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Title: Changes in charge density vs changes in formal oxidation states: The case of Sn halide perovskites and their ordered vacancy analogues

Abstract

Shifting the Fermi energy in solids by doping, defect formation, or gating generally results in changes in the charge density distribution, which reflect the ability of the bonding pattern in solids to adjust to such external perturbations. In the traditional chemistry textbook, such changes are often described by the formal oxidation states (FOS) whereby a single atom type is presumed to absorb the full burden of the perturbation (change in charge) of the whole compound. In the present paper, we analyze the changes in the position-dependence charge density due to shifts of the Fermi energy on a general physical basis, comparing with the view of the FOS picture. We use the halide perovskites CsSnX3 (X = F, Cl, Br, I) as examples for studying the general principle. When the solar absorber CsSnI3 (termed 113) loses 50% of its Sn atoms, thereby forming the ordered vacancy compound Cs2SnI6 (termed 216), the Sn is said in the FOS picture to change from Sn(II) to Sn(IV). To understand the electronic properties of these two groups we studied the 113 and 216 compound pairs CsSnCl3 and Cs2SnCl6, CsSnBr3 and Cs2SnBr6, and CsSnI3 and Cs2SnI6, complementing them by CsSnF3 and Cs2SnF6 in the hypothetical cubicmore » structure for completing the chemical trends. These materials were also synthesized by chemical routes and characterized by x-ray diffraction, 119Sn-Mössbauer spectroscopy, and K-edge x-ray absorption spectroscopy. We find that indeed in going from 113 to 216 (equivalent to the introduction of two holes per unit) there is a decrease in the s charge on Sn, in agreement with the FOS picture. However, at the same time, we observe an increase of the p charge via downshift of the otherwise unoccupied p level, an effect that tends to replenish much of the lost s charge. At the end, the change in the charge on the Sn site as a result of adding two holes to the unit cell is rather small. This effect is theoretically explained as a “self-regulating response” [Raebiger, Lany, and Zunger, Nature (London) 453, 763 (2008)] whereby the system rehybridizes to minimize the effect of the charge perturbation created by vacancy formation. Rather than having a single preselected atom (here Sn) absorb the full brunt of the perturbation producing two holes, we find that the holes are distributed in a complex pattern throughout the octahedral systems of X6 ligands, forming hole orbitals with some specific symmetries. This clarifies the relation between FOS and charge transfer that can be applied to a wide variety of materials.« less

Authors:
; ; ; ; ; ;
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1377072
DOE Contract Number:
AC02-06CH11357
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Materials; Journal Volume: 1; Journal Issue: 2
Country of Publication:
United States
Language:
English

