Structural Investigation of Si-Ge Epitaxial Layers by Convergent Beam Electron Diffraction (CBED)

現今電晶體閘極(Gate)寬度持續微縮下，為了更進一步提升載子於源極(Source)與集極(Drain)通道間的遷移率，應變矽(Strained Si)與矽鍺(Si1-xGex)材料已經普遍被應用於現今微電子工業。對於奈米尺度範圍內的應變分析，以穿透式電子顯微鏡(Transmission electron microscopy, TEM)技術為主之高解析穿透式電子顯微鏡配合幾何相位比對分析(Geometrical phase analysis)、收斂電子束繞射、奈米束繞射與電子全像技術(Electron holography)具有相當的成效。在這些技術當中，由於收斂電子束繞射對於晶格常數變化擁有高度敏感性與準確性，因此相當備受關注。 本研究為藉由超高真空化學氣相沉積系統，將4 μm厚Si0.95Ge0.05與50 nm厚Si0.8Ge0.2薄膜磊晶於(001)方向之p型矽基板上。由明場影像、高解析晶格影像與相應之快速傅立葉空間影像、掃描穿隧式電子顯微鏡影像、能量散佈光譜分析，Si0.95Ge0.05與Si0.8Ge0.2磊晶薄膜擁有相當均一的薄膜厚度、成分分布與優異的結晶特性。在收斂電子束繞射上選用[430]晶帶軸(Zone axis)，與以[430]晶帶軸為基準往[001]方向傾轉1o(偏[430]晶帶軸)為Si-Ge磊晶材料之晶帶軸，並於FEI TECNAI F30穿透式電子顯微鏡加裝10 eV狹縫(Slit)之能量過濾器(Energy filter)、300 kV電壓(有效電壓為298.6 kV)與掃描穿隧(STEM)模式下進行操作。本實驗之收斂電子束繞射圖譜可以完全藉由MacTempas軟體進行模擬、重合與更進一步晶體結構分析。 當接近Si0.95Ge0.05/Si介面收集收斂電子束繞射圖譜時，無論是在[430]晶帶軸或是偏[430]晶帶軸上，都可以明顯觀察到分裂之高次Laue晶帶線(High order Laue zone line)與模糊的收斂電子束繞射圖譜。相較於正[430]晶帶軸，偏[430]晶帶軸對於減緩成對菊池線(Kikuchi line pairs)所產生之多重條紋干擾與非彈性電子散射具有相當的成效，因此呈現出更多之高次Laue晶帶線資訊與更清楚之收斂電子束繞射圖譜。故，運用偏[430]晶帶軸收斂電子束繞射技術，可以更進一步提升收斂電子束繞射的影像品質與空間解析度。在藉由50 nm Si0.8Ge0.2磊晶薄膜進行偏[430]晶帶軸技術之收斂電子束繞射的實驗上，50 nm內的空間解析度已經可以達到。 分裂之高指數Laue晶帶線可以根據下列兩種假設模型之靜態模擬收斂電子束繞射圖譜來呈現，分別是晶格平面沿著TEM試片厚度方向彎曲(-0.03o, 0, 0.03o)與晶格常數改變(0.549 nm±0.06 nm)。藉由模擬與實驗上(008)、(1-17)、(-573)、(-575)線之分裂寬度的相互比較(特別是(008)線的顯著分裂)，指出在Si1-xGex磊晶於Si基板時，晶格平面沿著TEM試片厚度方向的彎曲為產生分裂高指數Laue晶帶線最有可能的原因。更進一步研究高指數Laue晶帶線分裂的起始距離與TEM試片厚度關係，在Si0.95Ge0.05磊晶層與Si基板上，分裂的高指數Laue晶帶線在280 nm、430 nm與550 nm的TEM試片厚度下，分別起始於距離Si0.95Ge0.05/Si介面170 nm、255 nm與310 nm處。薄TEM試片的製備過程中所產生之自由表面應力釋放效應為造成此現象的主要原因。測定在280 nm、430 nm與550 nm的TEM試片厚度下的高指數Laue晶帶線的分裂寬度，晶格平面沿著TEM試片厚度方向所產生的二維彎曲分佈便可被描繪出來，且具有相當優異的空間解析度(50 nm)與角度解析度(0.02o)。 在應變的估計上，晶格平面沿著TEM試片厚度方向的彎曲可以藉由扭轉應變(Distortion strain)模型來加以描述。藉由高角度Laue晶帶線的分裂寬度上所測得之晶格平面彎曲數據，扭轉應變估計與二維扭轉應變分佈狀況已經成功地被描繪，且清楚地顯示出介面扭轉應變與自由表面應力釋放現象。 最後，在Si0.95Ge0.05與Si0.8Ge0.2磊晶薄膜中的晶格常數與鍺濃度可以藉由高指數Laue晶帶線的偏移來進行估計。對於Si0.95Ge0.05與Si0.8Ge0.2磊晶薄膜，晶格常數與鍺濃度分別為0.544 nm (5 at%)與0.548 nm (19 at%)，此結果相當接近預測值，且更精準於能量散步光譜(EDS)分析的結果。In order to continually downscale the gate size of the transistor, strained Si and Si1-xGex materials have been applied in the modern electronics industry to enhance the carrier mobility of the channel between source and drain. Transmission electron microscopy (TEM) techniques, notably high-resolution TEM (HR-TEM) with geometrical phase analysis (GPA), convergent beam electron diffraction (CBED), nano-beam diffraction (NBD), and electron holography, are effective techniques for strain analysis in the nano-scale range. Of these techniques, CBED has attracted much attention due to its high sensitivity and accuracy in the determination of lattice parameters. In this study, 4 μm thick Si0.95Ge0.05 and 50 nm thick Si0.8Ge0.2 epitaxial layers were deposited on (001)-orientated p-type Si substrate in an ultra-high vacuum/chemical vapor deposition (UHV/CVD) system. Imaging with bright-field (BF), HR-TEM, corresponding fast Fourier transformation (FFT), scanning transmission electron microscopy (STEM), and energy dispersive spectroscopy (EDS) element line-profiles showed the uniformity of thickness and composition and the excellent crystal quality of the Si0.95Ge0.05 and Si0.8Ge0.2 layers. In the CBED experiment, [430] and 1º tilting toward the [001] direction from the [430] zone axis (the off [430] zone axis) were used on the Si-Ge epitaxial layers with an FEI TECNAI F30 TEM equipped with an energy filter of a 10 eV slit at 