Sapphire has a rhombohedral crystal structure with lattice constants a = 4.758 Å and c = 12.991 Å. Because of the significant differences in structure and lattice parameters, it has been a challenge to grow high quality ZnO epitaxial films on sapphire. Besides, the significant difference in thermal expansion coefficient between ZnO and sapphire [14] introduces additional strain upon post-growth cooling. ZnO grown on c-plane sapphire usually has the epitaixal relationship of (0001)[1120]ZnO || (0001) [1010]sapphire, under which ZnO lattice is

rotated 30o _{against the c-axis of sapphire and lattice mismatch reduces from 32% to}

18%. Narayan et al. proposed that ZnO films grew on (0001) Al2O3 substrate by

domain matching epitaxy (DME) with 5 or 6 (2110) planes of ZnO matching 6 or 7 (3030) planes of sapphire at interface [13]. Consequently, most of the lattice mismatch is accommodated by the misfit dislocations (MDs) which are confined at the interface. However, there still exist high densities of threading dislocations (TDs) (typically 109_~1011 _cm-2_{) extending throughout the entire thickness of ZnO epitaxial}

6

films, which is still a major problem limiting the performance of ZnO based devices. Therefore, the reduction of defect density is a principal target to pursue for high-quality epitaxial ZnO growth.

The other attractive substrate is silicon because of many advantages, such as low costs, excellent crystalline quality, large-area availability of Si wafer and, most importantly, the unique opportunity of integrating well-established Si electronics with ZnO-based optoelectronic devices. Hence, many efforts have been put to grow high-quality ZnO on Si. Unfortunately, direct growth of epitaxial ZnO films on Si is a difficult task due to large diversity in lattice constants (15.4%) and thermal expansion coefficient (56%) as well as the formation of amorphous SiO2 layer at

ZnO/Si interface [15,16]. Either polycrystalline or highly textured ZnO films with (0001)-plane normal were commonly obtained on Si (111) substrates [17]. Therefore, significant efforts have been made to use various materials as the buffer layer for subsequent ZnO growth and quite some progress has been achieved. Nevertheless, the growth of high-quality ZnO epi-films on Si is still regarded as an arduous challenge.

7 1.2 Motivation

For heteroepitaxial systems with large mismatches in lattice parameters and thermal expansion coefficients between the deposited layer and substrate, significant strain is built up in the grown layer. When the stored strain energy exceeds certain threshold, the heterostructure becomes metastable and defects are generated to release the large strain energy. As revealed by many studies on another popular optoelectronic semiconductor - GaN thin films, which has the same wurtzite structure as ZnO, defects intimately affect the electrical and optical properties of the films, including the degradation of devices through carrier scattering [18], nonradiative recombination [19], and reverse-bias leakage current [20, 21]. However, the influence of defects on the physical properties of epi-ZnO films is still not well understood. A comprehensive knowledge of structural defects in ZnO epi-layer and their influence on the optical and electrical properties is valuable especially for the design of photoelectronic devices. In this dissertation, the growth of high quality ZnO epitaxial films by pulsed-laser deposition (PLD) on sapphire (0001) and Si(111) using various oxide buffer layers including γ-Al2O3 and Y2O3 is reported. The

microstructure of ZnO epi-films were thoroughly studied by X-ray diffraction (XRD), transmission electron microscopy (TEM) and atomic force microscopy (AFM). The electrical properties of these epi-films were examined by using scanning capacitance

8

microscopy (SCM) and conductive atomic force microscopy (C-AFM). photoluminescence (PL) was employed to characterize the optical properties of the ZnO films. Based on the obtained results, the correlations between structural properties, in particular the structural defects, and electric as well as optical properties are established.

1.3 Organization of the dissertation

This dissertation is organized as follows. A brief review of epitaxial growth,

crystal structures, dislocation theory, and defect analysis using XRD and TEM is given in chapter 2. The basic theory of the techniques used to characterize the samples including XRD, scanning probe microscopy (SPM) and PL are also summarized in the same chapter. Chapter 3 contains the details of sample preparation and a description of experimental setups. In chapter 4, the defect structures of high quality ZnO epitaxial films grown on c-plane sapphire are reported; the correlation between TDs and electrical properties, characterized by SCM and C-AFM, of these films is also discussed. Chapter 5 consists of the study on the structural and optical characteristics of ZnO epitaxial films on Si(111) substrates with a thin γ-Al2O3 buffer layer; the correlation between various types of TDs and the

9

crystalline and optical properties of ZnO epi-films grown on Si (111) substrates using a nano-thick Y2O3 buffer layer and a discussion of the role of MDs at the ZnO/Y2O3

interface in stabilizing the structure of this heteroepitaxial system is also presented. Finally, chapter 7 contains the conclusion of the studies in the ZnO epi-films and the topics proposed for future studies.

