How MEMS Capacitive Accelerometers Measure Acceleration

Micro-Electro-Mechanical Systems (MEMS) capacitive accelerometers are the tiny components that allow smartphones, fitness trackers, and automotive airbags to detect motion and orientation. This article explores the internal mechanics of these sensors, focusing on how microscopic interdigitated silicon combs shift during movement, alter electrical capacitance, and convert physical linear acceleration into readable digital signals for consumer electronics.

The Core Components: Proof Mass and Silicon Springs

At the heart of a MEMS capacitive accelerometer is a microscopic mechanical structure etched directly into a silicon wafer. The primary moving part is called the "proof mass" (or seismic mass).

This proof mass is suspended slightly above the silicon substrate by ultra-thin, flexible silicon beams that act as mechanical springs. Because of these springs, the proof mass is free to move back and forth along a specific axis when an external force is applied, while the surrounding silicon frame remains completely rigid and fixed in place.

What Are Interdigitated Silicon Combs?

To measure the movement of the proof mass, the sensor uses a series of microscopic "fingers" etched into the silicon. One set of silicon fingers extends outward from the movable proof mass. Another set of fingers extends inward from the fixed outer frame.

These two sets of fingers are "interdigitated," meaning they are interlocked like the teeth of two zippers or the fingers of twoclasped hands, without actually touching one another. There are microscopic air gaps between each movable finger and its neighboring fixed fingers.

In physics, two conductive plates separated by an insulator (in this case, air) form a capacitor, which stores electrical energy. Therefore, every pair of adjacent silicon fingers acts as an individual microscopic capacitor. By using hundreds of these interdigitated fingers—known as a comb drive—the sensor maximizes the surface area and creates a measurable amount of electrical capacitance in a space smaller than a grain of salt.

The Physics of Motion: Newton’s Second Law

When the consumer device experiences linear acceleration—such as a smartphone being tilted or a car suddenly stopping—Newton’s laws of motion take over.

As the device accelerates in one direction, the fixed frame of the MEMS sensor moves immediately with the device. However, due to inertia, the suspended proof mass resists this sudden change and lags behind. This causes the silicon springs to stretch or compress, resulting in a physical displacement of the proof mass relative to the fixed frame. Once the acceleration stops, the silicon springs pull the proof mass back to its neutral, centered position.

Measuring the Shift: Differential Capacitance

The physical shift of the proof mass directly changes the spacing between the interdigitated silicon combs.

Capacitance is inversely proportional to the distance between the conductive plates. When the proof mass shifts, its movable fingers move closer to the fixed fingers on one side, and further away from the fixed fingers on the other side.

• Decreased Gap: Where the fingers move closer together, the electrical capacitance increases.
• Increased Gap: Where the fingers move further apart, the electrical capacitance decreases.

MEMS accelerometers use a technique called "differential capacitance" to measure this change accurately. Instead of just measuring one side, the sensor compares the increasing capacitance on one side of the comb with the decreasing capacitance on the other. This differential approach cancels out environmental noise, such as temperature fluctuations, and doubles the sensitivity of the measurement.

Signal Conversion: From Picofarads to Digital Data

The change in capacitance between the silicon combs is extremely small, often measured in femtofards or picofarads (trillionths of a farad). By itself, this tiny analog electrical change is useless to a smartphone's main processor.

To make the data usable, the MEMS mechanical chip is packaged alongside an Application-Specific Integrated Circuit (ASIC). The ASIC continuously applies a high-frequency voltage to the silicon combs to monitor their capacitance. When the capacitance shifts due to acceleration, the ASIC detects the imbalance, amplifies the microscopic electrical signal, and converts the analog voltage into a clean, digital value.

Because the stiffness of the silicon springs and the mass of the proof mass are known constants, the ASIC can calculate the exact amount of force required to cause that specific capacitance change, outputting a precise linear acceleration value (measured in g-forces) to the device's operating system.