We have demonstrated the characterizations the local electrical properties of ultrathin (1-4 nm) SiO2/Si(001) structures using a conducting atomic force microscopy with a nanometer-scale resolution in a vacuum (1 x 10(-5) Pa). The measurement in a vacuum enables to reduce the influence of adsorbed water on quantitative current measurements, while there is a problem at the measurement in air of 60% humidity. Fitting to the Fowler-Nordheim equation is good at thicker SiO2 films more than similar to 3 nm. We have also demonstrated the results of continuous current-voltage measurements during the breakdown process by charge injection through a conducting probe.