Polarization Independent Band Gaps in CMOS Back-End-of-Line for Monolithic High-Q MEMS Resonator Confinement

To pave the way for system-on-chip MEMS confinement up to 50 GHz, the mechanical properties of a CMOS back-end-of-line (BEOL) are studied by analytic and finite element approaches. In particular, the two main directions of vertical and horizontal wave propagation are investigated. With respect to the symmetry of the BEOL, the movement through the nonperiodic horizontal layers is described by the Rayleigh-Lamb equation. It is shown that our finite element method (FEM) approach, preventing Brillouin zone folding, can be employed in simulations of these structures, since the results are in excellent accordance to the corresponding analytical solutions. The vertical propagation through the periodic stack on the other hand is subject to phononic crystal effects resulting in Bragg-like band gaps (BGs) for either a certain or every polarization. Factoring in both types of propagation, it is demonstrated by our FEM simulations how these BGs can be tailored to specific values through variations in the BEOL layers to improve the quality factor of monolithically integrated MEMS devices.