Analytical modeling for bulk-micromachined condenser microphones

Abstract

The advent of silicon micromachining technology has opened up numerous opportunities for the commercialization of many miniaturized sensors and one of the beneficiaries is the silicon condenser microphone. Simple analytical expressions, such as those formulated by Škvor/Starr for mechanical-thermal noise calculation, are used to describe the mechanical performance of a microelectromechanical system ͑MEMS͒ microphone. However, the location effect of acoustic holes is usually not considered on both frequency response and mechanical-thermal noise. In this paper, the theory of a condenser microphone is reviewed and a new analytical modeling method for the MEMS condenser microphones is proposed based on Zuckerwar's model. With reference to a B&K MEMS microphone, the theoretical results obtained by the modeling method are in very good agreements with those experimental ones reported. It is also concluded that there is an optimum location for acoustic holes in the backplate. Finally, a new design for MEMS microphone with a polarization voltage of 10 V is proposed, which has an open-circuit sensitivity of 2.1 mV/ Pa ͑or −54 dB ref. 1 V / Pa͒, a bandwidth of 18 kHz, an A-weighted mechanical-thermal noise of 22 dB A, and a signal-to-noise ratio of 60 dB. This proposed microphone can be easily micromachined by using MEMS technology such as the deep reactive ion etching and wafer bonding technology.

Performance Enhancement by Substrate Perforation for a Wafer-Level Encapsulated RF MEMS DC Shunt Switch

“…4um without holes 6um without holes 8um without holes lOum without hole -4um with holes -6um with holes 8um with holes lOumwith holes -= cosh!iarccosh V2f 1 (5) f1(x) = f2(x)[f2(x)-66]+3f3(26) (6) f2(x)=3x+26-1 (7) f3(X)=X2- (1) Coating & pattering of polymer, and cavity formation by DRIE backplate silicon (300 tm thick) is firstly spin-coated and patterned with a CYTOP bonding layer. A cavity with a depth of 150 tm is then generated by deep reactive ion etching (DRIE).…”

“…The damping coefficient (Ba), also termed as air resistance, of a diaphragm due to the viscous damping losses in the air gap and the damping holes is governed by following equation [5][6][7] (1)…”

An analytical-numerical method for determining the mechanical response of a condenser microphone

“…The analysis in paper 10 shows also that by modifying the gap to 10[lm] it is possible to build with the same technique new MEMS microphones for nonmeasurement applications.…”

“…For determining the mechanical performance of the microphone, by using the method developed by Zuckerwar, Miao et al, 10 considered a model with a circular backplate and round holes. The analysis in paper 10 shows also that by modifying the gap to 10[lm] it is possible to build with the same technique new MEMS microphones for nonmeasurement applications.…”

“…9. Tan and Miao 10 in 2006 reviewed the theory of condenser microphones and proposed a new analytical modeling method for the B&K MEMS condenser microphone. The theoretical results obtained by this method were found to be in very good agreement with the experimental results reported in the case of a B&K MEMS microphone in Ref.…”