Numerical studies of variations in the gap and finger width ratio and travelled distance for the driving force of a radio-frequency microelectromechanical system device using the dual boundary element method

Abstract

Abstract

For the comb-drive design of microelectromechanical systems (MEMSs), the driving force due to the electrostatic field is very important, and an accurate electrostatic analysis is essential and indispensable. For various gaps, finger width ratios and travelled distances of the comb drive of MEMSs, the dual boundary element method (DBEM) has become a better method than the domain-type finite element method because the DBEM can provide a complete solution in terms of boundary values, with substantial saving in modelling effort. In this article, the DBEM is used to simulate the fringing field around the edges of the fixed and movable fingers of the comb drive of an MEMS for diverse design cases, and many electrostatic problems for typical comb drive designs of MEMSs are analysed, investigated and compared with a widely used approximate method. Results show that the driving force is obviously dependent on the travelled distance, and the approximate method cannot work well for all travelled positions because there is an apparent error (not less than 10 per cent), especially at the beginning and ends of the range of travel. In addition, the smaller the gap between movable and fixed fingers, the larger the driving force is, and the error of approximate method also becomes more and more predominant as the gap decreases. The results also demonstrate that the difference between the DBEM and the approximate method effect due to finger width ratio is very small. Using the DBEM presented in this article, an accurate and reasonable electrostatic field can be obtained, and the follow-up control method of driving force for the comb drive of an MEMS can be implemented more precisely.