An Analytical Model for Intrinsic Residual Stress Effect on Out-of-Plane Deflection in Chemical-Vapor-Deposited Free-Standing Thick Film

Abstract

ABSTRACTThe effect of residual stress on the out-of-plane deflection in a free-standing thick diamond films was investigated theoretically and experimentally. The deflection is believed to be caused by the variation in residual stress with film thickness. Key idea of this study is that the stress variation may be produced by gradually increasing substrate deformation resulting from the layer-by-layer deposition of the film. The layer-by-layer deposition was modeled by using infinitesimal plate-bending theory, considering the two deformation modes of contraction or expansion and bending. To verify the suggested model, several hundred micron thick diamond films were fabricated on Si, Mo and W substrates of varying thicknesses by microwave plasma assisted chemical vapor deposition. The model's predictions on bowing, based on intrinsic stress value measured by the curvature method, were in good agreement with the experimentally measured curvature of the as-released films. Finally, it is concluded that the bowing of CVD thick films depends on the intrinsic stress variation of the film associated with gradual increase in substrate deformation.