Influence of random roughness on cantilever curvature sensitivity

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.