Electroelastic field of a sphere located in the vicinity of a plane piezoelectric surface

The electric field generated by a scanning probe microscope is determined. Analytical expressions for the electroelastic field in a piezoelectric sample and the external electric field are derived for a spherical probe. It is demonstrated that the coupling of elastic and electrostatic fields in the piezoelectric material leads to energy redistribution between such fields. This circumstance causes variations in the normal component of the electric field strength at the interface and the capacitance of a probe.