Field emission: calculations supporting a new methodology of comparing theory with experiment

Abstract

This paper provides a demonstration-of-concept of a new methodology for comparing field electron emission (FE) theory and experiment. It uses the parameter κ in the mathematical equation I m = CV m κ exp[– B / V m ] (where B and C are weakly varying or constants) that is taken to describe how measured current I m depends on measured voltage V m for electronically ideal FE systems (i.e. systems that (i) have constant configuration during voltage application and (ii) have I m ( V m ) given by the emission physics alone). Experimental parameter values ( κ m ) are used to compare two alternative FE theories, for which allowable (but different) κ ranges have been established. At present, contributions to the ‘total theoretical κ ’ made by voltage dependence of notional emission area are not well known: simulations reported here provide data about four commonly investigated emitter shapes. The methodology is then applied to compare 1928/1929 Fowler–Nordheim (FN) FE theory and 1956 Murphy–Good (MG) FE theory. It is theoretically certain that the 1956 theory is ‘better physics’ than the 1928/1929 theory. As in previous attempts to reach known correct theoretical conclusions by experimentally based argument, the new methodology tends to favour MG FE theory, but is formally indecisive at this stage. Further progress needs better methods of establishing error limits and of measuring κ m .