Band Structure Engineering of Cs2AgBiBr6 Perovskite through Order

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Band Structure Engineering of Cs2AgBiBr6 Perovskite through Order-Disordered Transition: A First Principle Study Jingxiu Yang, Peng Zhang, and Su-Huai Wei J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b02992 • Publication Date (Web): 13 Dec 2017 Downloaded from http://pubs.acs.org on December 13, 2017

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The Journal of Physical Chemistry Letters

Band Structure Engineering of Cs2AgBiBr6 Perovskite through Order-Disordered Transition: A First Principle Study Jingxiu Yang,1,2 Peng Zhang2, Su-Huai Wei2*

1

Department of Materials Science and Engineering, Jilin Jianzhu University, Changchun, 130118, China

2

Beijing Computational Science Research Center, Beijing 100193, China

AUHOR INFORMATION Corresponding Author *Su-Huai Wei, [email protected]

ACS Paragon Plus Environment

The Journal of Physical Chemistry Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Cs2AgBiBr6 was proposed as one of the inorganic, stable, and non-toxic replacement of the methylammonium lead halides (CH3NH3PbI3, which is currently considered as one of the most promising light-harvesting material for solar cells). However, the wide indirect band gap of Cs2AgBiBr6 suggests that its application in photovoltaics is limited. Here, using the first principle calculation, we show that by controlling the ordering parameter at the mixed sublattice, the band gap of Cs2AgBiBr6 can vary continuously from a wide indirect band gap of 1.93 eV for the fully ordered double perovskite structure to a small pseudo-direct band gap of 0.44 eV for the fully random alloy. Therefore, one can achieve better light absorption simply by controlling the growth temperature, thus the ordering parameters and band gaps. We also show that controlled doping in Cs2AgBiBr6 can change the energy difference between ordered and disordered Cs2AgBiBr6, thus providing further control of the ordering parameters and the band gaps. Our study, therefore, provides a novel approach to carry out band structure engineering in the mixed perovskites for optoelectronic applications.

TOC GRAPHICS


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1. Introduction Given the low cost, suitable bandgap, high optical absorption and long carrier lifetime, the family of organic-inorganic perovskite halide AIBIIX3 (X=Cl, Br, I), especially CH3NH3PbI3, has become the most investigated light-harvest material for solar cells in the last few years1-4. Although solar cells based on CH3NH3PbI3 thin films have approached a high power conversion efficiency of more than 22%5, two serious problems including toxicity of the water soluble Pb2+ ions and thermodynamic instability of CH3NH3PbI3 in air against decomposition have presented major barriers to its commercial application6-7. It is proposed that to counteract these two issues, one may replace two toxic Pb2+ with a pair of group-I and group-III nontoxic BIBIII metal cations to form A2IBIBIIIX6 with ordered double perovskite structure8-9. If the averaged cation radius of BIBIII is smaller than Pb2+, the radius of cation AI can be decreased accordingly to preserve the geometric stability. In this way, inorganic cations such as Cs+ could possibly substitute CH3NH3+, forming stable inorganic perovskite halide. To keep lone pair states located at band edges, the most favorable candidate for BIII is Bi3+ and Sb3+, and the most desirable element for BI is In+ or Tl+. Unfortunately, double perovskite containing In+ is intrinsically instable and Tl+ is water soluble and toxic10. Therefore, other nontoxic and stable double perovskites have been tested, in which Na+, K+, Ag+, Au+, Cu+, etc. is proposed to take the site of BI 11-13. Among all the possible arrangement of A2BIBIIIX6, Cs2AgBiBr6 is one of the recent synthetic stable and nontoxic double perovskites, which has been recently reported to be an superior X-ray detector with a low detection limit.14 The synthetic Cs2AgBiBr6 has the predicted cubic double perovskite structure with the space group Fm3m, and a reported indirect band gap of 1.95 eV or 2.19 eV by photoluminescence and diffuse reflectance spectroscopy, respectively15-16. The indirect band gap and its corresponding low absorption in the visible light region has limited its application in solar energy conversion. This is consistent with the observation that light absorption of Pb free nontoxic (BI, BIII) double perovskite is not very efficient13. It is, therefore, quite interesting to see if band structure engineering for Cs2AgBiBr6, such as atomic disorder8, could be used to decrease the band gap of Cs2AgBiBr6 and increase its corresponding light absorption and power conversion efficiency. It is well known that changing the atomic arrangement in a semiconductor alloy can significantly modify its band structures17-18. For example, for ZnSnP2, its band gap can vary from 0.45 eV when the cation sublattice is random to 1.68 eV when the cation sublattice is fully ordered, forming the chalcopyrite structure17. Therefore, it is quite natural to investigate whether by changing the atomic arrangement in


