Thin film deposition is a key fabrication step in several opto-mechanical and electronics applications. For instance, thin film coatings can act as reflective interfaces, protective coatings or they can be used to modify the thermal behavior of the film-substrate system. For effective design, it is important to understand the deformation of the system in response to residual stresses during thin film deposition. The widely used Stoney’s equation to measure this deformation assumes isotropic elasticity of the substrate together with infinitesimal strains and rotations. In this work we relax both constraints, where we study the deformation of commonly used substrates made of single crystal Si(001) and Si(111) wafers that undergo large rotations. We derive relations between normalized substrate curvature and thin film mismatch strain and validate our analysis with numerical results. The methodology presented can be used for more accurate understanding of a broad range of film-substrate systems in semiconductors.

薄膜沉积是几种光电机械和电子应用中的关键制造步骤。例如，薄膜涂层可以充当反射界面，保护涂层，或者可以用来改变薄膜-基材系统的热性能。为了进行有效的设计，重要的是要了解系统在薄膜沉积过程中响应残余应力的变形。广泛用于测量此变形的Stoney方程假定基材具有各向同性的弹性以及极小的应变和旋转。在这项工作中，我们放宽了两个约束，在这里我们研究了由单晶Si（001）和Si（111）晶片制成且经常旋转的常用基板的变形。我们得出归一化衬底曲率和薄膜失配应变之间的关系，并用数值结果验证我们的分析。提出的方法可用于更准确地理解半导体中广泛的薄膜-衬底系统。