Simulating multi-scale gated field emitters—A hybrid approach

Multi-stage cathodes are promising candidates for field emission due to the multiplicative effect in local predicted by Schottky conjecture and its recently corrected counterpart [Biswas, J. Vac. Sci. Technol. B 38, 023208 (2020)]. Due large variation length scales even a 2-stage compound structure consisting of macroscopic base microscopic protrusion, simulation methodology gated emitting diode needs be revisited. As part this strategy, authors investigate on surface emitter near apex find that generalized cosine law continues hold locally tip multi-scale cathode. This is used emit electrons with appropriate distributions position velocity components knowledge only electric at apex. The consistent contemporary free-electron model follow from joint distribution launch angle, total energy, normal energy. For geometry enhancement factor around 1000, hybrid where vacuum calculated using COMSOL imported into Particle-In-Cell code PASUPAT, module implemented. Space charge effects incorporated adaptation PASUPAT truncated “open electrostatic boundary” condition. space field, combined particle-emission tracking.