Contact angle influence on the pull-in voltage of microswitches in the presence of capillary and quantum vacuum effects

Capillary condensation between the electrodes of microswitches influences the effective pull-in voltage in a manner that depends on the contact angle of the capillary meniscus and the presence of plate surface roughness. Indeed, surface roughening is shown to have a stronger influence on the pull-in potential for relatively small contact angles with respect to that of a flat surface when capillary condensation takes place. For long wavelength roughness ratios w/ξ≪1 with w the rms roughness amplitude and ξ the in-plane correlation length, the pull-in voltage increases with increasing theoretical contact angle θ₀ for flat surfaces. With decreasing correlation length ξ (increasing roughness), the pull-in potential decreases faster for smaller contact angles θ₀ In addition, with decreasing roughness exponent H (0≪H≪1), which characterizes short wavelength roughness fluctuation at short length scales (≪ξ), the pull-in potential shows a steeper decrease with decreasing correlation length ξ. Finally, with increasing relative humidity, the sensitivity of the pull-in voltage at small correlation lengths attenuates significantly with increasing contact angle θ₀.