10 References

[1] D. P. Norton, Y. W. Heo, M. P. Ivill, K. Ip, S. J. Pearton, M. F. Chisholm, and T. Steiner, Materials Today 7, 34 (2004).

[2] D. M. Bagnall, Y. F. Chen, Z. Zhu, T. Yao, S. Koyama, M. Y. Shen, andT. Goto,

Appl. Phys. Lett. 70, 2230 (1997).

[3] Y. F. Chen, D. M. Bagnall, H. J. Koh, K. T. Park, J. Hiraga, Z. Zhu , and T. Yao,

J. Appl. Phys. 84 3912 (1998).

[4] L. K. Singh and H. Mohan, Indian J. Pure Appl. Phys. 13, 486 (1975).

[5] A. Ohtomo, K. Tamura, M. Kawasaki, T. Makino, Y. Segawa, Z. K. Tang, G. Wong, Y. Matsumoto, and H. Koinuma, Appl. Phys. Lett. 77, 2204 (2000).

[6] D. C. Look, J. W. Hemsky, and J. R. Sizelove, Phys. Rev. Lett. 82, 2552 (1999) [7] B. J. Jin, S. H. Bae, S. Y. Lee, and S. Im, Mater. Sci. Eng, B 71, 301(2000). [8] D. M. Hofmann, A. Hofstaetter, F. Leiter, H. Zhou, F. Henecker, B. K. Meyer, S.

B. Orlinskii, J. Schmidt, and P. G. Baranov, Phys. Rev. Lett. 88,045504 (2002). [9] C. G. Van de Walle, Phys. Status Solidi B 229, 221 (2002).

[10] S. F. J. Cox, E. A. Davis, P. J. C. King, J. M. Gil, H. V. Alberto, R. C. Vilao, J. Piroto Duarte, N. A. De Campos, and R. L. Lichti, J. Phys.: Condens. Matter 13, 9001 (2001)

11

[12] A. Tsukazaki, A. Ohtomo, T. Onuma, M. Ohtani, T. Makino, M. Sumiya, K. Ohtani, S. F. Chichibu, S. Fuke, Y. Segawa, H. Ohno, H. Koinuma, and M. Kawasaki, Nature Mater. 4 42 (2005)

[13] J. Narayan, andB. C. Larson, J. Appl. Phys. 93, 278 (2003).

[14] F. Vigué, P. Vennéguès, S. Vézian, M. Laügt, and J.-P. Faürie, Appl. Phys. Lett.

79, 194 (2001).

[15] Y. Z. Yoo, T. Sekiguchi, T. Chikyow, M. Kawasaki, T. Onuma, S. F. Chichibu, J. H. Song, and H. Koinuma, Appl. Phys. Lett. 84, 502(2004).

[16] A. Nahhas, H. K. Kim, and J. Blachere, J. Appl. Phys. Lett. 78, 1511(2001). [17] H. M. Cheng, H. C. Hsu, S. Yang S.C. Y. Wu, Y. C. Lee, L.J. Lin, and W. F.

Hsieh, Nanotechnology 16, 2882 (2005).

[18] H. M. Ng, D. Doppalapudi, T. D. Moustakas, N. G. Weimann, and L. F. Eastman,

Appl. Phys. Lett. 73, 821 (1998).

[19] T. Sugahara, H. Sato, M. Hao, Y. Naoi, S. Tottori, K. Yamashita, K. Nishino, L. T. Romano, and S. Sakai S. (1998). Jpn. J. Appl. Phys. Part 2, 37, L398 (1998). [20] J. W. P. Hsu, M. J. Manfra, R. J. Molnar, B. Heying, and J. S. Speck, Appl. Phys.

Lett. 81, 79(2002).

[21] E. J. Miller, D. M. Schaadt, E. T.Yu, C. Poblenz, C. Elsass, and J. S. Speck, J.

