Strong electron-phonon coupling and carrier self-trapping in Sb 2S3 Yun Liu Institute of High Performance Computing IHPC

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Strong electron-phonon coupling and carrier self-trapping in Sb2S3

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

Julia Wiktor

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

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

arXiv:2210.05907v2 [cond-mat.mtrl-sci] 6 Apr 2023

Abstract

Antimony sulphide (Sb2S3) is an Earth-abundant and non-toxic material that is under investiga-

tion 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 interfa-

cial defects and trap states. More recently, there has been some discussion in the literature about

the role of carrier trapping in the optoelectronic properties of Sb2S3, with some reporting self-

trapped exciton (STE) as the microscopic origin for the performance loss, while others have found

no evidence of carrier trapping with only large polaron existing in Sb2S3. By using ﬁrst-principles

methods, we demonstrate that Sb2S3exhibits 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 K to 300 K. When two electrons or holes are

added to the system, bipolarons are observed with localized charge density accompanying signiﬁ-

cant lattice distortion with the formation of Sb and S dimers. When the bipolarons are placed near

each other, a bi-STE with formation energy per exciton of −700 meV is observed, in general agree-

ment with the experimentally measured Stokes shift. Our results reconcile some of the controversy

in the literature regarding the existence of carrier trapping in Sb2S3, and demonstrate the impor-

tance of systematically investigating electron-phonon coupling and polaron and STE formation in

the antimony chalcogenide family of semiconductors for optoelectronic applications.

INTRODUCTION

Photovoltaic (PV) solar cells are one of the key technologies for realizing a decarbonized

economy as the Sun is an inexhaustible and clean energy source. Mainstream solar panels

have been mainly based on crystalline silicon, which oﬀers high power conversion eﬃciencies

(PCE) at over 25% and its cost has decreased substantially over the years[1]. While other

emerging materials such as organic-inorganic hybrid perovskites and thin ﬁlm technologies

such as CIGS and CdTe are making rapid improvements in PCE, they still face stability,

toxicity, and material scarcity issues[2]. To further increase the PCE and lower the cost

of PV generated electricity, tandem solar cells show great potential as they can break the

∗liu yun@ihpc.a-star.edu.sg

†bm418@cam.ac.uk

Shockley-Queisser limit of single junction solar cells[3]. The widely used silicon PV has

a bandgap of around 1.1 eV and is an ideal material for the bottom cell to absorb the

lower energy part of the solar spectrum. The search for top cell materials compatible with

crystalline silicon is an active area of research for the scientiﬁc and engineering communities,

with candidates ranging from III-V semiconductors to perovskites[4].

Among the many novel material candidates, the metal chalcogenide family has received

a lot of attention due to their Earth-abundant and low-toxicity elements[5–8]. They also

possess desirable band gaps and relatively benign synthesis conditions. In particular, an-

timony sulphide (Sb2S3) has a high absorption coeﬃcient in the visible region and a band

gap of 1.7 eV that is ideal for the top subcell in a Si-based tandem solar cell. Despite these

promising traits, the record PCE of Sb2S3is only about 7.5%[9], far from the minimum 18%

needed for an eﬃcient top cell[10]. This is due to the fact that Sb2S3suﬀers from high open

circuit voltage (Voc) losses, even though the internal quantum eﬃciency is near unity and

the ﬁll factor is up to 70%. Irrespective of fabrication methods, the Voc is only about 0.7 eV,

half the theoretical maximum allowed by its band gap. This large Voc loss has generally been

ascribed to the presence of localized point defects such as sulphur vacancies or interfacial

defects between Sb2S3and the carrier transport layers[11–14]. Such trap states in the band

gap can act as non-radiative recombination centres to reduce photocarrier populations[15].

Defects can also reduce the quasi-Fermi level splitting range under illumination and lead to

lower Voc and poor device performance.

Some recent reports have attributed the Voc loss in metal chalcogenides to intrinsic carrier

self-trapping[16–18]. In Sb2S3, the role of extrinsic defects was excluded by the observation

of a few picosecond carrier trapping without saturation at high carrier density of 1020 cm−3

and the polarized nature of trap emission from single crystals[16]. In Sb2Se3, lattice an-

harmonicity was observed with a 20 ps barrierless intrinsic self-trapping with associated

polaronic lattice distortion[18]. On the other hand, a ﬁrst-principles study found that po-

larons in these systems have rather large radii extending over several unit cells and moderate

Fr¨ohlich coupling constants[19]. Therefore, the debate on the role of small localized polaron

and carrier trapping in Sb2S3remains open.

A prerequisite for the formation of polarons is strong coupling between the carriers and

the lattice. Experimentally, the importance of electron-phonon coupling in Sb2S3has been

studied by Chong and co-workers, who observed coherent phonon generation in pump-probe

experiments, and assigned it to the B3glongitudinal optical phonon mode at 65 cm−1.

It was also reported that a Agoptical phonon mode at 194 cm−1is responsible for the

excited state relaxation in Sb2Se3[18]. The electronic structure and band gaps of Sb2S3were

also calculated at various levels of theory[20–22], and, separately, the phonon dispersion

and anisotropic thermal expansion [23, 24]. However, a full microscopic characterization of

electron-phonon coupling is still missing.

In this work, we perform a systematic ﬁrst-principles study of electron-phonon coupling

and polarons in Sb2S3. We reveal the presence of strong electron-phonon coupling, leading to

a large absorption edge renormalization of 200 meV when temperature increases from 10 K

to 300 K. We ﬁnd that there are negligible structural distortions when an electron is added or

removed from the supercell with the charge density remaining delocalized across the system.

In the presence of two excess electrons or holes per supercell, corresponding to a carrier

density of 1020 cm−3, we observe bipolarons associated with the formation of antimony and

sulphur dimers, respectively. When the electron and hole bipolarons are placed next to each

other, a bi-self-trapped-exciton (bi-STE) encompassing two neighbouring STE, is observed

with a formation energy of −700 meV per exciton. Our results contribute to the debate

regarding the existence and role of polarons and STE, and highlight the complex carrier

self-trapping properties in metal chalcogenide systems mediated by strong electron-phonon

coupling.

RESULTS AND DISCUSSIONS

A. Equilibrium properties

The orthorhombic phase of Sb2S3belongs to the space group Pbnm with 20 atoms per

unit cell. Its crystal structure is highly anisotropic with covalently bonded 1D ribbons of

Sb4S6along the [010] or bdirection (Figure 1(a)(b)). These ribbons are in turn weakly

bonded in a zigzag fashion in the (010) plane by van der Waals interactions. Due to the

presence of van der Waals interactions, we test the nonlocal vdW-DF functional optB86b

and SCAN+rVV10[26, 27] against some commonly used semi-local, metaGGA, and hybrid

functionals[28–31] (details in the Methods section). While most functionals are able to

reproduce the blattice parameter accurately, the vdW functional performs the best at si-

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Strongelectron-phononcouplingandcarrierself-trappinginSb2S3YunLiuInstituteofHighPerformanceComputing(IHPC),AgencyforScience,TechnologyandResearch(A*STAR),1FusionopolisWay,#16-16Connexis,Singapore138632,RepublicofSingaporeandCavendishLaboratory,UniversityofCambridge,CambridgeCB30HE,UnitedKingdomJuli...

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Strong electron-phonon coupling and carrier self-trapping in Sb 2S3 Yun Liu Institute of High Performance Computing IHPC

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