  We present the evidence of the low defect density at Ge/GeO$_2$ interfaces in
terms of first-principles total energy calculations. The energy advantages of
the atom emission from the Ge/GeO$_2$ interface to release the stress due to
the lattice mismatch are compared with those from the Si/SiO$_2$ interface. The
energy advantages of the Ge/GeO$_2$ are found to be smaller than those of the
Si/SiO$_2$ because of the high flexibility of the bonding networks in GeO$_2$.
Thus, the suppression of the Ge-atom emission during the oxidation process
leads to the improved electrical properties of the Ge/GeO$_2$ interfaces.
