Simulating multiscale gated field emitters -- a hybrid approach

TL;DR

This paper presents a hybrid simulation approach for multiscale gated field emitters, combining electrostatic modeling and particle tracking to accurately capture local fields and space charge effects in complex geometries.

Contribution

It introduces a hybrid modeling framework that integrates COMSOL and PASUPAT for simulating multiscale gated cathodes with space charge effects, addressing scale variation challenges.

Findings

The generalized cosine law holds locally near the emitter tip.

The hybrid model accurately predicts charge emission and space charge effects.

Validation against theoretical models confirms the approach's effectiveness.

Abstract

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