Optoelectronic Properties and Defect Physics of Lead-free Photovoltaic Absorbers Cs$_2$Au$^{I}$Au$^{III}$X$_6$ (X=I, Br)

TL;DR

This study explores lead-free gold mixed-valence halide perovskites Cs$_2$Au$_2$X$_6$ (X=I, Br, Cl) as promising, stable, and non-toxic photovoltaic materials with high efficiency potential, while analyzing defect physics that could impact performance.

Contribution

It introduces a new class of lead-free perovskites with favorable optoelectronic properties and provides insights into defect physics affecting their photovoltaic performance.

Findings

High optical absorption near the band gap.

Potential deep-level defects that can trap carriers.

Higher simulated efficiency than MAPbI$_3$.

Abstract

Stability and toxicity issues with the hybrid lead iodide perovskite MAPbI$_3$ necessitate a hunt for potential alternatives. Here, we shed light on promising photovoltaic properties of gold mixed-valence halide perovskites Cs$_2$Au$_2$X$_6$ (X = I, Br, Cl). They satisfy fundamental requirements such as nontoxicity, better stability, a band gap in the visible range, and a low excitonic binding energy. Our study shows a favorable electronic structure, resulting in a high optical-transition strength, and thus a sharp rise in the absorption spectrum near the band gap. This, in turn, yields a very high short-circuit current density and hence higher simulated efficiency compared with MAPbI$_3$. However, careful investigation of defect physics reveals the possibility of deep-level defects (such as V$_X$ , V$_{Cs}$, X$_{Au}$, X$_{Cs}$, Au$_i$, and Au$_X$ , X = I, Br), depending on the growth conditions. These can act as carrier traps and become detrimental to photovoltaic performance. The present study should help in taking necessary precautions in synthesizing these compounds in a controlled chemical environment, which should minimize performance limiting defects and pave the way for future studies on this class of materials.

Figures

Tables

Table 1. Table 1: Formation enthalpy ( Δ ​ H f Δ subscript 𝐻 𝑓 \Delta H_{f} ) simulated and experimental band gap ( E g subscript 𝐸 𝑔 E_{g} ), difference between electronic and optically allowed direct gap ( Δ Δ \Delta E g d ​ a superscript subscript 𝐸 𝑔 𝑑 𝑎 E_{g}^{da} ), short circuit current density (J sc ), open circuit voltage (V oc ), current density (J max ) and voltage (V max ) at maximum power, SLME and fill factor (FF) at 298 K for the three compounds. Various device related parameters are calculated at a film thickness of 500 nm. For comparison, relevant data for MAPbI 3 are also tabulated. a Liu et al. ( 1999 ) , b Filip and Giustino ( 2014 ) , c Yin et al. ( 2015 )

Compound	$\Delta H_f$	$E_g$(eV)	$E_g$(eV)	$\Delta$$E_g^{da}$	Jsc	Jmax	Voc	Vmax	SLME	FF
	(meV/atom)	HSE06+GW	(Expt.)a	(meV)	(mA/cm2)	(mA/cm2)	(V)	(V)	$\eta$%
Cs2Au2I6	-66.75	1.45	1.31	13.3	33.02	32.15	1.04	0.95	30.41	0.89
Cs2Au2Br6	-109.97	1.61	1.60	17.1	22.90	22.43	1.31	1.21	27.19	0.91
Cs2Au2Cl6	-138.14	2.08	2.04	16.2	12.20	12.01	1.72	1.62	19.40	0.92
MAPbI3	-71.65	1.72(SS-G0W0)b	1.50c	0	16.76	16.40	1.27	1.17	19.21	0.90

Equations

$$E^{form}[D^q]=E^{tot}[D^q]$$

$$2\Delta {\mu }_{Cs}+2\Delta {\mu }_{Au}+6\Delta {\mu }_X=\Delta H_f(X=Br,I)$$

$$\Delta {\mu }_i<0,i=Cs,Au,X$$

$$a\Delta {\mu }_{Cs}+b\Delta {\mu }_{Au}+c\Delta {\mu }_X<\Delta H_f(C{s}_{a}A{u}_b{X}_c)$$

