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We investigate the Allan variance of nanoresonators with random rough surfaces under the simultaneous influence of thermomechanical and momentum exchange noises. Random roughness is observed in various surface engineering processes, and it is characterized by the roughness amplitude w, the lateral correlation length ξ, and the roughness exponent 0<H<1. The roughness influence becomes significant for measurement time τA so that ωoτA∼1, with ωo the fundamental resonance frequency. The Allan variance increases significantly with increasing roughness (decreasing H and/or increasing ratio w∕ξ) if the quality factor due to gas collisions is smaller than the intrinsic quality factor associated with thermomechanical noise.

Allan variance of frequency fluctuations due to momentum exchange and thermomechanical noises