An analytical electrothermal model of a 1-D electrothermal MEMS micromirror

We have developed an analytical model that describes the steady-state thermal behavior of a 1-D electrothermal bimorph MEMS micromirror. The steady-state 1-D heat transport equation is used to solve for the temperature distribution of the device upon actuation. Three models are developed using different thermal conditions on the device. The models consider heat dissipation from conduction and convection and the temperature dependence of the actuator electrical resistor. The temperature distribution equation of each model is analyzed to find critical thermal parameters such as the position of maximum temperature, maximum temperature, average temperature, and equivalent thermal resistance. The simplest model, called the Case 1 model, is used to develop an electrothermal lumped element model that uses a single thermal power source. In the Case 1 model, it is shown that a parameter called the "balancing factor" predicts where the maximum temperature is located, the distribution of power flow, and the division of thermal resistances. The analytical models are compared to FEM simulations and agree within 20% for all of the actuation ranges and thermal conditions tested.