Influence of random roughness on cantilever curvature sensitivity

TL;DR

This paper investigates how random surface roughness affects cantilever sensitivity to surface stress-induced curvature changes, providing analytical models to optimize sensing performance.

Contribution

It introduces analytical expressions linking surface roughness parameters to cantilever sensitivity, enhancing understanding and design of sensitive surface stress sensors.

Findings

Sensitivity decreases with increased roughness and local surface slope.

Analytical formulas enable direct application in sensing system design.

Sensitivity is influenced by roughness amplitude, correlation length, and Hurst exponent.

Abstract

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.