Electron affinities and ionization energies of Cu and Ag delafossite compounds: A hybrid functional study

Abstract

Using density functional theory with a hybrid functional, we calculate the ionization energies and electron affinities of a series of delafossite compounds ($AM$O${}_{2}$: $A=\text{Cu}$, Ag; $M=\text{B}$, Al, Ga, In, Sc). The alignments of the valence band maximum and the conduction band minimum, which directly relate to the ionization energies and electron affinities, were obtained by calculations of supercell slab models constructed in a nonpolar orientation. Our calculations reveal that the ionization energy decreases with an increasing atomic number of group-III elements, and thus suggest an improved $p$-type doping propensity for heavier compounds. For keeping both a low ionization energy and a band gap of sufficient size, CuScO${}_{2}$ is superior to the Cu-based group-III delafossites. By analyzing the electronic structures, we demonstrate that the compositional trend of the ionization energies and electron affinities is the result of a combined effect of $d$-band broadening due to Cu(Ag)-Cu(Ag) coupling and a repositioning of the $d$-band center.