12

Chapter 2 Theoretical background and characterization

techniques

2.1 Epitaxy

Epitaxy refers to the growth on a crystalline substrate of a crystalline substance that mimics the orientation of the substrate. If a film is deposited on a substrate of the same compositions, the process is called homoepitaxy; otherwise it is called heteroepitaxy [1]. Depending on the degree of lattice mismatch, (af - as)/as, where af

and as, respectively, denote the lattice constants of film and substrate, the epitaxy of

heterosystems can be modeled by lattice mismatch epitaxy (LME) or domain match epitaxy (DME). A brief review of the two epitaxy models and the difference between them is given in the following.

2.1.1 Lattice mismatch epitaxy (LME)

The well-established lattice-matching epitaxy is suitable for describing systems with small lattice misfit (less than 7%–8%). The deposited layer grows by one-to-one matching of lattice constants across the film–substrate interface. The film grows pseudomorphically up to a ‘‘critical thickness’’ where it becomes energetically favorable for the film to contain dislocations [2, 3]. In this case, the dislocations are generated at the film surface and glide to the interface; therefore, the Burgers vectors and planes of the dislocations are dictated by the slip vectors and glide planes of the crystal structure of the film [4]. Smaller lattice misfit leads to

smaller elastic energy and coherent epitaxy is formed. Above this misfit, it was surmised that the film will grow textured or largely polycrystalline.

2.1.2 Domain mismatch epitaxy (DME)

The DME concept represents a considerable departure from the conventional LME for hetero-systems with lattice misfit less than 7–8%. For hetero-systems with larger lattice misfit, integral multiples of lattice planes - domains, instead of lattice constants, match across the film–substrate interface. The size of the domain equals integral multiples of planar spacing in the DME. The detailed description of DME model can be consulted in Ref [5].

The hetero-system of ZnO grown on c-plane sapphire is an example of DME. The lateral lattice constants of ZnO and sapphire are 3.249 and 4.758 Å, respectively, yielding a lattice mismatch of -31.7%. Figure 2-1(a) shows high-resolution TEM cross-section image taken with electrons incident along ZnO [1100] pole, in which an atomically sharp interface between ZnO epi-film and substrate is demonstrated. The Fourier-filtered image of Fig. 2-1 (b) is shown in Fig. 2-1 (b), in which the vertical lines above and below the interface are associated with the (2110) planes of ZnO film and the (0110) planes of sapphire substrate, respectively. The image clearly manifests the matching of 5 or 6 (2110) planes of ZnO with 6 or 7 (3030) planes of sapphire at the interface. The corresponding diffraction pattern, shown in

Fig. 2-1 (c), confirms the relative orientation between film and substrate. The

c-plane of ZnO lies on the basal plane of sapphire with a 30° in-plane rotation, as

illustrated in Fig. 2-1(d), which leads to the alignment of the {3030} planes of sapphire with the {2110} planes, i.e. a planes, of ZnO. Thus, the domain consisted of an average 5.5 ZnO {2110} lanes with size of 8.935 Å matches nicely with the domain made of an average 6.5 sapphire

p } 0 3 30 { s with size of 8.928 Å. The DME of ZnO on (0001) sapphire has also been demonstrated by in-situ x-ray diffraction measurement during initial stage of film growth [5]. Narayan et al. applies the time-resolved x-ray crystal truncation rod (CTR) measurements made after each excimer laser ablation pulse. They found the surface structure transients associated with ZnO clustering and crystallization last for about 2 sec. following the abrupt ~5 μs duration of laser deposition and discovered the rapid relaxation of ZnO films on sapphire. The relaxation process requires the creation of dislocations, which involves nucleation and propagation of dislocations. The rapid relaxation process in DME is consistent with the fact that the critical thickness under these large misfits is less than 1 monolayer [6]. As a result, dislocations can nucleate during initial stages of growth and most defects are confined to the region near the interface, leading to fewer defects in the interior of the deposited layer, the active region of the device.

plane

Fig. 2-1 (a) High-resolution TEM cross section image with (0110) foil plane of sapphire and (2110) plane of ZnO showing domain epitaxy in ZnO/apphire system; (b) Fourier-filtered image of the region near interface manifesting the matching of ZnO (2110) and sapphire (3030) planes with a 5/6 and 6/7 ratio; (c) corresponding electron diffraction pattern showing the alignment of planes in ZnO and sapphire; and (d) schematic of atomic arrangement in the basal plane of ZnO and sapphire. [5]

epitaxy 2 .2 Structural defect in

The structural defects in epitaxial film are generally categorized as threading and misfit dislocation, stacking fault, oval defect, and etc., as illustrated in Fig. 2-2. The most important structural defect in epitaxial films is the dislocation which also named as line defect. Dislocations can be further clarified into two sections according to their location in epitaxial films. One is threading dislocations (TDs) which extends throughout the entire thickness of an epitaxial film and the other one is misfit dislocation (MDs) located mainly at the interface between the substrate and the

deposited layer during initial stage of epitaxy. In following section, a brief review of dislocation theory is given.

