Porosification of Silicon from the Viewpoint of Nonlinear Dynamics

Anodic dissolution of silicon in HF solutions leads to formation of porous silicon. Formation of a wide variety of porous structures has been reported. In the course of the studies, electrochemical oscillations have been found in silicon anodization. Because a symmetry breaking is necessary for the formation of porous silicon, such oscillatory phenomena have attracted keen attention for the understanding of porous silicon formation.

   Formation of macroporous silicon, whose pore diameter is several micrometers, has been explained based on the current burst model proposed by Föll and his colleagues. In the current burst model, macropore formation has been explained based on desynchronization of local oscillators on a silicon surface. Recent studies on nonlinear dynamics in electrochemistry have shown that spatiotemporal pattern formation is closely related to a negative differential resistance (NDR) observed in the current density vs. potential curve. However, NDRs have not been considered in porous silicon formation so far. We have focused our attention on the emergence of NDR in anodization of silicon, and have discussed the spatial pattern formation on silicon.

   Recently, we have found that a clear S-shaped NDR is observed after the correction of iR-drop in the electrolyte solution, when using an HF solution containing alcohol such as 2-propanol. In the S-shaped NDR region, an array of microgrooves is spontaneously formed on the silicon surface. Since an S-shaped NDR is induced by a positive feedback which is independent on electrode potential, while electrode potential plays a role of an negative feedback. In the present case, we think that the microgroove array is induced by Turing instability. According to earlier studies, the size of Turing patterns observed in electrochemical systems is on the scale of millimeters. Astonishingly, the size of the present Turing pattern is on the scale of micrometers. In the present paper, the reason why the characteristic size is so small will be discussed in detail. In addition to the Turing pattern formation, formation of other spatiotemporal patterns in silicon electrochemistry, which is difficult to be explained in the classical framework of spatiotemporal pattern formation in electrochemistry, will be discussed.