國立中山大學材料與光電科學學系 博士論文
Department of Materials and Optoelectronic Science National Sun Yat-sen University
Doctorate Dissertation
低維度應力對寬能隙單晶半導體的機性和光電特性影響 Mechanical and Optoelectronic Response of Wide Band Gap
Semiconductors under Low Dimensional Stress
研究生：宋大豪 撰
Welson Ta-Hao Sung 指導教授：黃志青博士
Dr. Jacob Chih-Ching Huang
中華民國 一百零一 年 十二 月 December 2012
謝誌
十年，從大學部一路念上來到博士畢業才有資格寫的這個謝誌，真提筆時卻 不知該從何處謝起，原本想著：要謝的人太多了，不如寫個「謝天」就帥氣作結，
然而寒窗數載幾經波折，如果不是這些貴人，現在的我可能還在學海裡浮沈。在 這人生中的一個重要頓點，我想在這裡表達最誠摯的謝意：
首先我要感謝家人們給我的支持，蛋頭老爸感謝你給我這個書蠹蟲從小鐵與 血的教育，鍛鍊我的心智上能在逆境中堅持、在唸書之餘完成三項鐵人、全程馬 拉松、衝浪、龍舟金牌…等等，能讓你覺得驕傲的事情就是我會去做的事，你老
是掛在嘴邊「生命的意義在於創造宇宙繼起之生命」，而我存在的意義就是超越
你，讓你以我為榮。我也要感謝堅強的媽媽，謝謝妳在我叛逆的時候沒有放棄我，
妳犧牲掉所有人生中該享樂的時間去照顧家人，讓我們能無後顧之憂的成長並唸 完學位，妳用身教告訴我們什麼是孝順與無怨無悔的付出，並教導我們無論在怎 樣的困境中都要記得笑，畢業後最大的心願是帶妳環遊世界！感謝我兩個姊姊 Misty & Alice 對我這個么弟老是存著不知道哪裡來的信心，妳們在各自領域裡 的努力就是對我的砥礪。
再來要感謝我的指導教授黃志青老師，感謝您這十年來耐心地提攜我這個問 題學生，讓一頭藍髮的班代參加的您的秘密結社、碩一偷跑出國打辯論、論文計 畫口試前一天在校內搞學運、博班還在實驗室裡組樂團，感謝您常忍著高血壓上 升的風險改我大小錯不斷的論文，願意拉拔我到現在還沒踢出實驗室。謝謝老師 在家裡出事的時候給我極大的空間與諒解，讓我能在學業與家庭衝突時不放棄的 走出一條路來。我想這都要感謝老師，您不懈的努力與對研究上的熱情一直都是 我心目中的表率，期望日後的表現將不愧於您創立第一屆材光系的首位博士生。
此外，要感謝美國田納西大學的聶台岡教授，來台半年的時間給予我研究上莫大
的討論與幫助，不管是對科學的態度或是追求人生上的目標，都讓我瞻仰到國際 級大師的風範。系上徐瑞鴻老師在光電物理方面提共熱心與細心的指導使我獲益 良多，願意讓我擔任教學助理讓自己在就讀研究所時能不依靠家裡自食其力。還 有義守大學的簡賸瑞教授亦師亦友的關係，除了提供研究的題目找出實驗方向之 外，像個大學長一樣不斷鼓勵並指導我。也感謝系上老師與系辦小姐，從大學部 以來對我的幫助與包容，謝謝你們！
最後，要感謝好朋友小易，從大一室友到決定念博班，幾乎所有做過的好事 壞事都有你一份，我的好對手與好伙伴，很高興求學時的夢想能和你一起實現。
會救人的 Dr. 陳，你對自己目標無畏地堅持與對哲學的思考激發我對自己的要 求，感謝你不時的當聆聽者並適時的給予我支持。土地、阿強、大姊頭、大眼睛、
喜孜孜，謝謝你們這群好朋友在我最需要幫助的時候，有源源不絕的能量堅持住。
還有實驗室裡許多學長們是我學習的目標，會走路的百科全書大神學長教導我博 學與行萬里路的重要、有杰與宇庭學長遠負國外求學工作優異表現、家爸子翔學 長跟我分享博班的心路歷程、敬仁學長教我對實驗的嚴謹與自我要求、炎暉學長 教我超高 EQ 的自我控制、斯威特學長與 KB 浩然學長教我待人處事的道理。一起 在中山努力的肌溝、小雞、大牛以及材光第一屆老同學們、現在成為實驗室不可 或缺的棟梁阿官、碩士就發 APL 的 BASS 手婷子、還在努力的 GT 安迪、準備接手 光電組的 Nick 以及實驗室優秀的學弟妹們，謝謝這段時間裡你們對我的幫助與 陪伴，雖然你們不一定會看到，但是我想你們應該都能感受得到，我愛你們！（抱）
給自己：博士畢業，只是人生中的一個頓點，日後你可能會一再回顧這段求 學時光，這段你對未來迷惘，探索著一條屬於自己的路並不斷地嘗試改變自己，
期許成為更好的人、能幫助更多的人。我希望未來的你，能找到每天早晨起床的 意義以及願意奉獻的目標。我希望你正在做對的而且快樂的事情，因為這兩者是 不衝突的。我希望你記得自信不是你現在擁有著什麼，而是你相信著自己，相信
上天不會給人過不去的坎，在接下來的路程都能鼓起勇氣面對。記得，要做自己！
Aint busying living, Aint busying dying.
