We have derived a series of analytical formulas describing the motion of a nanotip elastically driven across a Gaussian potential well of depth $U_1$ and half width $\sigma$. The tip gets pinned if the impact parameter $y_0$ is below a well-defined threshold value. Together with $U_1$ and $\sigma$, this value determines the pinning force. The scenario is slightly modified by superimposing a periodic potential with amplitude $U_0$ in the background, provided that $U_0\ll U_1$. 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.

• Received 24 September 2023
• Revised 14 March 2024
• Accepted 25 March 2024

DOI:https://doi.org/10.1103/PhysRevB.109.134103