Distributed and lumped element models for a bimorph-actuated micromirror

A procedure to model electrothermally actuated devices is developed and demonstrated using a 1D scanning micromirror. The micromirror is actuated by thermal bimorphs and an embedded platinum (Pt) resistor is used for generating Joule heating. Electrothermal, thermal and thermomechanical models are developed and integrated to generate a compact electrothermomechanical model. The electrothermal model relates the thermal power generated in the device to the applied voltage. The thermomechanical model evaluates the mirror rotation angle. The thermal model is developed by drawing analogy between heat flow in the device and current flow through an electrical transmission line. It provides the temperature of the embedded heater and the bimorph actuators. The heat loss coefficient to the surrounding atmosphere is obtained from finite element (FE) simulations. The distributed thermal resistances are represented by an equivalent circuit model with a few elements. A simplification of the circuit model is proposed when small length scales are involved. Rotation angle per unit power input predicted by the circuit model has an error of less than 8% compared to experimental results.