Defect physics and electronic properties of Cu${}_3$PSe${}_4$ from first principles

The $p$-type semiconductor Cu${}_3$PSe${}_4$ has recently been established to have a direct band gap of 1.4 eV and an optical absorption spectrum similar to GaAs [Foster et al., Appl. Phys. Lett. 99, 181903 (2011)], suggesting a possible application as a solar photovoltaic absorber. Here we calculate the thermodynamic stability, defect energies and concentrations, and several material properties of Cu${}_3$PSe${}_4$ using a wholly GGA+$U$ method (the generalized gradient approximation of density functional theory with a Hubbard $U$ term included for the Cu-$d$ orbitals). We find that two low energy acceptor defects, the copper vacancy V${}_{\text{Cu}}$ and the phosphorus-on-selenium antisite P${}_{\text{Se}}$, establish the $p$-type behavior and likely prevent any $n$-type doping near thermal equilibrium. The GGA+$U$ defect calculation method is shown to yield more accurate results than the more standard method of applying post-calculation GGA+$U$-based band-gap corrections to strictly GGA defect calculations.

Figure 1

Partial density of states for the unit cell (Cu${}_3$PSe${}_4$)${}_2$. The large Cu-$d$ peak rises to a maximum of twice the height of the plot. The vertical dashed line at 0 denotes the valence band maximum.

Figure 2

Chemical potential domain with stable region of Cu${}_3$PSe${}_4$ in gray. The chosen Cu-rich growth condition is indicated by a circle.

Figure 3

Defect formation energies and transition energies. Where nonequivalent sites are calculated, the lowest energies for each charge state are shown. The self-consistent room temperature Fermi energy $E_{F,\text{SC}}$, assuming a formation temperature of 500 ${}^{\circ }$C, is shown by the vertical line at 0.031 eV. The (0/+) transition energy for shallow donor Zn${}_{\text{Cu}}$ has been raised to follow the conduction band correction.

Figure 4

Heat of formation (GGA+$U$) of interstitial and complex defects containing extra P atoms. Energy corrections $\Delta E_{\text{corr}}$ are neglected except for the P${}_{\text{Se}}$ defect.