25 research outputs found
Electron-Phonon Interactions and Charge Transport from First-Principles Calculations: Complex Crystals, Higher Order Coupling, and Steps Toward the Small Polaron Regime
Electron-phonon (e-ph) interactions quantify the strength of interplay between charge carriers and lattice vibrations and critically determine the transport properties in materials near room temperature. Depending on the coupling strength, charge carriers can exhibit behaviors ranging from propagating waves extending across crystals to trapped particles localized in space. Therefore, accurately describing e-ph interactions plays a central role in quantitative transport studies on real materials. Over the last few years, first-principles methods combining density functional theory (DFT) and related techniques with the Boltzmann transport equation (BTE) have rapidly risen and reached maturity for investigating transport in various metals, semiconductors, and insulators with weak e-ph coupling. The lowest-order e-ph scattering process can be investigated starting from e-ph interactions from DFT calculations; this first-principles approach provides unambiguous quantitative prediction of transport properties such as the conductivity and mobility in common semiconductors and metals over a wide temperature range without using any empirical parameter. Encouraged by the agreement of the computed transport properties with experiment for many simple materials, this thesis aims to extend the applicability of this first-principles methodology and to further our understanding of microscopic transport mechanisms, especially in the wide temperature window near room temperature where transport is governed by e-ph scattering. We present research that expands the state of the art in three distinct ways, focusing on three research directions we pursue in this work. First, we employ the BTE to calculate the hole carrier mobility of naphthalene, an organic molecular crystal containing 36 atoms in a unit cell, the record largest system for first-principles charge transport calculations to date. The results are in excellent agreement with experiments, demonstrating that transport in some high-mobility organic semiconductors can still be explained within the band theory framework, and show that low-frequency rigid molecular motions control the electrical transport in organic molecular semiconductors in the bandlike regime. The second topic is an attempt to go beyond the lowest-order theory of e-ph interactions and quantify the importance of higher-order e-ph processes. We derive the electron-two-phonon scattering rates using many-body perturbation theory, compute them in GaAs, and quantify their impact on the electron mobility. We show that these next-to-leading order e-ph scattering rates, although smaller than the lowest-order contribution, are not negligible, and can compensate the overestimation of mobility generally made by the lowest-order BTE calculation in weakly-polar semiconductors. In the third part of the thesis, we explore the opposite extreme case in which e-ph interactions are strong and lead to the formation of localized (so-called "polaron") electronic states that become self-trapped by the interactions with the atomic vibrations. We derive a rigorous approach based on canonical transformations to compute the energetics of self-localized (small) polarons in materials with strong e-ph interactions. With the aid of \textit{ab initio} e-ph interactions, we carry out the corresponding numerical calculations to investigate the formation energy of small polaron and determine whether the charge carriers favor localized states over the Bloch waves. Due to the low computational cost of our approach, we are able to apply these calculations to various compounds, focusing on oxides, predicting the presence of small polaron in agreement with experiments in various materials. Our work paves the way to understanding small polaron formation and extending these calculations to predict transport in the polaron hopping mechanism in materials with strong e-ph coupling
Charge Transport in Organic Molecular Semiconductors from First Principles: The Band-Like Hole Mobility in Naphthalene Crystal
Predicting charge transport in organic molecular crystals is notoriously
challenging. Carrier mobility calculations in organic semiconductors are
dominated by quantum chemistry methods based on charge hopping, which are
laborious and only moderately accurate. We compute from first principles the
electron-phonon scattering and the phonon-limited hole mobility of naphthalene
crystal in the framework of ab initio band theory. Our calculations combine GW
electronic bandstructures, ab initio electron-phonon scattering, and the
Boltzmann transport equation. The calculated hole mobility is in very good
agreement with experiment between 100300 K, and we can predict its
temperature dependence with high accuracy. We show that scattering between
inter-molecular phonons and holes regulates the mobility, though
intra-molecular phonons possess the strongest coupling with holes. We revisit
the common belief that only rigid molecular motions affect carrier dynamics in
organic molecular crystals. Our work provides a quantitative and rigorous
framework to compute charge transport in organic crystals, and is a first step
toward reconciling band theory and carrier hopping computational methods.Comment: 7 pages, 4 figures, Accepted by Phys. Rev.
