Quantum Correction to the Work Functions of Clean Tungsten Surfaces under Electric Fields

Tungsten has a relatively high work function, electron emission is largely limited. In this work, first-principles calculations are used to study the work functions of tungsten (100), (110), and (111) surfaces under different electric fields. We have carefully and systematically tested the convergence of density-functional-theory (DFT) calculations in the local-density approximation (LDA) and generalized-gradient approximation (GGA) with a plane-wave basis set with the projector-augmented wave (PAW) method as implemented in the Vienna ab initio simulation package (VASP). Detailed study of field emission by using VASP is performed and it is found when we increase the electric field strength, the work functions of tungsten surfaces are reduced accordingly. A new scaling law of work function reduction due to the charge transfer near the metal/vacuum interface caused by external electric field is obtained. The quantum effect is different from the classical Schottky effect of lowering work function due to an external electric field. With the quantum correction, the predictions of Richardson-Dushman and Fowler-Nordheim equations under strong electric fields for thermionic and field emissions, respectively can be improved.