Thermal boundary layer limitations on the performance of micromachined microphones

Abstract

This work examines the extent to which thermal boundary layer effects limit the performance of micromachined microphones. The acoustic impedance of the cavity formed by the microphone enclosure is calculated using both analytical and finite-element methods. A thermal correction to the cavity impedance is included to account for the transition of compression and expansion within the enclosure from adiabatic to isothermal when the thermal boundary layer that forms at the walls of the enclosure becomes large compared to the enclosure dimensions. The thermal correction to the cavity impedance contains a resistive term that results from thermal relaxation losses and contributes thermal-acoustic noise to the system. A lumped-element network model for the microphone response which includes the thermally corrected enclosure impedance is presented and compared to measured results for a case study device. The relative noise power contribution of each noise source considered in the model is calculated. It is shown that the noise due to the resistive term of the enclosure cavity impedance becomes significant when the enclosure volume is small. This sets a theoretical limit on the noise floor that can be achieved by a micromachined microphone with given enclosure dimensions.

A Novel MEMS Capacitive Microphone with Semiconstrained Diaphragm Supported with Center and Peripheral Backplate Protrusions

“…Equation ( 16) assumes the wall to be an isothermal boundary and ignores the influence of adjacent walls. The thermally corrected impedance for a thin parallelepiped enclosure with a height 2a is given by Equation ( 16) [33]:…”

“…βa (16) where C a is the adiabatic compliance of the air volume, β = jωρ 0 C p k , ρ 0 is the density, k is the thermal conductivity, γ is the ratio of specific heats for gas inside the enclosure, and C p is the specific heat at constant pressure of the gas inside the enclosure. For a more detailed discussion on this topic, see [33].…”

A Behavioral Non-Linear Modeling Implementation for MEMS Capacitive Microphones

“…3, the equivalent circuit is a coupled model for acoustical, mechanical and electrical energy domains. The model includes sound port geometry impedance elements as per [15] and back volume acoustic impedance defined as a ladder network [16] - [17]. The MEMS large signal block couples the acoustic and mechanical domains with the diaphragm effective area as the transduction coefficient.…”

Numerical simulations on the performance of optical-acoustic sensors of minimal dimensions

“…Finally, we present the coupled problem of diaphragm vibrations and thermoacoustics. Thermoacoustic effects on the movement of the diaphragm are the subject of papers [16][17][18][19][20][21][22].…”

“…A small gap between the diaphragm and the backplate is necessary to enhance sensitivity. As described by [19], thermal boundary limitations can affect the performance of micromachined microphones. In contrast, the optical-acoustic sensor does not require a backplate.…”