Surface roughness influence on the pull-in voltage of microswitches in presence of thermal and quantum vacuum fluctuations

In this work we investigate the influence of the combined effect from random self-affine roughness, finite conductivity, and finite temperature on the pull-in voltage in microswitches influenced by thermal and quantum vacuum fluctuations through the Casimir force and electrostatic forces. It is shown that for separations within the micron or sub-micron range the roughness influence plays a dominant role, while temperature starts to show its influence well above micron separations. Indeed, increasing the temperature leads to higher pull-in voltages since it leads to an increased Casimir force. The temperature influence is more significant for relatively large roughness exponent H ∼ 1, while its influence is significantly lower with increasing lateral roughness correlation length ξ or due to long wavelength surface smoothness.