A resonant method for determining the residual stress and elastic modulus of a thin film

By measuring the resonant frequencies of the first two symmetric vibration modes of a circular thin-film diaphragm and solving the Rayleigh-Ritz equation analytically, the residual stress and elastic modulus of the film were determined simultaneously. The results obtained employing this method are in excellent agreement with those obtained numerically in finite element modelling when tested using freestanding circular SiC diaphragms with residual tensile stress. The stress and modulus values are also in reasonably good agreement with those obtained from nanoindentation and wafer curvature measurements, respectively.