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Infra-red Dielectric Screening Determines the Low Exciton Binding Energy of Metal-halide Perovskites Paolo Umari, Edoardo Mosconi, and Filippo De Angelis J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b03286 • Publication Date (Web): 16 Jan 2018 Downloaded from http://pubs.acs.org on January 16, 2018
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The Journal of Physical Chemistry Letters
Infra-Red Dielectric Screening Determines the Low Exciton Binding Energy of Metal-Halide Perovskites
Paolo Umari,a,b* Edoardo Mosconi,c,e Filippo De Angelis c,d,e* a
Dipartimento di Fisica e Astronomia, Università di Padova, via Marzolo 8, I-35131 Padova, Italy
b
CNR-IOM DEMOCRITOS, Istituto Officina dei Materiali, Consiglio Nazionale delle Ricerche, Italy.
c
Computational Laboratory for Hybrid/Organic Photovoltaics (CLHYO), CNR-ISTM, via Elce di Sotto 8, I-06123, Perugia, Italy. d
e
D3-Computation, Italian Institute of Technology, Via Morego 30, Genova, Italy.
Consortium for Computational Molecular and Materials Sciences (CMS)2, Via Elce di Sotto, 8, I06123, Perugia, Italy.
*
E-mail:
[email protected];
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Abstract The performance of lead-halide perovskites in optoelectronic devices are due to a unique combination of factors, including highly efficient generation, transport and collection of photogenerated charge carriers. The mechanism behind efficient charge generation in lead-halide perovskites is still largely unknown. Here, we investigate the factors which influence the exciton binding energy (Eb) in a series of metal-halide perovskites using accurate first-principles calculations based on solution of the Bethe-Salpeter equation, coupled to ab initio molecular dynamics simulations. We find that Eb is strongly modulated by screening from low-energy phonons, which account for a factor ∼2 Eb reduction, while dynamic disorder and rotational motion of the organic cations play a minor role. We calculate Eb =15 meV for MAPbI3 , in excellent agreement with recent experimental estimates. We then explore how different material combinations (e.g. replacing Pb → Pb:Sn→ Sn; and MA → FA → Cs) may lead to different Eb values and highlight the mechanisms underlying Eb tuning.
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The first employment of lead-halide perovskites as the light absorbing layer in a dye-sensitized solar cell 1 triggered a perovskite revolution in solar cell research.2-4 Perovskite solar cells nowadays exhibit certified efficiencies exceeding 22%, with many laboratories worldwide routinely reporting >20% efficiency.5-6 These devices are extremely attractive from an industrial perspective, provided stability issues can be overcome, since their fabrication through wet chemistry techniques may allow for ease of production through e.g. printing techniques.7-8 Metal-halide perovskites display a typical ABX3 structure in which one metallic center (e.g. Pb or Sn or a combination of the two) occupies the center of an octahedron whose vertices are occupied by halides (Cl, Br, I), Scheme 1a. A-site cations, typically methylammonium (MA), formamidinium (FA) or cesium (Cs), fill the space among the octahedra and are only loosely bound to the inorganic sub-lattice. The prototypical lead-halide perovskite is methylammonium lead iodide, MAPbI3, which displays a tetragonal crystal structure at room temperature comprising four formula units (48 atoms) in the primitive cell,9 see Scheme 1b. As an attractive replacement of lead, the analogous MASnI3 perovskite, characterized by a lower band-gap than the Pb-analogue (1.2 vs 1.6 eV) has been widely explored, both in single junction10 and perovskite/perovskite tandem devices.11-12 Despite being less stable than Pb-perovskites, solar cells based on Sn-perovskites are steadily increasing their efficiencies; mixed Sn/Pb perovskites are also making their way through recent literature enabling both band gap engineering (by tuning the Sn:Pb ratio) and enhanced stability.13-15 Furthermore, the admixture of different A-site cations (e.g. MA, FA, Cs) and of different halides (typically I and Br) has given rise to superior photovoltaic performance and stability.16
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Scheme 1. a) Schematic representation of AMX3 perovskite. b) MAPbI3 in its tetragonal optimized structure from ref. 17.
The astonishing performance of lead-halide perovskites in optoelectronic devices are due to a unique combination of factors, including highly efficient generation, transport and collection of photogenerated charge carriers. While transport18 and recombination19 of charge carriers have received considerable attention in the literature, with the respective discovery of large polarons20 and defect tolerance in lead-halide perovskites,21 the initial stage of charge generation, i.e. exciton dissociation, has been scarcely investigated in recent reports after having raised an initial huge interest. Following an initial upper bound estimate of ∼55 meV,22 a steady decrease of the exciton binding energy (Eb) has been measured in subsequent papers,23-24 with most recent average values of ∼16 meV.25 In a sense, it was soon realized that exciton dissociation was not a big issue in this materials class; with the upper bound of Eb=55 meV ∼90% of the absorbed photons would still lead to free charge carriers at excitation densities relevant to photovoltaics (∼1016 cm-3),22 so that mainstream studies were afterwards mainly devoted to device efficiency and optimization. It is also worth noting that while a low Eb is desirable to allow the easy exciton dissociation into free charges, a small 4 ACS Paragon Plus Environment
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Eb value also implies a lower oscillator strength of the fundamental transition. In this sense, small (e.g.
