New convergence scheme for self-consistent electromechanical analysis of iMEMS

The simulation of integrated micro-electromechanical structures (iMEMS) such as electrostatically driven microactuators often fails to converge due to the strong geometrical non-linearity of the electric potential. We present a new convergence scheme that uses a first-order approximation for the relation between the mechanical deformation and the electrostatic force derived from an electrostatic formulation using the boundary element method (BEM). The overall computational complexity per iteration is the same as with direct relaxation. A Newton update of the surface displacement solves otherwise divergent simulations and reduces the number of non-linear iterations for a self-consistent result. This allows efficient modelling of electromechanical actuators subject to strong deformations such as electrostatic comb-drives and deflectable micro-mirrors.