December, 2012 於中山西子灣
Content
Content…… ... I
List of tables ... V List of figures ... VII Abstract . ………...XIV
中文摘要…………. ... XVI
Chapter 1. Introduction ... 1
1.1. GaN ... 1
1.2. ZnO ... 2
1.3. Other wide band gap semiconductors ... 3
1.4. Motivations ... 4
Chapter 2. Background and literature review ... 6
2.1. The direct and indirect band gap of optoelectronic materials ... 6
2.2. The polar, semi-polar and non-polar plane of the wurtzite structure ... 6
2.3. The substrates and buffer layer of hetero-epilayer GaN ... 7
2.3.1. Substrates ... 9
2.3.2. Buffer layer ... 12
2.4. The methods of fabricating single crystal thin films ... 13
2.4.1. Chemical vapor deposition (CVD) ... 14
2.4.2. Metal-organic chemical-vapor deposition (MOCVD) ... 15
2.5. Basic properties of the hexagonal wurtzite structure ... 15
2.5.1. Group theory of hexagonal systems ... 15
2.5.2. Characters of dislocations in the wurtzite structure ... 17
2.6. Introduction of nanoindentation testing ... 17
2.6.1. Mechanical properties ... 17
2.6.2. Deformation mechanisms ... 20
2.7. Introduction of microcompression testing ... 23
2.7.1. Micropillar preparation ... 23
2.7.2. Force loading and measurement ... 25
2.7.3. Parameters of microcompression tests ... 26
2.7.4. Microscale characterization of mechanical properties ... 28
2.8. Thermal treatment of ion implanted semiconductors ... 30
2.8.1. Defects and ion implantation ... 31
2.8.2. Defects recovery ... 33
2.9. Luminescence properties of semiconductors ... 35
2.9.1. Raman spectrum ... 36
2.9.2. Luminescence spectrum ... 38
Chapter 3. Experimental procedures ... 41
3.1. Sample preparation ... 41
3.2. Nanoindentation testing ... 42
3.3. Microcompression testing ... 42
3.3.1. Microcompression sample fabrication using FIB ... 43
3.3.2. Thermal treatment ... 43
3.3.3. Microcompression test using the nanoindentation system ... 44
3.3.4. TEM sample fabrication using FIB ... 44
3.4. Property measurement and analyses ... 45
3.4.1. X-Ray diffraction analyses ... 45
3.4.2. Scanning electron microscopy (SEM) analysis ... 46
3.4.3. Transmission electronic microscopy (TEM) analyses ... 46
3.4.4. Raman spectrometer analyses ... 47
3.4.5. Cathodoluminescence (CL) spectrum analyses ... 48
Chapter 4. Experimental results ... 49
4.1. Structure quality identifications ... 49
4.1.1. X-ray diffraction analyses ... 49
4.1.2. EBSD analyses ... 49
4.1.3. Theoretical values calculations ... 50
4.2. Nanoindentation testing ... 55
4.2.1. ZnO ... 55
4.2.2. GaN ... 58
4.3. Microcompression testing ... 58
4.3.1. ZnO ... 58
4.3.2. GaN ... 60
4.3.3. Raman spectrometer analyses ... 61
4.4. SEM observations ... 62
4.5. XTEM analyses ... 63
4.6. Cathodoluminescence analysis ... 64
Chapter 5. Discussion ... 67
4.7. Low dimensional stress comparison ... 67
4.7.1. Theoretical and experimental results ... 67
4.7.2. Nanoindentation testing ... 68
4.7.3. Microcompression testing ... 69
4.7.4. Low dimensional measurements ... 71
4.8. Deformation mechanisms ... 72
4.9. Thermal treatment effects ... 73
4.10. Polarity effects ... 74
4.11. Hexagonal and cubic structure influence ... 74
4.11.1. Elasticity ... 75
4.11.2. Deformation mechanisms ... 76
4.11.3. Deformation energy analysis ... 78
Chapter 6. Conclusions ... 80
Chapter 7. Prospective and future work ... 84
References….. ... 85
Tables...101
Figures...121
List of tables
Table 1 Fundamental properties of III-V group semiconductors [11]. ... 93
Table 2 The mechanical properties of polycrystalline ZnO, single crystallize ZnO wafer, thin films, nanowires, nanobelts measured by different testing techniques [59, 94, 100]. ... 94
Table 3 The plane abbreviation and polarity of two semiconductors which used in this thesis. ... 95
Table 4 Comparison of the relevant III-V nitride material properties with perspective substrate materials [11, 29, 30]. ... 96
Table 5 Structure, lattice constant, space group and density of five different LAO phases [89, 105]. ... 97
Table 6 Lattice mismatch and thermal expansion coefficient between (200) γ-LAO and GaN [90, 106]. ... 98
Table 7 Lattice parameters of a number of the prospective substrate materials for ZnO [16]. ... 99
Table 8 The elastic constants list of ZnO [18]. ... 100
Table 9 Hardness and Young’s modulus of GaN from different kinds of indentation methods [20, 91]. ... 101
Table 10 List of main luminescence lines and bands in GaN [72]. ... 102
Table 11 Valance and ionic radii of candidate dopant atoms [30]. ... 103
Table 12 Migration barriers for native defects in Wurtzite GaN [74]. ... 104
Table 13 Comparison of the theoretical and experimental mechanical properties of ZnO. ... 105 Table 14 The elastic constants and estimated mechanical properties of GaN [108].
... 106 Table 15 Comparison of the theoretical and experimental mechanical properties of GaN. ... 107 Table 16 The Raman spectra peak position and FWHM of bulk ZnO. ... 108 Table 17 The fundamental optical modes of the Wurtzite crystal (frequency expressed in cm-1) [82]. ... 109 Table 18 The measurement of Raman E2 peak position and FWHM of GaN films and micropillars [54]………...…...…110 Table 19 Young’s modulus measured from different kinds of indentation methods [56, 60, 70]. ... 111 Table 20 Comparison of the crystal structure, mechanical data, and dominant deformation modes in the four optoelectronic materials [54, 60, 110]. .... 112
List of figures
Figure 1 Three structure types of II-IV group binary compound (a) Rocksalt (b)
Zincblende (c) Wurtzite [16]. ... 113
Figure 2 The corresponding band gap range of luminescence semiconductors [13,
18]. ... 114
Figure 3 Schematic diagrams showing the transitions across (a) a direct band gap and (b) an indirect band gap [107]. ... 115
Figure 4 Direct band gap of GaN [11]. ... 116
Figure 5 Direct band gap of ZnO [16]. ... 117
Figure 6 Wurtzite hexagonal structure. ... 118
Figure 7 Wurtzite structure along [0001] c-axis. ... 119
Figure 8 A sketch of induce the intrinsic electric field [37, 51]. ... 120
Figure 9 Non-polarity directions of GaN. ... 121
Figure 10 The figures show the reflectance spectra of unstrained A-plane GaN with the light polarized parallel (a) and perpendicular (b) to the c-axis. Clearly, the A exciton is visible only in (b), demonstrating a polarization anisotropy of 100% in this spectral range [22-25]. ... 122
Figure 11 Growth of hetero-epilayer (a) pseudomorphic (b) strain free layer [92,
108]. ... 123
Figure 12 Schematic diagram showing the epitaxial relationships of c-plane ZnO grown on sapphire (0001) [16]. ... 124
Figure 13 Chemical vapor deposition (CVD) process [93, 109]. ... 125
Figure 14 Low temperature, pressure and high gas velocity conditions of CVD [93,
109]. ... 126
Figure 15 High temperature, pressure and low gas velocity conditions of CVD [93,
109]. ... 127
Figure 16 Two-Flow MOCVD (TF-MOCVD) [48]. ... 128
Figure 17 Projection of wurzite hexagonal structure [55]. ... 129
Figure 18 The sketch of the nanoindentation testing [52]. ... 130
Figure 19 The sketch of the nanoindentation load-displacement (p-h) curve [52]. . 131
Figure 20 Contour plot of the CRSS of Berkovich tip at (01 1 2) slip plane (a) and (2 1 1 3) slip plane (b), where distances r and z are normalized by the contact radius a [53]. ... 132
Figure 21 The bright field cross section TEM image of spherical indent in ZnO at maximum load of 50 mN, the black arrow point out the basal plane (0001) and the red arrow point out the pyramidal plane {10 1} [57]. ... 133
Figure 22 The sketch of slip directions. Red lines represent the first slip system. Blue lines represent the secondary slip system [53] ... 134
Figure 23 Typical nanoindentation load–displacement data for annealed (100) Ni obtained using a 0.58 m radius spherical indenter. Elastic contact (Hertzian) solutions are shown for the data below the pop-in loads [69]. ... 135
Figure 24 The sketch of resolve shear stress. ... 136
Figure 25 Annular milling patterns have been used to mill a roughly defined micropillar sample of Ni single crystal [48, 62]. ... 137
Figure 26 The microcompression samples were fabricated into (A) a Ni3Al alloy and (B) Ni-based superalloy by using lathe milling program. The diameter of microcompression samples are 43 m and 2.3 m, respectively [48, 62]. ... 138 Figure 27 SEM micrographs of the flat-punch tip: (a) top view and (b) side view and
(c) projected area of the punch tip. ... 139 Figure 28 Schematic of the microcompression test setup [64]. ... 140 Figure 29 Schematic of a cylindrical pillar and its base [64]. ... 141 Figure 30 Effect of fillet radius/pillar radius ratio on numerical simulation output. The inset shows an enlargement of the circled region to facilitate comparison [21]. ... 142 Figure 31 (a) Deformed configuration of a circular cylindrical pillar with an aspect ratio = 5 at a strain of 0.1. (b) Deformed configuration of the pillar at the same strain of 0.1, but now considering friction. (c) Input and output
stress- =2~5, both with
friction and without friction (NF) [21]. ... 143 Figure 32 Effect of taper on numerical simulation output [21]. ... 144 Figure 33 Effect of misalignment of the system on the error in elastic modulus [21].