Fig. 2-2 The typical structural defect in epitaxy

2.2.1 Dislocations

2.2.1.1 The theory of dislocation

A dislocation is a crystallographic defect, or irregularity, within a crystal structure. The presence of dislocations strongly influences the properties of materials. Some types of dislocations can be visualized as being caused by the termination of a plane of atoms in the middle of a crystal. In such a case, the surrounding planes are not straight but bend around the edge of the terminating plane so that the crystal structure is perfectly ordered on either side. According to the relationship between Burgers vector and dislocation line, there are two primary types of dislocations, screw and edge dislocations. Mixed dislocation is a combination of the two types of

dislocation [7-9]. Some characteristics of both screw and edge dislocations are summarized below.

1. Screw dislocations:

A screw dislocation is much harder to visualize. Imagine cutting a crystal along a plane and slipping one half across the other by a lattice vector, the halves will fit back together without leaving a defect. If the cut only goes part way through the crystal and then slipped, the boundary of the cut is a screw dislocation. It comprises a structure in which a helical path is traced around the linear defect (dislocation line) by the atomic planes in the crystal lattice, as shown in Fig.2-3 (a). For pure screw dislocations, the Burgers vector b is parallel to the dislocation line. A screw dislocation moves (in the slip plane) in a direction perpendicular to the Burger vector (slip direction) cause the strain and elastic stress field surrounding a screw dislocation, as shown in Fig. 2-4 (a) are written as

2 2

μ ε τ με

π = = πr (2-1)

Here r and μ are the radius of the Burgers circuit and the shear modulus of the

= b , b

r

material, respectively. According to the linear elasticity theory, the strain energy density in the stress field of the screw dislocation is τ2_{/2μ. The strain energy per unit}

length of the screw dislocation can be estimated with the following integration.

0 2 r' ₂ s _r μb 1 μb ' = ( ) ( )2 ln 2π 2μ π = 4π

∫

r W rdr r r0 (2-2) 17

18

where Ws is the energy per unit length of the screw dislocation, r0 is the inner radius

that excludes the dislocation core and r’ is an outer limiting radius for integration. It is normally assumed that linear elasticity does not hold below r0 ~ b.

2. Edge dislocations:

An edge dislocation is a line defect where an extra half-plane of atoms is introduced mid way through the crystal, distorting nearby planes of atoms. When enough force is applied from one side of the crystal structure, this extra plane passes through planes of atoms breaking and joining bonds with them until it reaches the grain boundary. The "extra half-plane" concept of an edge dislocation can be used to illustrate lattice defects such as dislocations, as shown in Fig. 2-3(b). An edge lies perpendicular to its Burgers vector and moves in the direction of the Burgers vector. The stress field surrounding an edge orientation is more complicated than that surrounding a screw dislocation. It is generally assumed that an edge dislocation lies in an infinitely large and elastically isotropic material. Assuming the dislocation line coincides with the z-direction, the stress at a point with polar coordinates r and θ, as shown in Fig. 2-4 (b), can be calculated based on the elasticity theory and has the following component:

sin .( ) 2 (1 ) rr b r θθ μ θ − σ σ π ν = = − , cos .( ) 2 (1 ) θ μ θ τ π ν = − r b r (2-3) and σ_θθ rr

σ are tensile stress components in the r and θ direction,

where the τ_rθ

length of edge dislocation, WE is given as 0 2 r' ₂ E _r μb 1 = ( ) ( )2 2 2 4 (1 μ π π μ = π

∫

W rdr ln4 ' ) ν − b r r b (2-4 3. Mixed dislocations

he combination of edge and screw dislocation.

)

The mixed type is t

(a) C b (b) E b (c) Fig. 2-3 Three types of dislocation are screw (a), edge (b), and mixed (c) types,

respectively.

(a) (b)

Fig. 2-4 The stress and strain associated with screw (a) and edge (b) dislocation.

