A self-consistent theoretical model for macropore growth in n -type silicon

In this work, a theoretical study on the growth of macropores fabricated from n -type silicon by photoelectrochemical etching in HF-based electrolytes is reported. By solving the diffusion equation into the pores, we deduce a self-consistent model which can be used for quantitative prediction of the growth speed and pore depth. The limiting factor of the growth, i.e., the HF concentration at the pore tip, is shown to be a nonlinear function of the pore depth, a fact not accounted for by the current literature. A reduced model with a closed analytical solution is presented as well. Finally, the predictions of the full and reduced models are compared with the experimental data. © 2005 American Institute of Physics.