薄膜微結構在複雜沈積過程中，薄膜大多會與基板接觸表面產生殘留應力，應力過大時容易造成基板彎曲變形而導致薄膜破裂損壞，因此準確地評估薄膜殘留應力問題是非常重要的課題。本論文主要在平板力學理論架構下，分析薄膜應力造成基板彎曲變形的數學架構與力學行為，推算出兩者間之精確解，與Stoney formula比較，探討二者推導機制之差異，進一步分析Stoney formula之誤差原因。並且配合電腦軟體ABAQUS建立合理之模型來提供數值解，探討數學模式之正確性。

During the process of thin film deposition, residual stress will be induced in most of the situations when the thin film gets in touch with the substrate. Deformation of the substrate usually occurs when the stress attains the limitation at a certain value. Therefore, it is informative to characterize the stress evolution of the thin film in a reasonable manner. Based on the classical plate theory, a mathematical framework is constructed and the mechanical behavior is estimated when the thin film stress is caused by the deformation of the substrate. We have derived the exact solutions based on the framework and compared the results with the well-known Stoney formula. The discrepancy of the two results will be addressed. Furthermore, the underlying reasons for the inaccuracy will be assessed. A reasonable model is also constructed to provide numerical solutions in contrast with the finite element calculations, ABAQUS.

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