Temperature Dependence of the Elastic Constants of Doped Silicon

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Resonators fabricated in heavily doped silicon have been noted to have a reduced frequency-temperature dependence compared with lightly doped silicon. The resonant frequency of silicon microelectromechanical systems (MEMS) resonators is largely governed by the material’s elastic properties, which are known to depend on doping. In this paper, a suite of different types and orientations of resonators were used to extract the first- and second-order temperature dependences of the elastic constants of p-doped silicon up to 1.7e20 $\mathrm{cm}^{\mathrm {\mathbf {-3}}}$ , and n-doped up to 6.6e19 $\mathrm{cm}^{\mathrm {\mathbf {-3}}}$ . It is shown that these temperature-dependent elastic constants may be used in finite element analysis to predict the frequency-temperature dependence of similarly doped silicon resonators. [2013-0331]