Ab-initio thermodynamics, as described e.g., by Reuter et al., starts with the assumption that interface structures are grown in thermal equilibrium. The adsorbed molecules are in thermodynamic equilibrium with an infinite reservoir of adsorbate molecules in gas phase. Together, the reservoir and the interface make up a thermodynamic system with a fixed number of particles. The surface and the reservoir share the same temperature, as they are in thermodynamic equilibrium. The pressure we consider in this thermodynamic system is the partial pressure of the adsorbate molecules being evaporated into the chamber for deposition. Furthermore, here we assume that the electric field F is constant and homogeneous within the whole gas phase reservoir.