Physics-Based Model for Nonuniform Thermionic Electron Emission from Polycrystalline Cathodes

Abstract

A physics-based model that predicts the emitted current from thermionic cathodes is developed, which accurately spans from the temperature-limited (TL) to full-space-charge-limited (FSCL) regions. Experimental observations of thermionic electron emission demonstrate a smooth transition between TL and FSCL regions of the emitted-current-density-versus-temperature (J-T) (Miram) curve and the emitted-current-density-versus-voltage (J-V) curve. Knowledge of the temperature and shape of the TL-FSCL transition is important in evaluating the thermionic electron-emission performance of cathodes, including predicting the lifetime. However, there are no first-principles physics-based models that predict the smooth TL-FSCL transition region for real thermionic cathodes without applying a priori assumptions or empirical phenomenological equations that are physically difficult to justify. Previous work detailing the nonuniform thermionic emission found that the effects of three-dimensional space charge, patch fields (electrostatic potential nonuniformity on the cathode surface based on local work-function values), and Schottky barrier lowering can lead to a smooth TL-FSCL transition region from a model thermionic cathode surface with a checkerboard spatial distribution of work-function values. In this work, we construct a physics-based nonuniform emission model for commercial dispenser cathodes. This emission model is obtained by incorporating the cathode surface grain orientation via electron-backscatter diffraction and the facet-orientation-specific work-function values from density-functional-theory calculations. The model enables the construction of two-dimensional emitted-current-density maps of the cathode surface and corresponding J-T and J-V curves. The predicted emission curves show excellent agreement with experiment, not only in the TL and FSCL regions but, crucially, also in the 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 of the relationship between thermionic emission and cathode microstructure, which is beneficial for the design of vacuum electronic devices.