Design of Capacitive Bulk-micromachined Accelerometers Using the Topology Optimization Method

A capacitive MEMS (Micro-Electromechanical Systems) accelerometer based on bulk-micromachining technology is generally fabricated using three wafers (glass, silicon, glass), bonded together one on top of the other, forming two sets of parallel plate capacitors: the middle layer is obtained by silicon etching processes and consists of an inertial mass supported by one or more beams (movable electrode); the top and bottom wafers form the fixed electrodes. The flexibility of the beams allows the mass to move proportionally to the external acceleration; the displacement is estimated by the change in capacitance of the two plates (differential measure). The design of such sensors is a complex task involving the maximization of the sensitivity, resolution, stability, bandwidth and the minimization of the power consumption, noise and cross-axis sensitivity. The main design parameters usually considered are: thickness of the gap, applied voltage, geometric dimensions of the inertial mass and beams, spatial configuration of the beams, thickness of the wafers, among others. In this paper, we apply the Topology Optimization Method (TOM) to the design of MEMS accelerometers using the SIMP (Solid Isotropic Material with Penalization) material model, in order to find the optimal topology for the middle layer of the sensor. The objective function is to maximize the sensitivity (V/g) and the bandwidth; a maximum volume restriction must also be satisfied. An algorithm implemented in Matlab uses the method of moving asymptotes (MMA) as optimizer and communicates with the software COMSOL to solve the finite element problem, which is based on the Reissner-Mindlin plate element, considering shear deformation, and the MITC (Mixed Interpolation of Tensorial Components) formulation. Finally, we present several topologies obtained for the sensor by varying the initial conditions.