Bismuth Iodide Perovskite Materials for Solar Cell Applications

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Bismuth Iodide Perovskite Materials for Solar Cell Applications: Electronic Structure, Optical Transitions and Directional Charge Transport Meysam Pazoki, Malin B. Johansson, Huimin Zhu, Peter Broqvist, Tomas Edvinsson, Gerrit Boschloo, and Erik M. J. Johansson J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b11745 • Publication Date (Web): 05 Dec 2016 Downloaded from http://pubs.acs.org on December 5, 2016

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The Journal of Physical Chemistry

Bismuth Iodide Perovskite Materials for Solar Cell Applications: Electronic Structure, Optical Transitions and Directional Charge Transport Meysam Pazoki1,2, Malin B. Johansson1, Huimin Zhu1, Peter Broqvist2, Tomas Edvinsson3, Gerrit Boschloo1 and Erik M. J. Johansson1* 1

Department of Chemistry, Physical Chemistry, Ångström Laboratory, Box 523, 752 20, Uppsala

University, Uppsala, Sweden. 2

Department of Chemistry, Structural Chemistry, Ångström Laboratory, Box 538, 752 21,

Uppsala University, Uppsala, Sweden. 3

Department of Engineering Sciences, Solid State Physics, Ångström Laboratory, Box 534, 752

21, Uppsala University, Uppsala, Sweden. AUTHOR INFORMATION Corresponding Author *[email protected]

ACS Paragon Plus Environment

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ABSTRACT

Cesium and methyl ammonium bismuth iodides (Cs3Bi2I9 and MA3Bi2I9) are new low-toxic and air stable compounds in the perovskite solar cell family with promising characteristics. Here, the electronic structure and the nature of their optical transitions, dielectric constant and charge carrier properties are assessed for photovoltaic applications with density functional theory (DFT) calculations and experiments. The calculated direct and indirect band gap values for Cs3Bi2I9 (2.17 and 2.0 eV) and MA3Bi2I9 (2.17 and 1.97 eV) are found to be in good agreement with the experimental optical band gaps (2.2, 2.0 eV and 2.4, 2.1 eV for Cs3Bi2I9 and MA3Bi2I9, respectively) estimated for solution-processed films. There is an error cancelation in the DFT calculated band gap similar to for lead perovskites. However, fully relativistic DFT calculations indicate that the size of the spin orbit coupling (SOC) error cancelation for bismuth perovskite (0.5 eV) is less than for lead perovskite (1 eV) and other factors are therefore also important. Band structure calculations show high effective masses of the charge carriers along the c-axis but on the other hand lower electron effective mass in the a-b planes, revealing the interesting possibility for a directional charge transport. Calculations of dielectric constants, absorption coefficients, carrier effective masses and exciton binding energies, emphasize the fundamental differences between the lead and bismuth iodide perovskites and clarify the reasons behind the lower power conversion efficiency of bismuth iodide perovskite solar cells. Also the calculations show that the orientational disorder of the MA dipoles in the lattice has meaningful impacts on the near valence- and conduction band edge of the electronic structure.


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1. INTRODUCTION Solar energy is a promising sustainable energy source that provides an environmentally friendly supply of energy and has been considered as one the main candidates to overcome the future energy crisis.1 Perovskite solar cells (PSCs) have emerged recently2,3 with very promising properties and power conversion efficiencies (PCE) similar to the well-known CIGS and CdTe solar cells. Interestingly, the perovskite solar cells consist of only abundant elements and can be prepared using a range of different wet-chemical and vacuum based techniques, which enables low-cost production.4,5 They have the highest ever PCE improvement rate amongst all solar cell technologies investigated so far, and have been introduced as “next big thing in photovoltaics”6. Methyl ammonium lead iodide perovskite (MALIP) is the main prototypical compound of the perovskite solar cells with the general perovskite structure of ABX3 where the dipolar MA+ cations occupies the large cubo-octahedral interstitial space in between the octahedrally coordinated B cation of Pb2+ coordinated with six iodides (X). MALIP has not only been investigated in high efficiency solar cells,7 but also in lasing applications8and LEDs9,10. There are however still issues such as long term device stability11 and environmental concerns regarding the lead toxicity.12,13,5 The possibility of cation exchange as well as mixed halogen exchange allow the tuning of PSC electronic structure

