Macropore formation in p-type silicon: toward the modeling of morphology

The formation of macropores in silicon during electrochemical etching processes has attracted much interest. Experimental evidences indicate that charge transport in silicon and in the electrolyte should realistically be taken into account in order to be able to describe the macropore morphology. However, up to now, none of the existing models has the requested degree of sophistication to reach such a goal. Therefore, we have undertaken the development of a mathematical model (phase-field model) to describe the motion and shape of the silicon/electrolyte interface during anodic dissolution. It is formulated in terms of the fundamental expression for the electrochemical potential and contains terms which describe the process of silicon dissolution during electrochemical attack in a hydrofluoric acid (HF) solution. It should allow us to explore the influence of the physical parameters on the etching process and to obtain the spatial profiles across the interface of various quantities of interest, such as the hole concentration, the current density, or the electrostatic potential. As a first step, we find that this model correctly describes the space charge region formed at the silicon side of the interface.