A semi-analytical model of electron source potential barriers

A simple method of evaluating the potential barrier profiles (and therefore work function) of materials under applied field is developed. The methodology is designed to computationally expedient, flexible and therefore amenable to complications that occur such as surface structure (existence of nanoprotrusions), tunneling between layers ("internal field emission"), and the presence of adsorbates which will modify the dipole potential at the surface of an emitter. An iterative approach to finding that barrier height is developed, and the resulting density profiles used to evaluate the Exchange and Correlation potentials which give rise to the image charge lowering of the barrier under applied field.