Local work functions of clean tungsten surfaces under electric fields based on ab initio calculations

Tungsten, the common choice for vacuum tube filaments, can survive under high temperatures and provide thermionic emission of electrons. However, the emission is largely limited due to its relatively high work function (approximately 4.5 eV). First principles or ab initio calculations are used to study the local work functions of tungsten (W) clean (100), (110), and (111) surfaces under external electric fields. The authors have systematically tested the convergence of density-functional-theory (DFT) calculations in the local-density approximation (LDA) and generalized-gradient approximation (GGA) with a planewave basis set the projector-augmented wave method as implemented in the Vienna Ab-initio Simulation Package (VASP). Several pseudo-potentials have been tested for comparison. With the tungsten model under electric fields applied on both sides, we can investigate the dependence of the local work function and effective work function on field strength. In addition to thermionic emission, tungsten has been considered for use as a field emission (FE) electron source.