... 145 Figure 34 (a) The microcompressive engineering stress-strain curve of the Ni76Al24
alloy with 2m diameter. (b) SEM micrograph of a micropillar after microcompression test. Strain bursts are indicated by arrows in figure (a), and appearance of slip lines are also observed on the micropillar surface, as also indicated by arrows [67]. ... 146 Figure 35 Typical load–penetration curve for a maximum load of 250 mN showing a pop-in event. Inset: Load–penetration curve for a maximum load of 50 mN showing multiple pop-in events at 28 and 34 mN [57]. ... 147 Figure 36 Room-temperature monochromatic CL images of spherical indents in GaN.
The maximum loads and horizontal field widths are (a) 25 mN and 15 mm, (b) 50 mN and 15 mm, and (c) 200 mN and 30 mm. CL imaging conditions: electron beam energy 520 keV, CL wavelength =366 nm, and
CL bandpass 52.5 nm [57]. ... 148 Figure 37 The threading dislocation density decreases with increasing thickness for thin film GaN/sapphire [80, 96]. ... 149 Figure 38 Formation energies as a function of Fermi level for native point defects in GaN [74]. ... 150 Figure 39 Transition levels and formation energy of native defects in GaN [74]. .. 151 Figure 40 Experimental set up of a micro-Raman spectrometer [82]. ... 152 Figure 41 The diagram of anti-Stokes scattering [82]. ... 153 Figure 42 The Raman spectra of back scattering, near forward scattering and right angle scattering modes [82]. ... 154 Figure 43 The backscattering diagram of wurtzite micro-Raman spectrum. (a) input-output z axis [0001], (b, c and d) input-output a-axis [10 1 0] [82].
... 155 Figure 44 The right angle scattering diagram of wurtzite micro-Raman spectrum [82].
... 156 Figure 45 The E1 phonon propagation in the (0001) plane. The transverse phonon is illustrated by the solid-line polarization vector, and the dashed line corresponds to the (11 2 0) polarization component of Raman spectrum.
The k2 and k3 lines represent the quasi QA peak between the E1(TO) and A1(TO) peaks. ... 157 Figure 46 Deconvolution of c-plane GaN XRD rocking curve (0002) Peaks. [80, 96].
... 158 Figure 47 Schematic illustration of TEM sample procedure using FIB [97]. ... 159 Figure 48 The XRD pattern shows GaN has a shark peak located at 2= 34.62o. . 160 Figure 49 The XRD pattern of GaN estimate by CaRine software. ... 161 Figure 50 The XRD Rocking curve pattern shows a broad peak ranging from 16.45o to
17o with full width of middle height (FWMH) = 0.341o. ... 162 Figure 51 The EBSD patterns and SEM SEI image of c-plane ZnO. ... 163 Figure 52 The EBSD pattern and SEM SEI image of c-plane GaN... 164 Figure 53 Showing the load-displacement and modulus-depth curves of c-plane ZnO at CSM constant displacement rate mode. ... 165 Figure 54 Representative nanoindentation load-displacement curves of the as-grown, annealed wafer and the curve predicted by the Hertzain contact theory.
... 166 Figure 55 Representative nanoindentation load-displacement curves of the c-plane, a-plane, m-plane ZnO wafer and the curve predicted by the Hertzain contact theory. ... 167 Figure 56 Showing the data of c-plane GaN CSM mode depth 1000 nm nanoindentation testing. ... 168 Figure 57 Showing the first pop-in data of CSM mode depth 500 nm (~10% to total thickness) indentation testing. ... 169 Figure 58 Representative as-grown preset 300 nm pillar and annealed preset 300 nm pillar stress-strain curves of microcompression testing. ... 170 Figure 59 Representative load-displacement curves for microcompression of c-plane GaN micropillars. ... 171 Figure 60 Representative load-displacement curves for microcompression of a-plane ZnO micropillars. ... 172 Figure 61 Representative load-displacement curves for microcompression of m-plane ZnO micropillars. ... 173 Figure 62 The recorded data and Gaussian fitting Raman spectra of film ZnO. ... 174 Figure 63 The Raman spectra of ZnO after Ufine, middle and rough beam FIB Ga implanted conditions. ... 175
Figure 64 The recorded data and Gaussian fitting Raman spectra of as-grown ZnO.
