Pull-in characteristics of electromechanical switches in the presence of Casimir forces: Influence of self-affine surface roughness

In this work we explore the influence of self-affine roughness on the pull-in parameters for switches used in micro/nanoelectromechanical devices in the presence of the Casimir force. The pull-in parameters are described, respectively, by the ratios of the Casimir and electrostatic forces with respect to that of an elastic restoring force. It is shown that the roughness exponent H, which for self-affine roughness characterizes the degree of surface irregularity at short length scales, has significant influence on the Casimir force and consequently on the pull-in parameters. Indeed, significant changes of the ratio of the Casimir to restoring force take place for roughness exponents H <0.5, while larger exponents (> 0.5) have an effect that saturates rather fast especially for values close to that of a smooth hill-valley topography (H similar to 1). For the ratio of the electrostatic to restoring force, the influence of the roughness exponent H is less prominent for relatively large normalized plate separations (with respect to the initial separation in the absence of any forces). In any case, the largest influence of the roughness exponent H on the ratio of the Casimir to restoring force takes place for relatively weak electrostatic forces