A Theory for the Resonant Response of an Electrochemical System: Self-Oscillating Domains, Hidden Oscillation, and Synchronization Impedance

We present a theory which is able to account for the resonant behavior of the electric response of electrochemical interfaces, such as observed recently for the anodic dissolution of silicon. The interface is viewed as a parallel collection of small self-oscillating domains. For a constant applied potential, the domains are uncorrelated, and a stable macroscopic current is observed. However, they can become synchronized in the presence of a small sinewave potential excitation, and a linear resonant response of the current may be observed at the natural frequency or its overtones. An associatedcontribution to the impedance, called “synchronization impedance,” is calculated in the framework of a specific model. The calculated impedance gives good fits to the experimental data. The noise spectrum of the current at constant potential is also expected to exhibit resonances, and its measurement should provide information on the domain size.