Preferential oxygen sputtering from Nb2O5

The bombardment of Nb₂O₅ with Kr⁺ or O⁺₂ ions leads to the development of a surface layer NbO. The layer begins to form at (2–4) × 10¹⁵ ions cm^-2 as random nuclei which can be resolved by transmission electron microscopy. It is half complete at (4–8) × 10¹⁶ ions cm^?2, a much higher dose than that required for sputter equilibrium to be half complete. The final thickness is roughly 31 nm. These features, together with the further result that the layer forms independently of the bombarding current provided beam heating is avoided, can be understood from a model which combines preferential oxygen sputtering at the surface, diffusion of the relevant point defects, and random nucleation of a phase with lower stoichiometry. The governing equation is an extended form of the diffusion equation

$\text{?C}\text{?t}\text{=}\text{D?}{}^2\text{C}\text{?x}{}^2\text{+}\text{υ?C}\text{?x}\text{?}\text{DC}\text{L}{}^2$

where υ is the velocity of the surface recession due to sputtering and L is the diffusion length for trapping. Appropriate solution of the equation suggests that the altered layer will have a mean thickness similar to L, will be formed with a half-dose given by $\text{0.693LN}\text{S}$ where S is the sputtering coefficient, and will involve a total amount given by $\text{DC}{}_0\text{υ}$ atoms cm^?2, where C₀ is the stoichiometry at the outer surface. Current independence follows if the diffusion is bombardment enhanced, so that D is approximately proportional to υ. The main difficulty with the model is that it is strictly valid only for low concentrations.