Square-extensional mode single-crystal silicon micromechanical RF-resonator

Abstract

A micromechanical 13.1 MHz bulk acoustic mode (BAW) silicon resonator is demonstrated. The vihration mode can be characterized as a 2-D plate expansion that preserves the original square shape. The prototype resonator is fabricated of single-crystal silicon by reactive ion etching a silicon-on-insulator (SOI) wafer. The measured high quality factor ( Q = 130000) and current output (&AX 160 PA) make the resonator suitable for reference oscillator applications. An electrical equivalent circuit based on physical device parameters is derived and experimentally verified.

Nonlinear Limits for Single-Crystal Silicon Microresonators

“…While the triangle is rather crude approximation to the mode shape given by (11), it allows easy order of magnitude estimation of the nonlinear spring force. The beam tensioning due to the elongation is and the resulting force in -direction is (13) Thus, the nonlinear mechanical spring is (14) Finite element analysis shows that this simple estimate is accurate within 30% for a typical bridge microresonator. The critical vibration amplitude given by (8) is for a 13 MHz bridge resonator with and dimensions of , , and .…”

“…Both the beam and plate BAW resonators show high quality factors exceeding 100 000 and operate at 11.7 MHz and 13.1 MHz respectively. Further details of these resonators are provided in [2] and [14].…”

Focussed ion beam based fabrication of micro-electro-mechanical resonators

“…Silicon micro-electro-mechanical (MEM) resonators have shown performances comparable to those of quartz resonators (Kaajakari et al 2003;Yu-Wei et al 2004) but they offer the advantage of higher levels of integration in electronic circuits. The research effort for these devices is currently focused on rather thick layers combined with deep sub-micron gaps (also referred to as nanogaps), as this allows reduction of the resonator's equivalent resistance (Kaajakari et al 2003).…”

Stability of wafer level vacuum encapsulated single-crystal silicon resonators

“…The vibration of the square-extensional (se) resonator ( Figure 3(a)) is characterized as plate expanding and contracting in-plane while preserving the square shape [8], [9]. The side length of the resonator corresponds to the half acoustic wavelength.…”

“…Unfortunately, the power handling capacity of clamped-clamped resonators limit the achievable phase noise [6], [7]. Orders-of-magnitude larger power handling capacity has been obtained with a bulk acoustic mode (BAW) silicon resonators leading to noise floor of -150 dBc/Hz at 13 MHz meeting the typical phase noise requirements for wireless communication [8], [9]. Recently, comparable noise performance has been obtained with a polycrystalline silicon disk resonator and integrated electronics [10].…”