Analytical modelling of MEMS Z-axis comb-drive accelerometer

One of the most crucial step in designing of MEMS devices is modelling. It allows estimating the performance of a device without its fabrication and it provides fast optimization process. Very often it is desired to perform a coupled electromechanical simulation when a device integrates sensor and read-out circuit. A classical method uses FEM simulation. Although it is very precise, it requires building 3-D model, solving complex equations and does not provide electrical simulation of IC circuit. Therefore, there are other commercial solutions available on the market that may be coupled with CADENCE environment. In this paper, we propose to use an analytical model that can be exported to CADENCE as a black-box cell described in Verilog-A language. As an example, we take MEMS Z-axis comb-drive accelerometer whose mechanical part behave like an torsional harmonic oscillator. We include also the influence of fringing field. The model is compared with MEMS+ software in terms of electrical parameters that are inputs for electrical simulation of read-out circuit.