14–16

, and have inspired many theoretical and

experimental studies aiming at understanding the device and material physics in these systems. Replacement of the lead with other metals16–19, is an important topic to meet the environmental concerns and a transition to more complex perovskite crystal structures. Cesium bismuth iodide perovskite (Cs3Bi2I9) and methyl ammonium (MA) bismuth iodide perovskite (MA3Bi2I9) are


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successful examples17 that represents a new class in the perovskite solar cell materials family with low toxicity, air stability20 and fair degree of tunability. It is a promising material not only in possible applications of tandem solar cells, but also for obtaining fundamental understanding and further engineering of the perovskite material family. In comparison with the prototypical ABX3 perovskite, the A3B2X9 perovskite has two metal ions in the crystallographic unit cell. The enlarged unit cell of Cs3Bi2I9 makes this class unique in the increased possibility of ion replacements where further tuning of the behavior can be achieved and possibly novel electronic or directional properties can be explored as we discuss here. For any device applications, understanding of the electronic structure, optical transitions and carrier effective masses of the material are important. In this paper, we investigate the fundamental electronic structure of the A3B2X9 perovskites cesium bismuth iodide (Cs3Bi2I9) and methyl ammonium bismuth iodide (MA3Cs2I9) by means of scalar relativistic, time dependent and also fully relativistic spin-orbit corrected density functional theory (DFT) calculations. The results are compared to experimental results for the Bi-perovskites, as well as to the lead based counterpart MAPbI3. Band structure, ground state electronic density of states (DOS), partial density of states (PDOS), static and high frequency dielectric constant and effective masses of the charge carriers are determined by DFT and interpreted for possible applications and impacts on the device performance especially regarding the directional charge transport and exciton binding energies. UV-vis spectra of as-synthesized perovskite films on quartz substrate are also presented and compared with band structure calculations. Moreover, the impacts of orientational disorder of the MA dipoles on the electronic structure of MA3Cs2I9 as well as the reasons behind the agreement of the DFT and experimental band gap values are discussed. 2. METHODS


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2.1 Experiments. Quartz substrates were cleaned by immersion in detergent, dionized water, ethanol and acetone respectively in ultrasonic bath for 20 minutes each. Bismuth iodide and cesium iodide mixed in the molar ratio of 1:1.5 in Dimethylformamin (DMF) in the nitrogen glovebox and spin coated on the quartz substrate at 2500 RPM. For the MA bismuth iodide perovskite MAI was used instead of CsI. The films were sintered on a 100 OC hotplate for 30 minutes and cooled down to room temperature. Transmittance and reflectance of the films were recorded by a double-beam UV/Vis/NIR spectrophotometer equipped with an integrating sphere, and a Spectral on reflectance standard. X-ray diffraction was recorded immediately after the film formation in a double split beam, grazing incident angle configuration ( Siemens D5000), using parallel plate collimator with a Copper-α beam (λ=1.54Å) , a step size of 0.02 and a scan speed of 1 degree per minute.

2.2 Computational Methodology. The electronic structure calculations were performed using the density functional theory in the implementation with plane waves and pseudopotentials using the pwscf code of the QUANTUM ESPRESSO (QE) package21. The exchange-correlation energy was approximated using the General Gradient Approximation (GGA) proposed by Perdew–Burke–Ernzerhof (PBE) 22. Norm-conserving scalar-relativistic pseudopotentials for the different atomic species were used in all calculations, treating explicitly the I(5s25p5), C(2s22p2), H(1s1), N(2s22p3), Cs(6s16p1) and Bi(6s25d106p3) electrons. The spin orbit coupling (SOC) calculations were performed using a full relativistic pseudo-potential for Bi, generated using the Atomic code of the QE package with the same parameters as that of PBE scalar relativistic pseudo-potential.21 The validity of generated pseudo-potential was checked by comparison of the band structure with the corresponding one calculated using the scalar relativistic pseudo-


