Erratum to: Nonhydrogenic exciton spectrum in perovskite CH 3 NH 3 PbI 3 (physica status solidi (RRL) - Rapid Research Letters, (2015), 9, 10, (559-563), 10.1002/pssr.201510265)

In a recent article, the authors reported calculations of the exciton binding energy in the orthorhombic phase (OP) of MAPbI₃. They solved the exciton effective mass equation, using electron–hole interaction potentials screened by a distance-dependent dielectric function, originally proposed by Pollmann and Büttner (PB) and Haken (H). They obtained binding energies of 24 meV (PB) and 37 meV (H), the first of which is in reasonable agreement with the experimental value of 16–19 meV. However, a bug in the computer code was discovered, upon which the corrected exciton binding energy was found to be only ≈3.7 meV for the PB model. This value is significantly smaller than the experimental binding energy, questioning the applicability of the PB model for MAPbI₃. Nevertheless, the experimental binding energies can be reproduced by the calculations by adjusting the effective LO phonon energy E_LO. This parameter, taken as 38.5 meV (≡311 cm⁻¹) in Ref, was the only parameter not obtained from ab initio calculations. Figure shows the corrected binding energy (E_x) as a function of E_LO. Also shown is the experimental value from Phuong et al., and the value calculated by Yu with the H model, using slightly different effective masses. The vertical lines indicate infrared absorption frequencies identified by Grechko et al. It can be appreciated that the experimental binding energies (12–19 meV) can be reproduced with different values of E_LO for each model. For the PB model, the range 32–63 cm⁻¹ seems appropriate, in coincidence with the frequencies of ref. This range of frequencies is within the band located at 0–120 cm⁻¹, associated with the vibrations of the PbI₃ sublattice. Optically active phonon modes in this band have been identified by density functional theory calculations,[10–13] Raman scattering, and infrared absorption. In particular, Perez-Osorio et al. identified two groups of normal modes in the ranges 31–35 cm⁻¹, and 53–62 cm⁻¹, that contribute strongly to the static permittivity. (Figure presented.) Binding energy of the ground state exciton state (E_x) for the Pollmann–Büttner (E₁^PB) and Haken (E₁^H) models, as a function of phonon energy E_LO = hω_LO On the other hand, the H model predicts exciton binding energies in agreement with experiments for E_LO ≈ 16 meV (≡129 cm⁻¹). Phuong et al., by means of photocurrent measurements, determined an exciton binding energy of 12.4 meV, and an effective phonon energy E_LO ≈ 16.1 meV. Nagai et al., by means of terahertz reflection spectroscopy, identified peaks at 33, 71, 82, 95, 103, and 161 cm⁻¹. They fitted the inverse dielectric function with an effective one-phonon LO frequency of 131 cm⁻¹, in close agreement with ref. It is not clear why the H and PB models predict such different exciton binding energies, considering that the PB model was proposed as an improvement over the H model. Both models can reproduce the experimental values of the exciton binding energy in MAPbI₃, provided that the appropriate LO phonon energy is selected. In both cases, the LO phonon energy can be matched with certain experimentally identified vibrations. Let us comment on the scattering of experimental binding energies (12–19 meV). This can attributed to differences in the time scale inherent to each experimental technique, and to variations in exciton lifetime. Melissen et al. have discussed the relationship between exciton lifetime and the effectiveness of the vibration modes to screen the electron-hole interaction. Vibrations with a period larger than the exciton lifetime cannot contribute to its dielectric screening. Therefore, the largest exciton lifetimes may correspond to the smallest binding energies, thanks to lower frequency normal modes contributing to the dielectric constant. The exciton lifetime depends not only on the MAPbI₃ quality, but also on the presence of interfaces where excitons can dissociate. The H and PB models provide approximate stationary solutions of the exciton–LO-phonon system, being appropriate when the other interactions that limit the exciton lifetime are much weaker than electron–hole, electron–LO-phonon, and hole–LO-phonon couplings. In contrast, in the Wannier–Mott exciton model, a strong Coulomb electron–hole interaction is assumed, along with weak interactions with the rest of the system, including the LO phonons.