中文摘要
在異質磊晶中薄膜的成長與基板之間一直存在著晶格不配合的問題，也因為這個問題導致無法長出高品質的薄膜，在發光二極體中晶格不配合的問題不只存在於基板與薄膜之間，也存在於披覆層與活性層間，使得發光二極體的發光效率不佳、壽命不長。
在本論文中，修正剪遲滯法在彈性非等向性的狀態下，考慮不配合應變、剪應力平衡與力矩平衡的影響，利用矩陣、特徵值以及邊界值問題，來探討薄膜的應力。
本研究是探討[1000]方向的氮化鎵薄膜成長於[0001]的藍寶石基板上的異質層狀結構，針對熱應力的問題與雙異質結構、單量子井結構、量子井結構中銦含量不同的發光二極體，利用修正剪遲滯法來探討其水平方向的正向應力，並討論應力對發光二極體光電效應的影響。

Lattice matching between epitaxial layer and substrate is one of the most important point required to be considered in heteroepitaxial growth. It may be the main reason why an epitaxial film with good crystal quality is always
difficult to achieve. There also exists lattice mismatch between the active layer and the cladding layer for light emission diodes. The devices, consequently, have a short life and a week emission.
In this thesis, a modified shear lag method is formulated based on the theory of anisotropic elasticity. The effects of misfit strain, shear and moment balance are taken into consideration in analysis. The stress distributions in epitaxial films are then evaluated by solving the eignvalue problems including equilibrium equations and associated boundary conditions expressed in matrices form. The distributions of stress in a variety of cases including double heterostructure, single quantum well and the different indium mole fraction of the light emission diodes are obtained under the condition of the [1000] GaN film grown onto a [0001] sapphire substrate. Finally, the influence of film stress on optoelectronic properties in LEDs are evaluated and discussed.

參考文獻
[1] S. Nakamara, S. Pearton, G. Fasol , The Blue Laser Diode, Springer ,
[2] S.O. Kasap, Optoelectronics and Photonics Principles and Practices , Prentice Hall, Canada, 2001
[3] N.F. Dow, G.E.C. Missile and Space-Division, Rep. No. R63SD61 (quoted by G. S. Holister and C. Thomas, Fiber reinforced materials, Elseverier, London, p. 23, 1966.)
[4] G. H. Olsen and M. Ettenberg, Crystal Growth Theory and Techniques, Vol. 2, (edited by C. H. L. Goodman), Plenum Press, New York, 1978
[5] A.S. Jordan, J. Crystal Growth, 49, pp. 631, 1980
[6] S. Ochiai and K. Osamura, Stress distribution in a segmented coating film on metal fiber under tensile loading, J. Mater. Sci. 21, pp. 2744-
[7] S. Ochiai, K. Schulte and P. W. M. Peters, Strain concentration factors for fibers and matrix in unidirectional composites, Compos. Sci. Technol. 237-256, 1991
[8] S. Ochiai, K. Osamura, K. Tokinori, M. Nakatani, and K. Yamatsuta, Stress concentration at a notch tip in unidirectional metal matrix composites, Metallurgical Transaction A. Vol. 22A,pp. 2085-2095, 1991
[9] S. Ochiai and M. Hojo, Stress disturbances arising from cut fiber and matrix in unidirectional metal matrix composites calculated by means ofa modified shear lag analysis, J. Mater. Sci. 31, pp. 3861-3869, 1996
[10] S. Ochiai and K. Osamura, Influence of fracture of coating layer on fiber strength, Mater. Sci. Eng. A154, pp. 149-154, 1992
[11] K. Nakajima, Calculation of stress in As Ga In 88 . 0 12 . 0 trinary bulk crystals with compositionally graded As Ga In x x − 1 layers on GaAs seeds. , J. Crystal Growth 113, pp. 447-484,1991
[12] K. Nakajima, Calculation of stresses in GaAs/Si strained heterostructures. , J. Crystal Growth 121, pp. 278-296, 1992
