本論文利用壓電調制反射光譜(PzR)、光子調制反射光譜(PR)以及光激發螢光光譜(PL)研究鍺磊晶層(Ge-epilayer)及其多重量子井(MQW)結構之光學特性。
利用壓電調制反射光譜與光子調制反射光譜可得到來自鍺磊晶層的光學躍遷訊號，並配合熱膨脹係數之理論計算可探討不同厚度之矽基板對於鍺磊晶層所產生之應變(Strain)與溫度變化之關係。
使用光子調制反射光譜可探討鍺量子井寬度分別為12與15 nm之Ge/Si0.15Ge0.85 MQW結構光學特性，並可得到量子井結構當中可能的光學躍遷訊號。利用理論計算(envelope function approximation)結果，可確認量子井結構中來自基態(ground state)至激發態(excited state)的躍遷訊號，並可得到導電帶平移(conduction band offset)約為0.68。此外，亦可使用壓電調制反射光譜觀察到在不同成長技術下且不同成分結構之Ge/Si0.15Ge0.85 MQW與Ge/Si0.16Ge0.84ˊMQW之光學躍遷訊號。而材料能隙相關躍遷及量子井中躍遷訊號隨溫度變化的結果，可利用Varshni及Bose-Einstein兩方程式來得到其相關的溫度參數並加以討論。
利用溫度變化之光激發螢光光譜可同時觀察到來自Ge/Si0.15Ge0.85 MQW結構中直接復合(direct recombination)與間接復合(indirect recombination)的光學訊號。在高於室溫下，直接復合的訊號隨溫度增加而有增強的趨勢，原因為位於間接能隙侷限態之載子受熱激發(thermal excitation)至直接能隙侷限態所造成的直接複合訊號增強。
從實驗結果可知調制光譜是具有非接觸性與非破壞性的量測技術，為研究鍺磊晶層及其量子井結構光特性與其應用於近紅外光電元件之有力工具。

In this thesis, we report a detailed optical characterization on Ge epilayer and their quantum well (MQW) structures by using piezoreflectance (PzR), photoreflectance (PR) and photoluminescence (PL) spectroscopy.
The PzR and PR spectroscopy were employed to study the optical transitions from Ge epilayer. The strain of Ge epilayer was induced by variable temperature according to theoretical calculations with different thermal expansion coefficients between Si and Ge have been discussed.
The PR technique was used to characterize two Si/SiGe MQW structures with different well widths. The nominal thicknesses of the Ge/Si0.15Ge0.85 MQW structures in the two samples were 15 and 12 nm, respectively. The PR spectra revealed a wide range of the possible optical transitions in the MQW structure. Using a theoretical envelope function approximation calculations, the ground state and higher order transitions were observed and identified. The conduction band offset was found to be 0.68. In addition, PzR has also been used to detect the transition energies form different structures of the Ge/Si0.15Ge0.85 MQW and Ge/Si0.16Ge0.84 MQW grown by using different manufacture processes. Furthermore, a detailed study on temperature dependence of the excitonic transition energies indicates that the main influence is related to the band gap of the constituent materials in the well. We also discussed the parameters of temperature dependence of the experimental results by using Varshni and Bose-Einstein equations.
PL of the Ge/Si0.15Ge0.85 MQW structure was studied above room temperature, Both direct and indirect radiative recombination PL features were observed. The relative intensity of direct to indirect recombination increases with the increase of temperature. The enhancement of PL from direct recombination above RT has been attributed to the thermal excitation of carriers from L-type to C-type confined states.
The results show the potential of using PzR, PR and PL as powerful techniques with contactless and nondestructive properties, and these techniques are suitably used for the study of optical characterization of Ge epilayer and their MQW structures for NIR optoelectronic device applications.