Full text

I. Introduction

Since its inception in 2009, hybrid lead halide perovskite has become the center of attention in the photovoltaic community. High optical absorption and defect tolerance made its efficiency as high as 22.1%, almost comparable to commercial silicon solar cells.Kojima et al. (2009); Qian et al. (2016); Yin et al. (2015) Despite being highly efficient, it still has not been commercialized till date, mainly due to two reason, (i) poor stability in ambient environment (ii) toxicity due to Pb. While replacing the organic cation with inorganic Cs has helped in stability, but the presence of Pb seems insurmountable till now. A lot has been proposed as alternatives but either they were even more unstable or the efficiency is low.Frolova et al. (2016); Kumar et al. (2016); Noel et al. (2014); Yokoyama et al. (2016) One of the key alternatives which emerges recently are double perovskite halides, A2BB${}^{{}^{\prime}}$X6Volonakis et al. (2016) where A is Cs, X is one of the halides, and B, B${}^{{}^{\prime}}$ are +1, +3 elements or vice versa. There exists various theoretical and experimental studies exploring different B, B${}^{{}^{\prime}}$ combinations, but most of these compounds either have indirect band gap (leading to higher recombination loss) or the gap is in high violet region due to the optically forbidden transition (leading to poor absorption).Chakraborty et al. (2017); Meng et al. (2017); Xiao et al. (2017) Some solution has been reported showing indirect to direct transition but toxicity was still a concern.Slavney et al. (2017); Tran et al. (2017); Kangsabanik et al. (2018)

Cs2Au2X6 (X=I, Br, Cl) are a class of compounds which show semiconducting behavior at ambient condition.Liu et al. (1999); Kojima and Matsushita (2000) Although the predicted band gaps for these materials are quite favorable for solar absorption, however they were never being investigated from the photovoltaic perspective. Very recently, Debbichi et al.Debbichi et al. (2018) reported a theoretical study on Cs2Au2I6 and proposed it as a promising photovoltaic absorber. This was further confirmed by Giorgi et al.Giorgi et al. (2018) who showed the presence of weakly bound excitons in this compound, (similar to MAPbI3) hinting towards good photovoltaic performance. However, few key points are not properly addressed in these studies e.g. (i) nature of band gap (ii) estimation of solar efficiency, etc. In addition, these studies are only focused on Cs2Au2I6 compound, although the other halide compounds also have band gap in the visible range. Apart from these, defect physics of these compounds has never been studied. This is extremely important because defects in photovoltaic materials play a crucial role in dictating the device efficiency. For example, presence of a deep level defect which can act as electron-hole recombination center, limits the carrier diffusion to a greater extent.Walsh and Zunger (2017) While synthesizing, it is therefore very important to create a chemical environment which minimizes the defect concentration in a compound.

In this paper, we have performed a detailed first principle calculation to study the electronic, structural, and optical properties of the full series Cs2Au2X6 (X=I, Br, Cl) from a perspective of photovoltaic applications. Careful analysis of band structure reveals slightly indirect nature of band gap, in contrast to earlier reports.Debbichi et al. (2018); Giorgi et al. (2018) However the optically allowed direct band gap remains within a few meV from the electronic gap, resulting in exciting optoelectronic behavior. Chemical, mechanical, and dynamical stability of all the compounds are also studied. In addition, we have investigated the possibility of point defect formation under various growth environments and found that even in anion rich condition, there is a possibility of the formation of deep level halide vacancies in Cs2Au2X6. In addition, few other deep level defects are likely to form depending on the material and chemical environment, which may hinder its performance as photovoltaic absorber. Additionally, we have also simulated the series of compounds made of organic cations in place of Cs i.e. MA(CH3NH${}_{3}^{+}$), FA(CH(NH2)${}_{2}^{+}$), and investigated their possibility of formation and potential as photovoltaic absorber. All the calculations are done by employing first principles Density Functional Theory (DFT)Kohn and Sham (1965) as implemented in Vienna Ab-initio Simulation Package (VASP).Kresse and Furthmüller (1996); Kresse and Joubert (1999) Other details of the calculations are given in Appendix A.

