在半導體之異質層狀結構中，薄膜的成長與基板間一直存在晶格不配合的問題，在製造過程中異質層狀結構自薄膜沉積時，由於基板與薄膜的晶格常數與熱膨脹係數不同，因此會產生殘留應力。
在本論文中，利用修正的剪遲滯法在彈性等向性的狀態下，考慮不配合應變、差排密度和力矩平衡的影響。利用矩陣和特徵值的技巧去解一組聯立線性常微分方程組。本研究是採用GaAs/GaP薄膜成長於Si基板上的異質層狀結構，在[100]和[111]兩個不同的晶軸方向，對平行的結構加以比較，藉以評估在不同晶軸方向以及三種材料同時存在於結構中，其對水平方向的正向應力和剪應力的影響。

Multilayered film heterostructures of semiconductors have been extensively used in many applications especially in electronic and optoelectronics devices in recent years. The residual stresses will be introduced due to large lattice mismatch and different thermal expansion coefficient between substrate and film. A modified shear lag method, which is formulated based on the theory of anisotropic elasticity and also takes account of both the effects of lateral deflection and moment balance, is proposed. The matrix and the eigenvalue method are applied to solve the linear systems of differential equations. The distributions of longitudinal stress in different shapes of GaAs/GaP/Si multilayered heterostructures are evaluated along [100] and [111] crystalline directions, respectively. Moreover, the influences of three different materials inserted between these islands upon the distributions of normal and shear stresses are investigated and discussed.

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