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Letter
Absorption f-Sum Rule for the Exciton Binding Energy in Methylammonium Lead Halide Perovskites Nicola Sestu, Michele Cadelano, Valerio Sarritzu, Feipeng Chen, Daniela Marongiu, Roberto Piras, Marina Manias, Francesco Quochi, Michele Saba, Andrea Mura, and Giovanni Bongiovanni J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.5b02099 • Publication Date (Web): 30 Oct 2015 Downloaded from http://pubs.acs.org on November 1, 2015
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The Journal of Physical Chemistry Letters
Absorption F-sum Rule for the Exciton Binding Energy in Methylammonium Lead Halide Perovskites. Nicola Sestu, Michele Cadelano, Valerio Sarritzu, Feipeng Chen, Daniela Marongiu, Roberto Piras, Marina Mainas, Francesco Quochi, Michele Saba*, Andrea Mura, Giovanni Bongiovanni*. Dipartimento di Fisica, Università degli Studi di Cagliari, I-09042 Monserrato, Italy. AUTHOR INFORMATION Corresponding Authors *M.S.: E-mail
[email protected] *G.B.: E-mail
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ABSTRACT. Advances of optoelectronic devices based on methylammonium lead halide perovskites depend on understanding the role of excitons, whether it is marginal as in inorganic semiconductors, or crucial, like in organics. However, a consensus on the exciton binding energy and its temperature dependence is still lacking, even for widely studied methylammonium lead iodide and bromide materials (MAPbI3, MAPbBr3). Here we determine the exciton binding energy based on an f-sum rule for integrated UV-Vis absorption spectra, circumventing the pitfalls of least squares fitting procedures. In the temperature range 80 K – 300 K, we find that the exciton binding energy in MAPbBr3 is 60 3 meV, independent of temperature; for
MAPbI3, in the orthorhombic phase (below 140K) 34 3 meV, while in the tetragonal
phase the binding energy softens to 29 meV at 170 K and stays constant up to 300 K. Implications of binding energy values on solar cell and LED workings are discussed.
TOC GRAPHICS
KEYWORDS. Methylammonium lead halide perovskites, exciton binding energy, optical properties, UV-Vis absorption, optical constants.
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The optical properties of methylammonium lead halide perovskite materials are of interest for a large community of researchers attempting to enhance the performances of perovskite-based solar cells and light-emitting diodes. Significant efforts have been devoted to determine the exciton binding energy, which is a fundamental parameter for a direct gap semiconductor, as it determines how tightly bound are excited electrons and holes, therefore affecting device design and workings. Lead halide perovskites are hybrid salts with an organic cation (methylammonium in our case) and their exciton binding energy lies in an interesting regime, intermediate between tightly bound organic Frenkel exciton and the loosely bound inorganic Wannier one. Recent literature has made clear that at room temperature the majority of excitations in perovskite materials are free carriers,1-7 much like in low-gap inorganic semiconductors, where excitons are ionized. Consensus however has not been reached on the value of the exciton binding energy, not even on the most widely studied materials, such as methylammonium lead iodide (MAPbI3) and methylammonium lead bromide (MAPbBr3).8-19 Particularly, the customary analysis of UV-Vis absorption spectra employed to estimate the exciton binding energy is somewhat ambiguous, as fitting procedures to the Elliott formula for Wannier excitons are employed, where the exciton binding energy and the linewidth are strongly interdependent when they have similar magnitude, as is the case for lead-halide perovskites at room temperature. Further complications arise in the analysis of absorption and ellipsometry data20-23 because of film roughness and spurious light scattering or absorption processes from crystal grain boundaries and defects. As a consequence, widely spread values for the binding energy have been reported, e.g. in MAPbI3 ranging from 2 to 50 meV. Uncertainty reigns also over the temperature dependence of the exciton binding energy, with some recent reports even suggesting that a significant softening of the exciton
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binding occurs from cryogenic to room temperature24-27 because of the screening of electron-hole Coulomb attraction provided by the methylammonium ion rotations.28-30 Here we present an analysis of the UV-Vis absorption spectra of perovskite materials based on an f-sum rule on the integrated absorption, leading to the unequivocal determination of the exciton binding energy that, unlike standard methods, only depends on parameters that can be readily extracted from the experimental data, without the ambiguities of fitting procedures. We applied the method to both MAPbBr3 and MAPbI3 films in the temperature interval 80 K - 300 K, covering most transitions between the three crystallographic phases, orthorhombic, tetragonal
and cubic.20,31-33 We found that the binding energy is constant through all phase transitions in
MAPbBr3 while in MAPbI3 there is a 20% jump at the orthorhombic-tetragonal phase transition.
Figure 1. Absorption spectrum computed according to Elliott formula. The black line is the absorption spectrum computed according to Elliott formula based on parameters typical of MAPbBr3 ( 50 meV, Γ 14 meV, 2.3 eV,
0.091 eV-1), with the two
contributions from exciton and continuum states, respectively, represented by the red and blue dashed lines.
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The absorption spectrum in direct semiconductors near the bandgap can be described by the Elliott formula,34 where the contributions of discrete exciton transitions are added to the
continuum transitions (bandgap ) and both are phenomenologically convoluted with a bellshaped function to account for the finite linewidth Γ:4 ∝ ! " ∑ $ + α ∝ ! " '∑*
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