在光通訊中，利用量子史塔克效應所製成的電致吸收光電調變器是十分重要的元件。另一方面，鍺與矽同是四族元素，擁有良好的批配，因此利用矽鍺做成的元件可以與以矽為基材的電子元件結合，能進一步地提升電子元件之間的傳輸效能。

在本篇論文裡，我們分析討論了波函數的分佈和對光子的吸收受非對稱量子井結構的影響及結果。並從中發現，當導帶和價帶的波函數侷限在不同位置時會有藍位移的現象產生。為此，我們提出了一個設計準則，使得元件擁有大幅度的藍位移。最後，我們依循該準則並利用模擬來驗証。

Optical electroabsorption modulators using quantum confinement Stark effect are important devices in optical commincation. Ge is group IV element that is compatible with Si process. It is possible to integrate Ge/SiGe quantum well devices with integrated circuite.

In this thesis, we study the eigen state of carrier and analyze the electroabsorption in an asymmetric quantum well. We find out that if the barrier height of carriers in conduction band and valance band are different, there exists blue shift when electric field is applied. We further suggest a design rule for engineering the blue shift, and with this rule, we demonstrate an example of elctroabsorption modulators with Ge/SiGe asymmetric quantum well.

[1] M CARDONA and FH POLLAK. Energy-band structure of germanium and silicon - k.p method. PHYSICAL REVIEW, 142(2):530, 1966.
[2] SHUN-LIEN CHUANG. PHYSICS OF PHOTONIC DEVICES, chapter 14, pages 683–691. Wiley, 7 edition, 2009.
[3] MV FISCHETTI. MONTE-CARLO SIMULATION OF TRANS- PORT IN TECHNOLOGICALLY SIGNIFICANT SEMICON- DUCTORS OF THE DIAMOND AND ZINCBLENDE STRUC- TURES .1. HOMOGENEOUS TRANSPORT. IEEE TRANSAC- TIONS ON ELECTRON DEVICES, 38(3):634–649, MAR 1991.
[4] Hartmut Hang. Quantum Theory of the Optical and Electronic Properties of Semiconductor, chapter 10. World Scientific Pub- lishing Co. Pte. Ltd., 5 edition, 2009.
[5] Christian Jirauschek. Accuracy of Transfer Matrix Approaches for Solving the Effective Mass Schrodinger Equation. IEEE JOURNAL OF QUANTUM ELECTRONICS, 45(9):1059–1067, SEP 2009.
[6] B JONSSON and ST ENG. SOLVING THE SCHRODINGER- EQUATION IN ARBITRARY QUANTUM-WELL PO- TENTIAL PROFILES USING THE TRANSFER-MATRIX METHOD. IEEE JOURNAL OF QUANTUM ELECTRONICS, 26(11):2025–2035, NOV 1990.
[7] A KAHAN, M CHI, and L FRIEDMAN. INFRARED TRANSI- TIONS IN STRAINED-LAYER GEXSI1-X/SI. JOURNAL OF APPLIED PHYSICS, 75(12):8012–8021, JUN 15 1994.
[8] Yu-Hsuan Kuo, Yong-Kyu Lee, Yangsi Ge, Shen Ren, Jonathan E. Roth, Theodore I. Kamins, David A. B. Miller, and James S. Har- ris. Strong quantum-confined stark effect in germanium quantum- well structures on silicon. Nature, 437:1334–1336, 10 2005.
[9] C. Lange, N. S. Koester, S. Chatterjee, H. Sigg, D. Chrastina, G. Isella, H. von Kaenel, M. Schaefer, M. Kira, and S. W. Koch. Ultrafast nonlinear optical response of photoexcited Ge/SiGe quantum wells: Evidence for a femtosecond transient population inversion. PHYSICAL REVIEW B, 79(20), MAY 2009.
[10] Lucien D. Laude, Fred H. Pollak, and Manuel Cardona. Effects of uniaxial stress on the indirect exciton spectrum of silicon. Phys. Rev. B, 3:2623–2636, Apr 1971.
