Non-equilibrium thermodynamics of thermionic emission processes in   abrupt semiconductor junctions, including the effects of surface states
  The methods of non-equilibrium thermodynamics of systems with an interface have been applied to the study of thermionic emission processes in abrupt semiconductor junctions, including the effects of surface states . Our analysis covers different situations of interest, concerning unipolar and bipolar systems, either degenerate or not, with or without interface states and under steady and non-steady conditions. In this way, a complete phenomenological modelling of thermionic emission-interface states processes has been proposed, overcoming some of the inherent limititations of the currently existing models. 
G. Gomila, A. Perez-Madrid and J.M. Rubi