Determining Exciton Binding Energy and Reduced Effective Mass in Metal Tri-Halide Perovskites from Optical and Impedance Spectroscopy Measurements

TL;DR

This work tackles the challenge of accurately determining the exciton binding energy $E_{xb}$ and the reduced effective mass $\mu$ in metal tri-halide perovskites, where polaron effects and lattice polarization strongly influence optoelectronic properties. The authors integrate an Elliott-based Band Fluctuations (EBF) optical dispersion model with the Pollmann–Büttner (PB) exciton-polaron framework, explicitly incorporating LO phonon polarization via the electronic and ionic dielectric constants $\varepsilon_{\infty}$ and $\varepsilon_{0}$ and the LO phonon energy $\hbar\omega_{LO}$. They obtain $E_{xb}$ from optical absorption using the EBF model, determine $\varepsilon_{\infty}$ from ellipsometry, $\varepsilon_{0}$ from impedance spectroscopy, and estimate $\hbar\omega_{LO}$ from the temperature dependence of exciton linewidth, then map $E_{xb}$ onto PB contour maps to extract $\mu$. The results across MAPbI$_3$, MAPbBr$_3$, MAPbCl$_3$, CsPbBr$_3$, and FAPbI$_3$ show $E_{xb}$ values in the tens of meV range and $\mu$ in the $0.10$–$0.14\,m_e$ range, in good agreement with high-field magnetoabsorption and ARPES measurements, underscoring the robustness of the combined EBF-PB approach. This methodology provides a practical, experimentally accessible route to quantify polaron-influenced carrier masses in polar perovskites and potentially other polar semiconductors with free exciton bands, facilitating improved design of optoelectronic devices.

Abstract

Accurate determination of the exciton binding energy and reduced effective mass in halide perovskites is of utmost importance for the selective design of optoelectronic devices. Although these properties are currently determined by several spectroscopic techniques, complementary theoretical models are often required to bridge macroscopic and microscopic properties. Here, we present a novel method to determine these quantities while fully accounting for polarization effects due to carrier interactions with longitudinal optical phonons. Our approach estimates the exciton-polaron binding energy from optical absorption measurements using a recently developed Elliott based Band Fluctuations model. The reduced effective mass is obtained via the Pollmann-Buttner exciton-polaron model, which is based on the Frohlich polaron framework, where the strength of the electron-phonon interaction arises from changes in the dielectric properties. The procedure is applied to the family of perovskites ABX3 (A = MA, FA, Cs; B = Pb; X = I, Br, Cl), showing excellent agreement with high field magnetoabsorption and other optical-resolved techniques. The results suggest that the Pollmann-Buttner model offers a robust and novel approach for determining the reduced effective mass in metal tri-halide perovskites and other polar materials exhibiting free exciton bands.

Figures (3)

• Figure 1: (a) Schematic view of the exciton-polaron system as a result of the lattice polarization of a cubic perovskite ABX$_3$ (A: MA, FA,Cs; B: Pb; X: I, Br, Cl). Here, exchange of phonons are represented as zizag arrows and the exciton as the ellipsoid with center of mass at CM. (b) Real ($\varepsilon_1$) and imaginary ($\varepsilon_2$) part of the dielectric function at different frequencies. The dipole, ionic and electronic polarizations are represented as $\varepsilon_s$, $\varepsilon_0$ and $\varepsilon_\infty$, respectively.
• Figure 2: (a) Phases of the analyzed tri-halide perovskites as a function of temperature. (b) Temperature-dependent optical absorption data from CsPbBr3, extracted from Wolf et al. cristoph, presented as open circles. The solid lines indicate the fitting with the EBF model. Contributions of discrete and continuum exciton states of the EBF model are presented as shaded regions. (c) Exciton binding energies as a function of the bandgap at different temperatures obtained from the EBF model. Note that the corresponding phases of perovskites are enclosed by ellipses and labeled as orthorhombic (O), tetragonal (T) and cubic (C). The inset present a zoom around 1.6eV for MAPbI$_3$ and FaPbI$_3$.(d) Evolution of the exciton broadening (FWHM) for temperatures in the range of the analyzed phases. The solid lines represent the fitting of Eq. (\ref{['eq.linewidth']}) to obtain the LO phonon energy.
• Figure 3: Exciton-polaron binding energy surface map, calculated with Pollmann's model, as a function of the electron (x-axes) and hole (y-axes) bare effective masses for the $\textrm{MAPbI}_{3}$ (a), $\textrm{MAPbBr}_{3}$ (b), MAPbCl$_3$ (c), $\textrm{CsPbBr}_{3}$ (d) and $\textrm{FAPbI}_{3}$ (e). Here, the exciton binding energy shown in Table \ref{['table:parameters']} is presented as the black shaded region. Note that the average reduced effective mass is presented in sky-blue lines. Reduced effective masses from other experimental reports are presented in yellow dashed lines where the superscript denotes the perovskite phase, orthorhombic (O), tetragonal (T) and cubic (C). The hole effective mass retrieved from ARPES measurements are presented as magenta horizontal lines. Note that the carrier effective masses are in terms of the electron mass