Theoretical model for early stages of porous silicon formationfrom n- and p-type silicon substrates

Abstract

We present a stability analysis of the silicon-electrolyte interface for the etching of both n- and p-type silicon. The description is based on the model that we have developed in a preceding paper for n-type silicon. The model incorporates the transport phenomena of holes in the semiconductor and ions in the electrolyte, together with surface tension of silicon. Here, we have incorporated the kinetic effects of the electrochemical reaction in a coherent and transparent manner. We shall also consider the p-type silicon as well. Our numerical analysis shows that for n- and p-type silicon the electrolyte-silicon interface become linearly unstable below a critical dissolution speed (depending on the operating parameters), identified as the boundary between the regime of pore formation and electropolishing. Moreover, we extract scaling laws for the wavelength of the most dangerous interface fluctuations, which is expected to give a magnitude on the order of the interpore spacing. The results obtained for n-type silicon is consistent with available experimental data. We expect rather macropores. For p-type silicon, we find nanostructures for intermediate doping levels. We discuss the implication of our results together with theoretical suggestions for future work.