Atsushi Togo

Point defects in ZnO: an approach from first principles

Abstract Recent first-principles studies of point defects in ZnO are reviewed with a focus on native defects. Key properties of defects, such as formation energies, donor and acceptor levels, optical transition energies, migration energies and atomic and electronic structure, have been evaluated using various approaches including the local density approximation (LDA) and generalized gradient approximation (GGA) to DFT, LDA+U/GGA+U, hybrid Hartree–Fock density functionals, sX and GW approximation. Results significantly depend on the approximation to exchange correlation, the simulation models for defects and the post-processes to correct shortcomings of the approximation and models. The choice of a proper approach is, therefore, crucial for reliable theoretical predictions. First-principles studies have provided an insight into the energetics and atomic and electronic structures of native point defects and impurities and defect-induced properties of ZnO. Native defects that are relevant to the n-type conductivity and the non-stoichiometry toward the O-deficient side in reduced ZnO have been debated. It is suggested that the O vacancy is responsible for the non-stoichiometry because of its low formation energy under O-poor chemical potential conditions. However, the O vacancy is a very deep donor and cannot be a major source of carrier electrons. The Zn interstitial and anti-site are shallow donors, but these defects are unlikely to form at a high concentration in n-type ZnO under thermal equilibrium. Therefore, the n-type conductivity is attributed to other sources such as residual impurities including H impurities with several atomic configurations, a metastable shallow donor state of the O vacancy, and defect complexes involving the Zn interstitial. Among the native acceptor-type defects, the Zn vacancy is dominant. It is a deep acceptor and cannot produce a high concentration of holes. The O interstitial and anti-site are high in formation energy and/or are electrically inactive and, hence, are unlikely to play essential roles in electrical properties. Overall defect energetics suggests a preference for the native donor-type defects over acceptor-type defects in ZnO. The O vacancy, Zn interstitial and Zn anti-site have very low formation energies when the Fermi level is low. Therefore, these defects are expected to be sources of a strong hole compensation in p-type ZnO. For the n-type doping, the compensation of carrier electrons by the native acceptor-type defects can be mostly suppressed when O-poor chemical potential conditions, i.e. low O partial pressure conditions, are chosen during crystal growth and/or doping.

Distributions of phonon lifetimes in Brillouin zones

Lattice thermal conductivities of zincblende- and wurtzite-type compounds with 33 combinations of elements are calculated with the single-mode relaxation-time approximation and linearized phonon Boltzmann equation from first-principles anharmonic lattice dynamics calculations. In 9 zincblende-type compounds, distributions of phonon linewidths (inverse phonon lifetimes) are discussed in detail. The phonon linewidths vary non-smoothly with respect to wave vector, which is explained from the imaginary parts of the self energies. It is presented that detailed combination of phonon-phonon interaction strength and three phonon selection rule is critically important to determine phonon lifetime for these compounds. This indicates difficulty to predict phonon lifetime quantitatively without anharmonic force constants. However it is shown that joint density of states weighted by phonon numbers, which is calculated only from harmonic force constants, can be potentially used for a screening of the lattice thermal conductivity of materials.

Thermal physics of the lead chalcogenides PbS, PbSe, and PbTe from first principles

The lead chalcogenides represent an important family of functional materials, in particular due to the benchmark high-temperature thermoelectric performance of PbTe. A number of recent investigations, experimental and theoretical, have aimed to gather insight into their unique lattice dynamics and electronic structure. However, the majority of first-principles modeling has been performed at fixed temperatures, and there has been no comprehensive and systematic computational study of the effect of temperature on the material properties. We report a comparative lattice-dynamics study of the temperature dependence of the properties of PbS, PbSe, and PbTe, focusing particularly on those relevant to thermoelectric performance, viz. phonon frequencies, lattice thermal conductivity, and electronic band structure. Calculations are performed within the quasiharmonic approximation, with the inclusion of phonon-phonon interactions from many-body perturbation theory, which are used to compute phonon lifetimes and predict the lattice thermal conductivity. The results are critically compared against experimental data and other calculations, and add insight to ongoing research on the PbX compounds in relation to the off-centering of Pb at high temperatures, which is shown to be related to phonon softening. The agreement with experiment suggests that this method could serve as a straightforward, powerful, and generally applicable means of investigating the temperature dependence of material properties from first principles.

Prediction of Low-Thermal-Conductivity Compounds with First-Principles Anharmonic Lattice-Dynamics Calculations and Bayesian Optimization.

Compounds of low lattice thermal conductivity (LTC) are essential for seeking thermoelectric materials with high conversion efficiency. Some strategies have been used to decrease LTC. However, such trials have yielded successes only within a limited exploration space. Here, we report the virtual screening of a library containing 54,779 compounds. Our strategy is to search the library through Bayesian optimization using for the initial data the LTC obtained from first-principles anharmonic lattice-dynamics calculations for a set of 101 compounds. We discovered 221 materials with very low LTC. Two of them even have an electronic band gap <1 eV, which makes them exceptional candidates for thermoelectric applications. In addition to those newly discovered thermoelectric materials, the present strategy is believed to be powerful for many other applications in which the chemistry of materials is required to be optimized.

