Acoustic, thermal, and viscous modes in MEMS perforated back plates

Abstract

The back plates of MEMS microphones are commonly perforated with holes with radii on the order of a few micrometers. The plates themselves are only a few micrometers thick. Acoustic propagation in small pores is usually described in terms of the fundamental acoustic mode whose solution can be derived using the Low Reduced Frequency method of Tijdeman. Higher order acoustic modes and the viscous and thermal modes are assumed to be highly attenuated and negligible in pores of longer tubes. Since the holes in MEMS are relatively short, it is possible that additional modes may be necessary to accurately calculate the acoustic losses in the back plate. To investigate this possibility, Rayleigh’s determinant is solved numerically and the behavior of the additional modes beyond the fundamental as the pore size is reduced determined. For larger tubes, all modes behave as expected, but as the tube radius is reduced, the higher order acoustic modes become non-physical, leaving only the viscous and thermal modes as possible contributors to the attenuation.