On parameterizations of the Nordheim function

TL;DR

This paper reviews and proposes various parameterizations for the Nordheim function and its complement, which are crucial for modeling field emission phenomena.

Contribution

It introduces new parameterizations of the Nordheim function and its complement based on tabulated data, enhancing modeling accuracy in field emission studies.

Findings

New parameterizations improve fit to tabulated data.

Enhanced models facilitate better predictions of field emission.

Simplified formulas aid practical applications.

Abstract

Several parameterizations of tabulated values of the Nordheim function $\vartheta (y)$ and its complementary function $t(y)$ are proposed. The function $\vartheta (y)$ plays essential role in description of field emission.