One-dimensional dynamics of nano-scale oxidation

A continuum model is proposed to describe the process of scanned probe oxidation in the presence of a thin water layer on the surface of a substrate. The model describes the electric field and ion transport in both the liquid and the oxide layers and incorporates the reaction mechanism at the substrate/oxide interface. Further, the influence of the space charge due to ions trapped near the substrate/oxide interface is taken into account.Separation of time scales for the chemical reactions and ion transport as well as the asymptotic limit in terms of a small aspect ratio of the oxide layer are used to reduce the complex system of partial differential equations to a one-dimensional system of ordinary differential equations. The analytical solution of the reduced system results in the evolution equation for the oxide thickness. Numerical simulations of the evolution equation predict features of oxide growth that qualitatively agree with the experimental observations. A parametric study is conducted to determine the influence of the key operating and material parameters on the thickness of the oxide, the electric field, and ion concentration in the system.