Highly Absorbing Lead-Free Semiconductor Cu2AgBiI6 for Photovoltaic Applications from the Quaternary CuI–AgI–BiI3 Phase Space

Since the emergence of lead halide perovskites for photovoltaic research, there has been mounting effort in the search for alternative compounds with improved or complementary physical, chemical, or optoelectronic properties. Here, we report the discovery of Cu2AgBiI6: a stable, inorganic, lead-free wide-band-gap semiconductor, well suited for use in lead-free tandem photovoltaics. We measure a very high absorption coefficient of 1.0 × 105 cm–1 near the absorption onset, several times that of CH3NH3PbI3. Solution-processed Cu2AgBiI6 thin films show a direct band gap of 2.06(1) eV, an exciton binding energy of 25 meV, a substantial charge-carrier mobility (1.7 cm2 V–1 s–1), a long photoluminescence lifetime (33 ns), and a relatively small Stokes shift between absorption and emission. Crucially, we solve the structure of the first quaternary compound in the phase space among CuI, AgI and BiI3. The structure includes both tetrahedral and octahedral species which are open to compositional tuning and chemical substitution to further enhance properties. Since the proposed double-perovskite Cs2AgBiI6 thin films have not been synthesized to date, Cu2AgBiI6 is a valuable example of a stable Ag+/Bi3+ octahedral motif in a close-packed iodide sublattice that is accessed via the enhanced chemical diversity of the quaternary phase space.


Single crystal X-ray diffraction (SCXRD)
Data were collected at 100K on a Rigaku MicroMax-007 HF diffractometer with a molybdenum rotating anode microfocus source and a Saturn 724+ detector using Rigaku Crystal Clear v2.0. Unit-cell indexation, data integration, and reduction were performed using Rigaku CrysAlisPro v171.38.43. The structure was solved and refined using SHELX-2013, 4 implemented through Olex2. 5

Compositional Analysis
Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray Spectroscopy (EDX) was used to measure the composition as a direct elemental analysis technique. Measurements were carried out using a Hitachi S-4800 SEM with an Oxford Instruments model 7200 EDS Xray detector. Quantification was carried out using the microanalysis suite of the Inca Suite software (Version 4.15). All powders and crystals were sputtered with 15 nm Au to limit charging effects. Transmission Electron Microscopy (TEM) EDX was carried out using an JEOL JEM 2000FXII TEM microscope operating a W electron source operated at 200 kV, using an EDAX EDX detector, with quantification carried out using EDAX Genesis Spectrum (Version 5.217, 21-Jan-2008). All samples were prepared by spreading a finely ground powder onto carbon coated Au grids. Beam intensity had to be lowered, by increasing the spot size of the beam, as to not decompose the samples. All compositions calculated from EDX measurements were normalised to the nominal iodide content unless otherwise stated. The one standard deviation (1σ) spread in compositions measured for powder standards CuI and AgI, as well was the synthesised BiI3, CuBiI4 and Cu2AgBiI6 samples, are shown in Table S4.

Photostability
For the experiments, a Solar Light Model 16S-300-002 Solar Simulator was used which has a spectral output that complies with air mass 1.5 (AM1.5) per the ASTM standard definition. The combination of neutral density filters and lamp-to-sample distance allowed for the tuning of the intensity of the incident light to 1000 W m −2 as measured by a Solar Light Pyranometer PMA2144 and datalogging radiometer PMA2100. Sample temperatures were monitored using a T-type thermocouple and were found to stay below 35°C. For measurements in sealed atmospheres, powder was loaded into thin-walled (0.01 mm wall thickness) borosilicate capillaries under ambient air, dry synthetic air, and helium, and these were sealed with a gas-oxygen torch. The capillaries were then placed in the solar simulator and subjected to the full solar spectrum at an intensity of 1000 W m −2 .

Raman Spectroscopy
The measurements were carried out on a Renishaw inVia Reflex with a Leica microscope utilising a 633 nm wavelength red laser with a maximum power of 6.5 mW. The powder samples were measured in borosilicate capillaries and were exposed to 0.5% of the maximum laser power to avoid decomposition of the sample. The spot size was 5 µm.

