 If there is a large density of surface states, then the work function of the semiconductor will show a very weak dependence on doping or electric field.Theoretical modeling of the work function is difficult, as an accurate model requires a careful treatment of both electronic many body effects and surface chemistry; both of these topics are already complex in their own right.One of the earliest successful models for metal work function trends was the jellium model, which allowed for oscillations in electronic density nearby the abrupt surface (these are similar to Friedel oscillations) as well as the tail of electron density extending outside the surface.