Mechanically Coupled Single-Crystal Silicon MEMS Resonators for TCF Manipulation

Abstract

This paper presents mechanically coupled single-crystal silicon (SCS) microelectromechanical system (MEMS) resonators for temperature coefficient of frequency (TCF) manipulation. The reported mechanically coupled square extensional (SE) mode resonator consists of two square plates coupled with a beam or a third square plate purposely vibrating in another bulk mode. The SE mode resonators and the coupled structure can be considered as two kinds of individual resonators with different TCFs. Within the specific dimensions of the coupled resonator, the resonant frequencies of the two components are assumed to be equal. Hence, the TCF of the mechanically coupled resonator could be manipulated by adjusting the sizes of the coupling parts. The design and fabrication of coupled resonators have been completed in a degenerate-doped (100) SCS wafer. Measurement results illustrate that the TCFs of the coupled resonators can be purposely manipulated by adjusting the volume and equivalent spring constant ratios of the individual resonators. The minimal measured frequency shift is roughly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm$</tex-math> </inline-formula> 10 ppm for an 18 MHz coupled SE mode resonator, over the entire industrial temperature range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$-$</tex-math> </inline-formula> 40 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> C to 85 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> C. This work highlights a novel and effective way to manipulate the TCFs of MEMS resonators via mechanical coupling. 2022-0197