Quantum Hydrodynamics Approach to Electron Emission Physics

The emission of charged particles from solid surfaces into electromagnetic devices remains a limiting technological challenge for high-power microwave devices, vacuum electronics sources, free-electron lasers, and particle accelerators, in addition to an area of fundamental physics study involving questions of electromagnetism and quantum mechanics. A particular challenge is understanding the fundamental role played by various solid-state physical quantities, such as the fermi level, work function, the charge exchange-correlation potential, the image charge potential, and the electron affinity in devices that also have free charge in vacuum adjacent to the material surface. These questions become particularly vexing when the energy in the applied electromagnetic field and the energy in the space-charge fields of the emitted particles become of comparable magnitude. While considerable progress has been made in practical models to see scaling laws for particle emission physics, as well as development of algorithms that support high-fidelity emission physics in large-scale particle-in-cell “gun-code” models, here, we strive to reconsider the fundamental nature of the solid-vacuum barrier in the context of a one-dimensional quantum hydrodynamics approach that employs an orbital-free dynamical density functional theory. In particular, we strive to separate the physical role of the image charge and the exchange-correlation potential. Our methods explicitly compare the fidelity of the basic Thomas-Fermi model, the Kirzhnits-corrected Thomas-Fermi model, the addition of an exchange-correlation functional, and finally all these components to isolate the role each of these models plays in the complex physical process of electron emission. In particular, we stress the role of boundary conditions and emphasize questions of steady-state and equilibrium behavior in an emitting high-power electron diode.