  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 arising 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 strongly dominate cantilever response in
electromechanical measurements and produce signals equivalent to few pm of
surface displacement. In combination with modeling, the measurements of the
force were used to determine 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 junctions is limited by about 0.5 V/nm. This field can be
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.