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potential (supporting information). The Cs3Bi2I9 super cells consisted of 28 atoms corresponding to its hexagonal phase17 and MA3Bi2I9 super cell consisted of

70 atoms with different

orientations of MA dipole in order to have zero net dipole in the hexagonal unit cell. Different orientations of MA dipoles proved to be the perovskite with the most stable phase as previously reported for MAPbI323. Lattice parameters of the super cell are a=8.395 Å and c=20.988 Å in a hexagonal Bravai lattice. All the atom coordinates are relaxed to have total force of lower than 0.001 (Ry/au). Cut off energy for the plane wave expansion of electron wave functions and function and charge density were 40 and 400 Rydberg respectively. Brillouin zone sampling was carried out by a 4X4X4 Monkhorst-Pack grid for all calculations. The XcrysDen package24 and VESTA were used for visualization of atoms,charge densities and simulation of XRD graphs for single crystals. Effective mass of electron/holes was estimated from the second derivative of CB minimum/VB maximum respectively along the Gamma-A path (the details are reported in the supporting information). Charge density responses to incoming light (UV light with 4.35 eV and green light with 2.39 eV excitation energies) with different polarizations were calculated by time dependent density functional perturbation theory (TDDFPT)25 within the QE package. Selfconsistent calculations were done in gamma point and the time dependent calculations were performed subsequently in 5000 iterations in the case of green (2.93 eV , 518 nm) or UV (4.35 eV , 285 nm) excitations in which the polarizability of the excitation light was chosen to be parallel or perpendicular to c axis of the unit cell. High frequency dielectric constants and effective Born charges were obtained respectively from the difference of unit cell dipole moment or forces acting on atoms in the presence and absence of a small electric field with were frozen ionic configuration using26 CP program within the QE package. The static dielectric constants were obtained in the same way while the


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ions were allowed to relax in 20 to 50 optimization steps to capture the ionic contributions to the total dielectric constant.

3. RESULTS AND DISCUSSIONS 3.1 Estimation of the Bandgap. The calculated (P) DOS for Cs3Bi2I9 and MA3Bi2I9, and the experimentally measured UV-vis spectra are presented in Figure 1 and 2, respectively. To confirm the validity of the hexagonal perovskite phase of the as-synthesized films, XRD measurements have been performed (Figure S1) that are in good agreement with the previously reported XRD data for cesium and methyl ammonium bismuth perovskite films17. The DFT calculated band gap values are in good agreement with the experimentally determined values (Figure 2b and c). Here in, Tauc plots (Figure 2) have been implemented to determine the direct and indirect optical bandgaps, in which the onset of the absorption for (αhυ)1/r versus hυ corresponds to the direct (exponent r=1/2) or indirect (exponent r=2) band gap of bismuth perovskite, where α is absorption coefficient, h is Planck constant and υ is frequency.27 From the results in Figure 2, we can conclude that cesium bismuth iodide perovskite has an indirect bandgap of 2.0 eV (2.02 eV from DFT) and a direct bandgap of 2.2 eV (2.17 eV from DFT) while the methyl ammonium bismuth perovskite has an indirect gap of 2.1 eV (1.97 eV from DFT) and direct gap of 2.4 eV (2.17 eV from DFT). A summary of the calculated and experimentally estimated band gap values are listed and compared to the reported values from other groups in Table 1. Furtheremore, the near band edge peak observed in the UV-vis spectra of bismuth perovskites (Figure 2) can be related to the similar Guassian peak feature in the calculated PDOS spectra (Figure 1) at the bottom of conduction band. However, the possibility of an excitonic absorption peak cannot be excluded here, since the expected low dielectric


