Temperature Compensation of Silicon Lamé Resonators Using Etch Holes: Theory and Design Methodology

We present a new approach to the temperature compensation of MEMS Lamé resonators, based on the combined effect of the doping concentration and of the geometry of etch holes on the equivalent temperature coefficients of silicon. To this purpose, we develop and validate an analytical model which describes the effect of etch holes on the temperature stability of Lamé resonators through comparison with experiments available in the literature and finite-element method (FEM) simulations. We show that two interesting regions of the design space for Lamé resonators exist, where a cancellation of the first-order temperature coefficient of the resonance frequency is possible: [100]-oriented silicon with n-doping of 2.5 ·10¹⁹ cm ^-3 , and [110]-oriented silicon with p-doping higher than 1.4 ·10²⁰ cm ^-3 .