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

Measured field electron emission (FE) current–voltage I m ( V m ) data are traditionally analysed via Fowler–Nordheim (FN) plots, asln { I m/ V m 2 } versus 1/ V m . 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 plot has the form ln ⁡ { I m/V m ( 2 − η / 6 ) } versus 1/ V m , where η ≅ 9.836239 (eV/ ϕ ) 1/2 and ϕ is the local work function. Modern (twenty-first 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 I m ( V m ) data (among them, use of ‘smooth planar emitter methodology'). Careful use of MG plots could also help remedy other problems in FE technological literature. It is suggested that MG plots should replace FN plots.