... 176 Figure 65 The recorded data and Gaussian fitting Raman spectra of preset 40 nm
ZnO pillar. ... 177 Figure 66 The recorded data and Gaussian fitting Raman spectra of preset 300 nm ZnO. ... 178 Figure 67 The recorded Raman spectra of GaN film, as-milled pillar, preset 100 nm pillar and preset 200 nm pillar. ... 179 Figure 68 Showing the SEM image of (a) as-grown c-ZnO pillar and (b) annealed c-ZnO pillar after microcompression. ... 180 Figure 69 Showing the SEM image of m-ZnO pillar after microcompression. ... 181 Figure 70 Showing the SEM image of a-ZnO pillar after microcompression. ... 182 Figure 71 SEM images of (a) mark, (b) carbon protection layer and (c) side view of c-plane ZnO HR-XTEM sample. ... 183 Figure 72 Representative c-plane GaN (a) 1 m as-FIB-milled pillar SEM images and (b) first strain burst micropillar SEM image. ... 184 Figure 73 Showing the SEM image of (a) r-GaN thin film morphology, (b) cross section and (c) as-milled micropillar. ... 185 Figure 74 (a) XTEM bright filed image of the ZnO micropillar compressed to a preset displacement of 300 nm, and (b) the associated selected area diffraction pattern, with an indexed zone axis of [10 0]. ... 186 Figure 75 TEM characterization of the GaN micropillar compressed to a preset displacement of 200 nm: (a) bright field image from the longitudinal section, (b) selected area diffraction pattern for the upper region, and (c) selected area diffraction pattern for the lower region of the compressed pillar, with an indexed zone axis of [10 0]. ... 187
Figure 76 XTEM characterization of the 200 mN nanoindentation mark of the c-plane GaN thin film, with an indexed zone axis of [10 0].
Figure 77 The recorded cathodoluminescence spectrum of GaN from NSYSU. .... 189 Figure 78 The recorded cathodoluminescence spectrum of bulk ZnO from ISU. ... 190 Figure 79 The a-plane ZnO pillar CL spectra of just focus and over focus plane. .. 191 Figure 80 Representative c-plane ZnO CL spectra, and corresponding SEM SEI image and CL image of 383 nm. ... 191 Figure 81 The m-plane ZnO CL spectra of wafer, preset 50, 300 and 400 nm pillars.
... 201 Figure 82 Representative c-plane ZnO X-CL spectra, and corresponding SEM SEI image. ... 194 Figure 83 The center dark field (0001) image of c-plane ZnO micropillar, with an
indexed zone axis of [10 0].
Abstract
Wide band gap semiconductors ZnO/GaN attracted a great deal of interests for decade, due to their wide direct band, high electron binding energy, excellent chemical and thermal stability, good heat conductivity and capability, high electron mobility and transparent properties at room temperature. They have many potential applications such as laser, biosensor, piezoelectric power generator, nano-electromechanical systems and flat panel field emission displays. However, unexpected contact loading during processing or packaging may induce residual stresses and/or an increase in defect concentration in ZnO/GaN wafer or thin film, causing possible degenerated reliability and efficient operation of the piezoelectric and photonic device. To ensure and improve the performance of devices based on ZnO/GaN, a better understanding of the mechanical/optoelectronic response under different processing and loading conditions and even the measuring methods are necessary.
In this thesis, our aim is to reveal a comprehensive investigation of the mechanical responses on polar/non-polar GaN/ZnO single crystal under low dimensional stress. We try to provide the fundamental theoretical and experimental studies for further application and researches, such as tension testing, residual stress, low temperature cathodoluminescence and Raman spectroscopy analysis.
In this study, the theoretical Young’s modulus and Poisson ratio of ZnO/GaN are extracted from elastic constants for comparison and further estimation. The nano-scaled mechanical properties, such as Young’s modulus, hardness and yield
stress, are identified by using the nanoindentation system. The experimental values were fitting by the Hertzian contact theory. The results are in good agreement with the theoretical predictions. No significant strain rate influence is observed over the strain rate from 1x10-2 s-1 to 1x10-4 s-1. The comparisons of mechanical properties between the polar and non-polar planes of ZnO are firstly examined. The results reveal that the non-polar planes are softer than the polar plane. Both a-plane and m-plane ZnO have lower hardness and yield stress than c-plane ZnO. The microstructure and deformation mechanism are analyzed by using X-TEM and SEM. No pop-out or slope changing was found in their load-displacement curves, suggesting no phase transformation, twining or crack domain deformation occurred under microcompression and nanoindentation testing. Taking all considerations for the higher resulting Schmid factor and lower Burgers’ vector, the most possible slip system for c-plane hexagonal structures is the pyramidal plane. The a-plane has shorter burger’s vector on the slip plane which leads the lower yield stress than c-plane.
To erase the effect of FIB induced Ga ion implantation, the c-plane ZnO was annealed at 900oC for 1 hour. We found that the yield stress under microcompression decreases and the intensity of the cathodoluminescence spectrum increases after the annealing process. This result indicates that the thermal treatment is a good way to refine the crystal quality and decrease the defects density. The E2 peak of Raman spectrometer exhibits high residual compression stress constrain in the c-plane GaN thin film. Due to the high surface/volume ratio of pillar, nil residual stress remains in the GaN pillar after the FIB milling process. Even after the yield point, nil residual stress remains in the c-GaN pillar. Results indicate that the one dimensional geography is a good way to erase residual stress.
中文摘要
近數十年來，寬能隙氧化鋅與氮化鎵半導體引起科學界廣泛與熱烈的興趣。
主因於其優異的室溫物理性質，諸如：直接能隙、高電子束縛能、良好的化學與 熱穩定性、優異的熱傳導、高電子移動能力與其光學透明性。他們被廣泛的利用 於雷射、生物偵測器、壓力發電機、奈米機電系統，並被視為取代現有平面顯示 器核心元件之潛力材料。然而在製造元件或封裝過程中，外在的接觸應力會造成 材料內部的殘留應力或增加材料缺陷濃度，造成光電或壓電性元件其效能降低。
為了確保以及改善元件品質，更深入的瞭解氧化鋅與氮化鎵，在施加應力的情況 下其光電性質與機械性質的反應是必需的。
本研究主要是先利用彈性常數去估算理論楊氏模數與波松比，再將理論波松 比帶入實驗結果，將實驗楊氏模數與理論值做確認，確保波松比在更進一步計算 中準確。此外，利用奈米壓痕實驗探討奈米尺度下的楊氏模數與硬度，並與微奈 米尺度的一維壓應力實驗結果做比較。再將實驗結果帶入 Hertzian 彈性模型，得 出破壞降伏強度與臨界剪切應力。實驗結果與理論值吻合，在奈米與微奈米尺度 下均無應變速率對機械性質影響，非極性面與極性面比較結果發現，非極性面有 較低的硬度。利用掃瞄式與穿透式電子顯微鏡做塑性變形的圍觀組織分析結果得 知，在二維奈米壓痕與一維壓應力測試中都沒有發現相變化、雙晶與裂縫。差排 滑移為主要變形機制，變形系統為錐面。在熱處理、光電性質與幾何形狀部分相
關研究，我們發現但氧化鋅在常壓 900oC 下加熱一小時，可有效提升晶體表面品
質，減少因離子殖入造成非晶層的厚度，而陰極射線光譜藍光帶之強度也增加了 1.5 倍。拉曼光譜分析發現長在藍寶石基版的氮化鎵薄膜中含有的殘留應力，可 以經由高表面/體積比的幾何形狀得到釋放。釋放殘留應力後，由高斯分佈分析
拉曼光譜 E2波峰發現有紅位移的現象。
本論文試圖對六方對稱之氧系與氮系發光半導體材料提出廣泛的研究，對於 日後更深入的探討理論機械性質、變形機制、缺陷分析、殘留應力、極性與非極 性、熱處理、發光性質、微觀結構、幾何形狀與尺寸效應，提出理論與實驗基礎。
最後，我們比較了四種常見半導體材料的機械性質與破壞機制，並對於日後的實 驗發展提出粗略的方向。
Chapter 1. Introduction
Over the past few decades, scientific researchers raised a great deal of interests in the wide (>3 eV) band gap semiconductors, such as GaN and ZnO. Because of their high exciton binding energy, high thermal conductivity, high chemical stability, they have been widely used in electrically pumped ultraviolet–blue light-emitting diodes (LED), lasers, piezoelectric generator and photon detectors [1, 2]. At the end of 80’s, Akasaki et al. [3-6] and Nakamura et al. [7, 8] successfully grew high quality GaN on the (0001) sapphire substrate, and hence, produced high efficiency blue light LED. It is a landmark of lighting evolution and gives rise to a great series of researches on extensive issues, e.g. substrate, size effect, polarity, mechanical properties, or optoelectronic properties.
