Theoretical assessment of transitions across thermionic, field, and space-charge-limited emission

As electron emission devices continue to push technological limits of device size, electric field, and temperature, characterization of device limitations due to thermionic (TE), field (FE), and space-charge-limited emission (SCLE) becomes increasingly important for device reliability and performance. While various theoretical studies have examined the transitions between any two of these mechanisms using asymptotic nexus theory and more detailed multiphysics solutions, a full assessment across all three regimes simultaneously using a single theory remains incomplete. Using a single-particle theory and the thermofield representation of current density, we derive equations that recover the asymptotic solutions for the Richardson-Laue-Dushman, Fowler-Nordheim, and Child-Langmuir laws for TE, FE, and SCLE, respectively. Various transitions are observed from this full solution, including TE to FE to SCLE, the Miram curve transitioning TE to SCLE, and the discovery of a field-enhanced Miram curve. Equating two of these asymptotic solutions yields a second-order nexus; a third-order nexus arises when all three asymptotic solutions match, yielding conditions for transitions from TE or FE to SCLE. We add Ohm's law and SCLE at pressure, modeled by the Mott-Gurney law, to nexus theory, generating diode parameter phase plots showing the areas of influence for all five mechanisms. This provides additional insight into mechanistic transitions to elucidate experimental results and guide system design under more extreme design requirements.