Photoluminescence (PL) Spectroscopy
The Cu2AgBiI6 film was mounted in a gas-exchange helium cryostat (Oxford Instruments, OptistatCF2) and photoexcited by a 398 nm picosecond pulsed diode laser (Picoquant, LDH-D-C-405M). The resultant PL was collected and coupled into a grating spectrometer (Princeton Instruments, SP-2558), which directed the spectrally dispersed PL onto a photon-counting detector (PDM series from MPD), whose timing was controlled with a PicoHarp300 TCSPC event timer. A laser fluence of 200 nJ cm -2 was used for both the spectral and transient measurements of Cu2AgBiI6, which were both taken at a temperature of 295 K. The PL decay trace in Figure S16b was measured at a wavelength of 720 nm. The PL decay trace was fitted by a stretched exponential function I = I0 exp(−(t/τ) β ), where β is the distribution coefficient and τ is the time taken for the PL intensity to drop to I0/e. Such stretched exponential functions have been used to phenomenologically account for the presence of a local distribution of monoexponential decay rates, whose average lifetime is given by τav = (τ/β) Γ(1/β), where Γ is the gamma function. [6][7] The PL spectrum for MAPbI3 in Figure S15 was measured using the same experimental setup, except it was mounted in a cold-finger cryostat (Oxford Instruments, MicrostatHe) and detected with an iCCD (PI-MAX4, Princeton Instruments), under a laser excitation fluence of 490 nJ cm -2 .The spectrum was previously published in Wright et al. 8

UV-Visible absorption measurements using FTIR spectrometer
The UV-Visible absorption spectra in Figure 3 in the main text were measured using a Bruker Vertex 80v Fourier transform infrared (FTIR) spectrometer, configured with a tungsten halogen lamp illumination source, a CaF2 beamsplitter and a silicon detector. The samples were mounted in a gas-exchange helium cryostat (Oxford Instruments, OptistatCF2). The MAPbI3 absorption spectrum was previously published in Davies et al. 9 THz photoconductivity An amplified laser system (Spectra Physics, MaiTai-Empower-Spitfire) with a central wavelength of 800 nm, 35 fs pulse duration and 5 kHz repetition rate was used to generate THz radiation via the inverse spin Hall effect, using an emitter made of 2 nm of tungsten / 1.8 nm of Co40Fe40B20/ 2 nm of platinum, supported by a quartz substrate. The transmitted THz radiation was detected using free-space electro-optic sampling with a 1 mm thick ZnTe (110) crystal, a Wollaston prism and a pair of balanced photodiodes. The THz pulse was measured in transmission geometry. The pump beam was frequency-doubled to 400 nm by a β-barium-borate (BBO) crystal. Charge-carrier mobilities 4 were calculated from the initial transmitted signal at time = 0 ps at fluences of 7.8, 15.3 μJcm −2 , as outlined in Wehrenfennig et al., 10 and measurements were carried out under vacuum (< 10 −2 mbar).

J-V characterisation
J-V characterisation was measured using a Keithley 2400 sourcemeter and simulated air-mass 1.5 global tilt (AM1.5G) solar irradiation using a Wavelabs Sinus-220 light-emitting diode array, calibrated with a certified Si reference cell. The areas being measured were defined by using a black anodised aluminium mask placed directly in contact with glass side of the substrate and an enclosed sample holder, to shadow the rest of the device.

Photothermal deflection spectroscopy (PDS)
PDS is an ultrasensitive absorption measurement technique that detects heating of the sample due to the non-radiative relaxation of absorbed light and is insensitive to reflection and scattering. PDS enables the detection of absorbance signals with 5-6 orders of magnitude weaker than the band edge absorption. For the measurements, a monochromatic Pump light beam is shined on the sample (film on Quartz substrate), which on absorption produces a thermal gradient near the sample surface via non-radiative relaxation induced heating. This results in a refractive index gradient in the area surrounding the sample surface. This refractive index gradient is further enhanced by immersing the sample in an inert liquid FC-72 Fluorinert® (3M Company) which has a high refractive index change per unit change in temperature. A fixed wavelength CW laser probe beam is passed through this refractive index gradient producing a deflection proportional to the absorbed light at that particular wavelength, which is detected by a photo-diode and lock-in amplifier combination. Scanning through different wavelengths gives us the complete absorption spectra. Because this technique makes use of the non-radiative relaxation processes in the sample, it is immune to optical effects like interference and scattering. Furthermore, PDS technique is a powerful technique to measure the sub-bandgap tail states in a semiconductor up to an absorption coefficient of 1 cm -1 .

Elliot Model Fitting
We use Elliott's formula 11 which expresses the absorption coefficient as a linear combination of the absorption of a bound exciton with the absorption by the joint continuum of states 9, 12 : Where E is the photon energy, Ex is the exciton binding energy, Eg is the band gap, n is the refractive index (at energy E), | | 2 = |⟨Ψ | |Ψ ⟩| 2 is the momentum matrix element, is the Dirac delta function, Θ( ) is the step function, is the reduced mass, m0 is the electron rest mass, e is the elementary charge, c is the speed of light in vacuum and ℏ is the reduced Planck's constant.
The experimental absorption spectrum is fitted with the following model: Where A is a fitting constant and the excitonic part of the absorption ( ′ ) and the continuum part ( ′ ) are convoluted with gaussian broadening functions and , respectively.

