A model for electrochemical oscillations at the Si ∣ electrolyte contact: Part I. Theoretical development

We present a mathematical model that describes current oscillations of silicon in fluoride-containing solutions. The model is based on the relationship between a set of thickness oscillators (which represent the local thickness of the SiO2 layer) and the resulting current oscillations. We introduce a probability distribution for the periods of the thickness oscillators. During a cycle, a so-called synchronization state describes the temporal drift of the instant at which the thickness oscillators pass the smallest thickness. A convolution of the synchronization state with the probability distribution for the periods determines the synchronization state of the next cycle. A convolution of the superposition of all synchronization states with an elementary current peak leads to the current.