Effective AFM cantilever tip size: methods for in-situ determination

In atomic force microscopy (AFM) investigations, knowledge of the cantilever tip radius R is essential for the quantitative interpretation of experimental observables. Here we propose two techniques to rapidly quantify in-situ the effective tip radius of AFM probes. The first method is based on the strong dependency of the minimum value of the free amplitude required to observe a sharp transition from attractive to repulsive force regimes on the AFM probe radius. Specifically, the sharper the tip, the smaller the value of free amplitude required to observe such a transition. The key trait of the second method is to treat the tip-sample system as a capacitor. Provided with an analytical model that takes into account the geometry of the tip-sample's capacitance, one can quantify the effective size of the tip apex fitting the experimental capacitance versus distance curve. Flowchart-like algorithms, easily implementable on any hardware, are provided for both methods, giving a guideline to AFM practitioners. The methods' robustness is assessed over a wide range of probes of different tip radii R (i.e. 4 < R < 50 nm) and geometries. Results obtained from both methods are compared with the nominal values given by manufacturers and verified by acquiring scanning electron microscopy images. Our observations show that while both methods are reliable and robust over the range of tip sizes tested, the critical amplitude method is more accurate for relatively sharp tips (4 nm < R < 10 nm).