The development of ${\text{Si}}_{1\text{−}x}{\text{Ge}}_x$ alloys has prompted interest in exploring the nature of point defects, particularly vacancies. This study employs Heyd-Scuseria-Ernzerhof hybrid functional to investigate the electronic properties of the vacancy in ${\text{Si}}_{1\text{−}x}{\text{Ge}}_x$ alloys, focusing specifically on Si, ${\text{Si}}_{504}{\text{Ge}}_8$, and ${\text{Si}}_{488}{\text{Ge}}_{24}$ compositions. It is found that for a fixed vacancy configuration, variations in alloy composition lead to nearly similar formation energies. The calculated $(1-/2-)$ levels for vacancies of the 0-0-0, 0-0-1, and 0-1-0 configuration in the two alloys are generally consistent with the experimental value of $E_C-0.29\mathrm{eV}$. For the $(0/1-)$ level, the results for the vacancy in Si and the vacancy of the 0-0-0 configuration in ${\text{Si}}_{504}{\text{Ge}}_8$ are very close. The acceptor levels of the vacancy in Si are found to be $E_C-0.29\mathrm{eV}$ for $(0/1-)$ level and $E_C-0.33\mathrm{eV}$ for $(1-/2-)$ level. These results are consistent with the corresponding acceptor levels obtained for the vacancy of the 0-0-0 configuration in ${\text{Si}}_{504}{\text{Ge}}_8$. These findings underscore the importance of alloying and local configuration in determining vacancy electronic properties and suggest that ${\text{Si}}_{1\text{−}x}{\text{Ge}}_x$ alloys offer a valuable platform for more accurate probing of vacancy acceptor levels in silicon.

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• Defects
• First-principles calculations
• Disordered alloys
• Semiconductors
• Density functional theory
• Electronic structure