Proposed Heuristic Model for Fuzz Growth on Metal Surfaces

The growth of nano-scale rods, or fuzz, is observed experimentally on tungsten and molybdenum surfaces exposed to an incident He flux with ion energies $>$10 eV. It is experimentally determined that the growth of fuzz follows a diffusion-like equation as a function of the He exposure time $t$: \textit{x $\sim $ (2Dt)}$^{1/2}$, where $x$ is the fuzz thickness and $D$ is the effective diffusion coefficient. This growth is consistent with the incident He flux \textit{$\Gamma $}$_{o}$ being reduced at a rate of \textit{d$\Gamma $(x)/dx = -$\alpha \Gamma $(x)}$^{3/2}$ as the He ions traverse the fuzz. \textit{$\alpha $} is an integration constant. Based on the above assumption, we derived a relation between $x$, \textit{$\Gamma $}$_{o}$, and $t$: \textit{x + 2$\alpha $ }$^{-1}$\textit{$\Gamma $}$_{o}^{-1/2}$\textit{ = (2Dt)}$^{1/2}$. The notable features of this equation, for a fixed exposure time, are: 1) the saturation of the fuzz thickness as \textit{$\Gamma $}$_{o}$ approaches\textit{ $\infty $} and 2) the minimum threshold value of the incident He flux \textit{$\Gamma $}$_{o}$ required to initiate fuzz growth. Both of these features are experimentally observed. Another notable feature is that it requires a minimum He fluence \textit{$\Gamma $}$_{o}t_{min}$ at the metal surface to initiate fuzz growth.