Integration of MEMS resonators with CMOS to form a single chip allows operation at GHz-frequencies, while reducing size, weight, and power consumption of the overall system. This technology is a method for creating acoustic localization structures, such as PnCs and ABRs, to surround a MEMS resonator and form an acoustic cavity. PnCs are structures with periodic variations in space in their mechanical properties, which lead to the existence of frequency bandgaps. ABRs are composed of periodic layers which are usually two or more materials alternatively located in space. By applying ABRs on the side of unreleased resonator, it is possible to reestablish the desired free or fixed boundary condition. In CMOS technology, such material combinations are effectively created using metal layers, vias, and the dielectric used to electrically isolate neighboring metal layers which naturally surrounds the vias.