20

2.2.1.2 The influence of dislocation on electrical and optical properties

Dislocations are known to exhibit a wide variety of effects that can have a significant impact on the mechanical, electrical, and optical properties of materials [8, 10]. As reported in a large number of studies in GaN, dislocations indeed influence

the optical properties and device performance through nonradiative recombination. Table 2-1 summarizes the influence of threading dislocations (TDs) on electrical and optical properties for GaN epitaxial film.

Table 2-1. The influence of TDs on electrical and optical properties of GaN epitaxial film

TDs type Electrical property Optical property Screw TDs

Leakage current under reverse bias voltage

[11, 12]

Degradation of PL intensity at NBE

[13, 14] Edge TDs

Extra negative charge [15], nonconductive

[16]

Enhancement of PL intensity at DLE

2.3 Characterization techniques

2.3.1 X-ray diffraction (XRD)

The reciprocal lattice plays a fundamental role in most analytic studies of periodic structures, particularly in the theory of diffraction. Using the information collected in reciprocal space, one can infer the atomic arrangement of a crystal in real space. The following sections give an introduction of crystal structure and corresponding reciprocal space, the basic theory of diffraction, a description of both the Laue and Bragg condition for diffraction, and the formula for defect analysis based on XRD data [19, 20].

2.3.1.1 The equivalence of Bragg law and reciprocal lattice

For three-dimensional (3D) lattice, the lattice is given by a set of vectors Rn of

the form ; where a1, a2, and a3 are the lattice vectors, and n1,

n2, and n3 are integers. These vectors a1, a2, and a3 define the unit cell. To

describe a crystal structure completely, we need to associate a basis, consisting of atoms or molecules, with each lattice point. The construction of a 2D crystal from a “lattice+basis” is illustrated schematically in Fig. 2-5. The position of each atom in the crystal can be written as Rn+rj , where Rn specifies the origin of the nth unit cell

and rj denotes the position of the jth atom within the unit cell. The scattering

amplitude for a crystal can be factorized into two parts and written as

1 1 2 2 3 3

n

R = n a +n a +n a

( ) ( ) j n

unit cell structure factor lattice sum iq r iq R crystal j j n F q ₌

∑

f q e ⋅

∑

e ⋅   (2-5)

The first part is the scattering amplitude from the single unit cell and is know as the structure factor

. ._{( ) ( )} iq rj

u c

j j

F q =

∑

f q e ⋅ (2-6)

where fj denotes the scattering cross section of atom j. It is a linear combinational of

atomic form factor f, weighted by the corresponding phase factor eiq r⋅j to taken into account the path difference of scattered x-rays. The structure factor is a function of scattering vector.

Lattice

Basis

Crystal

Fig. 2-5 The construction of a 2D crystal structure from ‘lattice+basis”.

The second term is the lattice sum to add up the contribution of all the unit cells. The sum of phase factors is negligible except when the phases associated with all the unit cells are different by 2π or its multiple, i.e.

2 integer

n

q R⋅ = π × for all n’s (2-7)

In such a case, all the atoms interfere constructively and the lattice sum will be equal to a huge number. To express the periodic atomic arrangement of a crystal, we can construct a corresponding lattice in the reciprocal space (which has dimensions of reciprocal length) spanned by basis vectors (a1*, a2*, a3*) which fulfill a a_i⋅ ∗_j =2πδ_ij,

where δij

= a +

is the Kronecker delta function which equals to 1 if i=j and is zero otherwise. Similarly, a lattice point in the reciprocal lattice can be specified by , where h, k, l are all integers. It is now apparent that any reciprocal lattice vector g satisfies Eq. (2-7) since the scalar product of g and Rn

1 2 ∗ ∗₊ g h ka la 2 ( 3 ∗ 1 2 3) π ⋅ _n = +

g R hn kn +ln is always a multiple of 2π. In other word, only if q

coincides with a reciprocal lattice vector will the scattered amplitude of a crystallite be non-vanishing. This is known as the Laue condition for X-ray diffraction: . To satisfy the requirement of

=

q g

2π ⋅ _n =

g R n , the reciprocal lattice basis vectors can

be expressed by 1 2 3 2 3 1 3 1 2 2 2 2 π π π ∗ _{= ×} ∗ _{= ×} ∗ _{= ×} c c c a a a a a a a a V , V , V a ) (2-8) where is the volume of the unit cell. Each point (hkl) in the reciprocal lattice corresponds to a set of lattice planes with the miller indices of (hkl) in the

1 ( 2 3

c

V = ⋅a a ×a

real space lattice. The direction of the reciprocal lattice vector corresponds to the normal of the real space planes, and the magnitude of the reciprocal lattice vector

