General formulation of thermal, field, and photoinduced electron emission

The canonical equations of electron emission are the Richardson-Laue-Dushman equation for thermionic emission, the Fowler-Nordheim equation for field emission, and the Fowler-Dubridge equation for photoemission. They are widely used and experimentally well vetted for the determination of current density from electron sources. While all three may be obtained from a general underlying formulation, they are treated as distinct as their domains of applicability do not overlap. Here, a tractable analytical model is given that not only devolves to the canonical equations, but also and more importantly is effective in the transition regions when the emission currents from tunneling, thermal emission, and/or photoemission become comparable but where the canonical equations are inapplicable. The resulting thermal-field-photoemission equation has application to emerging advanced electron sources as well as for emission models required by beam simulation codes.