Use of energy-space diagrams in free-electron models of field electron emission

An improved method is reported for deriving the equations for cold field electron emission from a free-electron metal. It is shown that the derivation of these equations can be presented as a straightforward double integral in a space where the vertical axis represents the total electron energy, and the horizontal axis represents the component of electron kinetic energy parallel to the emitter surface. A general approach is developed that applies to a tunnelling barrier of any shape. It is shown that the temperature-correction factor derived by Murphy and Good for emission through an image-rounded barrier also applies to a more general barrier. For the standard image-rounded barrier the results coincide with those of Murphy and Good, but the derivation is more straightforward mathematically and the physics involved can be visualized more easily. The method developed here should be a good foundation for developing an improved theory of cold field electron emission from semiconductors: the main object of the paper is to lay this foundation. Copyright (C) 2004 John Wiley Sons, Ltd.