# The Murphy-Good plot: a better method of analysing field emission data

## TL;DR

The paper introduces the Murphy-Good plot as a superior method for analyzing field emission data, providing more accurate parameter extraction compared to traditional Fowler-Nordheim plots, and argues it should replace them.

## Contribution

It presents the theoretical foundation and practical advantages of the Murphy-Good plot for analyzing field emission data, improving parameter extraction accuracy.

## Key findings

- MG plots are nearly straight for theoretical data.
- MG plots enable more precise extraction of emission parameters.
- The paper advocates replacing FN plots with MG plots in practice.

## Abstract

Measured field electron emission (FE) current-voltage Im(Vm) data are traditionally analysed via Fowler-Nordheim (FN) plots, as ln{Im/(Vm)**2} vs 1/Vm. These have been used since 1929, because in 1928 FN predicted they would be linear. In the 1950s, a mistake in FN's thinking was found. Corrected theory by Murphy and Good (MG) made theoretical FN plots slightly curved. This causes difficulties when attempting to extract precise values of emission characterization parameters from straight lines fitted to experimental FN plots. Improved mathematical understanding, from 2006 onwards, has now enabled a new FE data-plot form, the "Murphy-Good plot". This plots ln{Im/(Vm)**(2-({\eta}/6)} vs 1/Vm, where {\eta} depends only on local work function. Modern ("21st century") MG theory predicts that a theoretical MG plot should be "almost exactly" straight. This makes precise extraction of well-defined characterization parameters from ideal I_m(V_m) data much easier. This article gives the theory needed to extract characterization parameters from MG plots, setting it within the framework of wider difficulties in interpreting FE Im(Vm) data (among them, use of the "planar emission approximation"). Careful use of MG plots could also help remedy other problems in FE technological literature. It is argued MG plots should now supersede FN plots.

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Source: https://tomesphere.com/paper/1905.07585