Physics-Based Model for Nonuniform Thermionic Emission from Spatially Heterogeneous Cathodes

Experiments show that there exists a smooth roll-off or knee transition between the temperature-limited (TL) and full-space-charge-limited (FSCL) emission regions of the emission current density-temperature J - T (Miram) and current density-voltage J - V curve for a thermionic emission cathode. We construct a physics-based model for nonuniform thermionic emission, including 3-D space charge, patch fields, and Schottky barrier lowering effects, which can accurately predict the J - T and J - V curves for a given 2-D work function map of the cathode surface. Our model does not require empirical equations or a priori assumptions of a continuous distribution of work functions on the cathode surface. We find the smooth transition arises as a natural consequence of the physics of nonuniform emission. To predict the emission from commercial dispenser cathodes, we obtain the work function map by incorporating the surface grain orientation via electron backscatter diffraction (EBSD) and the orientation-specific work function values from density functional theory (DFT) calculations. The predicted J - T and J - V curves show excellent agreement with experiment, not only in TL and FSCL regions but also in the smooth TL-FSCL transition region. This model provides a method to predict the thermionic emission from the microstructure of a commercial cathode and improves the understanding on the nonuniform electron beam from spatially heterogeneous cathodes.