  The relationship between the presence of defects at the stacking structure of
the Si/SiO$_2$ interface and leakage current is theoretically studied by
first-principles calculation. I found that the leakage current through the
interface with dangling bonds is 530 times larger than that without any
defects, which is expected to lead to dielectric breakdown. The direction of
the dangling bonds is closely related to the performance of the oxide as an
insulator. In addition, it is proved that the termination of the dangling bonds
by hydrogen atoms is effective for reducing the leakage current.
