The first consistent and complete model of current oscillations at the Si electrode is presented. The only basic assumption needed is an ionic breakthrough mechanism which is postulated to occur in thin oxides under oxidizing electrode conditions, leading to an enhanced and localized ion transport to the Si-SiO2 interface. Choosing reasonable values for three corresponding physical parameters and using a Monte Carlo simulation technique, first-principle calculations yield quantitative data in excellent agreement with numerous experimental results, including the value of the current, surface roughness, the average oxide thickness, and the capacitance as a function of the phase of oscillations, and the frequency of the oscillations as a function of applied voltage, current density, etching rate or HF concentration, and temperature.