24

is equal to 2π times of the reciprocal of the interplanar spacing of the real space planes. The Laue condition can be equivalently expressed by the Bragg’s Law. In Fig. 2-6 (a) the proof of this equivalence is illustrated for the case of a 2D square lattice. X-rays are reflected from atomic planes with a spacing of d. The requirement that the path length difference between x-rays reflected by the adjacent planes is a multiple of the wavelength leads to the well-known statement of Bragg’s law: λ = 2dsinθ, where θ is the angle between incident x-rays and reflecting planes. Replot the Bragg diffraction condition in reciprocal space using the outgoing wave vector k´ and incoming x-ray wave vector k, both of which have magnitude of 2π/λ in the elastic scattering process, and scattering vector q ≡ k´ – k = 2ksinθ, we can obtain the same diffraction condition q = g, the Laue condition [19]. The reciprocal lattice in this case is also a square lattice with a lattice spacing of 2π/d as shown in Fig. 2-6 (b) and the corresponding scattering vector q equals to g = 2π/d (01). Hence, each set of parallel planes (hkl) in real space can be expressed by a corresponding reciprocal lattice vector ghkl. The relationship between the reciprocal lattice point and

the planes in real space are concluded by two points:

1. ghkl is perpendicular to the planes with Miller indices (hkl).

Bragg λ = 2dsin θ d k k' θ θ Real θ θ q _2π/d Laue q=g k k' (0,1) (1,1) (1,0) (0,0) Reciprocal (a) (b)

Fig. 2-6 The equivalence of Bragg’s Law and the Laue condition for a 2D square lattice

Considering a 3D cubic crystal with lattice parameters a, Fig. 2-7 shows the lattice points in real and corresponding reciprocal space, respectively. As for a hexagonal symmetric crystal, including ZnO studied in this work, with lattice parameters a0 and

c0 (a = b = a0 ≠ c0, α = β = 90ο, γ = 120ο, 3 ₀2 ₀ 2

c

V = a c ) we also plot the real and

corresponding reciprocal space, as shown in Fig. 2-8.

3D

sc

Real space Reciprocal space

x a aK₁′=2π ˆ y a aK₂′=2π ˆ z a aK₃=2πˆ x a a1= ˆ K y a a2= ˆ K z a a3= ˆ K V = a3 Primitive vectors x a a z y x a a 0 0 1 2 ˆ 0 1 0 ˆ ˆ ˆ 2 ₃ 2 1 π π = = ′ K Primitive vectors 2π/a sc ′ 1 aK a2′ K ′ 3 aK

Fig. 2-7 The diagram of direct and the reciprocal lattice of a cubic symmetric crystal.

G a G b G c G' a G' b G' c a = b= a₀≠ c α = β =90°; γ = 120°

⊥

Projection

z-axis

Real space Reciprocal space

G K & ' c c , , ⊥ ⊥ G G K G G K ' ' a b c b a c ' o γ = 60 ' ' o α = β = 90 ' c 0 ' c 0 ' c 0 bcsinα 2 a = = V a 3 acsinβ 2 b = = V a 3 absinγ 1 c = = V c Hexagonal system

Fig. 2-8 The diagram of direct and the reciprocal lattice for a hexagonal symmetric crystal.

Derived from Eq. (2-8) reciprocal lattice vector ghkl of a cubic lattice and ghkil of a

hexagonal lattice can be expressed by

2 2 2

2 2

hkl hkl

g h k l for cubic lattice

d a π π = = + + and 2 2 2 ( ) 2 2 ( ) 0 0 2 4 | | 3 hkil hkil h hk k l

g for hexagona lattice

d a c

π _π ⎛ + + ⎞

= = _{⎜ ⎟}+

⎝ ⎠ (2-9).

Here the (hkl) is the three-axis Miller indices. Conventionally, for crystals with hexagonal and rhombohedral symmetry, crystallographic planes are denoted using the four indices based on a four-axis Miller-Bravias coordinate system, consisting of three basal plane axes (a1, a2, a3) at 120° angles to each other and a fourth axis (c)

perpendicular to the basal plane. The Miller-Bravias indices (hkil) satisfy the

27

conditions i = -(h+k). When using the Miller-Bravias indices one may clearly see the equivalence of the respective directions and planes in the crystal. In this thesis, 4-digit Miller-Bravias indices are used for materials with hexagonal and rhombohedral symmetries including ZnO and sapphire to distinguish them from those with cubic symmetry, e.g. Si, Y2O3 and γ-Al2O3 where 3-digit Miller indices are

employed.