Moreover, one dimension (tip-like or needle-like) semiconductors have attracted considerable attention in various applications, such as biosensor, laser and field emitted displays (FED). It can replace the carbon nanotubes (CNTs) and become one of the potential materials to make the key devices of field emitted displays. It is because ZnO has good chemical stability, mechanical stability and work functions electron affinities (4.5 eV) [9]. The fundamental properties of GaN, ZnO, and other wide band gap semiconductors are briefly introduced in the following sections.
1.1. GaN
Gallium nitride is a binary III/V semiconductor with a 3.3 eV direct band gap. The
compound is very hard and stiff (hardness H ~15 GPa and Young’s modulus E ~272 GPa). There are two structure types, namely, the most common hexagonal wurtzite structure (space group C6v/P63mc) and cubic zincblende structure, depending on substrate symmetry and growing conditions [10]. The lattice constant c/a ratio of hexagonal GaN is ~1.626 which is close to the ideal hexagonal closed packing (~1.633), and the Poisson ratio is about 0.35 (alone the c-axis). Its high thermal stability (melting point Tm ~2500oC), high electron mobility (440 cm2/V-sec), high exciton binding energy (25 meV), high thermal conductivity (1.3 W/cm-K at room temperature) and good chemical stability make it possible to be applied in high power and frequency optoelectronic devices or solar cell array in satellites. Table 1 [11] shows the rest properties of III-nitride group compounds.
1.2. ZnO
Zinc oxide is an inorganic II/VI group semiconductor with 3.4 eV direct band gap.
Compared with GaN, ZnO has relatively soft mechanical properties (H ~4.2 GPa and E
~140 GPa). In comparison with GaN/sapphire, ZnO/sapphire has approximately equivalent X-ray-diffraction (XRD) and photoluminescence (PL) line width, and even lower dislocation densities [12]. ZnO has three phases. The most stable structure is hexagonal wurtzite which is usually observed at ambient condition. The cubic zincblende structure can be grown by using cubic substrate. The cubic rocksalt structure (NaCl type) is high pressure phase (pressure greater than 10 GPa). The lattice parameter c/a ratio is about ~1.633 (a=3.252 Å and c= 5.313 Å ) and the Poisson ratio is about 0.34 (alone the c-axis). ZnO has high electron binding energy ~60 meV (which means electrons need higher energy to escape from molecule orbits onto its surface). Its high iconicity ~0.616 (cp. GaN ~0.5) causes the best piezoelectricity in III/V and II/VI
groups. Moreover, the good chemical and thermal stability, heat conductivity, high electron mobility and transparent properties make ZnO possible to be applied in non-toxicity transparent thin film, transparent thin film transistor, piezoelectric power generator (~7% efficiency) [16] and flat panel field emission displays.
1.3. Other wide band gap semiconductors
The bandgap of GaN can be changed by doping other group III nitrides, such as InN or AlN. The adapted bandgap can fully cover the range from infrared to ultra-violet light wavelength. The single crystal indium nitride InN exhibits a narrow direct band gap (~0.7 eV) which is slight function of temperature. InN has the same hexagonal wurtzite structure with a lattice parameter c/a ratio ~1.623 in ambient condition. It is usually mixed with GaN as a ternary group III nitride InxGa1-xN (where x is between 0.02~0.3) to apply in blue/green optoelectronic devices. But when the In/Ga ratio >0.4, non-radiation defects and phase separation dominated which degenerated the efficiency of high frequency light emitting diodes [13]. The single crystal aluminum nitride AlN exhibits the largest direct band gap (6.2 eV at room temperature), high melting point (Tm ~3237 K), relatively high thermal conductivity (285 W/m-K), electron mobility (~300 cm2/V-sec) in semiconductor ceramics [14]. It has loose hexagonal wurtzite structure (c/a ratio ~1.600). It can be used to fabricate UV LED or high electron mobility transistor (HEMT) [15].
For ZnO, group II-IV semiconductor magnesium oxide and cadmium oxide have three kinds of structures, which are hexagonal wurtzite, cubic rocksalt and zincblende, as shown in Figure 1 [16]. By composing these three oxides, the wide band gap can be adopted from 161 nm (7.7 eV) to 539 nm (2.3 eV) wavelength [17]. Figure 2 shows
various band gaps of the II-IV groups, III-V groups and other semiconductors [13, 18].
1.4. Motivations
The unexpected contact loading during processing or packaging might induce residual stress and/or defect concentration of the wide bandgap semiconductors, causing possible degradation of the device performance. Thus, to improve the successful fabrication of devices, based on epitaxial thin films and wafer, a better understanding of the mechanical characteristics is necessary and meaningful.
So far, there have been some reports addressing the macroscaled or microscaled mechanical responses of the bulk or thin film crystalline by using indentation (Table 2), but there is appreciable disparity in the measured values among various samples (e.g., shape and size), in particular single crystals. Microcompression testing can provide a simple uniform stress to study the mechanical properties and the corresponding luminescence responses for the single crystal wide bandgap semiconductor which is hard to be fabricated into bulk scale.
In this thesis, our aim is to reveal a comprehensive investigation of the mechanical responses on polar/non-polar GaN and ZnO single crystal under low dimensional stress. In addition, we try to investigate the luminescence responses of the defects, residual stress, thermal treatment by using Raman and cathodoluminescence spectroscopy, particularly in the sub-microscale and nanoscale region [21].