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constant and rather high effective mass of charges (calculated in Table 2) in bismuth iodide perovskites are in agreement with the presence of rather high binding energy excitons in the material. The calculated band structures are shown in Figure 3, together with the corresponding crystal structures. A 2x1x2 periodic view for unit cells of Cs3Bi2I9 and MA3Bi2I9 are presented in Figure S2 of Supporting Information. A good agreement from theoretical generalized gradient approximation (GGA) DFT has previously been reported also for MALIP23,28, for which the commonly underestimated band gap within GGA DFT surprisingly corresponds well with the experimentally determined optical band gap. GW calculation and comparison with spin orbit coupling and scalar relativistic DFT calculations for MALIP reveals that neglecting the spin orbit coupling (SOC) effects in the heavy element lead are responsible for error cancelation of the DFT underestimated band gap, leading to a similar value as the experimental band gap.29 The same effect can be expected here for bismuth, which is the heavier neighbor of lead in periodic table of elements. SOC calculations for MA and Cs bismuth iodide perovskites (Figure 3c,d) results in a narrowing of the band gap in agreement with previous reports for Cs3Bi2I9 30 and for lead perovskite29 and we can conclude that the SOC has a large contribution for the error cancelation also here. However, the SOC error cancelation value for bismuth perovskite is about 0.5 eV, which is less than the value for lead perovskite. Similar to MALIP, the main contribution to the valence band comes from iodide and a very low contribution from the metal and A cation (Figure 1).

3.2 Electronic Structure. The PDOS spectrum (Figure 1a) shows two separated conduction bands with a gap of around 500 meV between the two separate CBs where the first belongs mainly to bismuth/iodide molecular orbital states and the second one (with higher energy)


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belongs mainly to Cs states. The first CB with bismuth and iodide electronic states is extended in the unit cell with interconnected Bi and I atoms. The direct transition from VB to the CB is at the Gamma point for both cesium and MA bismuth iodide perovskites (Figure 3). The indirect transition occurs from the K to the Gamma point for both cesium and MA bismuth iodide perovskites. The calculated band diagrams show that the indirect transition has a slightly lower energy, which also was confirmed by the experimental results in Figure 2. The transition wavelength from VB to the high energy conduction band is estimated to be around 270 nm from the DFT calculation (Figure 2), which is not detectable in the UV-vis spectrum and other transitions may also cover this part of spectrum. In the case of dipolar cations such as MA+ in MA3Bi2I9, different orientations of the MA cation dipoles in unit cell were employed in order to have a net zero dipole and the properties for a nonferroelectric material. Larger unit cells with alternative cation orientations is needed to study the full dipole effects in the estimated spectrum of MA3Bi2I9 perovskite (see Figure S3 of supporting information for calculated DFT results for another dipole-distribution-phase of MA3Bi2I9 perovskite). In the case of lead analogue MAPbI3 perovskite, different orientations of MA+ dipoles in the unit cell has low impact on the band gap but has been reported to affect the effective masses of the charge carrier and charge recombination to some more extent.28 Here this effect was also observed for MA3Bi2I9. The calculated static dielectric constant (Table 2), band structure (Figure S3) and simulated XRD peaks(Figure S1) show meaningful changes by different orientations of the dipoles within the unit cell. However the experimentally measured values for multi crystalline films, would be an ensemble average of the polarizability domains in the case of their presence. Hence, similar to the lead perovskite, orientational order of MA dipoles indeed may play a role in the solar cell device performance. A reorientation of MA


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molecules has been observed in the dielectric constant calculations in the presence of electric fields (data is not shown), which is in agreement with other perovskite materials and indicative for possible reorientation and rotation of MA molecules in the device under working conditions. The effective masses of the charge carriers are important in the device performance through their contribution to the mobility of the photo-generated charges and the conductivity of the material. The calculated band structures of Cs3Bi2I9 and MA3Bi2I9, presented in Figure 3a and 3b, have been used to derive the effective masses of CB electrons (m*e) and VB holes (m*h) from the second derivative of corresponding energy state (E(k)) versus crystal momentum k (Table II) according to:

(∗ ) = ℏ () ( ∗ ) = ℏ () (1)