II. Structural details and Stability

Under the ambient condition, Cs2Au2X6 (X=I, Br, Cl) crystallizes in double perovskite structure with space group I4/mmm( #139). In this structure, Cs atoms sit at 4d Wyckoff site, Au(1) and Au(2) at 2b and 2a respectively while the anions sit at two inequivalent 4e(X(1)) and 8h(X(2)) sites. Here Au(1) and Au(2) possess +1, and +3 oxidation state respectively, making it possible to have all the features of double perovskite. Halogens form alternate linear [Au(1)X2]-, and square-planar [Au(2)X4]- complexes.Kojima and Matsushita (2000); Liu et al. (1999) The presence of alternately arranged elongated, and compressed AuI6 octahedra can be seen in Fig. 1(a), and can be confirmed from respective Au-X bond lengths (see SMsup ), which matches well with previous experimentally reported data.Riggs et al. (2012)

First, we checked the chemical, mechanical, and dynamical stability of these compounds. For chemical stability, we have calculated the formation enthalpy ($\Delta H_{f}$) against the binary halides in the following pathway: $\text{M}_{2}\text{Au}_{2}\text{X}_{6}\rightarrow 2\text{MX}+\text{AuX}+\text{AuX}_{3}$ (M=Cs, MA, FA; X=I, Br, Cl). They are presented in Table 1 (for inorganic compounds). Going from I $\rightarrow$ Br $\rightarrow$ Cl, the chemical stability increases. For mechanical stability, we calculated the elastic constants (tabulated in SMsup ) which satisfies the Born Huang mechanical stability criteria for all three halides.Born and Huang (1954) Calculated phonon dispersions (shown in SMsup ) show no imaginary frequencies, and hence confirms the dynamical stability.

III. Electronic structure

Figure 1(c, d, e) shows the electronic band structure calculated using hybrid (HSE06) functionalKrukau et al. (2006) for the three compounds. Cs2Au2I6 forms an intermediate band comprised mainly of Au(2) $5d_{x^{2}-y^{2}}$ and I-p orbitals, which is responsible for its band gap (1.31 eV) in the visible range.Kojima and Kitagawa (1994); Giorgi et al. (2018) The valence band maxima (VBM) consists mainly of Au(1) $5d_{z^{2}}$ and I-p orbital. In the case of Br and Cl, orbital contributions seem to be similar, but the band gap increases due to increase in nearest neighbors Coulomb interaction and Jahn-Teller distortion.Liu et al. (1999) For better accuracy, we have used HSE06 functional to simulate the band edge information, whereas, the band gap values are calculated using quasiparticle G0W0 calculations starting from wavefunction obtained using HSE06 functional. Our calculation reveals that all these materials have a slightly indirect band gap, having VBM and conduction band minima (CBM) at different points along $\Gamma$ to $\Sigma^{{}^{\prime}}$ direction, in contrast to the previous reports Debbichi et al. (2018); Giorgi et al. (2018), where a direct band gap is predicted at high symmetry N-point. This is due to the fact that, a more detailed Brillouin zone sampling (i.e. considering an important $\Gamma$-$\Sigma^{{}^{\prime}}$ direction in the band structure, where the actual VBM and CBM lies) is done in our study. We have also calculated the dipole transition matrix elements (aka transition probability) showing allowed optical transition at direct band gap [see Fig. S3 of SMsup ]. High transition strength indicating the possibility of high absorption can be attributed to the mixing of halogen p and Au d orbitals.Heo et al. (2017) Table 1 shows our simulated band gap along with the difference between indirect and optically allowed direct gap (\Delta$$E_{g}^{da}). Incorporation of spin orbit coupling (soc), does not show any significant effect on the optoelectronic properties of Cs2Au2I6 (band gap (Eg) changes by 0.07 eV and $\Delta$E${}_{g}^{da}$ remains same). This in turn, shows a negligible change in simulated efficiency. That is why, we have not used soc in our calculation for the other compounds, for which the effects are expected to be even less. Our simulated band gaps matches fairly well with previously reported experimental values.Liu et al. (1999) We have also checked the properties of organic cation namely MA and FA counterpart of these compounds. Our calculated lattice parameters for MA2Au2I6 agrees well with previous experimental data.Evans et al. (2017) All the other electronic structure data along with the band structure and transition probabilities are shown in SM.sup All the organic mixed valence gold perovskite compounds show fairly large band gap, restricting their application as photovoltaic absorber.