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Cs2AgBiBr6, that is introducing cation disorder on Ag-Bi sublattice, one can modify the band structure and optoelectronic properties of Cs2AgBiBr6. It is expected that disordered arrangement of Ag+ and Bi3+ can adjust the size of the band gap and may even change the indirect band gap character into more direct band gap character due to the band hybridization in the reduced crystal symmetry. In the following, using first principle calculation, we will investigate these possibilities. We find that manipulating ordering in Cs2AgBiBr6 can indeed lead to enhanced light absorption in the visible and near infrared region.

2. Results and Discussion 2.1 The ordered Cs2AgBiBr6 The primitive cell of the ordered double perovskite Cs2AgBiBr6 contains two Cs+, one Bi3+, one Ag+ and six I- bonded to the neighboring Bi3+ and Ag+ ions, as shown in Figure 1 (a). The cubic supercell containing 40 atoms (a 2×2×2 supercell of cubic AIBIIX3) is shown in Figure 1 (b). In the ordered structure, each Bi3+ is surrounded by six Ag+ in the B sublattice, and vice versa. The optimized lattice parameter is 11.18 Å, in good agreement with the experiment value15. Figure 1(c) shows the band structure of the primitive cell of the ordered Cs2AgBiBr6, which is calculated by HSE06 functional with the spin-orbit coupling (SOC). The calculated band gap of ordered Cs2AgBiBr6 is indirect with the valence band maximum (VBM) and the conduction band minimum (CBM) located at X and L points in the primitive Brillouin Zone (BZ), respectively, and the calculated band gap value of 1.93 eV is quite close to the estimated band gap in the photoluminescent experiment15. The calculated optical absorption of the ordered Cs2AgBiBr6 is shown as the black line in Figure 2. For the ordered Cs2AgBiBr6, the light absorption threshold (3.13 eV) is significantly higher than the band gap of 1.93 eV, which is a typical character of indirect band gap structure. 2.2 The fully disordered Cs2AgBiBr6 alloys Distinguished from the ordered Cs2AgBiBr6 compound, Bi3+ and Ag+ ions might occupy the B site in a random way, especially at high temperature. To describe the fully disordered (random) Cs2AgBiBr6 alloy, we have adopted the special quasirandom structures (SQS) approach19 in which a small finite supercell is

of the cluster (k, m) is closest to the generated so that its averaged atomic correlation functions targeted atomic correlation functions of the random alloy. Here, k represents the number of vertices in the polyhedron figures such as pairs (k=2), triangles (k=3), tetragons (k=4) and m represents the mth-neighbored



distance. Using the language of Ising models, we can assign to each B-site i a spin variable Si, which is set to be +1 if it is occupied by Ag+, or -1 if it is occupied by Bi3+. The atomic correlation function, is the

is -1, whereas in random product of the spin variables. For ordered Cs2AgBiBr6, the averaged product should be zero for all figures. Cs2AgBiBr6 structure, Following the above approach, we have constructed the SQS of Cs2AgBiBr6 in a 40-atom and a 320-atom cubic supercell. In the 40-atom SQS cell, the averaged atomic correlation functions of the pairs and triangles up to the second neighbor are zero. In the 320-atom model, the averaged atomic correlation functions of the first and second neighbored pairs, triangles and tetragons are all the same as the perfect random solid solution (not shown). Comparing the band structures of the small supercell to the large one, the band structure of the 40-atom cell is almost the same as that of the 320-atom cell with slightly larger band gap. Therefore, the 40-atom supercell is used to represent the random alloy structure. The band structure of the random Cs2AgBiBr6 in 40-atom supercell is shown in Figure 3(a). Quite different to the ordered Cs2AgBiBr6, the band gap of the random Cs2AgBiBr6 is reduced to be 0.44 eV. Both the VBM and the CBM appear to locate at Γ in the folded BZ. However, to get a better picture of the directness of the random alloy, we need to unfold the band structure of the supercell to the primitive BZ as shown in Figure 3(b). The blue dots in Figure 3(b) shows all the states unfolded from the supercell to the primitive cell for the random Cs2AgBiBr6. For the supercell used in the current study, the states at Γ in the folded BZ are derived from the states at Γ and X in the primitive BZ. However, the spectral weights of the VBM and CBM are quite different. The red dots in Figure 3(b) shows the band edge states with the spectral weight over 50%. We find that about 54% of the VBM for the random Cs2AgBiBr6 is folded from X and the rest 46% is folded from Γ. In contrast with the VBM, over 90% of the CBM is folded from Γ and only 10% of CBM is folded from X. Given the CBM is dominantly contributed by Γ states, whereas the VBM is mainly contributed by X states, the band structure of the random structure is recognized as only pseudo-direct, because unlike the fully ordered system, it now contains significant amount of direct band gap components in random Cs2AgBiBr6, as reflected by the calculated optical absorption of the random Cs2AgBiBr6 [red line in Figure 2], which indicates that in the near infrared and the visible light region (0.5 eV to 3 eV), the light absorption of the random Cs2AgBiBr6 alloy is considerably enhanced with the threshold at 0.44 eV. 2.3 Order-disorder phase transition The energy difference of the ordered and the random Cs2AgBiBr6 is estimated to be 0.141 eV per mixed


