DIFFUSION-INDUCED NUCLEATION MODEL FOR THE FORMATION OF POROUS SILICON

We propose a diffusion-induced nucleation model for the formation of p orous silicon based on two primary processes. The diffusion of holes f rom the bulk to the surface is controlled mainly by (a) the depletion- layer width (Delta W) and (b) the drift-diffusion length (l) of holes inside the lattice. The relevance of the two control parameters is dis cussed in the context of the existing physical models. We also conside r pore propagation as a self-avoiding random walk with a finite termin ation probability p(t). Pore morphologies obtained for both p- and n-t ype substrates are in agreement with TEM micrographs. Further, our mod el reproduces experimentally observed phenomena such as (i) a constant rate of growth, (ii) the dependence of the rate of growth on the anod ization potential, (iii) high-porosity structures similar to samples e xhibiting visible photoluminescence, and (iv) electropolishing of sili con in the high-potential limit. The effect of quantum confinement on porosity is illustrated.