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

Abstract

Resonant body transistors (RBTs) are solid state, actively sensed microelectromechanical systems (MEMS) resonators that can be implemented in commercial CMOS technologies. With small footprint, high-Q, 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-ofline (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.[2014-0364] IndexTerms-CMOS-microelectromechanical systems (MEMS), radio frequenty (RF) MEMS, resonators, resonant body transistor (RBT), phononic crystals.

Three-Dimensional Nano-Acoustic Bragg Reflectors for CMOS Embedded NEMS

“…This shows the extreme importance of performing 3D simulations to have a better estimation of the behavior of the designed structures. This is in contrast with some previous works in the literature which have only performed 2D simulations [19,28,29]. Comparing Figure 3.d with Figure 3.b offers also a visual proof that the confinement in 3D is not as good as in the case of 2D.…”

“…A similar point has already been made before comparing performance within different CMOS nodes [19]. In this case, the comparison is done by only changing the material properties and not the critical dimensions associated with the node.…”

“…In this case, a purely hybrid CMOS-MEMS is developed, and the integration is optimized as no post-processing is required. This approach was first introduced by Weinstein et al [19,20], where they defined the resonator using front-end-of-line (FEOL) layer(s), i.e. using silicon as the structural material, in the same way that had been already demonstrated before using an in-house technology [21].…”

“…The release is partially bypassed by creating an acoustic bandgap using a phononic crystal (PnC) structure (acoustic metamaterial) [22] the bottom substrate, only the buried oxide layer is present. These devices were successfully fabricated and exhibited a maximum quality factor of 252 at a frequency of almost 3 GHz [19], dropping from a quality factor close to 1000 according to simulations. Most of the acoustic energy loss is due to dissipation through the substrate, as the acoustic shielding is very poor.…”

Release-free silicon-on-insulator cavity optomechanics

“…This makes obtaining total internal reflection of mechanical waves in silicon clad with silicon oxide impossible. One approach to obtaining confinement that has been used in piezoelectric bulk acoustic wave devices [7] and more recently in silicon resonant body transistors [8] is to pattern a mechanical reflector directly into the substrate to prevent the mechanical waves from leaking away. A different approach is to sufficiently reduce the mechanical wave propagation phase velocity in the silicon layer so that the leakage is eliminated.…”