  The detailed analysis of the structural variations of three GeO$_2$ and
SiO$_2$ polymorphs ($\alpha$-quartz, $\alpha$-cristobalite, and rutile) under
compression and expansion pressure is reported. First-principles total-energy
calculations reveal that the rutile structure is the most stable phase among
the phases of GeO$_2$, while SiO$_2$ preferentially forms quartz. GeO$_4$
tetrahedras of quartz and cristobalite GeO$_2$ phases at the equilibrium volume
are more significantly distorted than those of SiO$_2$. Moreover, in the case
of quartz GeO$_2$ and cristobalite GeO$_2$, all O-Ge-O bond angles vary when
the volume of the GeO$_2$ bulk changes from the equilibrium point, which causes
further deformation of tetrahedra. In contrast, the tilt angle formed by
Si-O-Si in SiO$_2$ markedly changes. This flexibility of the O-Ge-O bonds
reduces the stress at the Ge/GeO$_2$ interface due to the lattice-constant
mismatch and results in the low defective interface observed in the experiments
[Matsubara \textit{et al.}: Appl. Phys. Lett. \textbf{93} (2008) 032104; Hosoi
\textit{et al.}: Appl. Phys. Lett. \textbf{94} (2009) 202112].
