Layer-by-layer oxidation of Si surfaces has been studied by scanning reflection electron microscopy, which allowed us to obtain plan-view images of buried SiO₂/Si interfaces. We observed atomic steps at the SiO₂/Si(111) interfaces and the periodic reversal of terrace contrast during oxidation of Si(001) surfaces. We found that the initial surface structure was preserved at the interface and that the interfacial steps did not move laterally during oxidation. These results mean that layer-by-layer oxidation is governed by random nucleation of nanometer-scale oxide islands and lateral island growth. We also studied the kinetics of initial layer-by-layer oxidation of Si(001) surfaces. Our results showed that barrier-less oxidation of the first sub-surface layer, as well as oxygen chemisorption onto the top-layer, occurred at room temperature. The energy barrier of the second-layer oxidation was found to be 0.3eV. The initial oxidation kinetics is discussed based on first-principles calculations.