A Fast Method for Electronic Band Structure Calculations (original) (raw)

Algorithms for Korringa-Kohn-Rostoker electronic structure calculations in any Bravais lattice

1997

We present some algorithms for improvements of band theory calculations based on the Korringa-Kohn-Rostoker method and on the coherent potential approximation, in the cases of ordered metals and random alloys. The purpose of our work was to develop a code flexible enough to deal on equal footing with any lattice geometry. The algorithms proposed are designed to achieve an arbitrary accuracy and to minimize the required computational efforts. In particular, we describe ͑i͒ an efficient and accurate method for the calculation of the KKR structure constants, and ͑ii͒ an adaptive method for the Brillouin zone integration. These algorithms have been tested for a free-electron Green's function and by explicit calculations for a number of systems and, when possible, discussed in comparison with other methods. Ab initio calculations for hexagonal close packed and face centered cubic Ti and for Cu 0.75 -Pt 0.25 random alloys are presented.

High-throughput electronic band structure calculations: Challenges and tools

Computational Materials Science, 2010

The article is devoted to the discussion of the high-throughput approach to band structures calculations. We present scientific and computational challenges as well as solutions relying on the developed framework (Automatic Flow, AFLOW/ACONVASP). The key factors of the method are the standardization and the robustness of the procedures. Two scenarios are relevant: 1) independent users generating databases in their own computational systems (off-line approach) and 2) teamed users sharing computational information based on a common ground (on-line approach). Both cases are integrated in the framework: for off-line approaches, the standardization is automatic and fully integrated for the 14 Bravais lattices, the primitive and conventional unit cells, and the coordinates of the high symmetry k-path in the Brillouin zones. For on-line tasks, the framework offers an expandable web interface where the user can prepare and set up calculations following the proposed standard. Few examples of band structures are included. LSDA+U parameters (U, J) are also presented for Nd, Sm, and Eu.

A hybrid method for the efficient calculation of the band structure of 3-D metallic crystals

IEEE Transactions on Microwave Theory and Techniques, 2004

In this paper, we propose a new hybrid method to characterize the band structure of three-dimensional metallic crystals. We formulate an auxiliary problem that has the same spectrum as the metallic crystal. We prove that the spectrum of the auxiliary problem can be efficiently computed using the plane-wave method and the method of moments. Thus, the band structure of the metallic crystal can also be efficiently calculated. Our approach is much more effective than root-searching methods, because all of the eigenvalues are obtained at once and degenerate cases pose no difficulty. This is a generalization of a previously proposed method for two-dimensional structures.

Numerical Methods for Electronic Structure Calculations of Materials

SIAM Review, 2010

The goal of this article is to give an overview of numerical problems encountered when determining the electronic structure of materials and the rich variety of techniques used to solve these problems. The paper is intended for a diverse scienti£c computing audience. For this reason, we assume the reader does not have an extensive background in the related physics. Our overview focuses on the nature of the numerical problems to be solved, their origin, and on the methods used to solve the resulting linear algebra or nonlinear optimization problems. It is common knowledge that the behavior of matter at the nanoscale is, in principle, entirely determined by the Schrödinger equation. In practice, this equation in its original form is not tractable. Successful, but approximate, versions of this equation, which allow one to study nontrivial systems, took about £ve or six decades to develop. In particular, the last two decades saw a ¤urry of activity in developing effective software. One of the main practical variants of the Schrödinger equation is based on what is referred to as Density Functional Theory (DFT). The combination of DFT with pseudopotentials allows one to obtain in an ef£cient way the ground state con£guration for many materials. This article will emphasize pseudopotentialdensity functional theory, but other techniques will be discussed as well.

Energy Band Structures of Semiconductors

The physical properties of semiconductors can be understood with the help of the energy band structures. This chapter is devoted to energy band calculations and interpretation of the band structures. Bloch theorem is the starting point for the energy band calculations. Bloch functions in periodic potentials is derived here and a periodic function is shown to be expressed in terms of Fourier expansion by means of reciprocal wave vectors. Brillouin zones are then introduced to understand energy band structures of semiconductors. The basic results obtained here are used throughout the text. Nearly free electron approximation is shown as the simplest example to understand the energy band gap (forbidden gap) of semiconductors and the overall features of the energy band structure. The energy band calculation is carried out first by obtaining free-electron bands (empty lattice bands) which are based on the assumption of vanishing magnitude of crystal potentials and of keeping the crystal periodicity. Next we show that the energy band structures are calculated with a good approximation by the pseudopotential method with several Fourier components of crystal potential. Also k · p perturbation method for energy band calculation is described in detail. Another method "tight binding approximation" will be discussed in connection with the energy band calculation of superlattices in Chap. 8. 1.1 Free-Electron Model It is well known that the physical properties of semiconductors are understood with the help of energy band structures. The energy states or energy band structures of electrons in crystals reflect the periodic potential of the crystals and they can be calculated when we know the exact shape and the magnitude of the crystal potentials. The shape and the magnitude of the potential are not determined directly from any experimental methods, and thus we have to calculate or estimate the energy bands by using the assumed potentials. Many different approaches to calculations of energy bands have been reported, but in this textbook we will deal with several methods, which are not so difficult to understand. We begin with the most simplified method to calculate electronic states in a model crystal.

