Ab-initio thermodynamics of deposition growth: surface terminations of CVD titanium carbide and nitride

We present a calculational method to predict terminations of growing or as-deposited surfaces as a function of the deposition conditions. Such characterizations are valuable for understanding catalysis and growth phenomena. The method combines ab-initio density functional theory (DFT) calculations and experimental thermodynamical data with a rate-equations description of partial pressures in the reaction chamber. The use of rate equations enables a complete description of a complex gas environment in terms of a few, (experimentally accessible) parameters. The predictions are based on comparisons between free energies of reaction associated with the formation of surfaces with different terminations. The method has an intrinsic non-equilibrium character. In the limit of dynamic equilibrium (with equal chemical potential in the surface and the gas phase) we find that the predictions of the method coincide with those of standard ab-initio based equilibrium thermodynamics. We illustrate the method for chemical vapor deposition (CVD) of TiC(111) and TiN(111), and find that the emerging termination can be controlled both by the environment and the growth rate.