[11] Leon Lever, Zoran Ikonic, Alex Valavanis, Jonathan D. Cooper, and Robert W. Kelsall. Design of Ge-SiGe Quantum-Confined Stark Effect Electroabsorption Heterostructures for CMOS Com- patible Photonics. JOURNAL OF LIGHTWAVE TECHNOL- OGY, 28(22):3273–3281, NOV 15 2010.
[12] A. C. H. Lim, R. Gupta, S. K. Haywood, M. J. Steer, M. Hop- kinson, and G. Hill. Electric field induced blueshift of the e1-hh1 exciton transition in a GaAs1-xNx/GaAs (x < 1%) stepped quan- tum well. APPLIED PHYSICS LETTERS, 89(26), DEC 25 2006.
[13] JF Liu, DD Cannon, K Wada, Y Ishikawa, DT Danielson, S Jongthammanurak, J Michel, and LC Kimerling. Deformation potential constants of biaxially tensile stressed Ge epitaxial films on Si(100). PHYSICAL REVIEW B, 70(15), OCT 2004.
[14] O. Madelung. Data in Science and Technology: Semiconductors Group IV Elements and III-V Compounds. Springer-Verlag, 1991.
[15] DAB MILLER, DS CHEMLA, TC DAMEN, AC GOSSARD, W WIEGMANN, TH WOOD, and CA BURRUS. ELECTRIC- FIELD DEPENDENCE OF OPTICAL-ABSORPTION NEAR THE BAND-GAP OF QUANTUM-WELL STRUCTURES. PHYSICAL REVIEW B, 32(2):1043–1060, 1985.
[16] S Richard, F Aniel, and G Fishman. Energy-band structure of Ge, Si, and GaAs: A thirty-band k center dot p method. PHYSICAL REVIEW B, 70(23), DEC 2004.
[17] Emre SARI. Ingan/gan quantum electroabsorption modulators with record breaking electroabsorption in blue, 2007.
[18] Rebecca K. Schaevitz, Jonathan E. Roth, Shen Ren, Onur Fi- daner, and David A. B. Miller. Material properties of Si-Ge/Ge quantum wells. IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, 14(4):1082–1089, JUL-AUG 2008.
[19] Virginia Semiconductor. The General Properties of Si, Ge, SiGe, SiO2 and Si3N4. Jun 2002.
[20] DS Shin. Effect of a step barrier on the quantum-confined Stark effect and applications to electroabsorption modulators with high saturation optical power. JOURNAL OF THE KOREAN PHYS- ICAL SOCIETY, 47(2):364–370, AUG 2005.
[21] DS Shin, PKL Yu, and SA Pappert. High-power electroabsorption modulator using intra-step-barrier quantum wells. JOURNAL OF APPLIED PHYSICS, 89(2):1515–1517, JAN 15 2001.
[22] MD STURGE. OPTICAL ABSORPTION OF GALLIUM AR- SENIDE BETWEEN 0.6 AND 2.75 EV. PHYSICAL REVIEW, 127(3):768–&, 1962.
[23] F Tekia, M Ferhat, and A Zaoui. Band-gap bowing in SixGe1-x alloy. PHYSICA B, 293(1-2):183–186, DEC 2000.
[24] S Vatannia and G Gildenblat. Airy’s functions implementation of the transfer-matrix method for resonant tunneling in variably spaced finite superlattices. IEEE JOURNAL OF QUANTUM ELECTRONICS, 32(6):1093–1105, JUN 1996.
[25] Su-Huai Wei and Alex Zunger. Predicted band-gap pressure coef- ficients of all diamond and zinc-blende semiconductors: Chemical trends. Phys. Rev. B, 60:5404–5411, Aug 1999.
[26] TH WOOD, JZ PASTALAN, CA BURRUS, BC JOHNSON, BI MILLER, JL DEMIGUEL, U KOREN, and MG YOUNG. ELECTRIC-FIELD SCREENING BY PHOTOGENERATED HOLES IN MULTIPLE QUANTUM-WELLS - A NEW MECH- ANISM FOR ABSORPTION SATURATION. APPLIED PHYSICS LETTERS, 57(11):1081–1083, SEP 10 1990.