The influence of surface topography on the electromechanical characteristics of parallel-plate MEMS capacitors

Variable parallel-plate microelectromechanical system (MEMS) capacitors have been used extensively in various applications. The performances of MEMS capacitors are traditionally predicted by considering the electrodes to be atomically smooth and, therefore, roughness effects are ignored. However, recent studies have shown the significant influence of surface topography on the performance and reliability of microelectronic capacitors and other solid-state devices. Hence, the objective of the present study is to yield insight into the impact of surface topography on the elecromechanical characteristics of MEMS capacitors. Specifically, closed-form analytical solutions are derived for the capacitance, electrostatic force, pull-in gap and voltage, electric field, and adhesion force by utilizing simple roughness representation. The significant effects of surface topography on the performance and reliability of MEMS capacitors are elucidated and discussed in the context of the presented results. Surface topography dominates the electromechanical characteristics of MEMS capacitors via the combinatorial influences of larger surface area and smaller effective gap between the electrodes. It is shown that adhesion forces, typically, have negligible influence on the pull-in phenomenon. More accurate description of the roughness by utilizing the statistical approach is also considered and a numerical example is presented for MEMS capacitors with polycrystalline silicon electrodes.