Efficient quasiparticle band-structure calculations for cubic and noncubic crystals

Physical review. B, Condensed matter, 1995

An efBcient method developed for the calculation of quasiparticle corrections to densityfunctional-theorylocal-density-approximation (DFT-LDA) band structures of diamond and zincblende materials is generalized for crystals with other cubic, hexagonal, tetragonal, and orthorhombic Bravais lattices. Local-field efFects are considered in the framework of a LDA-like approximation. The dynamical screening is treated by expanding the self-energy linearly in energy. The anisotropy of the inverse dielectric matrix is taken into account. The singularity of the Coulomb potential in the screened-exchange part of the electronic self-energy is treated using auxiliary functions of the appropriate symmetry. An application to the electronic quasiparticle band structure of wurtzite 2H-SiC is presented within the approach of norm-conserving, nonlocal, fully separable pseudopotentials and a plane-wave expansion of the wave functions for the underlying DFT-LDA.

Brillouin zone unfolding method for effective phonon spectra

Physical Review B, 2014

Thermal properties are of great interest in modern electronic devices and nanostructures. Calculating these properties is straightforward when the device is made from a pure material, but problems arise when alloys are used. Specifically, only approximate bandstructures can be computed for random alloys and most often the Virtual Crystal Approximation (VCA) is used. Unfolding methods [T. B. Boykin, N. Kharche, G. Klimeck, and M. Korkusinski, J. Phys.: Condens. Matt. 19, 036203 (2007).] have proven very useful for tight-binding calculations of alloy electronic structure without the problems in the VCA, and the mathematical analogy between tight-binding and valence-forcefield approaches to the phonon problem suggest they be employed here as well. However, there are some differences in the physics of the two problems requiring modifications to the electronic structure approach. We therefore derive a phonon alloy bandstructure (vibrational mode) approach based on our tight-binding electronic structure method, modifying the band-determination method to accommodate the different physical situation. Using the method, we study InxGa1−xAs alloys and find very good agreement with available experiments.

Linearized augmented plane-wave method for the electronic band structure of thin films

Physical Review B, 1979

We present a new method for treating the electronic structure of thin films Which is based on a generalization of the bulk linearized augmented-plane-wave (LAPW) method, This method avoids using the slab-superlattice geometry and combines the advantages of energy-independent muffin-tin Hamiltonian methods [fast root evaluation and rapid convergence for d-band metals as well as for nearly-free-electron (NFE) crystals] with the simple matrix element determination of the original augmented plane-wave (APW) method. As in the bulk LAPW method, the asymptote problem of the APW method is avoided, and the basis functions are everywhere continuous and differentiable. In addition, the film LAPW method retains such desirable features of the APW method as the ability to treat general potentials with no shape approximations, the ease with which relativistic effects can be included, and the fact that the basis size does not increase substantially for heavier elements. As a first application and test of the method, non-selfconsistent calculations are performed in the local-density approximation for exchange and correlation and with the one-electron potential constructed from a superposition of atomic charge densities. A semirelativistic formulation is employed in which the Dirac equation is Wived in the limit of zero spin-orbit coupling inside the muffin-tin spheres. Results' are reported for up to five atomic layer thin films (slabs) of the transition metals Fe, Co, Ni, and Cu and a nine-layer film of the NFE metal Al. The results are in generally good agreement with other theoretical calculations-. Some trends in the transition-metal band structures are discussed. A surface-state surface-resonance band for Al(001) is found to completely account for and clarify I behavior observed in very recent photoemission measurements.

A Model Order Reduction Method for Efficient Band Structure Calculations of Photonic Crystals

IEEE Transactions on Magnetics, 2000

The goal of this paper is to compute k 0 diagrams of photonic crystals, accurately and fast. For this purpose, we propose a multipoint model-order reduction scheme for the modal analysis of periodic structures, based on the finite element method. Our numerical example demonstrates that the new approach is significantly faster than conventional finite-element solutions, while error levels are very similar. The proposed method allows for an adaptive choice of the expansion points for the reduced model.