2.3.1.2XRD technique

X-ray diffraction is a well established technique for structure determination of three-dimensional crystals. The diffracted intensity from crystal is collected by proper arrangement of diffractometer to match the Laue condition in sample reciprocal lattice. The four-circle diffractometer utilized consist of four rotatable circles, which are θ, 2θ, χ and φ circle; the 2θ circle is the detector axis controlling the magnitude of scattering vector q. The φ, χ, and θ circles control the sample orientation. When the q vector coincides with the specific reciprocal lattice vector g, the Laue condition is satisfied. Conceptually, the φ angle is equivalent to the azimuthal angle and the χ angle is related to the polar angle of crystal.

[1] Radial scans

Radial scans collect scattered X-ray intensity while the scattering vector q is scanned along the any radial directions in reciprocal space. The most commonly

performed radial scan is the one along sample surface normal, which is often known as the θ−2θ or ω-2θ scan as shown in Fig. 2-9. From the positions of diffraction peaks we can determine the corresponding interplanar spacing along the direction of q and the linewidth of the diffraction peak can yield the structural coherence length (grain size) and inhomogeneous strain along the same direction. Similar to the radial scans along surface-normal, radial scans along in-plane and off-normal direction for reciprocal lattice of c-oriented ZnO are shown in (a) (0002) _(b) (1010) and (c)

(1012) planes of Fig. 2-10, respectively. They can provide the interplanar spacing, structural coherent length along corresponding direction.

θ θ _2θ q θ｀ θ｀ q｀ δq_z θ-2θ scan 2θ｀

Fig. 2-9 The diagram shows the radial scan along surface normal of XRD and corresponding variation of q vector in reciprocal space.

(0002)

₍₁₀₁₂₎

(1010)

(0110)

(000)

(0002)

Δq

(1012)

Δq

(1010)

Δq

60

o

90

o (0002)

Δq

(a)

(b)

(c)

Fig. 2-10 The diagram show the reciprocal lattice for c-oriented ZnO and the radial scans along surface-normal, in-plane and off- normal direction, respectively.

[2] Rocking curve (ω-scan)

For a given incident x-ray direction and detector position, scattered x-ray collected while the crystal is rotated or called rocked through the Bragg angle θB.

The resulting intensity vs the sample angular position θ or equivalently ω = θ−θB

yields the rocking curve. The width of a rocking curve is a direct measure of the range of orientation distribution, mosaicity, present in the irradiated area of the sample because each subgrain of a typical mosaic crystal successively comes into reflecting position as the crystal is rocked, as shown in Fig. 2-11(a). Rocking curve performed at reflections along surface-normal is sensitive the tilt (polar) angle distribution of the sample; on the other hand the rocking curved measured at surface Bragg peaks mainly reflect the twist (azimuthal) angle distribution of the sample, because the variation of

scattering vector Δq is perpendicular to the radial direction of corresponding reflections, as shown in Fig. 2-11(b).

(a) 30 δq_x θ θ (b) ω 2θ q q q rocking curve

Fig. 2-11 The diagrams show the orientation distribution of subgrains of a typical mosaic crystal (a) and the rocking curve of XRD and corresponding variation of q vector (b).

[3] Azimuthal scan

Azimuthal scan means measuring the diffraction intensity as a function of azimuthal angle φ by rotating the sample along an axis which is usually parallel to surface normal or, in some cases, to a specific crystallographic axis. Figure 2-12

illustrates schematically the reciprocal lattice of a c-oriented ZnO film. Using azimuthal scan, we can study the symmetry and crystal quality of the grown film and determine its relative orientation with substrate in epitaxy.

ZnO

Q

z 60o ₍₁₀₁₀₎ (0002) (0004) x Q (0110) (1014) (1014) φ‐scan (1014) Q | | ) 31 (000 y Q

Fig. 2-12 The diagram show azimuthal scan across the off-normal ZnO(1014)peak.

