Use of Capacitors in MEMS Accelerometers

This report was for a physics research project on capacitors to practice my citations.

What is MEMS?

Fig. 1 Diagram of a capacitive accelerometer.

Micro-electromechanical systems (MEMS) is a technology which combines mechanical and electrical parts into silicon-based, microscopic devices. These devices are typically made from a processing unit and a sensing unit. This sensing unit can either be capacitive or ohmic. The following report covers how the sensing unit of a capacitive MEMS accelerometer works, and the maths behind it.

How does a MEMS accelerometer work?

Any accelerometer is made of three components: a proof mass, a suspension system, and a sensing system. When the proof mass shifts relative to its original position, its displacement will be proportional to the applied acceleration. This movement will alter a property of the sensing element, which is then measured in some way. (SkyMEMS, 2025)
For a capacitive MEMS accelerometer, the sensing element is a parallel plate capacitor formed from the movable proof mass and a fixed conductive electrode separated by a small gap (Yazdi et al, 1998). When the device undergoes acceleration, the distance between the proof mass and the electrode will vary, altering the capacitance. This can then be read and understood by the processing unit.

How can the acceleration be found from variations in capacitance?

Fig. 2 Diagram of spring-mass system.

To determine the acceleration of the proof mass, relative to the accelerometer’s frame, the properties of the suspension system can be used to turn the variations in capacitance to changes in acceleration. If we simplify the suspension system such that it can be considered as a simple spring of spring constant k. When the proof mass moves due to an acceleration the spring will extend. This extension can be used to determine the force exerted on the spring using:

F=kΔxF=k\Delta x

Since this force was exerted on the spring by the proof mass, there will be an equal and opposite force exerted on the proof mass by the spring. This can be used to determine the acceleration of the proof mass: (Johnson, 2013)

F=maF=ma
ma=kΔxma=k\Delta x
a=kΔxma=\frac{k\Delta x}{m}
Fig. 3 Diagram of varying capacitance

In order to turn the variation in  into a value which can be measured, we will use the capacitance between the proof mass and the fixed conductive electrode. The capacitance of a parallel plate capacitor can be found using the equation: (Johnson, 2013)

C=Kϵ0AdC=K\epsilon_0\frac{A}{d}

In an ideal situation, only  will vary, so it can be said that  for the spring. This can then be substituted to determine a relationship between acceleration of the accelerometer and capacitance:

ΔC=Kϵ0AΔx\Delta C=K\epsilon_0\frac{A}{\Delta x}
Δx=Kϵ0AΔC\Delta x=K\epsilon_0\frac{A}{\Delta C}
a=kmKϵ0AΔCa=\frac{k}{m}\frac{K\epsilon_0A}{\Delta C}
a=kKϵ0Am1ΔCa=\frac{kK\epsilon_0A}{m}\frac{1}{\Delta C}

so it can be shown that:

a∝1ΔCa\propto\frac{1}{\Delta C}

Sources

Johnson, C. (2013). Process Control Instrumentation Technology, 8th ed., Harlow, Pearson Education Limited


SkyMEMS (2025), How does a MEMS accelerometer work? [online] Last accessed 16 June 2026: https://www.skymems.com/how-does-a-mems-accelerometer-work/


Yazdi, N., Ayazi, F., Najafi, K. (1998), ‘Micromachined Inertial Sensors’, Proceedings of the IEEE, vol. 86, no. 8, pp. 1640-1659

Images are taken from (Johnson, 2013) and (Yazdi et al, 1998)

Oscar Giacalone

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