Diffusion-induced nucleation model for the formation of porous silicon

We propose a diffusion-induced nucleation model for the formation of porous silicon based on two primary processes. The diffusion of holes from the bulk to the surface is controlled mainly by (a) the depletion-layer width (ΔW) and (b) the drift-diffusion length (l) of holes inside the lattice. The relevance of the two control parameters is discussed in the context of the existing physical models. We also consider pore propagation as a self-avoiding random walk with a finite termination probability ${\mathit{p}}_{\mathit{t}}$. Pore morphologies obtained for both p- and n-type substrates are in agreement with TEM micrographs. Further, our model reproduces experimentally observed phenomena such as (i) a constant rate of growth, (ii) the dependence of the rate of growth on the anodization potential, (iii) high-porosity structures similar to samples exhibiting visible photoluminescence, and (iv) electropolishing of silicon in the high-potential limit. The effect of quantum confinement on porosity is illustrated.