The calculated effective masses at the VB and CB edges are given in Table 2 for Cs3Bi2I9 and MA3Bi2I9. These estimated values are rather large, corresponding to relatively flat bands. The high effective masses suggest that the charge mobility is rather low in this material. SOC calculated bands have similar curvature while the bottom of CB has even a somewhat lower curvature (Figure 2). However, from the calculations, we can observe that there is a higher curvature at the CB minimum along the A->H and K->Gamma paths. The higher curvature shows that in these directions (within the a-b plane) the electron effective mass is lower, leading to an increased charge mobility, which may be important in many device applications. In the Cs3Bi2I9 unit cell, there is a longer distance between the atoms along the z direction in the terms of bonds and charge density distribution (Figure 4a, b). This can explain the differences in calculated effective masses along the z direction compared to the a-b direction and a light polarizability dependent conductance of single crystals may also be expected for this


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material. Moreover, the higher curvature in the second conduction band (CB2) is indicative of a faster charge transport in c direction when the electrons are in Cs-I hybridized states.

3.3 Charge Distribution. The ground state charge density plot (Figure 4) shows that the electronic cloud is distributed along the iodide bonds and also along the iodide-bismuth bonds in the unit cell (Figure 4 plane 1 and 2), while the large Cs+ and MA+ cations don’t share any charge density with iodide/bismuth atoms (Figure 4a,b plane 3). However the charge density distribution along the iodide-bismuth bonds is not very high and smaller compared to in MAPbI3.19 The unit cell volume for the bismuth perovskite ( ̴1274 Å3) is more than five times higher than for the cubic phase of lead perovskite ( ̴ 238 Å3) while the number of valence electrons within the bismuth perovskite unit cell (119) is less than three times higher than the lead perovskite valence electrons (43). This gives a lower expected charge density in the bismuth perovskite. Interestingly, the density of states at the CB minimum (integration of DOS from CBmin till CBmin +kBT) is higher in bismuth than the lead perovskite, which might lead to a higher charge conductivity in the excited state. However, on the other hand, the higher electron and hole masses would instead result in lower expected mobility for bismuth compared to the lead perovskite. Also, for a comparable absorption as the lead perovskite, a bismuth based perovskite absorber demands an increased film thickness, and the poor charge mobility along the c-axis require that the materials is applied with the c-axis parallel to the substrate, thereby utilizing the better conductivity in the a-b plane for directional charge extraction

in the

photoactive layer. The side view plot of the charge density (Figure S4 of supporting information) further shows that there is no significant connection between the charge planes for example between iodide or bismuth iodide atoms along the c axis. The bismuth iodide perovskites


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therefore shows a two-dimensional character, which is in agreement with the lower electron mass in the a-b plane and higher electron mass along the c axis. To further clarify the excited state charge distribution at operational condition of solar cell, the charge density response to light excitation was calculated by time dependent density functional perturbation theory (TDDFPT) considering different excitation polarizabilities and wavelengths (Fig S2 and S4 of supporting information), and also to investigate the possible differences of transitions to CB1 (visible range) and CB2 (UV range) contributions at excited state. UV excitation can excite electrons from the middle of the VB to CB1 minimum and also from the VB maximum to CB2, which complicates the separation of the different processes in the charge response density, unless the Cs charge density is representative of its occupied states in CB2. In the case of ab plane polarizability, the charge response distribution is rather similar for both green (excitation to CB1) and UV light (Figure S5 of supporting information), however the main difference appears for z polarizability where the transition arise from different networks of Bi-I bonds (related to CB1 states mainly) and Cs-I bonds (related to CB2 mainly) in the a-b plane. The dipolar and un-symmetric nature of excited state therefore induces a crystal direction dependence of the charge response for green and UV illuminations by which fundamental differences of CB1 and CB2 can be noted from the TDFPT calculations (Figure S5 and S6).