Chapter 2. Background and literature review
2.1. The direct and indirect band gap of optoelectronic materials
Wide band gap semiconductors have been used in order to produce high power lightening devices. The band gap can be simply distinguished as direct and indirect band gap. Figure 3 shows the schematic diagrams of direct and indirect band gap. For direct band gap materials, such as III-V series semiconductor (GaN/AlN/InN in Figure 4 [11]) or II-IV series semiconductors (ZnO/MgO/CdO in Figure 5 [16]), the electron-hole pairs can be produced by giving electric or solar energy. The electron-hole pairs are then recombined in a very short time and released most energy by photon. Only energy conservation should be considered in the recombination process of direct band gap. In comparison, the electron-hole pairs of indirect band gap material, such as GaAs, have to obey both energy and momentum conservation during the recombination process. Energy was released into photon and phonon which lead the degeneration of the lightening efficiency. In this thesis, we focus on the direct band gap material (GaN and ZnO) because of their better transition efficiency than the indirect band gap materials.
2.2. The polar, semi-polar and non-polar plane of the wurtzite structure
Single crystal wurtzite structure (Figure 6) has anisotropic properties in different directions. The c-plane has polarity in [0001] (c-axis) direction. The cations and anions stock at different layers of the (0001) c-plane. Although the whole structure
remains electrical neutrality, there is a little distance between the cation and anion atoms along the c-axis (Figure 7). The small deviation from ideal position causes an electrical dipole momentum and induces the intrinsic electric field along the c-axis (Figure 8). The c-plane is regarded as a polar plane and for those planes which include partial quantity of c-plane, such as, r-plane (1 1 02), is regard as the semi-polar plane.
Both of them would cause the decrease of the luminescence efficiency of optoelectronic devices. On the other hand, the non-polar planes (Figure 9), such as the m-plane (10 1 0) and the a-plane (2 1 1 0), have no intrinsic electric field along the <10
1 0> and <2 1 1 0> directions. Figure 10 reveals that light polarized parallel to the non-polar plane can stimulate higher energy excitons than light polarized perpendicular to the polar plane, thus enable to fabricate higher energy ultraviolet light-emitting devices [22-25]. In this thesis we focus on the anisotropic material properties on polar, semi-polar and especially non-polar plane. Table 3 lists the plane abbreviation and polarity of two semiconductors used in this thesis.
2.3. The substrates and buffer layer of hetero-epilayer GaN
Because it is difficult and expensive to grow some macro-scaled high quality single crystal semiconductor wafers as homo-epitaxy substrates, to find a suitable substrate material becomes an important issue, especially for producing thin film material. The threading dislocations, residual stress and other defects from hetero-epitaxy substrate could greatly change the performance of the luminescence device.
The affection of threading dislocation density on thin film can be confirmed by the nanoindentation system and cathodoluminescence spectroscopy (CL). The pop-in
event in load-displacement curve of nanoindentation system is related to the threading dislocation density. The load of the critical pop-in decreases with increasing pre-existing threading dislocation density [26]. The CL spectrum reveals the non-radiation zone at the threading dislocations and indentation points. Which means the high threading dislocation density not only creates non-radiation regions at the surface but also makes the non-radiated dislocations easier to be increased under the pressure.
To ensure the high crystal quality, three important coefficients should be considered when choosing a suitable hetero-epitaxy substrate:
1. lattice mismatch, 2. buffer layer, 3. thermal expansion
The formula of lattice mismatch strain can be represented by
f
e e s
a a a
, (2-1)
where as is lattice constant of substrate, ae is lattice constant of epitaxy thin film, and positive f is tension strain and negative f is compression strain. If f < 1%, the thin film structure will be strongly influenced by the substrate. The pseudomorphic layer will grow on the substrate (Figure 11 [92, 108]). If f > 1%, the lattice mismatch will create a residual stress field. As the thickness increases, more energy would be stored in the sample. When the thickness grew over a critical thickness, dislocations are then
created to release the strain energy. The large lattice mismatch leads the higher build-in threading dislocation density [27, 28].
The other consideration is the difference of the thermal expansion. The epilayers are often cracked after post-growth cooling due to the large thermal strain difference between substrate and thin film. The comparison of the relevant III-V and II-IV group material properties with perspective substrate materials is shown in Table 4 [11, 29, 30].
To reduce the lattice mismatch and thermal expansion difference, some buffer layers are grown not only on the hetero-epitaxy substrates but on the homo-epitaxy substrate as well. The threading dislocations density and residual stress can be reduced by growing hetero-buffer layers, defect free wires or low temperature buffer layers between the substrate and the targeting thin film.
Thus, substrates play an important role in producing high quality semiconductor wafer and thin film. Both mismatch and thermal strain will strongly affect the dislocation density. The following sections list some brief considerations of common substrates as well as buffer layer in the wide band gap semiconductor growing process.
2.3.1. Substrates
Silicon has been widely researched in various fields by silicon industry for decades. Its relatively mature procedure and adaptable semiconductor properties, such as larger size, cheaper cost, good thermal conductivity and electrical conductivity,
make it become one of the main substrates to produce single crystal GaN. However, the mismatch between Si and GaN is 16.9% (c-GaN on (111)Si) [22, 31]. To reduce misfit dislocations, AlN (hexagonal structures) epitaxy thin film is usually grown between (Si-AlN-GaN) as a buffer layer. The cubic (111)Si plane is used to be the growing plane.
The direction and plane between GaN, AlN and Si are shown as following [32, 33]:
[1120]GaN // [1120]AlN // [110]Si, (0001)GaN // (0001)AlN // (111)Si . (2-2)
The other popular substrate for growing is sapphire (Al2O3). Single-crystal films have been grown on sapphire with a high degree of surface flatness, which is essential for device fabrication. It is another common material which is chosen to be the substrate of GaN thin film in this study. The benefit of choosing sapphire to be the substrate of growing process is because it has relatively small lattice mismatch than single crystal cubic silicon. The c-plane GaN thin film can grow on (0001)Sapphire and the a-plane GaN epilayer can grow on (1100)Sapphire. The lattice mismatch between a-axis sapphire and c-axis GaN is 13.6% [34] and the difference of thermal expansion coefficient is 34% [35]. The lattice mismatch and thermal expansion difference will form a compression stress field in the film during process. For ZnO grown on sapphire, films usually display large mismatch and high residual strain, it is most likely due to defect-induced native centers carrier concentrations (in the 1017 cm−3 range), and low mobility (less than 100 cm2 V−1 s−1 at room temperature) as compared to an electron concentration of 1015 cm−3 and Hall mobility of 200 cm2 V−1 s−1 typical for bulk single crystals. The epitaxial relationship of
[0001]ZnO // [0001]sapphire, [1010]ZnO // [1120]sapphire [16]. (2-3)
A low temperature AlN buffer layer can reduce the threading dislocation density and residual stress. Although the sapphire substrate has good chemical and thermal stability, the good stability brings out another tough issue of processing thin film into a free standing sample.
