Zinc oxide thin films grown via atomic layer deposition have been under intense research for the past few years. Here we present a comprehensive density functional theory study on the atomic layer deposition of zinc oxide. The adsorption of diethyl zinc and subsequent surface reactions are studied on an ideal (100) ZnO surface as well as on a stepped surface in order to compare an ideal and a nonideal surface structures. Our results show that diethyl zinc adsorbs and reacts rapidly on the surface to form monoethyl zinc. Our calculations also show that the initial ligand-exchange reactions are preferred on the planar surface over the step surface. Further reaction from monoethyl zinc to adsorbed zinc atoms has a high reaction barrier. We present two surface structures for the saturated zinc oxide surface at the end of the diethyl zinc pulse corresponding to a low and a high temperature approximations that are in good agreement with the experiments.