300 kV (effective voltage was 298.6 kV) and STEM mode. A good match was achieved with CBED patterns simulated by MacTempas calculating software. CBED patterns taken close to the Si0.95Ge0.05/Si interface revealed split high order Laue zone (HOLZ) lines and blurred CBED patterns with the on [430] and off [430] zone axes. More HOLZ lines and clearer CBED patterns could be found by off [430] zone axis than by exact [430] zone axis. The off [430] zone axis provides a good method for the reduction of the influences of multi-fringes caused by Kikuchi line pairs and inelastic scattering, and hence the image quality of CBED patterns and spatial resolution can be improved. The spatial resolution of the CBED technique by off [430] zone axis in this study can reach 50 nm, as shown by examination of a 50 nm thick Si0.8Ge0.2 layer. Using the off [430] zone axis, according to the assumptions of bending of lattice planes along the direction of TEM specimen thickness by -0.03o, 0, and 0.03o and lattice constant changes by 0.549 nm±0.06 nm, the split HOLZ lines in CBED patterns were successfully reproduced by kinematical simulation. From the comparison of split widths of (008), (1-17), (-573), and (-575) lines with the experimental results, especially for the wide splitting of the (008) line, the bending of lattice planes along the direction of TEM specimen thickness is the most likely cause in the case of Si1-xGex layer on Si substrate. Furthermore, at variant specimen thicknesses of 280 nm, 430 nm, and 550 nm, the HOLZ line splitting began at points 170 nm, 255 nm, and 310 nm away from the Si0.95Ge0.05/Si interface on both sides of Si0.95Ge0.05 and Si, respectively, which can be interpreted as the effect of free surface relaxation during the preparation of the thin TEM specimen. From these CBED patterns at 290 nm, 430 nm, and 550 nm thick TEM regions, a 2-D bending map of lattice planes along the direction of the TEM specimen can be reconstructed with high spatial resolution (50 nm) and angle sensitivity (0.02o). In the strain estimation, the bending of lattice planes along the direction of the TEM specimen can be completely described by the model of distortion strain. From the bending consequences of the lattice plane, measured from the split widths of HOLZ lines, distortion strain has been successfully estimated and used to reconstruct a 2-D distortion strain distribution. Interface distortion strain and free surface relaxation can be clearly observed. Finally, from the shifts of HOLZ lines, the lattice constants and Ge concentrations in the Si0.95Ge0.05 and Si0.8Ge0.2 layers could be estimated. The lattice constants and Ge concentrations of the Si0.95Ge0.05 and Si0.8Ge0.2 layers were 0.544 nm (5 at%) and 0.548 nm (19 at%), respectively, which were very close to the expected results and much more accurate than the EDS results.致謝.......................................................I 摘要.....................................................III Abstract...................................................V Contents..................................................IX Figure Content...........................................XII Table Content............................................XXV Chapter 1 Introduction.....................................1 Chapter 2 Background Review: Si-Ge Epitaxial Layer.........5 2.1 Development of Si-Ge Materials [1].....................5 2.1.1 Early Work of Si-Ge materials........................7 