Strong electron-phonon coupling and bipolarons in ${\text{Sb}}_{2}{\text{S}}_{3}$

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Strong electron-phonon coupling and bipolarons in ${Sb}_{2} S_{3}$

Yun Liu, Bartomeu Monserrat, and Julia Wiktor

Phys. Rev. Materials 7, 085401 – Published 7 August 2023

Abstract

Antimony sulfide $({Sb}_{2} S_{3})$ is an Earth-abundant and nontoxic material that is under investigation for solar energy conversion applications. However, it still suffers from poor power conversion efficiency and a large open circuit voltage loss that have usually been attributed to point or interfacial defects. More recently, there has been some discussion in the literature about the role of carrier trapping in the optical properties of ${Sb}_{2} S_{3}$ , with some reporting self-trapped excitons as the microscopic origin for the performance loss, while others have found no evidence of carrier trapping with only large polarons existing in ${Sb}_{2} S_{3}$ . By using first-principles methods, we demonstrate that ${Sb}_{2} S_{3}$ exhibits strong electron-phonon coupling, a prerequisite for carrier self-trapping in semiconductors, which results in a large renormalization of $200 meV$ of the absorption edge when temperature increases from 10 to $300 K$ . When two electrons or holes are added to the system, corresponding to a carrier density of $1.6 \times 10^{20} {cm}^{- 3}$ , we find wave function localization consistent with the presence of bipolarons accompanying a significant lattice distortion with the formation of Sb and S dimers. The formation energies of the electron and hole bipolarons are $- 330$ and $- 280$ meV per carrier, respectively. Our results reconcile some of the controversy in the literature regarding carrier trapping in ${Sb}_{2} S_{3}$ and demonstrate the existence of large electron-phonon coupling and carrier self-trapping that might place a fundamental limit on the open circuit voltage and, consequently, the maximum efficiency of the photovoltaic cells.

Received 13 April 2023
Revised 20 June 2023
Accepted 20 July 2023

DOI:https://doi.org/10.1103/PhysRevMaterials.7.085401

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Electronic structure First-principles calculations Phonons Polarons Solar energy Thermal expansion

Energy Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Yun Liu ^*

Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, 16-16 Connexis, Singapore 138632, Republic of Singapore and Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom

Bartomeu Monserrat ^†

Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom and Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB3 0FS, United Kingdom

Julia Wiktor ^‡

Department of Physics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden

^*liu_yun@ihpc.a-star.edu.sg
^†bm418@cam.ac.uk
^‡julia.wiktor@chalmers.se

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Vol. 7, Iss. 8 — August 2023

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Figure 1
(a) ${Sb}_{2} S_{3}$ crystal structure viewed from the [010] axis, with the unit cell enclosed by the black box. Brown and yellow spheres represent Sb and S atoms, respectively. One $[{Sb}_{4} S_{6}]$ ribbon is encircled by the green dashed line. The intraribbon bonds are indicated by the solid brown-yellow lines, and the interribbon van der Waals interactions are indicated by black dashed lines. (b) ${Sb}_{2} S_{3}$ crystal structure viewed from the [001] axis, with the ribbon enclosed in a green dashed box. (c) The projected band structures along high-symmetry lines of the Brillouin zone calculated at the optB86b level, with the orbital contributions drawn as a series of stacked circles. (d) The phonon dispersion of ${Sb}_{2} S_{3}$ along high-symmetry lines of the Brillouin zone, with the total phonon density of states in the right panel.
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Figure 2
(a) Relative Helmholtz free energy as a function of the unit cell volume for temperatures between 0 and $400 K$ . The black dashed vertical line indicates the volume at the static DFT level, and the black squares indicate the minima of fitted free-energy curves at each given temperature with the Rose-Vinet equation of state. (b) The unit cell volume as a function of temperature as calculated by the QHA. The QHA data are also shifted by $- 2.5 Å^{3}$ to guide the comparison with experimental volumes [62]. (c) Absorption coefficient at temperatures from 10 to 400 K including phonon-assisted processes. A scissor operator of $0.5 eV$ is applied to all the spectra to align the static DFT band gap to the HSE06 level.
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Figure 3
Bond distortions arising from excess electrons and holes. (a) and (b) The crystal structure and selected bond lengths of ground state ${Sb}_{2} S_{3}$ , with characteristic interchain S-S (blue) and intrachain Sb-Sb (purple) and Sb-S (red) distances. (c) and (d) Distorted structures in the presence of an electron bipolaron, with Sb-Sb antimony dimer bond lengths at 2.89 Å. (e) and (f) Distorted structures in the presence of a hole bipolaron, with S-S sulfur dimer bond lengths at 2.08 Å.
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Figure 4
Electronic structures of the polaronic states. (a) and (d) Projected density of states (PDOS) of the relaxed bipolaronic structures with two excess electrons and holes, respectively. The energetic locations of the electron bipolaron and hole bipolaron states are circled. (b) and (c) Wave function isosurface of the electron bipolaron as viewed from the $b$ and $c$ axes. (e) and (f) The difference between the total charge density of the hole bipolaron and the pristine ${Sb}_{2} S_{3}$ as viewed from the $b$ and $c$ axes. Blue and red represent positive and negative values.
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Physical Review Materials

Strong electron-phonon coupling and bipolarons in Sb2S3

Yun Liu, Bartomeu Monserrat, and Julia Wiktor

Phys. Rev. Materials 7, 085401 – Published 7 August 2023

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Strong electron-phonon coupling and bipolarons in ${Sb}_{2} S_{3}$