Capillary condensation and quantum vacuum effects on the pull-in voltage of electrostatic switches with self-affine rough plates

In this work, we study the influence of capillary forces in combination with electrostatic and quantum vacuum generated forces on the pull-in voltage of microswitches having self-affine rough surfaces. This type of roughness is described by the rms roughness amplitude w, the in-plane correlation length ξ, and the roughness exponent H that quantifies the degree of surface irregularity at short length scales (<ξ). It is shown that an attractive capillary force decreases more the effective pull-in voltage when the plate surfaces are rougher. The latter corresponds to smaller roughness exponents H and/or larger long wavelength roughness ratios w∕ξ. Notably, the capillary contribution increases the sensitivity of the effective pull-in voltage on the roughness exponent H. This behavior takes place for values of H close to its experimental accuracy.