Fringing field modelling in MEMS capacitive comb-drive accelerometers

Modelling is a crucial step in designing MEMS devices. It is needed to estimate the device performance without its fabrication. Initially, simple calculations are needed to verify the possibility of device production with a given performance and to know the basic parameters necessary to achieve the desired goals. Further, optimization is commonly performed in order to improve the design. Both steps require simulation methods that are very fast and precise enough to reduce time to market. In many cases, classical, precise FEM simulations are not necessary and simple analytical models are used. MEMS devices like accelerometers, commonly uses elements of simple shapes that can be easily described with simple analytical formulas. However, analytical modelling is getting more complicated in case of capacitive transduction. Typically, these devices operate in the range of linear response but nothing can be done to avoid the influence of non-uniform electric field. Due to fringing field, a capacitance is often underestimated when using classical parallel plate formula. Therefore, there is a need for proper fringing field modelling. In this chapter, analytical modelling of fringing field on an example of MEMS accelerometer is presented. Specific structure type known as comb-drive consists of many small capacitors that enhance the impact of fringing field. Accelerometers in all axes are analyzed. Moreover, Z-axis accelerometer induces different electric field distribution due to the use of thinned fingers. Thus, analytical formulas are derived for various conditions. Finally, the model is compared with Coventor MEMS+ and fabricated strictures are measured in order to validate analytical approach.