Optical Modelling
The generalised transfer matrix method was used to model the optical response of the stack. 13 The python libraries Numpy and Scipy were used to perform the calculations. Transfer matrix calculations take the complex refractive index spectrum and thickness for each layer as input. The calculation provides us with absorptance of each layer, and the transmittance and reflectance of the stack. We assumed perfect internal quantum efficiency and calculated the short circuit current as the overlap integral of the AM1.5 solar spectrum with the absorptance. The JV curve of each sub-cell was modelled as a single diode: = − 0 . Here, is the ideality factor. The recombination current 0 is calculated through the principle of detailed balance: 0 = ∫ ( ) ⋅ ,300 ( ) ⋅ ∞ 0 . Here ,300 ( ) is the blackbody photon flux at 300K, and ( ) is the absorptance calculated from the transfer matrix calculation. The following diode parameters were assumed for the Cu2AgBiI6 sub-cell: 14  (20-200nm), and Cu2AgBiI6 (1200−1800nm) were varied with the indicated bounds using a differential evolution algorithm till a PCE maximum was obtained. The stack used as input for the Transfer Matrix Calculations is given in Table S5. The source of optical constants for each layer are also cited. For Cu2AgBiI6, a "synthetic" absorption co-efficient was created by splicing a 74 meV tail (gradient 1/0.074 eV) between 1.0 eV−1.88 eV, extracted from the gradient of the absorption onset from the combined PDS and FTIR datasets, to the absorption co-efficient obtained from FTIR measurements. The absorption co-efficient was set to zero below 1.0 eV. This was then converted into the extinction coefficient ( Figure S21) which was transformed into the refractive index using the Kramer's Kronig relation: 16 . The described method assumes the following: 1. Transfer Matrix Model Limitation: Layer roughness is much smaller than the wavelength of light (~550nm).
2. The "synthetic" absorption coefficient created by appending a tail of energy 74 meV between 1.88-1.45 eV characterises the material well.
3. The same transport materials conventionally used for hybrid perovskites, C60/SnO2 and PolyTPD are used. This is a relatively minor assumption as most transport layers are thin and poorly absorbing in comparison to the absorber layer, so the precise transport layer does not matter.
4. The Cu2AgBiI6 sub-cell can be optimised to bring it to the same radiative efficiency (EQEEL = 1%) as a well-performing hybrid lead halide perovskite cell. The same shunt and series resistances ( ℎ = 5 Ω ⋅ 2 , = 4.2 Ω) can also be achieved.

