Interatomic force laws that corrupt their own measurement

TL;DR

This paper investigates the ill-posed nature of force recovery in frequency-modulation AFM, showing how force law concavity affects measurement reliability and proposing conditions to ensure robust atomic-scale force spectroscopy.

Contribution

It identifies the role of force law concavity in causing ill-posed measurements and provides practical conditions to mitigate this issue, enhancing AFM force measurement accuracy.

Findings

Concavity of force law affects measurement stability.

Rapid concavity changes induce unphysical artifacts.

Experimental verification of conditions to prevent ill-posedness.

Abstract

Atomically-resolved imaging and force measurements using the atomic force microscope (AFM) are performed most commonly in a frequency-modulation (FM) mode. This has led to spectacular results, including direct observation of the atomic structure of complex molecules and quantification of chemical and frictional forces at the atomic scale. We address here a critical question: Is recovery of force from the measured frequency shift experienced by the AFM cantilever ill-posed - that is, unreliable in the presence of (unavoidable) measurement uncertainty? Resolution of this issue underlies all force measurements using FM-AFM, but remains outstanding. It is shown that concavity of the force law's distance dependence controls ill-posed behavior, with a rapid concavity change corrupting force measurements by inducing spurious and unphysical effects - such rapid change is not uncommon. Practical conditions to eliminate ill-posed behavior are formulated which are verified experimentally. This study lays the foundations for robust atomically-resolved force spectroscopy and future work that will seek to regularize ill-posed force measurements.