Combined short scale roughness and surface dielectric function gradient effects on the determination of tip-sample force in atomic force microscopy

The contribution of tip roughness to the van der Waals force between an atomic force microscopy probe tip and the sample is calculated using the multilayer effective medium model, which allows us to consider the relevant case of roughness characterized by correlation length and amplitude in the nanometer scale. The effect of the surface dielectric function gradient is incorporated in the tip-sample force model. It is concluded that for rms roughness in the few nanometers range the effect of short scale tip roughness is quite significant