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cation site, which is quite large and, therefore, can lead to the difficulty in synthesizing the solid solution. To investigate the phase transition through ordered and disordered state, the relationship between energy and the ordering parameter should be established. Based on the method of cluster expansion19, the energy of the structure with the configuration σ could be calculated as the following:

= + ∑

(1)

In Eq. (1), E σ is the total energy of the structure with the configuration σ, ER is the total energy of the fully random solid solution, is the effective interaction within clusters consisting of k atoms separated

is the average of the atomic correlation functions of cluster (k, m). Mapping the by m neighbors, calculated energy to the structure, and could be easily obtained. In this case, as shown in Eq. (2), the energy difference of and is related to the averaged correlation functions of pairs up to the 4th neighbors.

+

+ + ≈ +

(2)

The value of J21 (103.4 meV) is much larger than J22 -20.4 meV, J23 12.3 meV or J24 -26.7 meV, therefore, the interaction of the nearest neighbored pair has the dominant effect on the energy and the phase

can be treated as an ordering parameter varying from 0 for random alloy to -1 for the transition, and η= double perovskite structure. Based on the cluster expansion Hamiltonian of Eq. (2), we have performed Monte Carlo simulation using a large supercell containing 1280000 atoms at various temperature. Figure 4(a) shows the excess energy as a function of temperature and the corresponding averaged atomic correlation functions of pairs up to the 4th neighbor ( ) are shown in Figure 4(b). When the temperature increases from 0 K, the total energy per mixed cation site hardly changes until 800K, as well as the corresponding averaged atomic correlation functions as shown in Figure 4(b), indicating the structure remains ordered under 800K. Beyond 800K, the energy climbs slowly as the temperature increases. Between 1100K and 1200K, there is a phase

. The transition where energy increases sharply, so are the variation of the atomic correlation functions energy keeps increasing with the temperature after the phase transition. As the temperature increases, all of the correlation functions are approaching zero, which is the value for the random alloy, and the band gap of the solid solution becomes narrow. 2.4 The partial disordered Cs2AgBiBr6 Alloys The fully disordered phase is usually unachievable under the equilibrium growth condition for this nonisovalent solid solution because of the high mixing energy. In most cases, partial disordered solid



solution is obtained instead20. In this work, partial disordered Cs2AgBiBr6 could be obtained by quenching from temperature above 1200K. The higher of the temperature, the more disordered of the alloy is. In this work, we only studied the electronic and optical properties of the partial disordered alloy at the transition temperature. From the calculated atomic correlation functions at 1200 K, we have constructed a partial disordered supercell structure consisting of 160 atoms with tetragonal lattice vector a=11.18 Å, b=22.36 Å, and c=22.36 Å. The constructed partial disordered structure is disordered in the long range but ordered in the short range,

