Modeling of temperature frequency-compensation of doped silicon MEMS resonator

In this paper, an analytical model is presented to predict the temperature sensitivity of doped silicon MEMS resonator. Temperature coefficients of three elastic constants (C
11
, C
12
and C
44
) were predicted and found in good agreement (∼1%) with the experimental values previously reported in the literature. The model was then extended to find relationship between doping and temperate-compensated frequency. Our model shows that the Lame mode frequency of a MEMS resonator can be compensated via an optimum n-doping of around 4×10
¹⁹
cm
⁻³
for working temperature between −40°C to 100 °C.