# Mathematical analysis of the operation of a scanning Kelvin probe

## TL;DR

This paper provides a mathematical framework for understanding and implementing the scanning Kelvin probe, focusing on deriving operational equations and discussing design considerations for contact potential difference measurements.

## Contribution

It introduces a detailed mathematical analysis of the Kelvin probe's operation and describes the implementation of the off-null method for accurate contact potential difference determination.

## Key findings

- Derived equations governing Kelvin probe operation
- Described implementation of off-null measurement method
- Discussed design considerations for improved accuracy

## Abstract

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.