Mathematical analysis of the operation of a scanning Kelvin probe

The scanning Kelvin probe is a tool that allows for the contactless evaluation of contact potential differences in a range of materials, permitting the indirect determination of surface properties such as work function or Fermi levels. In this paper, we derive the equations governing the operation of a Kelvin probe and describe the implementation of the off-null method for contact potential difference determination, we conclude with a short discussion on design considerations.