Impact of dopants and strains on the oxygen vacancy formation in VO2

We perform first-principles calculations to examine the relationship of the oxygen vacancy ($V_O$) formation with dopants and mechanical strains in metallic tetragonal VO₂. Both compressive and tensile biaxial strains lower the formation energy of $V_O$, and the lowering of the formation energy is more pronounced under tensile strain. When six dopants, which possess different charge state and ionic radius, are introduced, the formation energy of $V_O$ increases, indicating that the dopants may suppress the $V_O$ formation in VO₂. Strains lead to similar trends in the undoped case, i.e., strains reduce the $V_O$ formation energy in the doped VO₂. Based on the results, we suggest that the difference in atomic relaxations of the two kinds of V–O bonds plays an important role in determining the formation energy of $V_O$.