## Coupled electrothermomechanical analysis of hybrid actuation in microsystems

## Citation

, "Coupled electrothermomechanical analysis of hybrid actuation in microsystems", *10th US National Congress on Computational Mechanics*, July 16-19, 2009

## Abstract

Bimorph-type electrothermal actuators are widely used in microelectromechanical systems (MEMS) to produce large displacements/forces using low drive voltages. However they are not ideal for applications where a constant deflection is to be maintained for significant periods of time because they consume a lot of power. Electrostatic actuators are preferred for low-power applications, but they typically require much higher drive voltages to produce the same displacement. In this paper, we develop a novel actuation design that integrates these two classes of actuators to combine the benefits of low drive voltage and low power operation. Previous work in this area focused on using electrothermal actuation in an RF-MEMS switch to close the switch contact and then shifting to electrostatic force as a low power latching mechanism to maintain the contact. We argue that it is possible to increase the efficiency of operation by intimately coupling the two actuation mechanisms so that they are both active at the same time. We develop a steady state model for hybrid electrothermomechanical actuators that accounts for the coupled interaction in electrical, thermal and mechanical domains. To solve for the mechanical displacement, we perform a geometrically nonlinear analysis on the structure. Motion in the actuator is governed by thermal stresses in the entire body and traction on the boundary that results from electrostatic pressure. We solve the steady state inhomogeneous current conduction equation to obtain the electric potential in the entire domain, which is used to calculate both the Joule heating inside the actuator as well as the electrostatic traction on its boundary. The Joule heating serves as the source term for thermal analysis to compute the temperature distribution in the actuator, which yields the thermal stress. Finite element method is used for thermal and mechanical analysis. The current conduction equation is solved on the entire domain, including the dielectric medium surrounding the electrodes. To reduce computational cost, we transform this equation into a boundary integral form defined on the electrode surfaces, which facilitates the use of a boundary element method for the electric potential. We perform a numerical analysis of a few test cases to demonstrate that hybrid actuation improves efficiency by achieving the same displacement using smaller drive voltages than those needed by pure electrothermal or electrostatic actuation. The hybrid ETM model is able to compute electrothermal and electrostatic forces in the presence of potential gradients in the electrodes. By merely changing the potential boundary conditions, we are able to transition between electrothermal and electrostatic configurations. Thus we see that the hybrid ETM model opens up a new class of actuators that combine the advantages of low drive voltage and low power consumption, while improving efficiency.