Optimal shape design of an electrostatic comb drive in microelectromechanical systems

Polynomial driving-force comb drives are synthesized using numerical simulation. The electrode shapes are obtained using the indirect boundary element method. Variable-gap comb drives that produce combinations of linear, quadratic, and cubic driving-force profiles are synthesized. This inverse problem is solved by an optimization procedure. Sensitivity analysis is carried out by the direct differentiation approach (DDA) in order to compute design sensitivity coefficients (DSCs) of force profiles with respect to parameters that define the shapes of the fingers of a comb drive. The DSCs are then used to drive iterative optimization procedures. Designs of variable-gap comb drives with linear, quadratic, and cubic driving force profiles are presented in this paper.