LiAlO2 (LAO) is another potential substrate material of producing free standing thin film. Due to its various advantages, such as lower lattice mismatch and thermal expansion mismatch than silicon and sapphire. Furthermore, LAO can be easily cleaved off from substrate by thermal decomposition. It is easier to produce the free standing sample. LAO was firstly compounded by Weyberg in 1906. Table 5 [89, 105]
lists the structure, lattice constant, space group and density of five different phases of LAO. In particular, the (200) -LAO has been used as a substrate of non-polar GaN because of its lowest misfit ratio (<2% for a-plane). Table 6 [90, 106] lists the misfit between LAO, c-plane and a-plane GaN. Because of the small misfit ratio, there is of no need to grow a buffer layer between the substrate and thin film which can simplify the process. Nevertheless, there is still some problem to be solved out. The difference of thermal expansion coefficient between LAO and GaN is still large (55% along [100]
and 63% along [001]). It will induce high threading dislocation density, cracks and even stripping during the cooling process.
For ZnO, homoepitaxy with its perfect lattice matching in-plane and out-of-plane has the potential for providing no strain induced by thermal-expansion mismatch, absence of highly defective substrate-layer interface, lower overall defect density, easy control over the material polarity by using Zn-face or O-face (0001) substrate, and simple device design ZnO substrates can be made very conductive. In addition to homoepitaxy, ZnO single-crystal substrates could also be useful for heteroepitaxy of
GaN-based active layers. The stacking order of ZnO is the same as that of GaN, with a lattice mismatch of only 1.8% [16]. Due to the complexity of the growing process, it should be mentioned that availability of high-quality ZnO substrate does not automatically pave the way for high-quality epitaxial layers.
Although high-quality ZnO substrates are available, making homo-epitaxy possible, most of the growth still has been done on sapphire (Figure 12 [16]). Despite its poor structural and thermal match to ZnO, it still has advantages such as low cost and availability as large-area wafers and its wide energy-band gap. Hetero-epitaxial ZnO layers have been grown on several other substrates, such as CaF2 [36], Si [37], GaAs [38, 39], and ScAlMgO [40] as well as on GaN/sapphire templates [41]. Table 7 [16] lists the lattice parameters of a number of prospective substrates. There is much work remains to be done to attain epitaxial layer matching the bulk in quality.
2.3.2. Buffer layer
The large differences of the lattice parameter and the thermal expansion would induce internal stress field during the cooling process. The residual stress field would cause high density threading dislocations or film cleavage to the single crystal film. To solve this problem, growing a buffer layer by different methods can highly improve the thin film quality.
Yoshida et al. found that growing an AlN buffer layer could substantially improve the quality of epitaxy GaN grown on the sapphire substrate [42]. The same research team has done a series of studies to find the role of AlN buffer layer. Firstly the AlN will deposit as an amorphous structure at low temperatures. The amorphous
layer can cover the surface and improve the substrate uniformly. The temperature then heated to the normal growth temperature, the AlN phase transformed into crystalline structure (which has only 2.4% lattice mismatch along a-axis, as listed in Table 1 [11]). It provided an excellent template for epitaxy [3-6]. The procedure of GaN growing on AlN buffer layers successfully improved 10 times of carrier concentration and mobility, two orders of intense detected by photoluminescence (PL) and one fourth narrower of the full height at middle width (FHMW) by X-Ray diffraction peak.
2.4. The methods of fabricating single crystal thin films
The GaN thin films and ZnO wafers can be grown on various substrates by following methods: molecular beam epitaxy (MBE) [43-46], halide vapor phase epitaxy (HVPE) [41, 47], chemical vapor deposition (CVD) and metal-organic chemical-vapor deposition (MOCVD) methods [41, 48].
The mechanism of growing single crystal semiconductor on hetero-epitaxy substrates in different geometric shape should consider the surface energy and molecular mobility. Take the free surface energy between substrate-film (γi), film (γf) and substrate (γs) into consideration. There are three different growing modes: the Frank-van der Merwe mode (thin film), the Volmer-Weber mode and the Stranski-Krastanov mode [106]. According to thermodynamics, if single crystal epi-layer thin film needs to be deposited on substrate without peeling off, the total surface energy of film and interface should be less than the free surface energy of substrate.
△γ = γf + γi - γs < 0. (2-4)
Using the Frank-van der Merwe mode to deposit a flat 2D thin film, substrate-film interface free surface energy can be neglected by small lattice mismatch, the free surface energy of film should be larger than the free surface energy of substrate (γf).
Substrate would be easily wet if lattice mismatch0 and γf＜γs[49]. The following is the briefly introduction of the manufacturing procedures of epi-layer GaN thin film by CVD and MOCVD in laboratory.
2.4.1. Chemical vapor deposition (CVD)
The chemical vapor deposition process can be separated into five steps (Figure 13 [93, 109]):
1. Input highly volatile reactant (precursor) into reaction tube.
2. Reactant diffuses in by main gas flow, passes through boundary layer and reaches the surface of substrate.
3. Reactant is absorbed by surface.
4. Precursor reacts and becomes deposition.
5. Product (gas) desorbs, diffuses out and excludes by main gas flow.
The last step determines the deposition rate. Total gas flux, tube pressure and orientation, surface area, geometric direction of substrate could also affect the deposition rate. At low temperatures, pressure and high gas velocity conditions (Figure 14 [93, 109]), reactant can easily reach surface, but reaction will become slower, and dynamics dominate whole process due to the lack of kinetic energy. At high
temperatures and high pressures with low gas velocity, Figure 15 [93, 109] shows when the reaction rate increases, boundary layer becomes thicker and diffusion rate dominates the whole process.
2.4.2. Metal-organic chemical-vapor deposition (MOCVD)
At the end of 1980s, Nakamura of Nichia chemical company modified MOCVD as two-flow MOCVD (TF-MOCVD, Figure 16 [48]) and produced high quality GaN in Figure 17 [55], based on the reaction below:
(CH3)3Ga + NH3 → GaN + 3CH4. (2-5)
Substrates should be heated to at least 800oC to deposit the high quality GaN. 1050oC was the right temperature to gain highest quality of GaN. Once the temperature was higher than 1100oC, GaN would crack due to the high vacancy density [50].
2.5. Basic properties of the hexagonal wurtzite structure
In this study, two wurzite structure materials (GaN and ZnO) in four orientations (Table 3) are analyzed of their mechanical properties and the luminescence performance. For clarity of presentation, the following sections list the basic group theory, formulas of mechanical properties, deformation mechanism and defects.
2.5.1. Group theory of hexagonal systems
Both GaN and ZnO are hexagonal system, four indices direction [uvtw] and three
indices system [UVW] can be converted by the following relations:
h=u-t u=(2h-k)/3,
k=v-t v=(2k-h)/3, (2-6)
l=w t=-(h+k)/3, w=l.
