Temperature Dependence of the Elastic Constants of Doped Silicon

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 cm^-3, and n-doped up to 6.6e19 cm^-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.