Effects of air damping and residual stress on micromechanical resonators were studied theoretically and experimentally.We qualitatively analysed the dependence of the non-dimensional added virtual mass incremental factor on the residual stress.
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.
By measuring the resonant frequencies of cantilever beams without and with thin films deposited and with the use of the Euler–Bernoulli beam theory, elastic modulus and density of thin films can be determined simultaneously. This simple resonant method was validated using a sputtered Ni film/Si substrate system. The elastic modulus of the Ni film obtained from this method was in excellent agreement with that measured by use of nanoindentation.