[Paper Review] Capturing Excitonic Effects in Lead Iodide Perovskites from Many-Body Perturbation Theory

Pooja Basera, Arunima Singh+2 more|arXiv (Cornell University)|Aug 7, 2020

Perovskite Materials and Applications5 references4 citations

TL;DR

This study employs an integrated first-principles approach combining hybrid DFT, GW, Bethe-Salpeter equation (BSE), model-BSE (mBSE), Wannier-Mott theory, and DFPT to accurately predict the electronic, optical, and excitonic properties of APbI₃ perovskites (A = MA, FA, Cs). It resolves inconsistencies in prior GW calculations by tuning the exact exchange parameter (α) in HSE06, achieving excellent agreement with experiment for bandgap, exciton binding energy (5–15 meV), and radiative exciton lifetime, while identifying Rashba-Dresselhaus splitting and low-energy phonons as key factors in long-lived excitons.

ABSTRACT

Lead iodide perovskites have attracted considerable interest in the upcoming photovoltaic technologies and optoelectronic devices. Therefore, an accurate theoretical description of the electronic and optical properties especially to understand the excitonic effects in this class of materials is of scientific and practical interest. However, despite several theoretical research endeavours in past, the most accurate analysis of the key electronic parameters for solar cell performance, such as optical properties, effective mass, exciton binding energy (E$_B$) and the radiative exciton lifetime are still largely unknown. Here, we employ state-of-the-art first-principles based methodologies viz. hybrid functional(HSE06) combined with spin-orbit coupling (SOC), many-body perturbation theory (GW, BSE), model-BSE (mBSE), Wannier-Mott (WM) and Density Functional Perturbation Theory (DFPT). By taking a prototypical model system viz. APbI$_3$ (A = Formamidinium (FA), methylammonium (MA), and Cs), an exhaustive analysis is presented on the theoretical understanding of the optical, electronic and excitonic properties. We show that tuning of exact exchange parameter ($α$) in HSE06 calculations incorporating SOC, followed by single shot GW, and BSE play a pivotal role in obtaining a reliable predictions for the experimental bandgap. We demonstrate that mBSE approach improves the feature of optical spectra w.r.t experiments. Furthermore, WM approach and ionic contribution to dielectric screening (below 16 meV) ameliorate the E$_B$. Our results reveal that the direct-indirect band gap transition (Rashba splitting) may be a factor responsible for the reduced charge carrier recombination rate in MAPbI$_3$ and FAPbI$_3$. The role of cation ''A'' for procuring the long-lived exciton lifetime is well understood. This proposed methodology allows to design new materials with tailored excitonic properties.

Motivation & Objective

• To resolve inconsistencies in prior GW calculations of the bandgap in lead halide perovskites by optimizing the exact exchange parameter in hybrid DFT.
• To provide a reliable theoretical framework for predicting optical, electronic, and excitonic properties, including exciton binding energy and radiative lifetime.
• To investigate the role of cation A (MA, FA, Cs) in modulating exciton lifetime and recombination dynamics.
• To quantify the contributions of ionic dielectric screening and spin-orbit coupling to excitonic behavior.
• To establish a predictive methodology for designing perovskite materials with tailored excitonic properties.

Proposed method

• Hybrid DFT with HSE06 functional and spin-orbit coupling (SOC) to improve bandgap prediction, with systematic tuning of the exact exchange parameter α from 25% to 53%.
• Single-shot GW calculations to correct quasiparticle energies, using three times the number of occupied orbitals for unoccupied states.
• Solution of the Bethe-Salpeter equation (BSE) to describe electron-hole interactions and excitonic effects, with convergence tested over k-point grids and band counts.
• Application of model-BSE (mBSE) with denser k-point sampling to improve agreement with experimental optical spectra.
• Use of Density Functional Perturbation Theory (DFPT) with a 12×12×12 k-grid to compute ionic contributions to dielectric screening and low-energy optical phonon modes.
• Wannier-Mott model combined with k.p perturbation theory to estimate exciton binding energy and radiative lifetime, validated via mBSE peak broadening.

Experimental results

Research questions

• RQ1 How does tuning the exact exchange parameter α in HSE06 improve the accuracy of the bandgap prediction in APbI₃ perovskites compared to standard GW calculations?
• RQ2 To what extent do ionic contributions to dielectric screening and low-energy phonon modes (below 16 meV) influence the exciton binding energy in MAPbI₃ and FAPbI₃?
• RQ3 How does Rashba-Dresselhaus splitting due to spin-orbit coupling affect the optical absorption and charge carrier recombination rate in hybrid perovskites?
• RQ4 What is the role of the organic cation (A = MA, FA) versus inorganic cation (Cs) in determining the radiative exciton lifetime?
• RQ5 Can the mBSE approach improve the agreement between theoretical optical spectra and experimental measurements compared to standard BSE?

Key findings

• Tuning the exact exchange parameter α in HSE06 with SOC yields a reliable starting point for GW calculations, resolving inconsistencies in prior bandgap predictions for APbI₃ perovskites.
• The model-BSE (mBSE) approach significantly improves the agreement between theoretical optical spectra and experimental measurements by capturing excitonic features more accurately.
• Exciton binding energies are predicted to range between 5 and 15 meV, with the highest values observed in FAPbI₃ and MAPbI₃, consistent with experimental trends.
• The presence of low-energy optical phonon modes below 16 meV contributes significantly to ionic dielectric screening, reducing the effective exciton binding energy.
• Rashba-Dresselhaus splitting in MAPbI₃ and FAPbI₃ leads to a direct-indirect bandgap transition, which suppresses non-radiative recombination and enhances exciton lifetime.
• The Wannier-Mott model and mBSE-based peak broadening both predict longer exciton lifetimes in MA- and FA-based perovskites compared to Cs-based systems, confirming the role of cation chemistry in excitonic stability.