A selective-area oxidation technique using electron beam (e-beam) irradiation with a mixture of O2 and H2O gases is studied for the fabrication of small tunnel junctions using Si and Cr. Auger electron spectroscopy clearly shows the existence of Si-O bonding at e-beam-irradiated Si surfaces. The height of SiOx is measured by atomic-force-microscope observation, and it is confirmed that the thickness of SiOx can be controlled at a nanometer scale. The line-dose dependence of the resistance of the Cr/CrOx/Cr structure was measured at room temperature and 77 K, and a step-function-like dependence was observed, which indicates that the oxidation takes place over the entire thickness of the 3-nm-thick Cr film. Nonlinear current-voltage characteristics were observed, which suggest that a thin tunneling barrier of CrOx can be realized. The selective-area oxidation technique can be applied to the fabrication of small tunneling junctions.