Tapio T. Rantala

Electronic structure calculations with GPAW: A real-space implementation of the projector augmented-wave method

Electronic structure calculations have become an indispensable tool in many areas of materials science and quantum chemistry. Even though the Kohn-Sham formulation of the density-functional theory (DFT) simplifies the many-body problem significantly, one is still confronted with several numerical challenges. In this article we present the projector augmented-wave (PAW) method as implemented in the GPAW program package (https://wiki.fysik.dtu.dk/gpaw) using a uniform real-space grid representation of the electronic wavefunctions. Compared to more traditional plane wave or localized basis set approaches, real-space grids offer several advantages, most notably good computational scalability and systematic convergence properties. However, as a unique feature GPAW also facilitates a localized atomic-orbital basis set in addition to the grid. The efficient atomic basis set is complementary to the more accurate grid, and the possibility to seamlessly switch between the two representations provides great flexibility. While DFT allows one to study ground state properties, time-dependent density-functional theory (TDDFT) provides access to the excited states. We have implemented the two common formulations of TDDFT, namely the linear-response and the time propagation schemes. Electron transport calculations under finite-bias conditions can be performed with GPAW using non-equilibrium Green functions and the localized basis set. In addition to the basic features of the real-space PAW method, we also describe the implementation of selected exchange-correlation functionals, parallelization schemes, ΔSCF-method, x-ray absorption spectra, and maximally localized Wannier orbitals.

Kohn-Sham potential with discontinuity for band gap materials

We model a Kohn-Sham potential with a discontinuity at integer particle numbers derived from the GLLB approximation of Gritsenko et al. We evaluate the Kohn-Sham gap and the discontinuity to obtain the quasiparticle gap. This allows us to compare the Kohn-Sham gaps to those obtained by accurate many-body perturbation theory based optimized potential methods. In addition, the resulting quasiparticle band gap is compared to experimental gaps. In the GLLB model potential, the exchange-correlation hole is modeled using a GGA energy density and the response of the hole to density variations is evaluated by using the common-denominator approximation and homogeneous electron gas based assumptions. In our modification, we have chosen the PBEsol potential as the GGA to model the exchange hole, and add a consistent correlation potential. The method is implemented in the GPAW code, which allows efficient parallelization to study large systems. A fair agreement for Kohn-Sham and the quasiparticle band gaps with semiconductors and other band gap materials is obtained with a potential which is as fast as GGA to calculate.

Three real-space discretization techniques in electronic structure calculations

A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the main approaches include finite-difference methods, various types of finite-elements and wavelets. This paper reports on the results of several code development projects that approach problems related to the electronic structure using these three different discretization methods. We review the ideas behind these methods, give examples of their applications, and discuss their similarities and differences.

Localized surface plasmon resonance in silver nanoparticles: Atomistic first-principles time-dependent density-functional theory calculations

We observe using ab initio methods that localized surface plasmon resonances in icosahedral silver nanoparticles enter the asymptotic region already between diameters of 1 and 2 nm, converging close to the classical quasistatic limit around 3.4 eV. We base the observation on time-dependent density-functional theory simulations of the icosahedral silver clusters Ag-55 (1.06 nm), Ag-147 (1.60 nm), Ag-309 (2.14 nm), and Ag-561 (2.68 nm). The simulation method combines the adiabatic GLLB-SC exchange-correlation functional with real time propagation in an atomic orbital basis set using the projector-augmented wave method. The method has been implemented for the electron structure code GPAW within the scope of this work. We obtain good agreement with experimental data and modeled results, including photoemission and plasmon resonance. Moreover, we can extrapolate the ab initio results to the classical quasistatically modeled icosahedral clusters.

Possible structures of nonstoichiometric tin oxide: the composition Sn2O3

Structural aspects of crystalline tin oxide and its interfaces with composition Sn2O3 are considered computationally based on first principles density functional calculations. The possibility of formation of different nonstoichiometric tin oxide crystals and SnO2/SnO interfaces is shown. The lowest total energy per Sn2O3 unit was evaluated for a layered Sn2O3 crystal, where oxygen vacancies are arranged into the (101) plane in a rutile structure system. Interface structures with orientations SnO2(101)/SnO(001) and SnO2(100)/SnO(100), corresponding to composition Sn2O3 are only slightly less stable. Their estimated interface energies are 0.15 J m−2 and 0.8 J m−2, respectively. All geometries have components similar to well-known rutile structure SnO2 and litharge structure SnO geometries. Most stable Sn2O3 crystals include SnO6 octahedra similar to those found in rutile structure SnO2.

Atomistic understanding of semiconductor gas sensors

Abstract Oxide semiconductors form a group of compounds whose specific properties of surfaces and interfaces are used for gas sensing. Our fundamental understanding of the operation principles of these devices is still insufficient. The abundance of phenomena on open oxide–semiconductor surfaces at elevated operation temperatures of the sensors is a central reason for the situation, in addition of the effects originating in the electrode–semiconductor contacts. The exchange of lattice oxygen with the surrounding atmosphere and a possible diffusion of oxygen through oxygen–vacancy donors in n -type oxides, especially at elevated temperatures, have also strong effects on the behaviour of semiconductor gas sensors. Atomistic understanding of surfaces is the basis for the understanding of both the receptor and transducer functions of semiconductor gas sensors. The rutile structure tin dioxide, SnO 2 , together with its most stable (110) face is the example material here. Especially, we consider the oxygen chemistry at the SnO 2 (110) surface together with its connection to dipole layers and band-gap surface states. For example, the role of tin (II) ions at the reduced SnO 2 (110) surface is discussed. A “transistor model” is also given to describe the transducing properties of semiconductor gas sensors.

