Experimental use of the inflection point test for force deconvolution in frequency-modulation atomic force microscopy to turn an ill-posed situation into a well-posed one by proper choice of amplitude

摘要

Frequency-modulation atomic force microscopy allows one to measure the force between a sharp tip and a sample and, ultimately, the force between two single atoms with outstanding precision. To extract forces from the measured frequency shifts, a deconvolution algorithm is required. Mathematically, the deconvolution problem is an inversion problem. It has been shown that deconvolution can be ill-posed, resulting in erroneous forces values. Whether the deconvolution is well-posed or ill-posed is determined by two factors: the shape of the force-distance curve and the oscillation amplitude used for the measurement. Recently, a test was proposed by Sader et al. [Nat. Nanotechnol. 13, 1088 (2018)] to determine whether a given deconvolution is well-posed for a specific amplitude. Here, we experimentally validate this test by means of two experimental situations measured with a set of different amplitudes: force-distance spectra over a single carbon monoxide molecule as well as over a Fe trimer on Cu(111). We verify the validity of the test by showing that for a given experimental situation, a specific amplitude may result in a well-posed deconvolution while a different amplitude might result in an ill-posed result. Furthermore, we comment on typical pitfalls that are caused by the discrete nature of experimental data and provide MATLAB code that can be used by everyone to perform this test with their own data.