Next-to-Leading Order Ab Initio Electron-Phonon Scattering
Electron-phonon (e-ph) interactions are usually treated in the lowest order
of perturbation theory. Here we derive next-to-leading order e-ph interactions,
and compute from first principles the associated two-phonon e-ph scattering
rates. The derivation involves Matsubara sums of the relevant two-loop Feynman
diagrams, and the numerical calculations are challenging since they involve
Brillouin zone integrals over two crystal momenta and depend critically on the
intermediate state lifetimes. Using random grids and Monte Carlo integration,
together with a self-consistent update of the intermediate state lifetimes, we
compute and converge the two-phonon scattering rates, using GaAs as a case
study. For the longitudinal optical phonon in GaAs, we find that the two-phonon
scattering rates are as large as nearly half the value of the leading-order
rates. The energy and temperature dependence of the two-phonon processes are
analyzed. We show that including the two-phonon processes is important to
accurately predicting the electron mobility in GaAs.Comment: 5 pages, 5 figure
Ab initio electron-two-phonon scattering in GaAs from next-to-leading order perturbation theory
Electron-phonon (e–ph) interactions are usually treated in the lowest order of perturbation theory. Here we derive next-to-leading order e–ph interactions, and compute from first principles the associated electron-two-phonon (2ph) scattering rates. The derivations involve Matsubara sums of two-loop Feynman diagrams, and the numerical calculations are challenging as they involve Brillouin zone integrals over two crystal momenta and depend critically on the intermediate state lifetimes. Using Monte Carlo integration together with a self-consistent update of the intermediate state lifetimes, we compute and converge the 2ph scattering rates, and analyze their energy and temperature dependence. We apply our method to GaAs, a weakly polar semiconductor with dominant optical-mode long-range e–ph interactions. We find that the 2ph scattering rates are as large as nearly half the value of the one-phonon rates, and that including the 2ph processes is necessary to accurately predict the electron mobility in GaAs from first principles
Facile ab initio approach for self-localized polarons from canonical transformations
Electronic states in a crystal can localize due to strong electron-phonon (e-ph) interactions, forming so-called small polarons. Methods to predict the formation and energetics of small polarons are either computationally costly or not geared toward quantitative predictions. Here we show a formalism based on canonical transformations to compute the polaron formation energy and wavefunction using ab initio e-ph interactions. Comparison of the calculated polaron and band edge energies allows us to determine whether charge carriers in a material favor a localized small polaron over a delocalized Bloch state. Due to its low computational cost, our approach enables efficient studies of the formation and energetics of small polarons, as we demonstrate by investigating electron and hole polaron formation in alkali halides and metal oxides and peroxides. We outline refinements of our scheme and extensions to compute transport in the polaron hopping regime
Facile ab initio approach for self-localized polarons from canonical transformations
Electronic states in a crystal can localize due to strong electron-phonon (e-ph) interactions, forming so-called small polarons. Methods to predict the formation and energetics of small polarons are either computationally costly or not geared toward quantitative predictions. Here we show a formalism based on canonical transformations to compute the polaron formation energy and wavefunction using ab initio e-ph interactions. Comparison of the calculated polaron and band edge energies allows us to determine whether charge carriers in a material favor a localized small polaron over a delocalized Bloch state. Due to its low computational cost, our approach enables efficient studies of the formation and energetics of small polarons, as we demonstrate by investigating electron and hole polaron formation in alkali halides and metal oxides and peroxides. We outline refinements of our scheme and extensions to compute transport in the polaron hopping regime