IV. Absorption coefficient and Spectroscopic Limited Maximum Efficiency (SLME)

Finite values of calculated transition probability encourage us to simulate the next relevant parameters for photovoltaic applications, i.e. absorption coefficients and spectroscopic limited maximum efficiency (SLME). Details about SLME formulation is given in SM,sup which is a better indicator of photovoltaic efficiency than the bare Shockley-Queisser limit.

Figure 2(a) and 2(b) show the absorption coefficients ($\alpha$) and SLME respectively for the three systems. For comparison, corresponding simulated data for MAPbI3 are also shown. From Fig. 2(a), one can see that the absorption coefficient in xy-plane is order of magnitude higher than those in the z-direction, confirming strong optical anisotropy of the material.Debbichi et al. (2018); Giorgi et al. (2018) This gives us an idea about appropriate alignment of the crystal axes, so as to maximize the photo absorption. Careful analysis reveals that the first optical peak along xy-direction can be attributed to vertical transition between two highest valence states (comprising of mainly Au(1) $5d_{z^{2}}$ orbitals) and two lowest conduction states (Au(2) $5d_{x^{2}-y^{2}}$ and I $p_{z}$ orbitals), whereas along z-direction it is due to the transition from lower part of the valence band (Au(1) $5d_{xz,yz}$) to the intermediate band, explaining the significantly higher optical absorption in xy-plane.Giorgi et al. (2018)

Looking at the absorption spectra one can see a sharp rise in absorption coefficient ($\alpha$) near the band gap for all three halides. Although in lower wavelength region the absorption coefficient is higher for MAPbI3, but a lower band gap (for Cs2Au2I6), and sharper rise of absorption spectra near band edge for both iodide and bromide compounds indicate better utilization of the solar spectrum. This can further be confirmed by our simulated short-circuit current density (Jsc). For completeness, we have tabulated room temperature (298 K) simulated values of few important device parameters, such as Jsc, open-circuit voltage(Voc), current density(Jmax) and voltage(Vmax) at maximum power output, SLME and fill factor(FF) at film thickness 500 nm for all three halides in Table 1, and compared the same with MAPbI3. Notice that, Jsc and Jmax are almost twice for Cs2Au2I6 as compared to MAPbI3, which becomes almost 1.5 times at saturation thickness. Slightly lower attainable voltage makes the efficiency 1.5 times at lower film thicknesses, and at least 3% higher at saturation thickness. A little higher band gap makes Cs2Au2Br6 to have higher attainable voltage making the SLME much higher than MAPbI3 at lower film thicknesses, while it becomes comparable when thickness goes near saturation (see Fig. 2). For Cl, efficiency remains much lower compared to the other two halides, mainly due to higher band gap resulting in much lower attainable current.

V. Defect Physics

Defects play a major role in dictating the carrier mobility, lifetime, and recombination rate for a given semiconductor. Unlike extended defects (e.g. grain boundaries, surface passivation, etc.), intrinsic point defects (vacancies, interstitial, antisites, etc.) are very difficult to control.Wallace et al. (2017); Walsh and Zunger (2017); Park et al. (2018) For example, in case of MAPbI3, shallow dominant point defectsYin et al. (2014) result in high carrier diffusion length aiding to its high efficiency. Whereas presence of deep level defects, acting as Shockley-Read-Hall (SRH) recombination centers, are known to be one of the main reasons behind significantly lower efficiency in case of kesterite (CZTS) solar cells.Wallace et al. (2017) In order to gain better insight, we performed a detailed ab-initio study of all the possible point defects in Cs2Au2I6 and Cs2Au2Br6, which are predicted to have comparable or higher theoretical efficiency than MAPbI3.