3.4 Directional Transport and Photovoltaic Application. Although the band gap obtained for the bismuth perovskites is not optimum for a solar cell based on a single light absorber layer, it would be close to ideal for a top cell in a tandem configuration with silicon or CIGS in the bottom cell. Combining a top cell with 2.1 eV band gap with a bottom cell of 1.1-1.3 eV band gap is expected to reach over 25% efficiency under 1 sun illumination.31 The bismuth perovskite


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would therefore be an interesting alternative as a low-toxic material to use as a top cell in a tandem solar cell. However, the nature of the unit cell charge planes and the high effective masses limits the mobility and diffusion length of charge carriers along the c axis. Therefore the orientation of the crystals and the thickness of the film need to be controlled, in order to achieve high efficiency solar cells. Also the lower absorption coefficient (Figure 2) compared to lead perovskite4 together with lower estimated dielectric constant and mobility (Table 2) compared to lead counterpart4 explain the lower device efficiency of bismuth perovskite found so far, using the same thickness and device engineering as in the lead perovskite. Therefore, the device fill factor (FF) and current density can be influenced by the lower mobility and lower light absorption within the bismuth iodide perovskite compared to the lead perovskite. In solar cells, after light absorption the separation of electrons and holes is important to obtain a photocurrent. In conventional crystalline solar cells for example silicon solar cells, the interaction between the photo-generated electron and hole is rather weak, but in other solar cell materials, such as organic materials for solar cells there may be a strong exciton binding energy between the electron and the hole. The exciton binding energy (Ebin) is proportional to: Ebin ∝ (m*/є) (3) The rather high effective masses m* (Table 2) together with the low dielectric constant ε (Table 2) therefore result in rather high expected exciton binding energies and a more difficult charge separation process for the bismuth perovskites. The differences in effective masses in different directions may also be of importance for the mechanism of exciton dissociation and exciton


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transport in the material. This is very important in solar cells based on this material, and may also be of importance for application in LED, where the control of direction and efficiency of exciton recombination also are highly important. Besides, low charge mobility negatively affects the diffusion length (L) through Einstein relation by which diffusion coefficient and mobility are directly proportional. The collection of charges may therefore be difficult in solar cells of bismuth perovskite where the thickness should be large enough to absorb most of the solar light. Non symmetric directional charge conduction in the separate ab planes, having two separate conduction bands and expected high exciton binding energy are factors that depending whether all the criteria are satisfied or not, could also open up a lot of interesting other applications and are worth further investigations. Based on the presented data, the bismuth perovskite devices have lower light harvesting ability, lower dielectric constant and carrier mobility and possibly lower charge separation efficiency which may explain their lower device conversion efficiency in comparison to the champion lead perovskite devices. 4. CONCLUSIONS In summary, the electronic structure of the cesium and MA bismuth iodide perovskites are investigated by DFT calculations and the possible impacts on the device applications are discussed. GGA based DFT calculations can predict the experimental indirect and direct band gaps. The cancellation effects between the normal DFT band gap underestimation and the effects from neglecting SOC as in methyl ammonium lead iodide perovskite are investigated by comparing spin orbit splitting and fully relativistic pseudo-potential calculations . The PDOS shows two separate conduction bands with a gap of 0.5 eV was obtained from the calculations in which the lowest CB has extended states of bismuth and iodide, and the higher conduction band states mainly consists of cesium iodide hybridized states. High effective masses of electron and


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holes corresponding to rather low mobilities are obtained from the band structure spectra for the VB maximum and CB minimum. However, a lower electron mass was obtained in the a-b plane, which suggests that higher electron mobility is possible within this plane. Therefore, the results suggest that the bismuth iodide perovskites are promising materials for implementation in lowtoxic solar cells, and especially as the top cell material in tandem solar cells, due to the relatively high band gap and electron mobility in the a-b plane. The presented results with lower absorption coefficient, lower static dielectric constant, and expected higher exciton dissociation energy may explain the lower device performance found so far for bismuth iodide perovskite compared to its lead counterpart. For devices based on the bismuth perovskite, a slightly different device structure may therefore be needed, with a control of the crystal direction of the perovskite grains and combination with another material for efficient charge separation.

