Intrinsic stress in chemical vapor deposited diamond films: An analytical model for the plastic deformation of the Si substrate

Abstract

The intrinsic stress in diamond film deposited on a Si substrate is difficult to measure because high-temperature deposition induces plastic deformation in the Si and so renders useless an elastic solution. In this study, an analytical model is proposed to estimate intrinsic stress using a substrate-curvature technique and considering the plastic deformation of substrate. The stress distribution of the as-deposited film is affected not only by the intrinsic stress of the film but also by the bending and plastic deformation of the substrate. In this model, the distribution is formulated, based on elastic/plastic plate-bending theory, in terms of substrate curvatures, intrinsic stress in the film, and yield stress of the substrate. The intrinsic stress of the film together with the yield stress of the substrate can be obtained from experimentally measured substrate curvatures by solving two equilibrium equations and a moment-relaxation equation describing the film removal. Diamond films were deposited by microwave plasma chemical vapor deposition at varying film thicknesses and deposition temperatures. For the application of the model, the curvature of the film-removed substrate was measured as well as that of as-deposited substrate. The results show that overestimated intrinsic stress can be corrected successfully through this new model. The validity of the results was confirmed by stress measurement using a Raman-peak-shift method. In addition, the generation mechanism of intrinsic stress is analyzed as reflecting a competition between a grain-size effect and nondiamond carbon effect. (C) 2001 American Institute of Physics.