Formation energy for a defect $D$ at a charge state ‘$q$’ is defined as,

[TABLE]

Where $E^{tot}$[$D^{q}$] is the total energy for a supercell with the associated defect $D$ at a charge state ‘$q$’. $E^{tot}[bulk]$ is the total energy for pure bulk supercell of equivalent size. $\mu$i is the chemical potential of the associated defect with $n_{i}$ being the number of defects added ($n_{i}>0$) or removed ($n_{i}<0$). The next term accounts for the chemical potential for electrons added ($q<$0) or removed ($q>$0) to create various charged defect states. $E_{VBM}$ is the energy at valence band maxima, $\Delta E_{F}$ can be varied from 0 (at VBM) to band gap $E_{g}$ (at CBM). $E_{c}$ is the correction term which includes electrostatic and potential alignment corrections for charged defects.Freysoldt et al. (2009) We also include the correction for band gap underestimation by PBE exchange correlation functional,Perdew et al. (1996) via incorporating the band edge (both VBM and CBM) shifts obtained by more accurate quasiparticle G0W0 calculations.Lany and Zunger (2008) More details about band gap corrections are provided in Appendix B.

Three types of defects are considered, vacancies (VCs, VAu, VX), interstitials (Csi, Aui, Xi), and anti-sites (CsAu, CsX, AuCs, AuX, XCs, XAu), (X=I, Br), etc. Two inequivalent Wyckoff positions for both X and Au are considered. To accurately calculate various defect charge state energies, a 160 atom supercell is used. Further discussions on the choice of defects are presented in Appendix C.

It is extremely important to notice that, $E^{form}(D^{q})$ can vary depending on the particular choice of $\mu$. Experimentally, this chemical potential can vary depending on the growth environment. The choice of $\mu$ generally depends on the stability of the compound against possible elemental and/or competing secondary phases. As secondary phases, we have considered the most stable binary halides and other super-ordered structures of the cations.

First, for the compound to be stable the below thermodynamic equilibrium must be reached,

[TABLE]

Here, $\Delta H_{f}$ is the formation enthalpy of the compound against its elemental constituents. $\Delta\mu_{i}=\mu_{i}-\mu^{0}_{i}$ where $\mu^{0}_{i}$ is total energy of constituent ‘$i$’ at its elemental phase. Following are a set of equations, which should be satisfied to avoid co-existence of elemental and secondary phases,

[TABLE]

[TABLE]

where, a,b,c=0,1,2….Z.

Figure 3(a,b) shows the phase diagrams for Cs2Au2I6 and Cs2Au2Br6 against their possible competing elemental and secondary compound phases (taken from Materials Project database.Jain et al. (2013)) The brown shaded areas in both the figures show allowed chemical potential region for the constituents, keeping the intended material stable. We have taken seven different sets of allowed chemical potentials for each halide (shown as A,B,C,D,E,F,G points in respective diagrams), which represent various chemical environments, from cation poor/anion rich to cation rich/anion poor conditions. We have drawn the respective defect formation energy diagram for each of them. The related $\Delta\mu_{i}$ values and corresponding defect formation energy plots can be found in SM.sup

Figures 4 and 5 show the defect formation energies for various intrinsic defects as a function of Fermi level in three different chemical growth conditions, (a) cation poor/anion rich and (b) cation rich/anion poor, and (c) moderate cation/anion, for Cs2Au2I6 and Cs2Au2Br6 respectively. These three phases are marked as point $`$A’, $`$E’ ($`$D’ for X=Br) and $`$G’ in the respective phase diagrams in Fig. 3, and corresponding $\Delta\mu$ values can be found in SM.sup Most probable defects (setting a cut-off of Eform[Dq] $\sim$0.75 eV) are highlighted with respect to the Fermi level pinning in these figures. We have also considered a few other possible growth environments (points $`$A’-$`$G’ in Fig. 3), whose defect formation energies are shown in SM.sup Line styles (symbols) for various defects, in all the three growth environments, are shown in the right hand panel of Fig. 4(c) and 5(c). For Cs2Au2I6, at cation poor/anion rich environment (Fig. 4(a)), the dominant acceptor type defects are VCs, VAu(1), (IAu(1) will act as neutral defect at this Fermi level pinning) whereas VI and Au(1)i are dominant donors. There is another neutral defect Au(1)Cs, which can form at a high concentration, but because it does not show any charge state transition in the band gap, the Fermi level will be pinned at almost middle of the gap where VCs and VI(1) intersects. At cation rich/anion poor environment (Fig. 4(b)), donor defects (mostly iodine vacancies) are likely to drag the Fermi level more close to the CBM, where the main acceptor defects will be cation (Cs, Au(1)) vacancies and IAu(1). At this growth condition, the material will show low n-type carrier concentration. At moderate cation/anion condition (Fig. 4(c)), the Fermi level pinning will be at a position near the mid gap region, indicating very low intrinsic carrier concentration. Overall, one can see that iodine vacancies (along with VCs) are most dominant ones at all growth conditions, in which VI(1) is more probable than VI(2). Apart from these, there are other possible defects which are likely to dominate depending on the chemical environment. These defects show deep transition levels well in the band gap, and may act as SRH recombination centers, hindering the photovoltaic (PV) efficiency. In case of bromide compound, vacancy at two inequivalent halide sites show different formation energies, with VBr(2) being the more probable one. At cation poor/anion rich environment (Fig. 5(a)), contribution from acceptor VCs will be mainly compensated by donors VBr(2) and Au(1)i, pinning the Fermi level at the p-type side of the band gap. At this Fermi level pinning, a number of other deep level donor defects (such as Au(2)Cs, Au(2)Br(2), Au(2)i, VBr(1), etc.) and acceptor VAu(1) is likely to form. A very low n-type concentration is expected at cation rich/anion poor growth condition (see Fig. 5(b)). Most of the defects will still be present when a moderate cation/anion environment is maintained (Fig. 5(c)), pinning the Fermi level in the middle of the band gap. In all these growth environments, Fermi level pinning is mostly positioned near the mid gap region, which explains the experimental observation of high resistivity in these compounds. Riggs et al. (2012)

