The physics of generalized Fowler-Nordheim-type equations

The aim here is to generalise the standard FN-type equation, so that the physical equation where the local emission current density (ECD) J is related to the barrier field F becomes clearer for metals. This is a preliminary need before the above equation can be fully linked with cold field electron emission (CFE) theory for non-metals. Each generalisation step needs stating in detail; this paper deals with the first few.