Theory and Design of Phononic Crystals for Unreleased CMOS-MEMS Resonant Body Transistors

Resonant body transistors (RBTs) are solid state, actively sensed microelectromechanical systems (MEMS) resonators that can be implemented in commercial CMOS technologies. With small footprint, highQ, and scalability to gigahertz frequencies, they form basic building blocks for radio frequency (RF) front-ends and timing applications. Toward the goal of seamless CMOS integration, this paper presents the design and implementation of phononic crystals (PnCs) in the back-end-of-line (BEOL) of commercial CMOS technologies with bandgaps in the gigahertz frequencies to be used for enhanced acoustical confinement in CMOS-RBTs. Lithographically defined PnC dimensions allow for bandgap engineering, providing flexibility in resonator design, and allowing for multiple frequencies on a single chip. The theoretical basis for analyzing generic PnCs is presented, with focus on the special case of implementing PnCs in CMOS BEOL layers. The effect of CMOS process variations on the performance of such PnCs is also considered. The analysis presented in this paper establishes a methodology for assessing different CMOS technologies for the integration of unreleased CMOS-MEMS resonators. This paper also discusses the importance of uniformity of the acoustical cavity in the nonresonant dimension and its effect on overall resonator performance. A PnC implementation in IBM 32-nm silicon on insulator (SOI) BEOL layers is demonstrated to achieve 85% fractional-bandgap ~4.5-GHz frequency. With better energy confinement, the proposed CMOS-RBTs achieve a quality factor Q of 252, which corresponds to 8× improvement over the previous generation RBTs, which did not include PnCs. The presented devices have a footprint of 5 μm × 7 μm. This paper concludes with a discussion of the properties required of a CMOS technology for high performance RBT implementation.