Overall analysis of these two halides from stability (phase diagram) and defect tolerance perspective indicates that, utmost care needs to be taken while synthesizing these compounds because the single phase stability region for both of them are rather small. In addition, both the compounds show possibility of numerous deep level defects (even more so given the high temperature ($\sim$900 K) synthesis procedure reported in Riggs et al. (2012)) which may act as carrier traps and thus substantially reduce the VOC, in practice. As such, in spite of the excellent optoelectronic properties, Cs2Au2X6 may have limited PV performance due to the possibility of deep level defects. Nevertheless, there exists few well known compounds, such as CIGS, CZTS etc., where the formation of defect complexes has been reported to make the deep level defects electrically benign.Park et al. (2018) In case of gold mixed halides, a number of defect complexes can be possible, thus requiring further studies to get a deeper understanding.

VI. Conclusion

In summary, we have carried out a detailed analysis of optoelectronic properties and defect physics of Cs2Au2X6 (X=I, Br), two compounds with several favorable properties such as non-toxicity, better stability and simulated efficiency etc. First principles simulations predict these compounds to have slightly indirect nature of band gap, with optically allowed direct band gap remaining very close (within 20 meV) to the indirect gap, allowing the optical absorption to be very high. The value of band gap falling in the visible region and sharp rise of absorption coefficient near band edge yields reasonably high simulated efficiency (even at very small film thickness). Our study on defect physics, however, predicted the possibility of deep level defects in both of these materials. Halide vacancies are observed to be most dominant defects. Cation vacancies (VCs, VAu(1)), interstitials and few antisite defects will also form depending on the material and growth environment. The existence of deep level defects (which can act as trap states) will probably make the materials prone to carrier loss due to non-radiative recombination. Analysis of the defect physics (Fermi level pinning, dominant defects, etc.) explains some of the experimental observations reported earlier. Nevertheless, we believe that, the present study will guide experimentalists to employ optimal chemical growth conditions to carry out future studies on these compounds and also help theoreticians to work on similar aspects of related materials.Gajdoš et al. (2006); Yu and Zunger (2012); Shockley and Queisser (1961); Green (2004); Tiedje et al. (1984)

Acknowledgements

JK and SG have contributed equally to this work. They acknowledge financial support from IIT Bombay for research fellowship. AA and MA acknowledge National Center for Photovoltaic Research and Education (NCPRE) funded by Ministry of new renewable energy (MNRE), Government of India and IIT Bombay for possible funding to support this research.

