Journal of Adhesion Science and Technology, Vol.20, No.10, 1125-1146, 2006
Surface-forces-driven instability of comb-drive microcantilevers in MEMS
Comb-drive structures consisting of two opposing arrays of microcantilevers have widespread use in MEMS. In this paper, a novel method is developed to study jump-to-together instability of such comb-drive microcantilevers, each of which is attracted by two neighboring microcantilevers through surface forces. Based on a representative spring model given in the Appendix, it is verified that equilibrium deflections of all intermediate microcantilevers (except those at the ends of the array) would be negligibly small because two attractions from two opposing sides are almost equal but opposite. Thus, when the end-effect of the microcantilevers at the ends of the array is neglected, the critical value of the beam-beam interaction coefficient for instability of the array is found to be exactly a half of the critical value of the interaction coefficient for instability of a pair of opposing microcantilevers. The dependence of the critical value on the overlap length of opposing microcantilevers is demonstrated for varying ratios of lengths and bending stiffnesses. Furthermore, the end-effect on the critical value for instability of the comb-drive microcantilevers is examined by quantifying the effect on instability of the amplified interaction coefficients between neighboring beams at the two ends. In particular, it is found that the end-effect lowers the critical value for instability by 25-40%, irrespective of the overlap length. Finally, the validity of the present methods is confirmed by the good agreement between the results obtained by the present methods for the spring system and the exact data obtained by iteration numerical method with relative errors less than 5% or 10%, depending on whether the accurate amplified interaction coefficients at the two ends are known or must be estimated approximately by a simple method.