Atomic-scale stick-slip through a point defect

We have derived a series of analytical formulas describing the motion of a nanotip elastically driven across a Gaussian potential well of depth U₁ and half width σ. The tip gets pinned if the impact parameter y₀ is below a well-defined threshold value. Together with U₁ and σ, this value determines the pinning force. The scenario is slightly modified by superimposing a periodic potential with amplitude U₀ in the background, provided that U₀U₁. The formulas presented here can be applied to estimate the pinning energy and the linear extension of the perturbation created by a point defect such as an atomic vacancy on a crystal surface from atomic-scale friction force measurements performed by scanning probe microscopy.