Three indices direction system (UVW) can be converted to four indices system (uvtw) by adding t = -(U+V). In the other side, simply take t term away from four indices system can convert back into three indices system. In addition, unlike the cubic system, not all the indices of direction [abc] is the normal vector of plane (abc).
To get the normal directions of other planes, space directions should be converted into three indices. Then pick arbitrarily two vectors on the plane and cross them into one vector. The normal direction can be calculated by transforming back to four indices.
The following contains the name of the main planes and their plane directions:
Basal plane, c-plane {0001} <0001>,
m-plane ,
a-plane . (2-7)
Pyramidal plane ,
r-plane .
Reciprocal unit vectors and real lattice unit vectors share the following relation:
} 0 1 10
{ 1010 }
0 2 11
{ 1120 } 1 1 10
{ 1011 }
02 1 1
{ 1102
, ,
.
(2-8)
Because the reciprocal lattice has the property of orthonormality, reciprocal direction [hkl] would always be normal to reciprocal plane (hkl). For reciprocal lattice, the length of reciprocal vector g
( g
= hb1 + kb2 + lb3)equal to 1/dhkl, where d is d spacing of periodicity lattice.
2.5.2. Characters of dislocations in the wurtzite structure
The Burgers vector of threading dislocations in a hexagonal structure could be found by Thompson tetrahedron. For basal planes {0001}, there are 6 edge dislocations which lied on the plane (Burgers vector 1120
3
1 ) and two screw
dislocations (Burgers vector <0001>) which perpendicular to the plane. Combining edge and screw dislocations could get extra 12 sets of mixed dislocations (Burger vector 1123
3
1 ). The partial dislocations could be classified as Shockley partial
dislocation 1100 3
1 (lied on the basal plane) and Frank partial dislocation
0001 3
1 (perpendicular to the basal plane). Combining Shockley and Frank partial
dislocations can gain another partial dislocation group 2203 6
1 [37, 51] .
2.6. Introduction of nanoindentation testing
2.6.1. Mechanical properties
3 2 1
3 2
1 a a a
a b a
3 2 1
1 3
2 a a a
a b a
3 2 1
2 1
3 a a a
a b a
The basic mechanical properties, hardness (H) and Young’s modulus (E) can be calculated by using the Oliver-Pharr model (Figure 18) [20, 52]. The formula of hardness is:
Ac
H Pmax
, (2-9)
where Pmax is the maximum indentation load in load-displacement curve (Figure 19 [52]), Ac is the projected contact area which can be extend to a series:
5 1/168 / 1 4 4 / 1 3 2 / 1 2 1
2
0 c c c c c c
c C h Ch C h C h C h C h
h F
A
. (2-10)
C0 to C5 can be obtained by testing a standard sample, in this case silica, and hc is the contact depth. In the limit of hc ≪ R (here R is the radius of indenter tip), the relationship can approximately reduce to
c c
c C h Ch
Rh
A2 0 2 1 . (2-11)
The tip radius R can then be extract from the projected contact area of the shallow depth [53]. The formula of reduced Young’s modulus Er is:
s c r
A
E 1
2
1 2
, (2-12)
where s is Poisson ratio of the sample. Considering the displacement from the tip, the Young’s modulus of the sample can be extract by
i i s
s
r E E
E
2
2 1
1
1
. (2-13)
The Ei and vi are the Young’s modulus and Poisson’s ratio of the diamond indenter.
Our MTS nanoindentation system gives the measured value of diamond tip, the Young’s modulus is Ei = 1141 GPa and the Poisson’s ratio is i =0.07. The Poisson ratio of sample act important role in both formula. For anisotropic material, the Poisson ratio s of different direction can be derived by the elastic constant matrix Cij. For Hexagonal wurtzite structure, the symmetry can simplify the matrix as following:
6 5 4 3 2 1
66 44 44 33 13 13
13 11 12
13 12 11
6 5 4 3 2 1
0 0 0 0 0
0 0
0 0 0
0 0 0
0 0
0 0 0
0 0 0
0 0 0
C C C C C C
C C C
C C C
, (2-14)
where andis the normal stress along a1-axis, a2-axis and c-axis, respectively.
The elastic constants C11, C12, C13, C33, C44, and C66 are listed in Table 8 [16]. The equation of stiffness (S) and dampling (C) are
1 1 2
max / ( ))cos ( )
(
1
f
s
m K K h
S P
, (2-15)
sin
) (
max
h
C P
,
where is the phase angle between Pmax and h(w), m is the mass of the indentation column, Ks is the is spring constant in the vertical direction, Kf is frame stiffness, w is angular speed which equals 2πf, f is the driven frequency of the ac signal of 45 Hz for CSM mode [54]. Table 9 summarizes the mechanical properties by using different kinds of indentation methods [20]. Because m, Ks and Kf are all constant values for the specified indentation system, there are deviation of E and H between different indentation tips. E and H values extracted by Berkovich tip are larger than other shape of tips.
2.6.2. Deformation mechanisms
So far, there is no evidence of twining or phase transformation induced during deformation in GaN and ZnO. It is believed the dislocation is the dominated deformed mechanism. The preferred slip plane would be changed as c/a ratio is changed.
According to theoretical lattice strength:
0
max 2
a Gb
, (2-16)
where G is shear modulus, b is Burger’s vector, a is distance between planes, 0 is critical shear stress. Dislocations are preferred to slip on close packing planes (amax) and along close packing direction (bmin).
For nanoindentation system, the Berkovich tip creates a complex stress field into the specimen (Figure 20 [53]). For hexagonal close packed structure, the c/a ratio is 1.633. The close packed plane and main prefer slip plane is basal plane (0001). The c/a ratio of epitaxial layer GaN (hexagonal wurtzite structure) is ~1.626, which is close to the hexagonal close structure [11]. As the loading increasing along the c-axis, the structure is compressed. Dislocations preferred to slip on other plans, such as {2113} or {1012} pyramidal plane, during nanoindentation testing (Figure 17, [55]). On the other hand, when the c/a ratio is over the ideal value >1.633, the preferred slip plane remain on basal plane. As the indent depth increasing, more dislocations slip on the basal plane and pyramidal plane. The slip planes keep extending by dislocation stacking. Two planes eventually cross together (Figure 21 [57]). To keep the deformation going, the secondary slip planes starts to be active at deeper depths (Figure 22 [53]).
To determine the prefer slip plane, we have to look back to the fundamental theory of the resolved shear stress.
rss =× (cos × cosφ)max , (2-17)
where (cos×cosφ) is usual seen as the Shimid factor, φ represents the angle between the normal vector of the slip plane and the applied stress and represents the angle between the slip and stress directions.
The yield stress is the transition point between elastic and plastic deformation.
The yielding point can be extracted from the pop-in effect of the nanoindentation load-displacement curve. The load-displacement relationship (P-h) can be well fitted
