Nano- and macropore formation in p-type silicon

We present an analytical model describing the instability of the interface during anodization of p-type resistive silicon in HF electrolyte, leading to porous silicon formation. Our analytical approximations are applicable to p-type amorphous and crystalline silicon with resistivities in the range from about 0.1 to 10,000 Ω cm. For all kinds of p-type silicon, nanopore formation is predicted to occur first, as it is governed by properties of the silicon/electrolyte barrier. Then, pores of increasing diameter are expected to grow, up to sizes of the order of a characteristic cutoff length. Structures above that size occur only when the resistivity of silicon is larger than that of the electrolyte.