Notes The authors declare no competing financial interests. ACKNOWLEDGMENT Swedish energy agency, Swedish research council (VR), Swedish research council FORMAS, ÅForsk, Stand-UP energy program are appreciated for the financial supports of this work. The computations were performed on resources provided by SNIC through Uppsala Multidisciplinary Center for Advanced Computational Science (UPPMAX) under Project snic2015-6-65 and snic2015-1-281. MP thanks Jolla Kullgren for the insightful discussions.


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ASSOCIATED CONTENT Experimental and simulated XRD graphs of bismuth iodide perovskite films, extended view of the bismuth iodide perovskite unit cells, data for MA3Bi2I9 with different orientation of dipoles, Side view plot of CS3Bi2I9 charge response density, plots of charge density response to an abplane and c-axis polarized UV/green excitation lights for CS3Bi2I9, zoom in plot of Cs3Bi2I9 CB, analysis and assertion of the validity of the generated pseudo-potential, and band structure of Cs3Bi2I9 along K to Gamma. The Supporting Information is available free of charge via the Internet at http://pubs.acs.org.

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Figures

Figure 1. Calculated partial and total DOS for (a) Cs3Bi2I9 and (b) MA3Bi2I9 perovskite. The energy scale 0 eV is set at the valence band edge.


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Figure 2. (a) Measured UV-Vis spectra of Cs3Bi2I9 and MA3Bi2I9 perovskites and corresponding (b) direct and (c) indirect optical bandgaps estimated from absorption coefficient α.


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Figure 3. (a,b) band structure of Cs3Bi2I9 along Gamma-A-H-K path without (a) and with (b) SOC and (c) schematic of the unit cell. d,e) band structure of MA3Bi2I9 along Gamma-A-H-K path without (d) and with (e) SOC and (f) schematic of the unit cell. Primitive vector c is also presented in the figure. Red, cyan ,gray, yellow , blue and white spheres are representative of Bismuth, cesium, iodide, carbon, nitrogen and hydrogen atoms respectively.


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Figure 4. Top view plot of charge density in the (a) Cs3Bi2I9 and (b) MA3Bi2I9 unit cells along three different planes marked in the schematic of unit cell by numbers 1-3.


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Table 1. Estimated band gap values (eV) for bismuth iodide perovskites. Material/method DFT (PBE) Cs3Bi2I9

MA3Bi2I9

DFT (SOC)

Experiment

Theory

Experiment

-

Direct

2.2

1.7

2.2

-

Indirect

2.0

1.6

2.0

1.9a

2.3a

Direct

2.4

1.6

2.2

2.1b

2.1b

Indirect

2.1

1.5

2.0

2b

2.0b

a

Ref. 25 Theory (from DFT_HSE+SOC) and experiment (from UV-vis). b Ref. 21 Direct band gap has obtained from a combination of experiment and DFT calculations. Theory values are estimated from the presented DOS graph in the Ref 21(figure 4).

Table 2. Effective masses of charge carriers and dielectric properties of A3Bi2I9 perovskites. Static (ε0) and high frequency (ε∞) dielectric tensors, and effective mass of electrons (m*e) and holes (m*h) (in units of free electron mass m0). The values in parentheses are from Ref 25.

Material

εx0

ε z0

m*e Γ-A

m*e A-H

m*h Γ-A Γ

m*h H-A†

Cs3Bi2I9

3.46

1

4.5

1.1

13.04 3.98(5.5a)

9.1

MA3Bi2I9

→∞

0.54

110

0.95

39.89

5.43

9.62 4.67

MA3Bi2I9

119.56

3.66

→∞

4.14

5.78

7.08

4.55 46.83

εx∞

ε z∞

4.34(4.2 a)

different oriented MA (Fig. S3) a

Ref. 25 Theory (from DFT_HSE+SOC) †For MA3Bi2I9 with different oriented MA it presents m*h A-H


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TOC GRAPHICS

Table of Contents Graphic


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Bismuth Iodide Perovskite Materials for Solar Cell Applications

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