Phonon-phonon interactions in transition metals

In this paper the phonon self-energy produced by anharmonicity is calculated using second-order many-body perturbation theory for all bcc, fcc, and hcp transition metals. The symmetry properties of the phonon interactions are used to obtain an expression for the self-energy as a sum over irreducible triplets, very similar to integration in the irreducible part of the Brillouin zone for one-particle properties. The results obtained for transition metals shows that the lifetime is on the order of

Native defects in oxide semiconductors: a density functional approach

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Anharmonicity in the High-Temperature Cmcm Phase of SnSe: Soft Modes and Three-Phonon Interactions.

s. Moreover, the Peierls approximation for the imaginary part of the self-energy is shown to be reasonable for bcc and fcc metals. For hcp metals we show that the Raman-active mode decays into a pair of acoustic phonons, their wave vector being located on a surface defined by conservation laws.

Influence of the exchange-correlation functional on the quasi-harmonic lattice dynamics of II-VI semiconductors

We report a semilocal and hybrid Hartree-Fock density functional study of native defects in three oxide semiconductors: ZnO, SrTiO(3), and SnO. The defect that is responsible for the n-type conductivity of ZnO has been debated, in which the O vacancy, Zn interstitial, their complexes, and residual H impurity are considered candidates. Our results indicate that the O vacancy induces a deep and localized in-gap state, whereas the Zn interstitial is a shallow donor and hence can be a source of the carriers. In view of the formation energies, the O vacancy is likely to form with a substantial concentration under O-poor conditions, but the Zn interstitial is unlikely. We thus propose that the O vacancy is relevant to the nonstoichiometry of ZnO and that a source other than the native defects, such as the H impurity, needs to be considered for the n-type conductivity. For SrTiO(3), the O vacancy and its complexes have been regarded as the origins of some of the remarkable electrical and optical properties. We suggest significant roles of the Ti antisite for a new insight into the defect-induced properties. Two types of Ti antisite, both of which are off-centered from the Sr site but toward different directions, exhibit low formation energies under Ti-rich conditions as does the O vacancy. They can explain optical properties such as visible-light emission, deep-level absorption, and the ferroelectricity observed in reduced SrTiO(3). As an example of p-type conductors, SnO has been investigated with a focus on the acceptor-like native defects. Under O-rich conditions, the Sn vacancy and O interstitial are found to be energetically favorable. The Sn vacancy induces shallow acceptor levels and can therefore be a source of carriers. The O interstitial shows no in-gap levels and hence it is inactive in terms of the carrier generation and compensation. However, this defect is a key to the understanding of the structures of intermediate compounds between SnO and SnO(2).

Ab initio ORTEP drawings: a case study of N-based molecular crystals with different chemical nature

The layered semiconductor SnSe is one of the highest-performing thermoelectric materials known. We demonstrate, through a first-principles lattice-dynamics study, that the high-temperature Cmcm phase is a dynamic average over lower-symmetry minima separated by very small energetic barriers. Compared to the low-temperature Pnma phase, the Cmcm phase displays a phonon softening and enhanced three-phonon scattering, leading to an anharmonic damping of the low-frequency modes and hence the thermal transport. We develop a renormalization scheme to quantify the effect of the soft modes on the calculated properties, and confirm that the anharmonicity is an inherent feature of the Cmcm phase. These results suggest a design concept for thermal insulators and thermoelectric materials, based on displacive instabilities, and highlight the power of lattice-dynamics calculations for materials characterization.

First principles study of thermal conductivity cross-over in nanostructured zinc-chalcogenides

We perform a systematic comparison of the finite-temperature structure and properties of four bulk semiconductors (PbS, PbTe, ZnS, and ZnTe) predicted by eight popular exchange-correlation functionals from quasi-harmonic lattice-dynamics calculations. The performance of the functionals in reproducing the temperature dependence of a number of material properties, including lattice parameters, thermal-expansion coefficients, bulk moduli, heat capacities, and phonon frequencies, is evaluated quantitatively against available experimental data. We find that the phenomenological over- and under-binding characteristics of the local-density approximation and the PW91 and Perdew-Burke-Enzerhof (PBE) generalised-gradient approximation (GGA) functionals, respectively, are exaggerated at finite temperature, whereas the PBEsol GGA shows good general performance across all four systems. The Tao-Perdew-Staroverov-Scuseria (TPSS) and revTPSS meta-GGAs provide relatively small improvements over PBE, with the latter being better suited to calculating structural and dynamical properties, but both are considerably more computationally demanding than the simpler GGAs. The dispersion-corrected PBE-D2 and PBE-D3 functionals perform well in describing the lattice dynamics of the zinc chalcogenides, whereas the lead chalcogenides appear to be challenging for these functionals. These findings show that quasi-harmonic calculations with a suitable functional can predict finite-temperature structure and properties with useful accuracy, and that this technique can serve as a means of evaluating the performance of new functionals in the future.