(-0.66) of the partial disordered phase at 1200K is more because the dominant ordering parameter close to the ordered phase (-1) instead of the fully disordered phase (0). In this case, the obtained band structure is still indirect with the band gap of about 1.46 eV, which is more close to the band structure of the ordered Cs2AgBiBr6. It is expected that partial disordered alloys with higher degree of disorder would be more like the fully disordered alloy with narrower band gaps. The light absorption of the partial disordered Cs2AgBiBr6 quenched from 1200K is shown as the blue line in Figure 2. The light absorption coefficient of the partial disordered Cs2AgBiBr6 shows the indirect character of the band structure, but compared to the fully ordered phase the visible light harvest is clearly enhanced with the threshold red-shifted from 3.13 to 1.82 eV. 2.5 Doping effect on the transition temperature The order-disorder transition diagram suggests that the fully disordered Cs2AgBiBr6 could only be synthesized beyond 3000K, which is almost impossible in experiment. The high synthetic temperature is directly caused by the large energy difference between the ordered and the random phases. If the energy difference reduces, the synthetic temperature will consequently decrease. Comparing the band alignment of the ordered and disordered Cs2AgBiBr6, as shown in Figure 5, it is obvious that the CBM of the fully disordered phase is 1.05 eV lower than the CBM of the ordered phase. If extra electrons were introduced to the CBM state, the random phase with lower CBM will gain more energy than the ordered one with higher CBM energy. Similarly, the random phase with higher VBM will gain more energy than the ordered phase, if extra holes were introduced to the VBM state. Therefore, we proposed that the energy difference between the random and the ordered phases could be reduced by introducing electrons or holes to the system. To examine the proposal, we have performed the calculation with large portion of Cs substituted by Ba and La. As shown in Table 1, if 12.5% Cs is substituted by Ba, the random phase is almost as stable as the ordered phase. When the doping concentration is doubled, the random phase is 0.153


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eV/mixed site more stable than the ordered phase. If 12.5% Cs is substituted by La, the fully disordered phase is 0.192 eV/site more stable than the ordered phase. Therefore, if the concentration of the n-type dopant is high enough, the fully disordered phase can be even more stable than the ordered phase energetically. When the concentration is decreased below the solubility limit, instead of the reversion of the thermal stability, reduced energy difference and decreased transition temperature is expected. Similarly, p-type doping could also stabilize the fully random phase by introducing extra holes. However, its effect is expected to be smaller than n-type doping due to the small band offset of the VBM as shown in Figure 5. Indeed, we find if 4.17% Br is replaced by Te, the energy difference between the fully ordered and disordered phase is only slightly reduced to 0.123 eV/site.

3. Conclusions In summary, we show that by introducing disorder to the cation occupancy of Ag and Bi in Cs2AgBiBr6 we could engineer the band structure of Cs2AgBiBr6. Using the Monte Carlo and the first principle calculation, we predict that a series of the disordered Cs2AgBiBr6 with the band structures changing from indirect band gap of 1.46 eV to pseudo-direct band gap of 0.44 eV could be synthesized by quenching from different temperature beyond 1200K. Introducing n-type dopants such as Ba or La on Cs site and p-type dopants such as Te on Br site into the alloy can reduce the energy difference and thus the transition temperature. Depending on the extent of disorder, the light absorption in the visible and the near infrared region for the disordered Cs2AgBiBr6 alloys is considerably enhanced, which has broaden the application of the compound. This work shows that introducing cation disorder is a useful way for band structure engineering of the perovskite materials for various applications.

Computational Methods: The first principle calculation in this work is performed by the VASP code21-22. The PAW pseudopotentials and PBEsol23 functional are employed with an energy cutoff of 350 eV. For the ordered Cs2AgBiBr6, all the atoms and the lattice vectors are fully relaxed until the force on each atom is less than 0.01 eV/Å. For the fully and partial disordered Cs2AgBiBr6, the lattice vectors are fixed to be the same as the corresponding ordered supercell. For the discussion of the electronic and optical properties, we have employed the hybrid functional HSE0624 with spin-orbit-coupling (SOC). The band unfolding of the disordered Cs2AgBiBr6 from the 40-atom supercell to the primitive cell of ordered Cs2AgBiBr6 is performed by the BandUP code25.



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The fully disordered solid solution in this work is mimicked by the SQS19 in the cubic supercell of 40 and 320 atoms, respectively. The cubic supercell of 40 and 320 atoms containing 4 and 32 primitive cells of Cs2AgBiBr6 are optimized with 4×4×4 and 2×2×2 k-point sampling, respectively. The partial disordered structure is also generated by the approach similar to that in generating SQS, that is finding a supercell structure with its relevant atomic correlation functions closest to the target partial disordered atomic correlation functions. The order-disorder transition is calculated using the cluster expansion approach as implemented in the ATAT code26. The cluster expansion coefficients are fitted to the energy calculated by the PBEsol functional. The equilibrium structures of the solid solution at the increasing temperatures are calculated by the Monte Carlo simulations in a supercell of 1280000 atoms.

