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First-Principles Study on Structural Properties of GeO$_2$ and SiO$_2$ under Compression and Expansion Pressure

The detailed analysis of the structural variations of three GeO$_2$ and SiO$_2$ polymorphs ($α$-quartz, $α$-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].