Spatiotemporal Patterns Formed on p-Type Silicon Electrodes during Electrochemical Dissolution

Formation of spatiotemporal patterns has been reported in many electrochemical systems [1]. Applications of spatiotemporal patterns to other fields such as materials science and biological science are important for further progress of nonlinear dynamical systems. Since there are lots of parameters for the emergence of the patterns, it is difficult to understand the mechanisms for pattern formation.

   Spatiotemporal patterns are often observed in electrochemical systems that show negative differential resistance (NDR) on their current density vs. potential curves. We have found that an S-shaped NDR was observed when a p-type silicon (p-Si) electrode was anodized in an HF solution containing organic solvents. A well-aligned microgroove array was formed after electrochemical dissolution at a potential in the S-shaped NDR. Although the spatial pattern was formed at the S-shaped NDR region, oscillatory instability in current or potential was not observed. In the present study, we report that an oscillatory instability in current is observed at the S-shaped NDR region.

   For the electrochemical measurements, p-Si (100) with a resistivity of 1-4.5 W cm was used as the working electrode. Platinum (Pt) rods were used not only as the counter electrode, but also as the indicator electrode. Electrolyte solution was a mixture of aqueous HF (47 wt.%), ultrapure water and methanol (MeOH) with a composition of 5:6:29 in volume. Since the resistance of the solution is significant to estimate the potential applied at the electric double layer, the resistance was measured by impedance spectroscopy. Temperature of the solution was controlled by a water bath.

   Figure 1 depicts current density vs. potential (j-U) curves together with current density vs. iR-corrected potential (j-f) curves measured in the solution at 20°C and 30°C. When using the solution at 20°C, an S-shaped NDR is observed after correcting the iR-drop in the solution. We have confirmed that an array of microgrooves is spontaneously formed at potentials on the NDR branch. No oscillatory instability is observed in the curves. In the solution at 30°C, a fluctuation in current is observed on the j-U curve. After the correction of iR-drop in the solution, a clear oscillatory instability is observed in the region where the S-shaped NDR is detected in the solution at 20°C.

   Time developments of current measured at a constant potential in the NDR region was plotted in Figure 2. Clear current oscillations are not observed in the solution at 20°C although the current fluctuates with time. In contrast, a current oscillation whose period is roughly 1 min is observed. This difference suggests that a bifurcation from the Turing to Turing-Hopf occurs by changing the temperature of the solution from 20 °C to 30°C.

[1] K. Krischer, N. Mazouz, P. Grauel, Angew. Chem. Int. Ed. 40, 850 (2001).