Figure 1. The primitive cell (a) and the 40-atom cubic supercell (b) of the ordered Cs2AgBiBr6. The Cs, Ag, Bi, and Br are represented by green, light blue, purple and brown balls, respectively, and the corresponding band structure in the primitive Brillouin Zone (c).


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105

Fully Ordered Partial Disordered Fully Disordered

α (cm-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


104

103

102 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Energy (eV) Figure 2. The calculated optical absorption coefficients (α) of the fully ordered (black line), partial disordered (blue line), and fully disordered (red line) Cs2AgBiBr6

Figure 3. The unfolding of the band structure of fully disordered Cs2AgBiBr6 (a) to the corresponding band structure of ordered double perovskite structure (b). The red dots in (b) represent the dots at the band edge with the spectral weight over 50%.



Figure 4. The Monte-Carlo simulation of the excess energy as a function of temperature (a) and the corresponding averaged atomic correlation functions of pairs up to the mth neighbor ( ) (b).

Figure 5. The band alignment of the ordered, partial disordered, and fully disordered Cs2AgBiBr6.


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Table 1. The relative energy of the ordered and disordered Cs2AgBiBr6 with dopants at different concentrations.

Ordered (eV/mixed-site)

Fully Disordered (eV/mixed-site)

Pure

0

0.141

12.5% Ba@Cs

0

0.001

25% Ba@Cs

0

-0.153

12.5% La@Cs

0

-0.192

4.17%Te@Br a

0

0.123

a. Note that for a given concentration, the number of dopants on the anion site is three time more than that at the cation site.



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ASSOCIATED CONTENT

AUTHOR INFORMATION Corresponding Author *Su-Huai Wei, [email protected]

ACKNOWLEDGEMENT: This work is financially supported by the National Key Research and Development Program of China under Grant No. 2016YFB0700700 and the Natural Science Foundation of China under Grant No. 51672023 and U1530401. We also acknowledge the computational support from the Beijing Computational Science Research Center (CSRC).

REFERENCES (1) Kojima, A.; Teshima, K.; Shirai, Y.; Miyasaka, T. Organometal Halide Perovskites as Visible-Light Sensitizers for Photovoltaic Cells. J. Am. Chem. Soc. 2009, 131 (17), 6050-6051. (2) Lee, M. M.; Teuscher, J.; Miyasaka, T.; Murakami, T. N.; Snaith, H. J. Efficient hybrid solar cells based on meso-superstructured organometal halide perovskites. Science 2012, 338 (6107), 643-647. (3) Yin, W.-J.; Yang, J.-H.; Kang, J.; Yan, Y.; Wei, S.-H., Halide Perovskite Materials for Solar Cells: A Theoretical Review. J. Mater. Chem. A 2014, 3, 8926-8942. (4) Yang, W. S.; Noh, J. H.; Jeon, N. J.; Kim, Y. C.; Ryu, S.; Seo, J.; Seok, S. I. High-performance photovoltaic perovskite layers fabricated through intramolecular exchange. Science 2015, 348, 1234–1237. (5) Nrel Efficiency Chart. https://www.nrel.gov/pv/assets/images/efficiency-chart.png (accessed 8, Nov, 2017). (6) Shi, Z.; Guo, J.; Chen, Y.; Li, Q.; Pan, Y.; Zhang, H.; Xia, Y.; Huang, W., Lead-Free Organic-Inorganic Hybrid Perovskites for Photovoltaic Applications: Recent Advances and Perspectives. Adv. Mater. 2017, DOI: 10.1002/adma.201605005. (7) Ono, L. K.; Park, N.-G.; Zhu, K.; Huang, W.; Qi, Y., Perovskite Solar Cells—Towards Commercialization. ACS Energy Lett. 2017, 2, 1749-1751. (8) Savory, C. N.; Walsh, A.; Scanlon, D. O., Can Pb-Free Halide Double Perovskites Support High-Efficiency Solar Cells? ACS Energy Lett. 2016, 1, 949-955. (9) Volonakis, G.; Filip, M. R.; Haghighirad, A. A.; Sakai, N.; Wenger, B.; Snaith, H. J.; Giustino, F., Lead-Free Halide Double Perovskites via Heterovalent Substitution of Noble Metals. J. Phys. Chem. Lett. 2016, 7, 1254-1259. (10) Xiao, Z.; Du, K.-Z.; Meng, W.; Wang, J.; Mitzi, D. B.; Yan, Y., Intrinsic Instability of Cs2In(I)M(III)X6 (M = Bi, Sb; X = Halogen) Double Perovskites: A Combined Density Functional Theory and Experimental Study. J. Am. Chem. Soc. 2017, 139, 6054-6057. (11) Zhao, X.-G.; Yang, J.-H.; Fu, Y.; Yang, D.; Xu, Q.; Yu, L.; Wei, S.-H.; Zhang, L., Design of Lead-Free Inorganic Halide Perovskites for Solar Cells Via Cation-Transmutation. J. Am. Chem. Soc. 2017, 139, 2630-2638. (12) Zhao, X.-G. G.; Yang, D.; Sun, Y.; Li, T.; Zhang, L.; Yu, L.; Zunger, A., Cu-in Halide Perovskite Solar Absorbers. J. Am. Chem. Soc. 2017, 139, 6718-6725.


