Fowler–Nordheim-type equations, in the J - F form, are (approximate) theoretical equations derived to describe the local current density J emitted from the internal electron states in the conduction band of a bulk metal. The emission current density (ECD) J for some small uniform region of an emitting surface is usually expressed as a function J (φ, F) of the local work-function φ and the local barrier field F that characterize the small region. For sharply curved surfaces, J may also depend on the parameter(s) used to describe the surface curvature.