[1] M. Haurylau, S.P. Anderson, K.L. Marshall, P.M. Fauchet, ”Electrically Tunable Silicon 2-D Photonic Bandgap Structures,” IEEE J. Sel. Topics Quantum Electron., vol. 12, pp. 1527-1533 (2006)
[2] V. Švrček, T. Sasaki, Y. Shimizu, N. Koshizaki, “Blue Luminescent Silicon Nanocrystals Prepared by Nanosecond Laser Ablation and Stabilized in Electronically Compatible Spin on Glasses,” J. Appl. Phys., vol. 103, pp. 023101-1-023101-8 (2008)
[3] H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An All-Silicon Raman Laser,” Nature (London), vol. 433, pp. 292-294 (2005)
[4] M. Bonfanti, E. Grilli, M. Guzzi, D. Chrastina, G. Isella, H. Von Känel, H. Sigg, “Direct Gap Related Optical Transitions in Ge/SiGe Quantum Wells,” Physica E, vol. 41, pp. 972-975 (2009)
[5] F. Schäffler, ”High-Mobility Si and Ge Structures,” Semicond. Sci. Technol., vol. 12, pp. 1515-1549 (1997)
[6] K. Ismail, M. Arafa, K. L. Saenger, J. O. Chu, B. S. Meyerson, “Extremely High Electron Mobility in Si/SiGe Modulation‐Doped Heterostructures,” Appl. Phys. Lett., vol. 66, pp. 1077-1079 (1995)
[7] E.M. Chumbes, A.T. Schremer, J.A. Smart, Y. Wang, N.C. MacDonald, D. Hogue, J.J. Komiak, S.J. Lichwalla, R.E. Leoni, III, J.R. Shealy, ”AlGaN/GaN High Electron Mobility Transistors on Si(111) Substrates,” IEEE Tran. Electron. Devices, vol. 48, no. 3, pp. 420-426 (2001)
[8] H. Daembkes, H.J. Herzog, H. Joke, H. Kibbel, E. Kaspar, ”The n-Channel SiGe/Si Modulation-Doped Field-Effect Transistor,” IEEE Tran. Electron. Devices, vol. ED-33, no. 5, pp. 633-638 (1986)
[9] P. Narozny, H. Dambkes, H. Kibbel, E. Kasper, “Si/SiGe Heterojunction Bipolar Transistor Made by Molecular-Beam Epitaxy,” IEEE Tran. Electron. Devices, vol. 36, no. 10, pp. 2363-2366 (1989)
[10] S. Huang, W. Lu, C. Li, W. Huang, H. Lai, and S. Chen, “A CMOS-Compatible Approach to Fabricate an Ultra-thin Germanium-on-Insulator with Large Tensile Strain for Si-Based Light Emission,” Opt. Express, vol. 21, no. 1, pp. 640-646 (2013)
[11] O. Madelung, Numerical Data and Functional Relationships in Science and Technology, Landolt-Börnstein, New Series, Group III, vol. 17, Pt. A., Springer-Verlag, Berlin (1982)
[12] Y. H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris, “Strong Quantum-Confined Stark Effect in Germanium Quantum-Well Structures on Silicon,” Nature (London), vol. 437, pp. 1334-1336 (2005)
[13] H. Kosaka, H. Shigyou, Y. Mitsumori, Y. Rikitake, H. Imamura, T. Kutsuwa, K. Arai, and K. Edamatsu, Coherent Transfer of Light Polarization to Electron Spins in a Semiconductor,” Phys. Rev. Lett., vol. 100, pp. 096602-1-096602-4 (2008)
[14] S. Tsujino, H. Sigg, G. Mussler, D. Chrastina, and H. von Känel, ”Photocurrent and Transmission Spectroscopy of Direct-gap Interband Transitions in Ge/SiGe Quantum Wells,” Appl. Phys. Lett., vol. 89, pp. 262119-1-262119-3 (2006)
[15] Y. Chen, C. Li, H. Lai, and S. Chen, “Quantum-Confined Direct Band Transitions in Tensile Strained Ge/SiGe Quantum Wells on Silicon Substrates,” Nanotechnology, vol. 21, pp. 115207-1-115207-5 (2010)
[16] P. Chaisakul, D. Marrie- Morini, G. Isella, D. Chrastina, X. Le. Roux, S. Edmond, J. R. Coudevylle, E. Cassan, and L. Vivien, “Polarization Dependence of Quantum-Confined Stark Effect in Ge/SiGe Quantum Well Planar Waveguides,” Optics Lett., vol. 36, no. 10, pp. 1794-1796 (2011)
