  In solid-state physics/chemistry, a precise understanding of defect formation
and its impact on the electronic properties of wide-bandgap insulators is a
cornerstone of modern semiconductor technology. However, complexities arise in
the electronic structure theory of defect formation when the latter triggers
partial occupation of the conduction/valence band, necessitating accurate
post-process correction to the energy calculations. Herein, we dissect these
complexities, focusing specifically on the post-process band-filling
corrections, a crucial element that often demands thorough treatment in defect
formation studies. We recognize the importance of these corrections in
maintaining the accuracy of electronic properties predictions in wide-bandgap
insulators and their role in reinforcing the importance of a reliable common
reference state for defect formation energy calculations. We explored solutions
such as aligning deep states and electrostatic potentials, both of which have
been used in previous works, showing the effect of band alignment on defect
formation energy. Our findings demonstrate that the impact of defect formation
on electronic structure (even deep states) can be significantly dependent on
the supercell size. We also show that within band-filling calculations, one
needs to account for the possible change of electronic structure induced by
defect formation, which requires sufficient convergence of electronic structure
with supercell size. Thus, this work emphasizes the critical steps to predict
defect formation energy better and paves the way for future research to
overcome these challenges and advance the field with more efficient and
reliable predictive models.
