Confronting interatomic force measurements

The quantitative interatomic force measurements open a new pathway to materials characterization, surface science, and chemistry by elucidating the tip–sample interaction forces. Atomic force microscopy is the ideal platform to gauge interatomic forces between the tip and the sample. For such quantitative measurements, either the oscillation frequency or the oscillation amplitude and the phase of a vibrating cantilever are recorded as a function of the tip–sample separation. These experimental quantities are subsequently converted into the tip–sample interaction force, which can be compared with interatomic force laws to reveal the governing physical phenomena. Recently, it has been shown that the most commonly applied mathematical conversion techniques may suffer a significant deviation from the actual tip–sample interaction forces. To avoid the assessment of unphysical interatomic forces, the use of either very small (i.e., a few picometers) or very large oscillation amplitudes (i.e., a few nanometers) has been proposed. However, the use of marginal oscillation amplitudes gives rise to another problem as it lacks the feasibility due to the adverse signal-to-noise ratios. Here, we show a new mathematical conversion principle that confronts interatomic force measurements while preserving the oscillation amplitude within the experimentally achievable and favorable limits, i.e., tens of picometers. Our theoretical calculations and complementary experimental results demonstrate that the proposed technique has three major advantages over existing methodologies: (I) eliminating mathematical instabilities of the reconstruction of tip–sample interaction force, (II) enabling accurate conversion deep into the repulsive regime of tip–sample interaction force, and (III) being robust to the uncertainty of the oscillation amplitude and the measurement noise. Due to these advantages, we anticipate that our methodology will be the nucleus of a reliable evaluation of material properties with a more accurate measurement of tip–sample interaction forces.