| A theoretical model for the influence of residual stress on the out-of-plane deflection in a free-standing thick diamond films (the bowing phenomenon) is presented. The variation in residual stress with film thickness is believed to be a cause of the bowing. In this study, the stress variation is assumed to be produced by a gradual increase of substrate deformation resulting from the layer-by-layer deposition of the film. The model was developed using infinitesimal plate-bending theory, considering the two deformation modes of contraction or expansion and bending. To verify the suggested model, diamond films were fabricated on Si, Mo and W substrates of varying thicknesses using 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 bowing curvature of the as-released films measured by a profilometer. This confirms that the bowing of thick films depends on the intrinsic stress variation of the film associated with gradual increase in substrate deformation. Finally, a method of eliminating bowing by depositing multi-layers with different stresses was discussed. |
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