Porous silicon formation: Stability analysis of the silicon-electrolyte interface

We have performed both analytically and numerically a stability analysis of the silicon-electrolyte interface for the photoelectrochemical etching of n-type Si. The model incorporates the transport of holes in the semiconductor, ion diffusion in the electrolyte, together with surface tension of silicon. A careful physical analysis of the governing equations allows us to identify the relevant ingredients. This renders the problem tractable analytically. Our analytical analysis, which shows a good agreement with the full numerical calculation, allows us (i) to express analytically the dissolution speed, (ii) to derive scaling laws for interpore spacing as a function of the doping level of Si and applied potential, and (iii) to obtain an analytical expression for the bifurcation curve in parameter space, which constitutes a boundary between the regime of pore formation and electropolishing. Our results are consistent with available experimental data on n-type Si. A possible extension to p-type semiconductors is outlined. Outlooks and speculations opening lines of future inquiries are also presented.