[13] K. Nakajima, Calculation of compositional dependence of stresses in GaInAs/GaAs strained multilayer heterostructures. , J. Crystal Growth, 126, pp. 511-524, 1993
[14] B.J. Spencer, P.W. Voorhees, S.H. Davis, Morphological instability in epitaxially strained dislocation-free solid films: Linear stability theory. , J. Appl. Phys. 73, pp. 4955-4970, 1993
[15] K. Nakajima, K. Furuya, Effect of Si interlayers on stress and curvature radius of GaAs/Si and GaAs/Si/GaAs/Si heterostructures with interfacial misfit dislocations., Jpn. J. Phys. 33, pp. 1420-1426, 1994
[16] T. Kozawa, T. Kachi, H. Kano, H. Nagase, Thermal stress in GaN epitaxial layers grown on sapphire substrates. , J. Appl. Phys. 77, 9, pp.4389-4392, 1995
[17] K. Nakajima and S. Ochiai, Effect of crack on stress reduction in GaAs/Si heterostructures. , Jpn. J. Phys. 34, pp. 3000-3007, 1995
[18] K. Nakajima, K. Kithana and S. Ochiai, Calculation of stress concentration at the edge of island layer: Demonstration for GaAs/Si. ,Jpn. J. Phys. 35, pp. 2605-2613, 1996
[19] V. Srikant et al., Mosaic structure in epitaxial thin films having large lattice mismatch. , J. Appl. Phys. , 82, 9, pp.4286-4294, 1997
[20] A.F. Wright, Elastic properties of zinc-blende and wurtzite AlN, GaN and InN. , J. Appl. Phys., 82, 6, pp.2833-2839, 1997
[21] . O rer o Gfr & & et al., Relaxation of thermal strain in GaN epitaxial layers geown on sapphire. , Material Science and Engineering , B43, pp.250- 252, 1997
[22] S. Krukowski et al., Thermal properties of Indium Nitride , J. Phys. Chem Solids, V59, N3, pp.289-295, 1998
[23] T.C. Chen, H.C. Wu, Stress and deflection in GaAs/Si layers Heterostructures by improved laminate theory. , J. Crystal Growth, 186, pp. 571-578, 1998
[24] Michael C.Y. Chan, Elaine M.T. Cheung, E. Herbert. Li, Atunable blue light emission of InGaN/GaN quantum well through thermal interdiffusion. , Materials Science and Engineering, B59, pp.283-287, 1999
[25] S. Heame, E. Chason, J. Han, J.A. Floro, J. Figiel, J. Hunter, Stress evolution during metalorganic chemical vapor deposition of GaN. , Appl. Phys. Letters ,V74 ,N3 ,pp.356-358, 1999
[26] H. Amano et al., Growth of GaN on highly mismatched substrate and its application to novel devices. ,Diamond and Relates Materials , 8, pp.302- 304, 1999
[27] S. Einfeldt et al., Strain relaxation in AlGaN under tensile plane stress. , J. 76 Appl. Phys., V88, N12, pp.7029-7036, 2000
[28] R. Jones, Do we really understand dislocation in semiconductors. , Materials Science and Engineering, B71, pp.24-29, 2000
[29] . T ttcher o B & & , S. Einfedldt, The role of high-temperature island colaescence in the development of stresses in GaN films. , Applied Physics Letters, V78, N14, pp.1976-1978, 2001
[30] L. Liu, J.H. Edger, Substrate for gallium nitride epitaxy, Materials Science and Engineering. , R37, pp.61-127, 2002
[31] T.M. Regan et al., Neutron irradiation of sapphire for compressive strengthening.Ⅱ. Physical properties changes. , J. Nuclear Materials, 300, pp.47-56, 2002
[32] 林家慶, 氮化鎵磊晶缺陷之研究, 國立海洋大學碩士論文, 2000
[33] 林進龍, 多層異質薄膜結構知熱應力分析, 國立成功大學碩士論文,2000
[34] 史光國, 現代半導體發光及雷射二極體材料技術, 全華科技, 台北,2001