I APPENDIX A: Computational Details

All the calculations are done using Density Functional Theory (DFT) Kohn and Sham (1965) as implemented in Vienna Ab-initio Simulation Package (VASP) Kresse and Furthmüller (1996); Kresse and Joubert (1999) with projector augmented Wave (PAW) basis set. Finding the equilibrium structure, calculation of decomposition enthalpy and other primary electronic structure (band structure, density of states etc.) were done using Perdew-Burke-Ernzerhof (PBE) exchange correlation functional.Perdew et al. (1996) Cs (5s25p66s1), Au (5d106s1), I (5s25p5), Br (4s24p5), Cl (3s23p5), C (2s22p2), N (2s22p3), and H (1s1) are used as valence electrons. An energy cutoff 500 eV with 6$\times$6$\times$6 $\Gamma$ centered k-mesh is considered for structural optimization and unit cells are relaxed until forces reached to the value less than 0.001 eV/Å for Cs2Au2X6; X=I, Br, Cl. For organic gold halides, we have replaced the Cs with MA (CH3NH3) and FA (CH(NH2)2) cations in the relaxed Cs2Au2I6 structure and then relaxed in 3 steps. At first, we did full geometrical relaxation then again performed relaxation with parameters keeping volume and shape fixed and at last we did full geometrical relaxation with 500 eV with 6$\times$6$\times$6 kpoints until forces converge to 0.01 eV/Å. Charge densities were calculated using energy cutoff of 450 eV, 8$\times$8$\times$8 k-mesh using the relaxed structures until energy converges up to 10*-6* eV. Next, we have used Heyd-Scuseria-Ernzerhof (HSE06)Krukau et al. (2006) functional to get the band edge information. To obtain more accurate value of band gap we have used G0W0 method along with HSE06 and PBE exchange correlation functional. Optical absorption coefficients are calculated within the independent particle approximation with PBE exchange correlation functional and then scissor shifted to experimental band gap while calculating the SLME. For simulation of various defects at different charge states, we have used 520 eV plane wave energy cutoff along with gamma centered k-mesh. For each defect in different charge states, we have only relaxed the ionic positions keeping the cell shape and volume fixed.

APPENDIX B: Corrections associated with charged defects and Band gap underestimation

For charged defects, there are a few sources of error that comes from the DFT approximation which uses a background charge to neutralize the supercell. This requires two corrections, one is electrostatic interaction term correction and the other is potential alignment term. We use the well documented Freysoldt, Neugebauer and Van de Walle (FNV) scheme to correct these errors.Freysoldt et al. (2009) Next we notice that for both the halides, PBE underestimates the band gap substantially. In practice, this can be seen as the shift of VBM (CBM) up (down) by $\Delta E_{VBM}$ ($\Delta E_{CBM}$) while showing a reduced band gap. This induces an underestimation in the defect formation energy by $\Delta E_{VBM}$ ($\Delta E_{CBM}$) per hole (electron) occupying the acceptor (donor) level, in case of acceptor (donor) type defects. Here to correct these, we calculate the shift in band edges from quasiparticle G0W0 calculations, which reproduce the experimental band gap very well in case of these two halides.Lany and Zunger (2008) We calculate the $\Delta E_{VBM}$ ($\Delta E_{CBM}$) to be 0.39 eV (0.26 eV) in case of Cs2Au2I6 and 0.49 eV (0.30 eV) for Cs2Au2Br6. All the defect formation energy calculations include the above mentioned corrections.

Note: We have used the same set of pseudopotentials for all the defect related calculations including phase diagrams, band edge shifts.

APPENDIX C: Choice of defects

Three types of defects are considered, vacancies (VCs, VAu, VX), interstitials (Csi, Aui, Xi), and anti-sites (CsAu, CsX, AuCs, AuX, XCs, XAu), (X=I,Br), etc.. For these compounds, there are two inequivalent Wyckoff positions for both halides, X and Au, which we have considered while considering the vacancy and anti-site defects. For the interstitials, we have considered all the possible positions and chosen the final position based on the total energy calculated at neutral charge state. As discussed earlier we denote Au*+1* and Au*+3* as Au(1) and Au(2) respectively. X(1) and X(2) (X=Br,I) represents halide anions at 4e and 8h Wyckoff sites respectively. Here we have used PYCDT codeBroberg et al. (2018) to generate the supercells with defects. To accurately calculate the various defect charge state energies a 160 atom supercell is used.