Kinetics of Oxide Film Growth on Metal Crystals: Electron Tunneling and Ionic Diffusion

Numerical computations have been made for the growth rate of oxide and other dielectric contact films for the case of ion transport by diffusion and electron transport by tunneling. In the early phase of growth, electronic equilibrium prevails and the oxide growth rate can be limited by the diffusion of ions aided by a relatively large negative electrical contact potential $V_M$ between metal and adsorbed oxygen. In the later phase of growth, ionic equilibrium prevails and the rate can be limited by the tunneling of electrons through the oxide aided by a positive electrical ionic diffusion potential $V_D$. The growth law in the early phase is of the Mott-Cabrera form, while in the later phase it is very nearly direct-logarithmic. The rather sharp transition between the two growth laws occurs at film thicknesses of the order of 20 to 30 Å, and is accompanied by a change in sign of the electrical potential across the oxide. The oxide growth rate in the early stages depends primarily on the value of the Mott potential $V_M$ (defined as the difference in metal Fermi level and the ${\mathrm{O}}^{-}$ level in adsorbed oxygen) and the parameters associated with ionic diffusion. For the later stages of growth, the metal-oxide electronic work function ${\chi }_0$ is the most important parameter, with the ratio of ionic boundary concentrations playing a lesser role through $V_D$. An increase in temperature increases the growth rate exponentially in the early growth stages, but increases the rate only moderately through $V_D$ in the later stages.