Citation Formats

Dalpian, Gustavo M., Liu, Qihang, Stoumpos, Constantinos C., Douvalis, Alexios P., Balasubramanian, Mahalingam, Kanatzidis, Mercouri G., and Zunger, Alex. Changes in charge density vs changes in formal oxidation states: The case of Sn halide perovskites and their ordered vacancy analogues. United States: N. p., 2017. Web. doi:10.1103/PhysRevMaterials.1.025401.
Dalpian, Gustavo M., Liu, Qihang, Stoumpos, Constantinos C., Douvalis, Alexios P., Balasubramanian, Mahalingam, Kanatzidis, Mercouri G., & Zunger, Alex. Changes in charge density vs changes in formal oxidation states: The case of Sn halide perovskites and their ordered vacancy analogues. United States. doi:10.1103/PhysRevMaterials.1.025401.
Dalpian, Gustavo M., Liu, Qihang, Stoumpos, Constantinos C., Douvalis, Alexios P., Balasubramanian, Mahalingam, Kanatzidis, Mercouri G., and Zunger, Alex. Sat . "Changes in charge density vs changes in formal oxidation states: The case of Sn halide perovskites and their ordered vacancy analogues". United States. doi:10.1103/PhysRevMaterials.1.025401.
@article{osti_1377072,
title = {Changes in charge density vs changes in formal oxidation states: The case of Sn halide perovskites and their ordered vacancy analogues},
author = {Dalpian, Gustavo M. and Liu, Qihang and Stoumpos, Constantinos C. and Douvalis, Alexios P. and Balasubramanian, Mahalingam and Kanatzidis, Mercouri G. and Zunger, Alex},
abstractNote = {Shifting the Fermi energy in solids by doping, defect formation, or gating generally results in changes in the charge density distribution, which reflect the ability of the bonding pattern in solids to adjust to such external perturbations. In the traditional chemistry textbook, such changes are often described by the formal oxidation states (FOS) whereby a single atom type is presumed to absorb the full burden of the perturbation (change in charge) of the whole compound. In the present paper, we analyze the changes in the position-dependence charge density due to shifts of the Fermi energy on a general physical basis, comparing with the view of the FOS picture. We use the halide perovskites CsSnX3 (X = F, Cl, Br, I) as examples for studying the general principle. When the solar absorber CsSnI3 (termed 113) loses 50% of its Sn atoms, thereby forming the ordered vacancy compound Cs2SnI6 (termed 216), the Sn is said in the FOS picture to change from Sn(II) to Sn(IV). To understand the electronic properties of these two groups we studied the 113 and 216 compound pairs CsSnCl3 and Cs2SnCl6, CsSnBr3 and Cs2SnBr6, and CsSnI3 and Cs2SnI6, complementing them by CsSnF3 and Cs2SnF6 in the hypothetical cubic structure for completing the chemical trends. These materials were also synthesized by chemical routes and characterized by x-ray diffraction, 119Sn-Mössbauer spectroscopy, and K-edge x-ray absorption spectroscopy. We find that indeed in going from 113 to 216 (equivalent to the introduction of two holes per unit) there is a decrease in the s charge on Sn, in agreement with the FOS picture. However, at the same time, we observe an increase of the p charge via downshift of the otherwise unoccupied p level, an effect that tends to replenish much of the lost s charge. At the end, the change in the charge on the Sn site as a result of adding two holes to the unit cell is rather small. This effect is theoretically explained as a “self-regulating response” [Raebiger, Lany, and Zunger, Nature (London) 453, 763 (2008)] whereby the system rehybridizes to minimize the effect of the charge perturbation created by vacancy formation. Rather than having a single preselected atom (here Sn) absorb the full brunt of the perturbation producing two holes, we find that the holes are distributed in a complex pattern throughout the octahedral systems of X6 ligands, forming hole orbitals with some specific symmetries. This clarifies the relation between FOS and charge transfer that can be applied to a wide variety of materials.},
doi = {10.1103/PhysRevMaterials.1.025401},
journal = {Physical Review Materials},
number = 2,
volume = 1,
place = {United States},
year = {Sat Jul 01 00:00:00 EDT 2017},
month = {Sat Jul 01 00:00:00 EDT 2017}
}
  • The advantageous performance of hybrid organic-inorganic perovskite halide semiconduc- tors in optoelectronic applications motivates studies of their fundamental crystal-chemistry. In particular, recent studies have sought to understand how dipolar, dynamic, and organic cations, such as methylammonium (CH 3 NH 3 + ) and formamidinium (CH(NH 2 ) 2 + ) affect physical properties such as light absorption and charge transport. Here, to probe the influence of organic- inorganic coupling on charge transport, we have prepared the series of vacancy-ordered double perovskite derivatives, A 2SnI 6, where A = Cs +, CH 3NH 3 +, and CH(NH 2) 2 +. Despitemore » nearly identical cubic structures by powder X-ray diffraction, replacement of Cs + with CH 3NH 3 + or CH(NH 2) 2 + reduces conductivity through a reduction in both carrier concentration and carrier mobility. We attribute the trends in electronic behavior to anharmonic lattice dynamics from the formation of hydrogen bonds that yield coupled organic-inorganic dynamics. This anharmonicity manifests as asymmetry of the inter-octahedral I-I pair correlations in the X-ray pair distribution function of the hybrid compounds, which can be modeled by large atomistic ensembles with random rotations of rigid [SnI 6] octahedral units. The presence of soft, anharmonic lattice dynamics holds implications for electron-phonon interactions, as supported by calculation of electron-phonon coupling strength that indicates the formation of more tightly-bound polarons and reduced electron mobilities with increasing cation size. Finally, by exploiting the relatively decoupled nature of the octahedral units in these defect-ordered perovskite variants, we can interrogate the impact of organic-inorganic coupling and lattice anharmonicity on the charge transport behavior of hybrid perovskite halide semiconductors.« less
  • The advantageous performance of hybrid organic-inorganic perovskite halide semiconduc- tors in optoelectronic applications motivates studies of their fundamental crystal-chemistry. In particular, recent studies have sought to understand how dipolar, dynamic, and organic cations, such as methylammonium (CH 3 NH 3 + ) and formamidinium (CH(NH 2 ) 2 + ) affect physical properties such as light absorption and charge transport. Here, to probe the influence of organic- inorganic coupling on charge transport, we have prepared the series of vacancy-ordered double perovskite derivatives, A 2SnI 6, where A = Cs +, CH 3NH 3 +, and CH(NH 2) 2 +. Despitemore » nearly identical cubic structures by powder X-ray diffraction, replacement of Cs + with CH 3NH 3 + or CH(NH 2) 2 + reduces conductivity through a reduction in both carrier concentration and carrier mobility. We attribute the trends in electronic behavior to anharmonic lattice dynamics from the formation of hydrogen bonds that yield coupled organic-inorganic dynamics. This anharmonicity manifests as asymmetry of the inter-octahedral I-I pair correlations in the X-ray pair distribution function of the hybrid compounds, which can be modeled by large atomistic ensembles with random rotations of rigid [SnI 6] octahedral units. The presence of soft, anharmonic lattice dynamics holds implications for electron-phonon interactions, as supported by calculation of electron-phonon coupling strength that indicates the formation of more tightly-bound polarons and reduced electron mobilities with increasing cation size. Finally, by exploiting the relatively decoupled nature of the octahedral units in these defect-ordered perovskite variants, we can interrogate the impact of organic-inorganic coupling and lattice anharmonicity on the charge transport behavior of hybrid perovskite halide semiconductors.« less