Shape Optimization of Eigenfrequencies in MEMS Gyroscopes

Microelectromechanical systems (MEMS) gyroscopes are widely used in consumer and automotive applications. They have to fulfill a vast number of product requirements which lead to complex mechanical designs of the resonating structure. Arriving at a final design is a cumbersome process that relies heavily on human experience in conjunction with design optimization methods. In this work, we apply node-based shape optimization to the design of a MEMS gyroscope. For that purpose, we parametrize the coordinates of the nodes of the finite element method (FEM) mesh that discretize the shapes of the springs. We then implement the gradients of the mechanical eigenfrequencies and typical MEMS manufacturability constraints, with respect to the design parameters, in a FEM code. Using gradient-based optimization we tune the gyroscope's frequency split and shift spurious modes away from the first three multiples of the gyroscope's drive frequency while manufacturability constraints are fulfilled. The resulting optimized design exhibits novel geometrical shapes which defy any human intuition. Overall, we demonstrate that shape optimization can not only solve optimization problems in MEMS design without required human intervention, but also explores geometry solutions which can otherwise not be addressed. In this way, node-based shape optimization opens up a much larger space of possible design solutions, which is crucial for facing the ever increasing product requirements. Our approach is generic and applicable to many other types of MEMS resonators.