Atomic layer deposition (ALD) has emerged as an important technique for thin film deposition in the last two decades. Zinc oxide thin films, usually grown via DEZ/H2O-process, have seen much interest both in application and in theoretical research. The surface processes related to the growth of the thin film are not entirely understood and the conceptual picture of the ALD process has been contradicted by recent experiments where ligands from the zinc pulse persist on the surface even after extended water pulse exposures. In this work, we investigate the overall growth of the zinc oxide thin films grown via DEZ/H2O-process by modelling the surface chemistry using first principles kinetic Monte Carlo for the first time. The kinetic Monte Carlo allows us to implement density functional theory calculations conducted on zinc oxide (100) surface into a kinetic model and extract data directly comparable to experimental measurements. The temperature dependent growth profile obtained from our model is in good qualitative agreement with the experimental data. The onset of thin film growth is offset from the experimentally data due to the underestimation of the reaction barriers within density functional theory. The growth per cycle of the deposited film is overestimated by 18% in the kinetic model. Mass-gain during an ALD cycle is in qualitative agreement with experimental quartz-crystal microbalance data. The main mass-gain within an ALD cycle is obtained during the DEZ pulse and mass-change during the water pulse negligible. The cause of low film growth at low temperatures is due to the high reaction barriers for ethyl-elimination during the water pulse. This kinetic barrier results in low film growth as no new DEZ can adsorb to the ethyl-saturated surface. At elevated temperatures ethyl-elimination becomes accessible, resulting in the ideal layer-by-layer growth of the film. However, a large fraction of ethyl-ligands persist on the surface after each ALD cycle even at high temperatures. This results in ethyl-ligands being encapsulated into the film lattice. This is likely due to an incomplete set of reaction pathways and it is likely that some yet unidentified process is responsible for the elimination of the ethyl-ligands from the surface as the deposition process progresses.