Effects of material and dimension on TCF, frequency, and Q of radial contour mode AlN-on-Si MEMS resonators

This paper investigates the effects of material and dimension parameters on the frequency splitting, frequency drift, and quality factor (Q) of aluminium nitride (AlN)-on-n-doped/pure silicon (Si) microelectromechanical systems (MEMS) disk resonators through analysis and simulation. These parameters include the crystallographic orientation, dopant, substrate thickness, and temperature. The resonators operate in the elliptical, higher order, and flexural modes. The simulation results show that i) the turnover points of the resonators exist at 55 ​°C, –50 ​°C, 40 ​°C, and –10 ​°C for n-doped silicon with the doping concentration of 2 ​× ​10¹⁹ ​cm^–3 and the Si thickness of 3.5 ​μm, and these points are shifted with the substrate thickness and mode variations; ii) compared with pure Si, the modal-frequency splitting for n-doped Si is higher and increases from 5% to 10% for all studied modes; iii) Q of the resonators depends on the temperature and dopant. Therefore, the turnover, modal-frequency splitting, and Q of the resonators depend on the thickness and material of the substrate and the temperature. This work offers an analysis and design platform for high-performance MEMS gyroscopes as well as oscillators in terms of the temperature compensation by n-doped Si.