Electronic structure calculations of an oxygen vacancy in $\mathrm{K}{\mathrm{H}}_2\mathrm{P}{\mathrm{O}}_4$

We present first-principles total-energy density-functional theory electronic structure calculations for the neutral and charge states of an oxygen vacancy in $\mathrm{K}{\mathrm{H}}_2\mathrm{P}{\mathrm{O}}_4$ (KDP). Even though the overall density of states profiles for the defective KDP are quite similar to those of the perfect KDP, the oxygen vacancy in the neutral and $+1$ charge states induces defect states in the band gap. For the neutral oxygen vacancy, one electron is localized in the O vacancy maintaining the charge that was at that site in the pure crystal, while the neighboring P atom to the vacancy gains about one electron relative to its charge state in pure KDP. For the $+1$ charge oxygen vacancy, the removal of an electron reduces the occupation of the filled gap states in the neutral case from two to one electron and produces a new empty state in the gap. The new empty gap state is very close to the highest occupied states, leading to a dramatic decrease of the band gap. In sharp contrast, no defect states appear in the energy gap for the $+2$ charge O vacancy, where the neighboring P atom to the O vacancy almost returns to its perfect-crystal charge state. For the $-1$ charge oxygen vacancy, the added electron does not localize on any of the atoms near the vacancy; rather it goes into the vacancy to spin-pair with the electron that was there in the neutral vacancy.

Figure 1

Schematic view of the local atomic structure of the O vacancy in a tetrahedral $\mathrm{P}{\mathrm{O}}_4$ unit in KDP (The $\mathrm{P}\mathrm{O}$ and $\mathrm{O}\mathrm{H}$ bond lengths are listed in Table ). The P, O, and H atoms are labeled by black, gray, and white circles, respectively. The O(4) atom belongs to a neighboring tetrahedral $\mathrm{P}{\mathrm{O}}_4$ unit. The position of the O vacancy is denoted with V(O).

Figure 2

Total density of states for the defect-free KDP (a), the neutral (b), $+1$ (c), $+2$ (d), and $-1$ (e) charged O vacancy, respectively. The valence-band maximum of the defect-free KDP is set at $0\mathrm{eV}$. The highest occupied (empty) band gap states for the defective KDP are denoted by solid (dotted) arrows.

Figure 3

Isosurface of the wave function of the highest occupied orbitals for the neutral O vacancy in KDP. The atomiclike orbitals are centered on the O vacancy as well as the neighboring O atoms.

Figure 4

Orbital- and atom-resolved partial density of states (PDOS) for the neutral O vacancy in KDP. The P, O(1), O(2), O(3), and O(4) atoms are shown in Fig. 1.

Figure 5

Orbital- and atom-resolved partial density of states (PDOS) for the $+1$ charged O vacancy in KDP. The positions of the P, O(1), O(2), O(3), and O(4) atoms are shown in Fig. 1.