A phononic crystal strip based on silicon for support tether applications in silicon-based MEMS resonators and effects of temperature and dopant on its band gap characteristics

Phononic crystals (PnCs) and n-type doped silicon technique have been widely employed in silicon-based MEMS resonators to obtain high quality factor (Q) as well as temperature-induced frequency stability. For the PnCs, their band gaps play an important role in the acoustic wave propagation. Also, the temperature and dopant doped into silicon can cause the change in its material properties such as elastic constants, Young's modulus. Therefore, in order to design the simultaneous high Q and frequency stability silicon-based MEMS resonators by two these techniques, a careful design should study effects of temperature and dopant on the band gap characteristics to examine the acoustic wave propagation in the PnC. Based on these, this paper presents (1) a proposed silicon-based PnC strip structure for support tether applications in low frequency silicon-based MEMS resonators, (2) influences of temperature and dopant on band gap characteristics of the PnC strips. The simulation results show that the largest band gap can achieve up to 33.56 at 57.59 MHz and increase 1280.13 % (also increase 131.89 % for ratio of the widest gaps) compared with the counterpart without hole. The band gap properties of the PnC strips is insignificantly effected by temperature and electron doping concentration. Also, the quality factor of two designed length extensional mode MEMS resonators with proposed PnC strip based support tethers is up to 1084.59% and 43846.36% over the same resonators with PnC strip without hole and circled corners, respectively. This theoretical study uses the finite element analysis in COMSOL Multiphysics and MATLAB softwares as simulation tools. This findings provides a background in combination of PnC and dopant techniques for high performance silicon-based MEMS resonators as well as PnC-based MEMS devices.