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Modelling a MEMS device


Micro-Electro-Mechanical-Systems and their variant Micro-Opto-Electro-Mechanical-Systems are typical objects that benefit from the use of simulation tools and expertise. They can act as a sensor or an actuator in the system they fit in, depending on their design. Modelling a MEMS device requires multiphysics capabilities in mechanics, electromagnetism, heat transfer or microfluidics. But acoustics simulation of a MEMS shows valuable information to help improve its design too. This is the case of MEMS mirrors.

Objectives from modelling a MEMS device

Found in several industries, MEMS mirrors make an essential part of video projectors. With the miniaturisation of portable devices and progress made to hardware and electronics, they even become a feature in some of our smartphones.

Besides mechanical and electrical behaviour of the MEMS, one can also investigate its noise. When activated, the MEMS mirror will vibrate at a resonance frequency. This concept is similar to the actuation of a piezoelectric transducer. These vibrations – many thousands per second – will produce some motion of air just near the mirror walls. And this motion will propagate to the surroundings as an acoustics wave thus making noise.

So, if one wants to prevent the microsystem to make too much noise, modelling and acoustics simulation can help control the sound pressure level measured.

Results from simulation and information extracted

Equations to model the acoustics of MEMS device

One can use linearised Navier-Stokes equations to solve for the pressure, velocity and temperature fluctuations around the MEMS. For miniaturised devices, one must account for viscous and thermal losses at a very short distance from the mirror walls. These losses occur in what we call boundary layers, similar to the layer we find in CFD simulations.
Size does not come from a geometrical aspect only, but also from the operating frequency of the system. Hence one derives the boundary layers from:

Viscous boundary layer size for acoustics simulation the viscous boundary layer
Thermal boundary layer size for acoustics simulation the thermal boundary layer
Where μ is the dynamic viscosity of air
ρ is the density of air
k is the thermal conductivity of air
Cp is the heat capacity of air
f0 is the operating frequency

Far-field sound pressure level

One can extract various data on various plots from such model of the MEMS device. The end user typically wanted to know the sound pressure level (SPL) from the frequency-domain simulation. This information is made available in the near-field but also in the far-field (outside of the computational volume) thanks to Helmholtz-Kirchhoff integral at the border.

The customer could visualise the magnitude and directivity of the SPL at 1 metre distance. Seeing the SPL was larger than 40 dB in some directions, it could modify the MEMS design accordingly and manufacture a final product which met the noise expectations.

Far-field sound pressure level

In this figure one can see SPL and the noise directivity at 1m from the MEMS. Red colours show largest SPL values and the shape of the coloured shell gives information about the direction.
Shell is partially cut to see the MEMS mirror in the centre (in grey and black colours).

Polar plot of SPL

The graphs shows the SPL in X = 0 plane and provides directivity and magnitude visualisation of the data. One can see the MEMS behaves like a dipole source and in which direction around it the SPL gets larger.

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