[17] Y. Rong, Y. Ge, Y. Huo, M. Fiorentino, M. R. T. Tan, T. I. Kamins, T. J. Oshalski, G. Huyet, and J. S. Harris Jr., “Quantum-Confined Stark Effect in Ge/SiGe Quantum Wells on Si,” IEEE J. Sel. Topics Quantum Electron., vol. 16, no. 1, pp. 85-92 (2010)
[18] Y. Chen, C. Li, Z. Zhou, H. Lai, S. Chen, W. Ding, B. Cheng, and Y. Yu, “Room Temperature Photoluminescence of Tensile-Strained Ge/Si0.13Ge0.87 Quantum Wells Grown on Silicon-Based Germanium Virtual Substrate,” Appl. Phys. Lett., vol. 94, pp. 141902-1-141902-3 (2009)
[19] H. Yaguchi, K. Tai, K. Takemasa, K. Onabe, R. Ito, Y. Shiraki, ” Characterization of Ge/SiGe Strained-Barrier Quantum-Well Structures Using Photoreflectance Spectroscopy,” Phys. Rev. B, vol. 49, no. 11, pp. 7394-7399 (1994)
[20] D. J. Paul, “8-Band k.p Modeling of the Quantum Confined Stark Effect in Ge Quantum Wells on Si Substrates,” Phys. Rev. B, vol. 77, pp. 155323-1-155323-7 (2008)
[21] M. Bonfanti, E. Grilli, M. Guzzi, M. Virgilio, G. Grosso, D. Chrastina, G. Isella, H. von Känel, A. Neels, “Optical Transitions in Ge/SiGe Multiple Quantum Wells with Ge-Rich Barriers,” Phys. Rev. B, vol. 78, pp. 041407-1-041407-4 (2008)
[22] E. Gatti, E. Grilli, M. Guzzi, D. Chrastina, G. Isella, and H. von Känel, “Room Temperature Photoluminescence of Ge Multiple Quantum Wells with Ge-Rich Barriers,” Appl. Phys. Lett., vol. 98, pp. 031106-1-031106-3 (2011)
[23] P. Chaisakul, D. Marris-Morini, G. Isella, D. Chrastina, X. Le Roux, E. Gatti, S. Edmond, J. Osmind, E. Cassan, and L. Vivien, ”Quantum-Confined Stark Effect Measurements in Ge/SiGe Quantum-Well Structures,” Opt. Lett., vol. 35, no. 17, pp. 2913-2915 (2010)
[24] J. Liu, M. Beals, A. Pomerene, S. Bernardis, R. Sun, J. Cheng, L. C. Kimerling, and J. Michel, “Waveguide-Integrated, Ultralow-Energy GeSi Electro-Absorption Modulators,” Nat. Photonics, vol. 2, pp. 433-437 (2008)
[25] L. Vivien, J. Osmond, J. M. Fédéli, D. Marris-Morini, P. Crozat, J. F. Damlencourt, E. Cassan, Y. Lecunff, and S. Laval, ” 42 GHz p.i.n Germanium Photodetector Integrated in a Silicon-on-Insulator Waveguide,” Opt. Express, vol.17, no. 8, pp. 6252-6257 (2009)
[26] P. Chaisakul, D. Marris-Morini, G. Isella, D. Chrastina, X. Le Roux, S. Edmond, J. Osmind, E. Cassan, J. R. Coudevylle, and L. Vivien, “Ge/SiGe Multiple Quantum Well Photodiode with 30 GHz Bandwidth,” Appl. Phys. Lett., vol. 98, pp. 131112-1-131112-3 (2011)
[27] Z. Liu, W. Hu, C. Li, Y. Li, C. Xue, C. Li, Y. Zuo, B. Cheng, and Q. Wang, “Room Temperature Direct-Bandgap Electroluminescence from n-type Strain Compensated Ge/SiGe Multiple Quantum Wells,” Appl. Phys. Lett., vol. 101, pp. 231108-1-231108-4 (2012)
[28] J. Liu, X. Sun, R. Camacho-Aguilera, L. C. Kimerling, and J. Michel, ”Ge-on-Si Laser Operating at Room Temperature,” Opt. Lett., vol. 35, no. 5, pp. 679-681 (2010)
[29] M. Cardona, Modulation Spectroscopy, Academic, New York, pp. 1-358 (1969)
[30] Y. Hamakawa, and T. Nishino, Optical Properties of Solids: New Developments, North-Holland, Amsterdam, p. 255 (1970)
[31] F. H. Pollak, “Modulation Spectroscopy of Semiconductors and Semiconductor Microstructures,” Handbook on Semiconductors, vol. 2, ed. M. Ballanski, North-Holland, New York, pp. 524-635 (1994)
[32] X. Yin, and F. H. Pollak, “Novel Contactless Mode of Electroreflectance,” Appl. Phys. Lett., vol. 59, no. 18, pp. 2305-2307 (1991)
[33]X. Yin, X. Guo, F. H. Pollak, G. D. Pettit, J. M. Woodall, T. P. Chin, and C. W. Tu, “Nature of Band Bending at Semiconductor Surfaces by Contactless Electroreflectance,” Appl. Phys. Lett., vol. 60, no. 11, pp. 1336-1338 (1992)
