Point defects in solids are promising single-photon sources with application in quantum sensing, computing and communication. Herein, we describe a theoretical framework for studying electric field effects on defect-related electronic transitions, based on density functional theory calculations with periodic boundary conditions. Sawtooth-shaped electric fields are applied perpendicular to the surface of a two-dimensional defective slab, with induced charge singularities being placed in the vacuum layer. The silicon vacancy (VSi) in 4H-SiC is employed as a benchmark system, having three zero-phonon lines in the near-infrared (V1, V1' and V2) and exhibiting Stark tunability via fabrication of Schottky barrier or p-i-n diodes. In agreement with experimental observations, we find an approximately linear field response for the zero-phonon transitions of VSi involving the decay from the first excited state (named V1 and V2). However, the magnitude of the Stark shifts are overestimated by nearly a factor of 10 when comparing to experimental findings. We discuss several theoretical and experimental aspects which could affect the agreement.
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