Computational design of low-band-gap double perovskites

Using density functional theory (DFT) based calculations, we propose a family of metastable, as-yet unmade V${}^{5+}$ and Cr${}^{6+}$ double perovskite compounds with low band gaps spanning much of the visible region of the solar spectrum. Through analysis of a related set of measured optical gaps of $d^0$ ABO${}_3$ perovskites and A${}_2$B${}^{\prime }$BO${}_6$ double perovskites, an ad hoc procedure is developed to correct DFT and many-body perturbation theory gaps, bringing them into quantitative agreement with experiment for measured compounds, and predicting that V${}^{5+}$ and Cr${}^{6+}$ double perovskites would have gaps ranging from approximately 1.1 to 2.4 eV, significantly lower than previous materials studied in this class. DFT calculations also establish that these V${}^{5+}$ and Cr${}^{6+}$ compounds are likely able to be synthesized, either in bulk form or as epitaxial thin films. These compounds would comprise a new class of semiconducting double perovskites for potential use in solar energy conversion and other optoelectronic applications.

Figure 1

(a) The double perovskite structure, with rock-salt B-site ordering. (b) LDA densities of states (DOS) of SrTiO${}_3$, Sr${}_2$ScVO${}_6$, and Sr${}_2$CaCrO${}_6$, in which the valence band maxima are defined as zero energy. (c) LDA (light red), $G_0{W}_0$@LDA (light blue), and HSE06 (light green) band gaps of twelve hypothetical V${}^{5+}$ and Cr${}^{6+}$ double perovskites with rock-salt B-site ordering. Estimated optical gaps (red, blue, green) based on the assumption that computational errors are equal to those of SrTiO${}_3$. Estimated optical gaps (black) based on the modification of LDA gaps using linear corrections in $\frac{1}{{\epsilon }_{\infty }}$ and ${\Delta }_{\mathrm{X}}$ (see text). Error bars ($\pm 0.20$ eV) indicate uncertainty, as determined by the standard deviations of the fits for known compounds. The dashed line represents the optical gap of SrTiO${}_3$.

Figure 2

LDA (red), $G_0{W}_0$@LDA (blue), and HSE06 (green) electronic gaps versus experimental optical gaps of compounds synthesized and measured in Ref. 11. Compounds are grouped according to the more highly charged B-site cation, the primary component of the conduction band.

Figure 3

(a) Differences between optical and LDA gaps (${\Delta }_{\mathrm{LDA}}$) versus $\frac{1}{{\epsilon }_{\infty }}$ for 30 compounds synthesized and measured in Ref. 11. (b) ${\Delta }_{\mathrm{LDA}}$ vs ${\Delta }_{\mathrm{X}}$ (see text). (c) ${\Delta }_{\mathrm{LDA}}$ versus both $\frac{1}{{\epsilon }_{\infty }}$ and ${\Delta }_{\mathrm{X}}$. Dashed lines and planes are least-squares fits to the data shown. Compounds are grouped according to the more highly charged B-site cation, the primary component of the conduction band.

Figure 4

(a) The most unstable phonon frequencies at the zone center of a $2\times 2\times 2$ perovskite unit cell for twelve hypothetical V${}^{5+}$ and Cr${}^{6+}$ double perovskites with rock-salt B-site ordering, with phonon modes in which B-site cations move (“translational”) shown separately from others (“rotational”). (b) Computed phonon dispersion relations of Ba${}_2$ScVO${}_6$ (left) and Ba${}_2$CaCrO${}_6$ (right) with undistorted rock-salt B-site ordering. Real frequencies indicate stability with respect to distortion.

Figure 5

(a) The six distinct B-site orderings of A${}_2$B${}^{\prime }$BO${}_6$ double perovskites in a $2\times 2\times 2$ perovskite unit cell. (b) Total energies per formula unit, relative to the rock-salt B-site ordering of each compound and in the absence of symmetry-breaking distortions. (c) The most unstable phonon frequencies at the zone center of a $2\times 2\times 2$ perovskite unit cell for the distinct B-site orderings of Ba${}_2$ScVO${}_6$ and Ba${}_2$CaCrO${}_6$, with phonon modes in which B-site cations move (“translational”) shown separately from others (“rotational”).

Figure 6

The DFT-LDA total energy per formula unit of the ferroelectric (FE) columnar ordering of twelve hypothetical V${}^{5+}$ and Cr${}^{6+}$ double perovskites relative to rock-salt ordering (blue), and DFT-LDA gaps of both geometries (green, red).