Nitrogen incorporation into GaInNAs lattice-matched to GaAs: The effects of growth temperature and thermal annealing

We have studied the effects of growth temperature and subsequent thermal annealing on nitrogen incorporation into lattice-matched dilute Ga0.942In0.058NAs-on-GaAs epilayers, which were grown by the molecular-beam epitaxy method. The samples were studied experimentally by means of x-ray diffraction and Raman spectroscopy and theoretically by calculations within the density-functional theory. Over the entire range of growth temperatures applied (410–470°C), nitrogen appeared to be mainly located on substitutional sites in “short-range-order clusters” as N–Ga4 and, to a lesser extent, as N–Ga3In. There were also indications of the presence of nitrogen dimers NN, as suggested by Raman spectroscopy, in qualitative agreement with the calculations. An increase in growth temperature reduced the amount of substitutional nitrogen and decreased the number of N–Ga4 clusters relative to N–Ga3In. Postgrowth thermal annealing promoted the formation of In–N bonds and caused a blueshift in the optical band gap, which incr...

Porphyrin adsorbed on the (101[combining macron]0) surface of the wurtzite structure of ZnO--conformation induced effects on the electron transfer characteristics.

Electron transfer at the adsorbate-surface interface is crucial in many applications but the steps taking place prior to and during the electron transfer are not always thoroughly understood. In this work a model system of 4-(porphyrin-5-yl)benzoic acid adsorbed as a corresponding benzoate on the ZnO wurtzite (101[combining macron]0) surface is studied using density functional theory (DFT) and time-dependent DFT. Emphasis is on the initial photoexcitation of porphyrin and on the strength of coupling between the porphyrin LUMO or LUMO + 1 and the ZnO conduction band that plays a role in the electron transfer. Firstly, ZnO wurtzite bulk is optimized to minimum energy geometry and the properties of the isolated ZnO (101[combining macron]0) surface model and the porphyrin model are discussed to gain insight into the combined system. Secondly, various orientations of the model porphyrin on the ZnO surface are studied: the porphyrin model standing perpendicularly to the surface and gradually brought close to the surface by tilting the linker in a few steps. The porphyrin model approaches the surface either sideways with hydrogen atoms of the porphyrin ring coming down first or twisted in a ca. 45° angle, giving rise to π-interactions of the porphyrin ring with ZnO. Because porphyrins are closely packed and near the surface, emerging van der Waals (vdW) interactions are examined using Grimmes D2 method. While the orientation affects the initial excitation of porphyrin only slightly, the coupling between the LUMO and LUMO + 1 of porphyrin and the conduction band of ZnO increases considerably if porphyrin is close to the surface, especially if the π-electrons are interacting with the surface. Based on the results of coupling studies, not only the distance between porphyrin and the ZnO surface but also the orientation of porphyrin can greatly affect the electron transfer.

Nitrogen interstitial defects in GaAs

We have studied nitrogen interstitial defects in GaAs with first-principles calculations. On the basis of calculated formation energies we have determined the most common nitrogen defects and the transition levels for various charge states. The lowest energy interstitial-type defects are found to be N-N and N-As split interstitials for most of the experimentally relevant conditions. We have also compared two different methods of obtaining the potential correction needed in an accurate calculation of the formation energies and transition levels.

Computational study of GaAs1−xNx and GaN1−yAsy alloys and arsenic impurities in GaN

We have studied the structural and electronic properties of As-rich GaAs1−x Nx and N-rich GaN1−yAsy alloys in a large composition range using first-principles methods. We have systematically investigated the effect of the impurity atom configuration near both GaAs and GaN sides of the concentration range on the total energies, lattice constants and bandgaps. The N (As) atoms, replacing substitutionally As (N) atoms in GaAs (GaN), cause the surrounding Ga atoms to relax inwards (outwards), making the Ga–N (Ga– As) bond length about 15% shorter (longer) than the corresponding Ga–As (Ga–N) bond length in GaAs (GaN). The total energies of the relaxed alloy supercells and the bandgaps experience large fluctuations within different configurations and these fluctuations grow stronger if the impurity concentration is increased. Substituting As atoms with N in GaAs induces modifications near the conduction band minimum, while substituting N atoms with As in GaN modifies the states near the valence band maximum. Both lead to bandgap reduction, which is at first rapid but later slows down. The relative size of the fluctuations is much larger in the case of GaAs1−x Nx alloys. We have also looked into the question of which substitutional site (Ga or N) As occupies in GaN. We find that under Ga-rich conditions arsenic prefers the substitutional N site over the Ga site within a large range of Fermi level values.