Crystallographic and eigenmode dependence of TCf for single crystal silicon contour mode resonators

Abstract

This paper reports the effects of crystal orientations on the temperature coefficient of frequency (TCf) of single crystal silicon square-plate micromechanical resonators vibrating in two distinct contour modes: Lamé mode and square extensional (SE). For the Lamé mode, the same TCf was found over several devices aligned to the <;110> direction, while much greater variation in the TCf was observed among the devices aligned against the <;100> direction. For the SE mode, the devices in both <;100> and <;110> orientations exhibit similar TCf values for varying doping levels. These observations are supported by Keyes' theory and close agreement between experiments and simulations is shown.