Measurement of the Effect of Temperature on Stress Distribution and Deformation in Multilayer Optical Thin Film Structur
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stresses are simply great enough to cause a large degree of curvature in the substrate without peeling, this might be sufficient to compromise device performance. If a large-area optical thin film device has a high stress-induced curvature, the optical properties may be significantly affected. There is a need to be able to characterize and predict the stresses and deformation in a device resulting from the interactions between the film layers and the substrate. This study focuses on several key issues in determining and fully understanding the stress state in layered thin film structures. Two elastic models are compared: the commonly used "Stoney's equation" for stress calculation, and a more complex elastic plate bending model. These methods are employed to predict elastic changes in curvature as a function of temperature and compared to the measured behavior of an actual sample of a layered thin film structure. The particular case in which diamond and silicon films are deposited on germanium substrates is investigated. The high deposition temperature and large difference in thermal expansion coefficient between the diamond film and the substrate cause a large amount of thermal elastic stress and deformation in the structure. In addition, it is likely that some plastic deformation occurs in the germanium substrate due to high temperature creep. This study is an attempt to accurately model the deformation and determine the actual stresses that exist in the structure. THIN FILM STRESS THEORY Thin film stresses are caused by both the difference in thermal expansion coefficients between the substrate and film(s) and by the film deposition process itself. The thermal stresses are 351 Mat. Res. Soc. Symp. Proc. Vol. 356 01995 Materials Research Society
referred to as extrinsic stresses and the deposition stresses as intrinsic. Intrinsic stresses are affected by the structure of the growing film, the rate of deposition, the amount of thermal energy present during deposition and the mobility of the arriving particles and impurities in the film[ 1,2]. Thermal stresses exist if the film and substrate have different thermal expansion coefficients and there is a temperature change in the structure after film deposition. Both the film and substrate would expand or contract to their new equilibrium dimensions if they were not constrained at their interface. The film stress as described here is the average one-dimensional stress in the plane of the film, ;,x and ryy. The stress models here do not take into account edge effects or any stress or strain components perpendicular to the plane in intermediate films in layered structures due to different Poisson's ratios of the films and substrate. The stress at the film-substrate interface results in a bending moment in the structure due to the interface being constrained. The substrate will bend until an equilibrium has been reached, leaving the structure with a curvature that may be directly related to the amount of film stress. The relation between thin film stress and curvature
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