Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

Carrier concentration profiles of two-dimensional electron gases are investigated in wurtzite, Ga-face AlxGa1−xN/GaN/AlxGa1−xN and N-face GaN/AlxGa1−xN/GaN heterostructures used for the fabrication of field effect transistors. Analysis of the measured electron distributions in heterostructures with AlGaN barrier layers of different Al concentrations (0.15<x<0.5) and thickness between 20 and 65 nm demonstrate the important role of spontaneous and piezoelectric polarization on the carrier confinement at GaN/AlGaN and AlGaN/GaN interfaces. Characterization of the electrical properties of nominally undoped transistor structures reveals the presence of high sheet carrier concentrations, increasing from 6×1012 to 2×1013 cm−2 in the GaN channel with increasing Al-concentration from x=0.15 to 0.31. The observed high sheet carrier concentrations and strong confinement at specific interfaces of the N- and Ga-face pseudomorphic grown heterostructures can be explained as a consequence of interface charges induced by ...

/pdf/two-dimensional-electron-gases-induced-by-spontaneous-and-11pht7aexp.pdf

Two-dimensional electron gases induced by spontaneous and piezoelectric polarization charges in N- and Ga-face AlGaN/GaN heterostructures

First-principles calculations have evolved from mere aids in explaining and supporting experiments to powerful tools for predicting new materials and their properties. In the first part of this review we describe the state-of-the-art computational methodology for calculating the structure and energetics of point defects and impurities in semiconductors. We will pay particular attention to computational aspects which are unique to defects or impurities, such as how to deal with charge states and how to describe and interpret transition levels. In the second part of the review we will illustrate these capabilities with examples for defects and impurities in nitride semiconductors. Point defects have traditionally been considered to play a major role in wide-band-gap semiconductors, and first-principles calculations have been particularly helpful in elucidating the issues. Specifically, calculations have shown that the unintentional n-type conductivity that has often been observed in as-grown GaN cannot be a...

First-principles calculations for defects and impurities: Applications to III-nitrides

The electronic ground state of a periodic system is usually described in terms of extended Bloch orbitals, but an alternative representation in terms of localized "Wannier functions" was introduced by Gregory Wannier in 1937. The connection between the Bloch and Wannier representations is realized by families of transformations in a continuous space of unitary matrices, carrying a large degree of arbitrariness. Since 1997, methods have been developed that allow one to iteratively transform the extended Bloch orbitals of a first-principles calculation into a unique set of maximally localized Wannier functions, accomplishing the solid-state equivalent of constructing localized molecular orbitals, or "Boys orbitals" as previously known from the chemistry literature. These developments are reviewed here, and a survey of the applications of these methods is presented. This latter includes a description of their use in analyzing the nature of chemical bonding, or as a local probe of phenomena related to electric polarization and orbital magnetization. Wannier interpolation schemes are also reviewed, by which quantities computed on a coarse reciprocal-space mesh can be used to interpolate onto much finer meshes at low cost, and applications in which Wannier functions are used as efficient basis functions are discussed. Finally the construction and use of Wannier functions outside the context of electronic-structure theory is presented, for cases that include phonon excitations, photonic crystals, and cold-atom optical lattices.

Maximally-localized Wannier Functions: Theory and Applications

https://th.fhi-berlin.mpg.de/site/uploads/Publications/CPC-180-2175-2009.pdf

Ab Initio Molecular Simulations with Numeric Atom-Centered Orbitals

As an alternative to the standard Kohn-Sham procedure, other exact realizations of density-functional theory ~generalized Kohn-Sham methods! are presented. The corresponding generalized Kohn-Sham eigenvalue gaps are shown to incorporate part of the discontinuity D xc of the exchange-correlation potential of standard KohnSham theory. As an example, a generalized Kohn-Sham procedure splitting the exchange contribution to the total energy into a screened, nonlocal and a local density component is considered. This method leads to band gaps far better than those of local-density approximation and to good structural properties for the materials Si, Ge, GaAs, InP, and InSb.

Generalized Kohn-Sham schemes and the band-gap problem

nextnano is a semiconductor nanodevice simulation tool that has been developed for predicting and understanding a wide range of electronic and optical properties of semiconductor nanostructures. The underlying idea is to provide a robust and generic framework for modeling device applications in the field of nanosized semiconductor heterostructures. The simulator deals with realistic geometries and almost any relevant combination of materials in one, two, and three spatial dimensions. It focuses on an accurate and reliable treatment of quantum mechanical effects and provides a self-consistent solution of the Schrodinger, Poisson, and current equations. Exchange-correlation effects are taken into account in terms of the local density scheme. The electronic structure is represented within the single-band or multiband kldrp envelope function approximation, including strain. The code is not intended to be a ldquoblack boxrdquo tool. It requires a good understanding of quantum mechanics. The input language provides a number of tools that simplify setting up device geometry or running repetitive tasks. In this paper, we present a brief overview of nextnano and present four examples that demonstrate the wide range of possible applications for this software in the fields of solid-state quantum computation, nanoelectronics, and optoelectronics, namely, 1) a realization of a qubit based on coupled quantum wires in a magnetic field, 2) and 3) carrier transport in two different nano-MOSFET devices, and 4) a quantum cascade laser.

nextnano: General Purpose 3-D Simulations

We present a Kohn-Sham method that allows one to treat exchange interactions exactly within density-functional theory. The method is used to calculate lattice constants, cohesive energies, Kohn-Sham eigenvalues, dielectric functions, and effective masses of various zinc-blende semiconductors (Si, Ge, C, SiC, GaAs, AlAs, GaN, and AlN). The results are compared with values obtained within the local-density approximation, generalized gradient approximations, the Krieger-Li-Iafrate approximation for the Kohn-Sham exchange potential, and the Hartree-Fock method. We find that the exact exchange formalism, augmented by local density or generalized gradient correlations, yields both structural and optical properties in excellent agreement with experiment. Exact exchange-only calculations are found to lead to densities and energies that are close to Hartree-Fock values but to eigenvalue gaps that agree with experiment within 0.2 eV. The generalized gradient approximations for exchange yield energies that are much improved compared to local-density values. The exact exchange contribution to the discontinuity of the exchange-correlation potential is computed and discussed in the context of the band-gap problem.

Exact exchange Kohn-Sham formalism applied to semiconductors

Relativistic and nonrelativistic empirical tight-binding theory is generalized to incorporate time-dependent electromagnetic fields in a gauge-invariant manner that does not introduce any extra adjustable parameters. Based on this approach, it is shown that explicit expressions can be derived for the effective mass tensor, the effective Land\'e g factor, the current, the frequency-dependent transverse dielectric function, and the wave-vector- and frequency-dependent longitudinal dielectric function. A finite basis analogue of the optical f-sum rule is derived and shown to impose a condition on tight-binding parameters.

Electromagnetic fields and dielectric response in empirical tight-binding theory.

A new Kohn-Sham method that treats exchange interactions within density functional theory exactly is applied to Si, diamond, GaN, and InN. The exact local exchange potential leads to significantly increased band gaps that are in good agreement with experimental data. Generalized gradient approximations yield exchange energies that are much closer to the exact values than those predicted by the local density approximation. The exchange contribution to the derivative discontinuity of the exchange-correlation potential is found to be very large (of the order of 5--10 eV).

P. Vogl

Papers

Generalized Kohn-Sham schemes and the band-gap problem

nextnano: General Purpose 3-D Simulations

Exact exchange Kohn-Sham formalism applied to semiconductors

Electromagnetic fields and dielectric response in empirical tight-binding theory.

Exact Kohn-Sham Exchange Potential in Semiconductors