The required voltage and current to produce a desired displacement with a MEMS electrothermal actuator can vary considerably between devices due to manufacturing process variation. This article presents a case for using resistance change divided by the ambient temperature resistance (ΔR/R0) as the quantity sensed in a feedback system to control the displacement, and avoid either melting the actuator with over drive, or not producing the desired actuation with under drive. The electrical resistance of a MEMS thermal actuator was calculated using a resistivity model that includes both the extrinsic and intrinsic conduction mechanisms in silicon. The model also accounts for the change in resistivity due to the strain in the silicon resulting from the confinement of the actuator by the two mounting posts. Using the model, it was shown that ΔR/R0 is a unique function of the effective temperature over the operating temperature range. The displacement of the actuator was calculated from a simple model, and was used to generate plots of the resistance change versus displacement. These plots were compared with the nearly universal plot of ΔR/R0 versus displacement found experimentally for thermal actuators with a range of dimensions. The calculated and measured curves were in reasonable agreement.

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