Temperature Compensated Bulk-Mode Capacitive MEMS Resonators With ±16 ppm Temperature Stability Over Industrial Temperature Ranges

Abstract

This letter reports temperature compensated single crystal silicon (SCS) bulk-mode capacitive microelectromechanical system (MEMS) resonators with high temperature stability of less than ±20 ppm over industrial temperature range. Degenerate doping is adopted to change the temperature coefficient of frequency ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$TCF$ </tex-math></inline-formula> ) and adjusting of crystal orientation is implemented to tune the turnover points for the MEMS resonators, thanks to the different temperature coefficient of elastic constants ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$TCE$ </tex-math></inline-formula> ) of the resonators along different crystal orientation. The adjustment effects are verified by using finite element method (FEM) simulations as well as measurement results. Two bulk-modes, namely length-extensional (LE) and square-extensional (SE) mode resonators along various crystal orientations in a degenerate-doped (100) SCS wafer are designed and fabricated. The measurement frequency shifts are approximately ±20 ppm for the LE mode resonator and ±16 ppm for the SE mode resonator as the resonators are placed along 22.5° from the <110> direction over industrial temperature range of −40°C to 85 °C, respectively. It highlights an effective way to reduce the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$TCF$ </tex-math></inline-formula> via degenerate doping and precisely adjust the turnover point by crystal orientation tuning for MEMS resonators. [2022-0046]