Because of its high dielectric constant, alumina (Al₂O₃) is a candidate gate oxide material for next-generation MOSFETs. As well as the increasingly stringent requirements for electrical performance, a new gate oxide must survive the demanding conditions of the manufacturing process. Layers of alumina are routinely grown on silicon by Chemical Vapour Deposition (CVD), but the underlying reactions are poorly understood. Our DFT slab calculations aim to elucidate CVD at the atomic-scale by considering the reaction of gas-phase precursors (AlMe₃ and H₂O) on the model alpha-Al₂O₃-(0001) surface. Computed structures of intermediates in the growth process are presented, along with quantitative surface energies and approximate dependence on precursor partial pressure.