  In this work we explore the influence of random surface roughness on the
cantilever sensitivity to respond to curvature changes induced by changes in
surface stress. The roughness is characterized by the out-of-plane roughness
amplitude w, the lateral correlation length x, and the roughness or Hurst
exponent H (0<H<1). The cantilever sensitivity is found to decrease with
increasing roughness (decreasing H and/or increasing ratio w/x) or equivalently
increasing local surface slope. Finally, analytic expressions of the cantilever
sensitivity as a function of the parameters w, x, and H are derived in order to
allow direct implementation in sensing systems.
