Unification of Photo- Thermionic, and Field Emission

Many theoretical studies have focused on unifying various electron emission mechanisms 1 due to their impact on numerous applications, including nano vacuum transistors, electric thrusters, multipactor, and time-resolved electron microscopy 2 . Recent theories have unified field emission through the Fowler-Nordheim (FN) law, space-charge limited emission (SCLE) in vacuum through the Child-Langmuir (CL) law, and SCLE with collisions through the Mott-Gurney (MG) law. 1 , 2 Subsequent studies extended this linkage to include Ohm’s law and thermionic emission through the Richardson-Laue Dushman (RLD) law 1,2,3 and then developed a complete non-dimensional scheme to link quantum SCLE through Paschen’s law 4 . This talk extends the prior theory linking thermionic emission 3 by replacing the general thermal field current density with the general thermal field photo current density to further assess photoemission through the Fowler-DuBridge (FD) equation. We numerically solve the current density as a function of voltage to demonstrate the transition between CL, MG, FN, RLD, and FD. We specifically outline the process for plotting each individual asymptotic solution as a function of temperature, laser frequency, mobility, or gap distance with the other parameters fixed to develop "nexus plots." Examining the nexuses between these asymptotic solutions determines whether we can use the simple emission laws to characterize emission behavior or we must resort to using either the full emission theory derived here or one of the previously derived coupled theories 1 , 3 .The implications of these results for determining operating conditions for practical devices for laser and plasma applications will be discussed.