Page 15 of 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(13) Meng, W.; Wang, X.; Xiao, Z.; Wang, J.; Mitzi, D. B.; Yan, Y. Parity-Forbidden Transitions and Their Impact on the Optical Absorption Properties of Lead-Free Metal Halide Perovskites and Double Perovskites. J. Phys. Chem. Lett. 2017, 8 (13), 2999-3007. (14) Pan, W.; Wu, H.; Luo, J.; Deng, Z.; Ge, C.; Chen, C.; Jiang, X.; Yin, W.-J.; Niu, G.; Zhu, L.; Yin, L.; Zhou, Y.; Xie, Q.; Ke, X.; Sui, M.; Tang, J., Cs2AgBiBr6 Single-Crystal X-Ray Detectors with a Low Detection Limit. Nat. Photonics 2017, 11, 726-732. (15) Slavney, A. H.; Hu, T.; Lindenberg, A. M.; Karunadasa, H. I., A Bismuth-Halide Double Perovskite with Long Carrier Recombination Lifetime for Photovoltaic Applications. J. Am. Chem. Soc. 2016, 138, 2138-2141. (16) McClure, E. T.; Ball, M. R.; Windl, W.; Woodward, P. M., Cs2AgBiX6 (X = Br, Cl): New Visible Light Absorbing, Lead-Free Halide Perovskite Semiconductors. Chem. Mater. 2016, 28, 1348-1354. (17) Scanlon, D. O.; Walsh, A., Bandgap Engineering of ZnSnP2 for High-Efficiency Solar Cells. Appl. Phys. Lett. 2012, 100, 251911. (18) Park, J.-S.; Yang, J.-H.; Kanevce, A.; Choi, S.; Repins, I. L.; Wei, S.-H. Ordering-induced direct-to-indirect band gap transition in multication semiconductor compounds. Phys. Rev. B 2015, 91 (7). (19) Wei; Ferreira, L. G.; Bernard, J. E.; Zunger, Electronic Properties of Random Alloys: Special Quasirandom Structures. Phys. Rev. B 1990, 42, 9622-9649. (20) Ma, J.; Deng, H.-X.; Luo, J.-W.; Wei, S.-H., Origin of the Failed Ensemble Average Rule for the Band Gaps of Disordered Nonisovalent Semiconductor Alloys. Phys. Rev. B 2014, 90,115201. (21) Kresse, G.; Furthmüller, J., Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169. (22) Kresse, G.; Furthmüller, J., Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comp. Mater. Sci. 1996, 6, 15-50. (23) Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Vydrov, O. A.; Scuseria, G. E.; Constantin, L. A.; Zhou, X.; Burke, K., Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces. Phys. Rev. Lett. 2008, 100, 136406. (24) Krukau, A. V.; Vydrov, O. A.; Izmaylov, A. F.; Scuseria, G. E., Influence of the Exchange Screening Parameter on the Performance of Screened Hybrid Functionals. J. Chem. Phys. 2006, 125, 224106. (25) Tomić, M.; Jeschke, H. O.; Valentí, R., Unfolding of Electronic Structure through Induced Representations of Space Groups: Application to Fe-Based Superconductors. Phys. Rev. B 2014, 90. (26) Van de Walle, A.; Tiwary, P.; de Jong, M.; Olmsted, D. L.; Asta, M.; Dick, A.; Shin, D.; Wang, Y.; Chen, L. Q.; Liu, Z. K., Efficient Stochastic Generation of Special Quasirandom Structures. Calphad 2013, 42, 13-18.


Band Structure Engineering of Cs2AgBiBr6 Perovskite through Order

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