2.3.1.3 Threading dislocation distortion for XRD analysis

The presence of TDs in materials gives rise to crystalline plane distortion [21]. Depending on the geometry of TDs, lattice is deformed in a different way. Have a thin film with hexagonal wurtzite crystalline symmetry and c-plane normal orientation as an example. Pure screw TDs along [0001] direction generate a pure shear strain field, where (hkil) crystalline planes with nonzero l are deformed. The width of (000l) rocking curve and radical scan are only sensitive to the screw TDs in the films. Therefore, the width of (000l) diffraction peaks is investigated to determine the strain field induced by screw TDs. The density of the screw dislocations Ns can be

obtained using the following equation [22, 23] 2 2 4.35 α_Ω = s c N b (2-10)

where bc is the Burgers vector of screw TDs and αΩ _{is the tilting angle. From the}

radial-scan line width of (000l) reflections, the inhomogeneous strain εs can be

obtained. Considering that each dislocation is accompanied by a strain field, it is possible to calculate the dislocation density from the strain induced broadening of Bragg reflections in the radial direction βεusing the following equations provided that

the slip planes and Burgers vectors of the dislocations are known [24].

( )

2 _{8 ln 2} 2 _tan

ε 2

β = ε_S θ (2-11)

<εs2> is the mean square strain and can be calculated for a pure screw dislocation by

[24, 25] 2 2 2 2 0 ln sin 4 ε π ⎛ ⎞ = _{⎜ ⎟} ⎝ ⎠ s s S s s b r r r 2_{Ψ (2-12)} s

Ψ is the angle between the Burgers vector bs and the normal of the diffracting lattice

plane and rS and r0 denote the upper and lower integration limits of the strain field,

respectively. For r0, a value of 10- 7 cm is assumed and rs is related to the screw

dislocation density Ns by 1/ 2 1 4 ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ s s r N (2-13)

On the other hand, pure edge TDs with dislocation line along [0001] direction and Burgers vector 1 1120

3

E

b = < > cause an azimuthal rotation of crystallites around the

surface normal, consequently, the crystalline planes (hkil) with l = 0 are twisted. The presence of pure edge TDs not only influences the width of rocking curve but also that of radical scan of (hki0) reflections. The twist angle α can be measured by _φ performing φ-scans. Using measured broadening βφof the φ−scans, the dislocation

density NE can be calculated from following equation when the broadening due to

small correlation lengths |L| can be neglected, i.e. βφ = α [22, 23] _φ

2 2 4.35 φ α = E E N b (2-14)

where bE is the Burgers vector of the edge dislocations. (In the case of ZnO, |bE| = a0 =

0.3238 nm.) This equation holds only for a strictly random distribution of dislocations.

If dislocations are piled up in small angle grain boundaries, the following formula should be used, ' ' 2.1 φ α = E E N b L (2-15)

where |L| is the average size of subgrains and '

E

α is again the twist angle. For a system with both dislocation distributions (randomly and piled up), as observed in the ZnO sample, the real dislocation density will fall between these two values. For the calculation of the mean square strain of edge dislocations < 2

E

ε >, the following equation is adapted:

(

)

(

)

(

)

2 2 2 2 2 2 0 5 ln , , , 2.45cos 0.45cos 64 E E E E E E b r f where f r r ε π ⎛ ⎞ = _{⎜ ⎟} Δ Ψ Δ Ψ = Δ + ⎝ ⎠ ΨE (2-16)

where Ψ is again the angle between the Burgers vector and the diffraction plane _E normal and Δ is the angle between the normal of the slip plane and the normal of the diffracting plane. The edge dislocation density NE is related to rE, the outer limit of

strain filed caused by edge dislocations, by:

1/ 2 1 4 E E r N ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ (2-17) As a cross examination, the line width broadening of an off-normal reflection which is sensitive to both screw and edge types of TDs is usually examined. Reflection(1014) is a proper choice. Because there are three distinct dislocation systems for pure edge dislocations in ZnO, i.e.

] 10 2 1 [ 3 1 and ], 110 2 [ 3 1 ], 0 2 11 [ 3 1 = E

b , the mean square strain < 2

E

ε > is influenced by all three possible orientations. In table 2-2, the angles Ψ and Δ as well as the _E corresponding values of f (Δ,Ψ ) are listed for the three individual slip systems _E {1010} for diffraction vector(1014). From Eq. (2-16) it is clear that pure edge threading dislocations with 1 1120

3

E

b = < > do not influence the (000l) reflections of ZnO since the angles Ψ and Δ are both 90_E o. In order to calculate the mean square strain due to screw and edge dislocations, the individual square strains are summed up as follows:

( )

2 _{8 ln 2 (} 2 2 _{) tan} ε 2 β = ε_S + ε_E θ (2-18) 34