Pattern Formation during Si Electrodissolution

Fig. 1: On top sketch of the illumination set-up.

Fig. 2: On top sketch of the ellipsometric imaging set-up.

The photoelectrodissolution of n-type silicon in fluoride-containing electrolytes is a prototypical model system for the study of patterns and synchronization phenomena in oscillatory media. The oscillations arise from the interaction between the formation and dissolution of an oxide layer on the silicon surface, and the patterns correspond to variations in the thickness of the oxide layer. They emerge when the reaction rate becomes illumination limited, which is a manifestation of the decisive role of the lateral transport of valence band holes for pattern formation and makes the illumination strength an important control parameter. In our experimental setup ellipsometric imaging is used to monitor the evolution of the patterns, and a spatial light modulator serves as a flexible device to illuminate the electrode.

The diverse patterns observed include multifrequency clusters, so-called chimera states characterized by the coexistence of synchronized and incoherently oscillating, as well as a variety of other coexistence patterns. In addition, the Si oscillator is birhythmic in a certain parameter range, so that the spatio-temporal dynamics of birhythmic systems can be studied experimentally.

As a bridge between nonlinear dynamics and electrochemistry, our studies aim to uncover the nature of spatial couplings in the system, correlate different coupling modes with the observed synchronization patterns, link the observed patterns to universal laws, and validate theoretical predictions on pattern formation in oscillating media.