Influence of germanium substitution on the structural and electronic stability of the competing vanadium dioxide phases

We present a density-functional theory (DFT) study of the structural, electronic, and chemical bonding behaviour in germanium (Ge)-doped vanadium dioxide (VO$_2$). Our motivation is to explain the reported increase of the metal-insulator transition temperature under Ge doping and to understand how much of the fundamental physics and chemistry behind it can be captured at the conventional DFT level. We model doping using a supercell approach, with various concentrations and different spatial distributions of Ge atoms in VO$_2$. Our results suggest that the addition of Ge atoms strongly perturbs the high-symmetry metallic rutile phase and induces structural distortions that partially resemble the dimerization of the experimental insulating structure. Our work, therefore, hints at a possible explanation of the observed increase in transition temperature under Ge doping, motivating further studies into understanding the interplay of structural and electronic transitions in VO$_2$.