Density Functional Theory Calculations
All periodic density functional theory calculations were performed using version 5.4 of the the VASP code 17 with the projector augmented wave method to describe core electrons. 18 The crystal structure prediction package ChemDASH 19 was used to generate low energy ordered configurations of atoms within (2a+b, a+2b, c) supercells of the disordered experimental structure. Four independent starting configurations were initially generated by randomly occupying the experimental mixed and partially occupied Bi, Ag and Cu sites within the cell. ChemDASH was then used to generate 249 further configurations from each starting configuration by swapping between Bi, Ag and vacancies on the octahedral sites, and Cu and vacancies on the tetrahedral sites. A basin hopping approach using a value for kBT of 0.01 eV/atom for the Metropolis acceptance criterion was used to ensure that low energy configurations were generated. The geometry of each configuration was optimised using the optB86b-vdW functional 20 to model the important van der Waals interactions between the large iodine anions within the structure. ChemDASH uses a multi-step approach to geometry optimisation, where the final step used here had a plane-wave energy cutoff of 500 eV and forces were minimised to below 0.02 eV/Å. The lowest energy configuration of the 249 generated starting from each of the four starting configurations were then taken forwards to calculate the electronic structure, giving four low energy configurations with significantly different Bi, Ag and Cu orderings. A more accurate geometry was obtained for each of these configurations by performing a further geometry optimisation with the optB86b-vdW functional but with a higher plane-wave energy cutoff of 550 eV and a denser k-point mesh with a k-point spacing of 0.1 Å −1 and to a tighter force threshold of 0.001 eV/Å for convergence ( Figure  S22). A single-point calculation using the SCAN meta-GGA functional 21 and including the effects of spin-orbit coupling was then used to compute the electronic structure of each of these four configurations, resulting in the partial density of states plots shown in Figure 3c and Figure S13. Band structure diagrams in Figure S14 for the lowest energy computed structure of Cu2AgBiI6 utilise the SCAN functional and including spin-orbit coupling effects Figure S1.   The number of octahedral sites occupied is ½ of the total allowed by the structure (due to the vacant layers), however in Cu2AgBiI6, the atomic occupancies of these sites are less than one (disordered). (d) The two tetrahedral sites of Cu2AgBiI6. Site Cu1 is found in the layers containing octahedral occupancy, and site Cu2 is found in the layers without octahedral occupancy. In Cu2AgBiI6, these Cu sites are not fully occupied (disordered) but do show layered ordering and therefore can be described as possessing partial layered ordering. Figure S4. The Pawley fit to room temperature laboratory PXRD data of CuBiI4. The PXRD pattern is fitted using a cubic unit cell with space group Fd3 ̅ m, previously reported by Fourcroy et al. 22 The extracted lattice parameter is a = 12.1580(2) Å.
G.OF. Χ 2 = 1.33 Figure S5. SEM EDX of the powder corresponding to nominal composition x = 0 Cu1-3xBi1+xI4, giving an average composition of Cu1.21(5)Bi1.11 (7)I4.00 (9), and referred to as CuBiI4 throughout the text. Figure S6. The PXRD patterns of (a) CuBiI4 as synthesised (b) CuBiI4 kept in the dark in air at room temperature for three weeks, and (c) CuBiI4 kept in the dark at -20°C for three weeks. The main peak of the BiI3 decomposition phase is marked by the asterisk. Figure S7. The PXRD patterns of AgBiI4 and Cu2AgBiI6 powders after being exposed to one week in the solar spectrum, sealed in capillaries in air. Also shown are the PXRD of the controls, which were kept in the dark in air. The range shown includes where the largest peaks would appear for possible decomposition phases AgI (black tick marks), CuI (red tick marks) and BiI3 (blue tick marks), should they have been present. Figure S8. (a) The Raman spectra of AgBiI4 and Cu2AgBiI6 control samples, showing the characteristic two peaks, which occur at low wavenumbers. The Raman spectra of AgBiI4 and Cu2AgBiI6 powders after being exposed to the AM1.5 solar spectrum in different atmospheres are shown in b and c, respectively. There are no significant changes in the spectra of either materials. The change in ratio of the two peaks in the AgBiI4 He 1 week spectra is likely due to the disorder of the Ag + and Bi 3+ cations. Figure S9. Pawley fit of PXRD pattern for Cu2AgBiI6 films spincoated on FTO glass, fitted to a rhombohedral phase associated with a quaternary phase (black tick marks), a rhombohedral phase consistent with a Cu3xBi1-xI3 phase (red tick marks), and SnO2 (blue tick marks).  Figure S13. The partial density of states plots for the lowest energy configurations arising from each of the four independent ChemDASH calculations shown in Figure S22. The electronic structure is computed using the meta-GGA functional, SCAN, 21 and including spin-orbit coupling. Shown on each plot is the value of the smallest gap between occupied and unoccupied bands. The plot for configuration 1, the lowest energy configuration overall is also shown in Figure 3c of the main text, but is included again here for comparison. Although changing the configuration of Ag + , Bi 3+ and Cu + cations within the computed cell does affect the position and shape of peaks in the density of states, in all configurations the Cu 3d-states dominate at the valence band edge, and the conduction band consists of mixed Bi 6p-states and I 5p-states.

S19.
The optical response of a Cs2AgBiBr6 on silicon tandem was modelled using the transfer matrix method. 13 The thickness of the Cs2AgBiBr6 (100 nm -1000 nm) and the anti-reflective coating LiF (10nm -150 nm) was varied using a differential evolution algorithm till the limiting tandem current was maximised. The optimised device structure was LiF (110 nm)/ITO (80 nm)/SnO2 ( Figure S21. The "synthetic" extinction co-efficient for Cu2AgBiI6 which was used as input for the optical calculations, as described in the optical modelling . Figure S22. The optimised geometry of the lowest energy configurations arising from each of the four independent ChemDASH calculations computed using the van der Waals functional, optB86b-vdW. 20 The computed energy for each configuration is given relative to configuration 1, the lowest energy overall. The green, blue, grey and pink spheres/polyhedra represent I − , Cu + , Ag + and Bi 3+ ions respectively. These low energy configurations represent different ordered arrangements of the cations consistent with the average structure determined experimentally.