2.1.2 Advent of the Relaxed Buffer of Si-Ge and Early Device.....................................................8 2.1.3 Fabricate on MOSFETs.................................9 2.1.4 High-mobility strained-layer MOSFETs................11 2.2 Defects in Si-Ge Epitaxial Layer......................13 2.3 Introduction of the Growth Methods of Si-Ge Epitaxial Layer.....................................................18 2.3.1 Molecular Beam Epitaxy (MBE)........................20 2.3.2 Chemical Vapor Deposition (CVD).....................21 Chapter 3 Literature Review: Advanced TEM on Strain Analysis..................................................27 3.1 Convergent-beam Electron Diffraction (CBED)...........30 3.2 Geometric Phase Analysis (GPA)........................35 3.3 Nano-beam Electron Diffraction (NBD) and Electron Holography................................................43 Chapter 4 Experimental Processes..........................51 4.1 Si1-xGex Epitaxial Layer(s) Deposition................51 4.2 TEM Sample Preparation................................52 4.3 TEM Equipment.........................................53 4.4 CBED Technique........................................54 4.6 EELS Spectroscopy.....................................55 4.7 EDS Spectroscopy/Line-scan............................56 Chapter 5 Results and Discussion: Off-Zone Axis Operation (CBED)....................................................63 5.1 The Basic TEM Studies on Si-Ge Epitaxial Layers.......63 5.2 Zone Axis Selection...................................65 5.3 Line Splitting of HOLZ lines at Si-Ge/Si interface....66 5.4 Off [430] Zone CBED Operation.........................68 Chapter 6 Results and Discussion: Analysis of Split HOLZ lines.....................................................85 6.1 Influence of Thickness on CBED Patterns...............85 6.2 The Relationship between Split HOLZ lines and Crystal Distortion................................................87 6.3 Two-dimensional Map of Crystal Rotation...............91 6.4 Crystal Rotation by X-ray Diffractometer..............93 Chapter 7 Results and Discussion: Strain Estimation......113 7.1 Geometric Phase Analysis (GPA).......................114 7.2 Crystal Distortion at the Si1-xGex/Si Interface......115 7.3 Strain Estimation by HR-STEM with GPA................118 7.4 Strain Estimation of Crystal Distortion..............121 Chapter 8 Results and Discussion: Lattice Constant and Ge Concentration............................................139 8.1 Lattice Constant in a Selected Local Region..........139 8.2 The Determination of Ge Concentration in Si-Ge Layers...................................................141 Chapter 9 Conclusion.....................................151 Chapter 10 Future Work...................................155 References...............................................157 Appendix.................................................165 Appendix A. Determination of Effective TEM Accelerating Voltage by CBED Method...................................165 Appendix B. Specimen-Thickness Measurement in the Thicker TEM Specimen by EELS spectrum............................170 Appendix C. Determination of Lattice Constant by CBED Technique................................................179 Appendix D. Concentration Calculation of Ge Doped into Si Structure................................................182 Abbreviations............................................18