Unusual defect properties in multivalent perovskite ${\mathrm{Cs}}_2{\mathrm{Au}}_2{\mathrm{I}}_6$: A first-principles study

Double halide perovskites have attracted increasing interest due to their great potential to eliminate the toxicity and instability issues in lead halide perovskites. Unfortunately, octahedral cation antisites easily form in common double halide perovskites and induce deep defect levels. Here, using first-principles calculation methods, we report unusual defect properties in the double halide perovskite ${\mathrm{Cs}}_2{\mathrm{Au}}_2{\mathrm{I}}_6$, including the coexistence of shallow and deep defect transition energy levels of iodine vacancies, absent of octahedral cation antisites, and different dominant donor defects such as interstitials $\left({\mathrm{Au}}_{\mathrm{i}}\right)$ and I substituting Au $\left({\mathrm{I}}_{\mathrm{Au}}\right)$. We attribute these unusual defect properties to the multivalence effect of Au and strong covalent bonding between Au and I. Based on the defect properties, we propose two possible applications of ${\mathrm{Cs}}_2{\mathrm{Au}}_2{\mathrm{I}}_6$. On one hand, ${\mathrm{Cs}}_2{\mathrm{Au}}_2{\mathrm{I}}_6$ could be a useful candidate for photodetectors under I-rich growth conditions due to its relatively low carrier densities because the Fermi level is pinned near the middle of the band gap due to the strong compensation of the dominant donors ${\mathrm{Au}}_{\mathrm{i}}$ and acceptor ${\mathrm{V}}_{\mathrm{Cs}}$. On the other hand, ${\mathrm{Cs}}_2{\mathrm{Au}}_2{\mathrm{I}}_6$ can be made $n$-type if it is grown under I-poor conditions, which can be further enhanced by growing the sample at 600 K and then quenching to 300 K. Consequently, ${\mathrm{Cs}}_2{\mathrm{Au}}_2{\mathrm{I}}_6$ has potential as an $n$-type photovoltaic absorber. Our studies not only enrich the defect physics in multivalent double halide perovskites but also provide useful information for advancing ${\mathrm{Cs}}_2{\mathrm{Au}}_2{\mathrm{I}}_6$ technologies.

Figure 1

(a) Primitive cell of ${\mathrm{Cs}}_2{\mathrm{Au}}_2{\mathrm{I}}_6$. The Cs, Au, and I atoms are shown with green, gold, and purple spheres, respectively. (b) The rock-salt-type ordering of the compressed and elongated octahedrons surrounding Au1 and Au2 atoms. The compressed and elongated octahedrons are shown with light yellow and dark yellow squares, respectively. Different octahedral environments make Au1 and Au2 exist as ${\mathrm{Au}}^{1+}$ and ${\mathrm{Au}}^{3+}$ valence, respectively, leading to different defect natures.

Figure 2

(a) Electronic band structures of ${\mathrm{Cs}}_2{\mathrm{Au}}_2{\mathrm{I}}_6$ using the PBE functional (red dashed lines) and the HSE hybrid functional (black lines). The energy difference between the direct band gap at N and the indirect band gap is within a few meV ensuring that the material remains an excellent light absorber. (b) Total and partial density of states of ${\mathrm{Cs}}_2{\mathrm{Au}}_2{\mathrm{I}}_6$, where the Fermi level is set at zero. (c) The partial charge density of the CBM of ${\mathrm{Cs}}_2{\mathrm{Au}}_2{\mathrm{I}}_6$. (d) The partial charge density of the VBM of ${\mathrm{Cs}}_2{\mathrm{Au}}_2{\mathrm{I}}_6$. In order to better display the partial charge densities in (c) and (d), Cs atoms in the original cell are removed. The CBM is mainly derived from the hybridization of ${\mathrm{Au}}^{3+}\text{−}5\mathrm{d}$ $\left({\mathrm{Au}}^{3+}\text{−}5{\mathrm{d}}_{x_2\text{−}{y}_2}\right)$ orbitals and $\mathrm{I}{2}^{\text{–}}\text{−}5\mathrm{p}$ orbitals while the VBM is mainly made up of the ${\mathrm{Au}}^{1+}\text{−}5\mathrm{d}$ $\left({\mathrm{Au}}^{1+}\text{−}5d_{z_2}\right)$ orbitals and ${\mathrm{I}}^{\text{–}}\text{−}5\mathrm{p}$ orbitals.

Figure 3

Calculated phase diagram of ${\mathrm{Cs}}_2{\mathrm{Au}}_2{\mathrm{I}}_6$ using the HSE hybrid functional against other competitive phases (Cs, Au, I, CsAu, CsI, ${\mathrm{CsI}}_3$, ${\mathrm{CsI}}_4$, AuI, ${\mathrm{Cs}}_2\mathrm{AuI}$). The purple blue polygon surrounded by A, B, C, D, and E points indicates the stable region of the single phase, where ${\mathrm{Cs}}_2{\mathrm{Au}}_2{\mathrm{I}}_6$ can be grown under thermodynamic equilibrium condition.

Figure 4

Calculated formation energies of intrinsic defects in ${\mathrm{Cs}}_2{\mathrm{Au}}_2{\mathrm{I}}_6$ as a function of ${\mathrm{E}}_{\mathrm{F}}$, when (${\mu }_{\mathrm{Cs}}$, ${\mu }_{\mathrm{Au}}$) is at the five representative chemical potential points (A, B, C, D, and E) in Fig. 3. The slopes of the lines indicate the defect charge states. Defects with very high formation energy are shown by the dashed lines. The materials grown at point A (I-poor) has good n-type, which has potential to be a suitable $n$-type photovoltaic absorber. ${\mathrm{Cs}}_2{\mathrm{Au}}_2{\mathrm{I}}_6$ could be a useful candidate for photodetectors under I-rich growth conditions (points B, C, D, and E) due to its relatively low carrier densities, because the Fermi level is pinned near the middle of the band gap.

Figure 5

Calculated transition energy levels for intrinsic donor (black lines) and acceptor (red lines) defects in ${\mathrm{Cs}}_2{\mathrm{Au}}_2{\mathrm{I}}_6$, which are referenced to the CBM and VBM of the host, respectively. The valence band below VBM and the conduction band above CBM are shown with shaded regions with ${\mathrm{E}}_{\mathrm{F}}<0\mathrm{eV}$ and ${\mathrm{E}}_{\mathrm{F}}>1.31\mathrm{eV}$, respectively.

Figure 6

(a) and (b) show the Fermi level, carrier density, and defect density as functions of the chemical potential of Cs under thermodynamic equilibrium growth condition at $T=300$ and 600 K, respectively. The quenched (to $T=300\mathrm{K}$) Fermi level, carrier density, and defect density from 600 K as functions of Cs chemical potential are shown in (c). The $n$-type property of ${\mathrm{Cs}}_2{\mathrm{Au}}_2{\mathrm{I}}_6$ can be further enhanced by growing the sample at 600 K and then quenching it to 300 K. (The unit of carrier density and defect density is $\mathrm{c}{\mathrm{m}}^{\text{–}3}$.)