An Analytical Model for Intrinsic Residual Stress Effect on Out-of-Plane Deflection in Chemical-Vapor-Deposited Free-Sta
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An Analytical Model for Intrinsic Residual Stress Effect on Out-of-Plane Deflection in Chemical-Vapor-Deposited Free-Standing Thick Film Jeung-hyun Jeong, Young-Joon Baik1 and Dongil Kwon School of Materials Science and Engineering, Seoul National University, Seoul 151-742, Korea 1 Thin Film Technology Research Center, Korea Institute of Science and Technology, Seoul 136791, Korea ABSTRACT The 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. INTRODUCTION Thick diamond films are considered very suitable for use as thermal spreaders for high-power electronic devices and microwave optical windows due to its very high hardness, stiffness and thermal conductivity, and very low electrical conductivity [1]. Polycrystalline diamond wafers for these thick-film applications are being developed using various chemical vapor deposition (CVD) [2-4]. However, CVD processes often results in out-of-plane film deflection when the diamond film is released from the substrate. This phenomenon is known as bowing. Bowing must be eliminated so that the diamond wafer can be used effectively, and thus very expensive process of mechanical and chemical polishing should be added. To reduce the production cost, it is essential to control the bowing of the diamond film at the deposition step. The film bowing is suspected to be the result of variations in residual stress with film thickness. The stress variation has been reported to be caused mainly by microstructural changes in the film with increasing thickness and is sometimes related to substrate deformation [4-7]. However, the origin of the stress variation and its effect on bowing are not fully understood. In case of diamond film, since the microstructure-induced variation in residual stress is limited to within 5-15 µm of an interface [5,6], its effect on the film bowing is very small in films several hundred µm thick, such as diamond wafers. Indeed, a substrate with thick film experiences a considerably larger defor
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