Stochastic surface effects in nanobeam sensors

This work analyzes the statistical properties of nanobeam deflections due to stochastic surface stresses, induced by the surface adsorption/desorption of surrounding particles. A mechanical model for a heterogeneous nanobeam is first introduced. The model considers combined axial forces and bending moments due to non-uniform surface effects. Then, local surface interactions are statistically derived from the Langmuir interaction model and their corresponding stochastic surface stresses are introduced. Two types of nanobeam sensor are studied: a cantilever beam with pure surface bending effect and a clamped beam with mixed surface force and bending moment effects. The advantages of each type are discussed. The deflection statistics are found analytically and validated by Monte Carlo simulations. An analytical relation between the adsorption/desorption rates and the maximum deflection variance is found.