[34] H. Shen, S. H. Pan, F. H. Pollak, and R. N. Sacks, “Electromodulation Mechanisms for the Uncoupled and Coupled States of a GaAs/Ga0.82Al0.18As Multiple-Quantum-Well Structure,” Phys. Rev. B, vol. 37, no. 18, pp. 10919-10922 (1988)
[35] H. Mathieu, H., J. Allègre, and B. Gil, “Piezomodulation Spectroscopy: A Powerful Investigation Tool of Heterostructures,” Phys. Rev. B, vol. 43, no. 3, pp. 2218-2227 (1981)
[36] C. H. Ho, H. W. Lee, and Z. H. Cheng, “Practical Thermoreflectance Design For Optical Characterization of Layer Semiconductors,” Rev. Sci. Instrum., vol. 75, no. 4, pp. 1098-1102 (2004)
[37] Z. Xu, and M. Gal, “Temperature Modulated Photoluminescence in Semiconductor Quantum Wells,” Superlatt. Microstruct., vol. 12, no. 3, pp. 393-396 (1992)
[38] D. E. Aspnes, Handbook on Semiconductor, vol. 2, ed. by T. S. Moss, North-Holland, New York, p.109 (1980)
[39] See, for example, F. H. Pollak and O. J. Glembocki in Proceedings of the Society of Photo-optical Instrumentation Engineers (SPIE, Bellingham 1988) vol. 946, p. 2. (1988)
[40] O. J. Glembocki and B. V. Shanabrook, ”Electromodulation Spectroscopy of Confined Systems,” Superlatt. Microstruct., vol. 5, pp. 603-607 (1989)
[41] M. Balkanaki , in Handbook on Semiconductors, vol. 2, ed. M. Balkanaki, North-Holland, New York, pp. 66-109 (1982)
[42] D. W. Aspnes, and A. A. Studna, “Schottky-Barrier Electroreflectance: Application to GaAs,” Phys. Rev. B, vol. 7, no.10, pp. 4605-4625 (1973)
[43] D. E. Aspnes, and B. O. Seraphin, “Electric Field Effects in Optical and First-Derivative Modulation Spectroscopy,” Phys. Rev. B, vol. 6, no. 8, pp. 3158-3160 (1972)
[44] Y. P. Varshni, “Temperature Dependence of Energy Gap in Semiconductors,” Physica (Amsterdam) vol. 34, no. 1, pp. 149-154 (1967)
[45] P. Lautenschlager, M. Garriga, S. Logothetidis, and M. Cardona, “Interband Critical Points of GaAs and Their Temperature Dependence,” Phys. Rev. B, vol. 35, no. 17, pp. 9174-9189 (1987)
[46] H. Mathieu, J. Allègre, and B. Gil, “Piezomodulation Spectroscopy: a Powerful Investigation Tool of Heterostructures,” Phys. Rev. B, vol. 43, no. 3, pp. 2218-2227 (1991)
[47] S. Adachi, Properties of Group-IV, III-V and II-VI Semiconductors, Wiley, New York, p. 82 (2009)
[48] B. Welber, M. Cardona, Y. F. Tsay, and B. Bendow, “Effect of Hydrostatic Pressure on the Direct Absorption Edge of Germanium,” Phys. Rev. B, vol. 15, no. 2, pp. 875-879 (1977)
[49] I. Balslev, “Direct Edge Piezo-reflectance in Ge and GaAs,” Solid State Commun., vol. 5, pp. 315-317 (1967)
[50] Y. A. Burenkov, S. P. Nikanorov, and A. V. Stepanov, Sov. Phys. Solid State, vol. 12, p. 1940 (1971)
[51] H. P. Singh, “Determination of Thermal Expansion of Germanium, Rhodium and Iridium by X-rays,” Acta Crys., vol. A24, pp. 469-471 (1968)
[52] Y. Okada and Y. Tokamaru, “Precise Determination of Lattice Parameter and Thermal Expansion Coefficient of Silicon between 300 and 1500 K,” J. Appl. Phys., vol. 56, no. 2, pp. 314-320 (1984)
[53] S. L. Chuang, Physics of Optoelectronic Devices, Wiley, New York, p. 144 (1995)
[54] C. Lange, N. S. Köster, S. Chatterjee, H. Sigg, D. Chrastina, G. Isella, H. von Känel, M. Schäfer, M. Kira, and S. W. Koch, “Ultrafast Nonlinear Optical Response of Photoexcited Ge/SiGe Quantum Wells: Evidence for a Femtosecond Transient Population Inversion,” Phys. Rev. B, vol. 79, pp. 201306-1-201306-4 (2009)
