[Cross posted to material modeling stack exchange as recommended in the comments, although I couldn’t find the policies for that.]
Some fairly basic conceptual questions arose as I was doing some DFT and getting the DOS of an ionic semiconductor system with a defect.
When the system is globally neutral, the defect is in the $-2$ charge state. I call this the empty trap state. If I introduce a hole in the system (the overall atomic system now has a net charge of +1), I observe localization of the hole on the defect(*) which is now in the $-1$ charge state. I call this the filled trap state.
The confusion comes up when I produce a DOS for both filled and empty traps. In both cases, the geometry is the same and the only thing that changes is the presence of a localized hole on the defect (well, and some settings as to how the spin is handled which I will align later. It might explain some discrepancies between both but not answer the central question).
In the “empty trap” case (no hole, $-2$ charge state), we have a peak in the middle of the band gap. Integrating the DOS over this peak shows me that it corresponds to two electronic states.
In the “filled trap” case (trapped hole, $-1$ charge state), the peak is sightly shifted, which might be due to the Coulombic interaction induced by the trapped charge. All good. But what I don’t understand, is that if I integrate the DOS over the trap state, I get this time only one state!
It seems that the addition of a hole made a trap state “disappear” in the band structure! (Looks like it re-distributed in the band edges). Now that doesn’t match my understanding of band structures and their occupancy. Adding or subtracting charge carriers might shift some state levels, sure. It will definitely impact how those energy states are occupied. But I don’t understand how it “deletes” some states. For me, the only difference when injecting a hole should be that a previously occupied state is now free (and potentially shifted), but it should not cease to exist.
Can anybody clarify this for me?
Bonus question: I was also surprised to see that a trap state with a $-2$ charge had its level in the middle of the bandgap, suggesting that it might be a trap for both electrons and holes, when simple coulombic considerations (as well as others) clearly suggest that it should preferentially be preferentially a hole trap.
(*)thanks to the use of appropriate self-interaction correction schemes for DFT
EDIT: it is worth noting that, in the ground state, the two electronic trap states are occupied by electrons when the trap is empty (no hole). They are just below the Fermi energy. When the hole is introduced, one of those states is occupied and moved back to the valence band. The remaining midgap trap state is now unoccupied by electrons (above Fermi energy)
