Quantification of in-contact probe-sample electrostatic forces with dynamic atomic force microscopy

Atomic force microscopy (AFM) methods utilizing resonant mechanical vibrations of cantilevers in contact with a sample surface have shown sensitivities as high as few picometers for detecting surface displacements. Such a high sensitivity is harnessed in several AFM imaging modes. Here, we demonstrate a cantilever-resonance-based method to quantify electrostatic forces on a probe in the probe-sample junction in the presence of a surface potential or when a bias voltage is applied to the AFM probe. We find that the electrostatic forces acting on the probe tip apex can produce signals equivalent to a few pm of surface displacement. In combination with modeling, the measurements of the force were used to access the strength of the electrical field at the probe tip apex in contact with a sample. We find an evidence that the electric field strength in the junction can reach ca. 1 V nm^-1 at a bias voltage of a few volts and is limited by non-ideality of the tip-sample contact. This field is sufficiently strong to significantly influence material states and kinetic processes through charge injection, Maxwell stress, shifts of phase equilibria, and reduction of energy barriers for activated processes. Besides, the results provide a baseline for accounting for the effects of local electrostatic forces in electromechanical AFM measurements as well as offer additional means to probe ionic mobility and field-induced phenomena in solids.