[55] J. P. Dismukes, L. Ekstrom, and R. J. Paff, “Lattice Parameter and Density in Germanium-Silicon Alloys,” J. Phys. Chem. vol. 68, no. 3, pp. 3021-3027 (1964)
[56] S. Adachi, “Model Dielectric Constants of Si and Ge,” Phys. Rev. B, vol. 38, no. 18, pp. 12966-12976 (1988)
[57] W. C. Dash and R. Newman, “Intrinsic Optical Absorption in Single-Crystal Germanium and Silicon at 77°K and 300°K,” Phys. Rev. vol. 99, no. 4, pp. 1151-1155 (1955)
[58] C. G. Van de Walle, “Band Lineups and Deformation Potentials in the Model-Solid Theory,” Phys. Rev. B, vol. 39, no. 3, pp. 1871-1883 (1989)
[59] J. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S. Jongthammanurak, J. Michel, and L. C. Kimerling, ”Deformation Potential Constants of Biaxially Tensile Stressed Ge Epitaxial Films on Si(100),” Phys. Rev. B, vol. 70, pp. 155309-1-155309-5 (2004)
[60] H. J. McSkimin and P. Andreatch, “Elastic Moduli of Silicon vs Hydrostatic Pressure at 25.0°C and 195.8°C,” J. Appl. Phys. vol. 35, no. 7, pp. 2161-2165 (1964)
[61] S. Adachi, Properties of Group-IV, III-V and II-VI Semiconductors, John Wiley & Sons, New York, p. 148 (2005)
[62] F. H. Pollak and H. Shen, ”Modulation Spectroscopy of Semiconductors: Bulk/Thin Film, Microstructures, Surfaces/Interfaces and Devices,” Mater. Sci. Eng., vol. R10, Nos. 7-8, pp. 275-374 (1993)
[63] G. Bastard and J. A. Brum, “Electronic States in Semiconductor Heterostructures,” IEEE J. Quantum Electron., vol. 22, no. 9, pp. 1625-1644 (1986)
[64] S. Adachi, Properties of Group-IV, III-V and II-VI Semiconductors, John Wiley & Sons, New York, p. 178 (2005)
[65] Y. Yin, D. Yan, F. H. Pollak, M. S. Hybertsen, J. M. Vandenberg, and J. C. Bean, “Temperature Dependence of The Fundamental Direct Transitions of Bulk Ge and Two Ge/SiGe Multiple-Quantum-Well Structures,” Phys. Rev. B, vol. 52, no. 12, pp. 8951-8958 (1995)
[66] P. A. Dafesh and K. L. Wang,” Temperature Dependences of The Eo Transitions in Bulk Ge and a Ge-rich (Si)m/(Ge)n Superlattice” Phys. Rev. B, vol. 45, no. 4, pp. 1712-1718 (1992)
[67] A. Kangarlu, H. R. Chandrasekhar, M. Chandrasekhar, Y. M. Kapoor, F. A. Chambers, B. A. Vojak, and J. M. Meese, “Temperature Dependence of The Quantized States in a GaAs-Ga1-xAlxAs Superlattice,” Phys. Rev. B., 37, no. 2, pp. 1035-1038 (1988)
[68] Y. S. Huang, H. Qiang, F. H. Pollak, G. D. Pettit, P. D. Kirchner, J. M. Woodall, H. Stragier, and L. B. Sorensen, ”Temperature Dependence of the Photoreflectance of a Strained Layer (001) In0.21Ga0.79As/GaAs Single Quantum Well,” J. Appl. Phys., vol. 70, no. 12, pp. 7537-7542 (1991)
[69] Y. Ishikawa, K. Wada, J. Liu, D.D. Cannon, H.C. Luan, J. Michel, L.C. Kimerling, “Strain-Induced Enhancement of Near-Infrared Absorption in Ge Epitaxial Layers Grown on Si Substrate,” J. Appl. Phys. vol. 98, pp. 013501-1-013501-9 (2005)
[70] L. Carroll, F. Imbert, H. Sigg, M. Süess, E. Müller, M. Virgilio, G. Pizzi, P. Rossbach, D. Chrastina, G. Isella, “Quantum-Confined Direct-Gap Transitions in Tensile-Strained Ge/SiGe Multiple Quantum Wells,” Appl. Phys. Lett., vol. 99, pp. 031907-1-013907-3 (2011)
[71] P. Chaisakul, D. Marrie-Morini, G. Isella, D. Chrastina, N. Izard, X. Le. Roux, S. Edmond, J. -R. Coudevylle, and L. Vivien, “Room Temperature Direct Gap Electroluminescence from Ge/Si0.15Ge0.85 Multiple Quantum Well Waveguide,” Appl. Phys. Lett., vol. 99, pp. 141106-1-141106-3 (2011)