Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set

We present a comprehensive, up-to-date compilation of band parameters for the technologically important III–V zinc blende and wurtzite compound semiconductors: GaAs, GaSb, GaP, GaN, AlAs, AlSb, AlP, AlN, InAs, InSb, InP, and InN, along with their ternary and quaternary alloys. Based on a review of the existing literature, complete and consistent parameter sets are given for all materials. Emphasizing the quantities required for band structure calculations, we tabulate the direct and indirect energy gaps, spin-orbit, and crystal-field splittings, alloy bowing parameters, effective masses for electrons, heavy, light, and split-off holes, Luttinger parameters, interband momentum matrix elements, and deformation potentials, including temperature and alloy-composition dependences where available. Heterostructure band offsets are also given, on an absolute scale that allows any material to be aligned relative to any other.

Band parameters for III–V compound semiconductors and their alloys

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Alternative energy technologies

The construction of accurate pseudopotentials with good convergence properties for the first-row and transition elements is discussed. We show that by combining an improved description of the pseudowavefunction inside the cut-off radius with the concept of ultrasoft pseudopotentials introduced by Vanderbilt optimal compromise between transferability and plane-wave convergence can be achieved. With the new pseudopotentials, basis sets with no more than 75-100 plane waves per atom are sufficient to reproduce the results obtained with the most accurate norm-conserving pseudopotentials.

https://iopscience.iop.org/article/10.1088/0953-8984/6/40/015/pdf

Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements

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

The structure and implementation of a new general iterative method for diagonalising large matrices (the 'residual minimisation/direct inversion in the iterative subspace' method of Bendt and Zunger) are described and contrasted with other more commonly used iterative techniques. The method requires the direct diagonalisation of only a small submatrix, does not require the storage of the large matrix and provides eigensolutions to within a prescribed precision in a rapidly convergent iterative procedure. Numerical results for two rather different matrices (a real 50*50 non-diagonally dominant matrix and a complex Hermitian 181*181 matrix corresponding to the pseudopotential band structure of a semiconductor in a plane wave basis set) are used to compare the new method with the competing methods. the new method converges quickly and should be the most efficient for very large matrices in terms both of computation time and central storage requirements; it is quite insensitive to the properties of the matrices used. This technique makes possible efficient solution of a variety of quantum mechanical matrix problems where large basis set expansions are required.

https://iopscience.iop.org/article/10.1088/0305-4470/18/9/018/pdf

A new method for diagonalising large matrices

First-principles total-energy and electronic-structure calculations for Si„Ge„superlattices grown epitaxially on an (001) Si substrate reveal a nearly direct band gap despite the pronounced indirectness of its constituents. Whereas the lowest conduction-band wave function extends over both Si and Ge sublattices, the (higher energy) lowest direct state shows strong confinement to Si states. We predict that a substrate with a larger lattice constant than Si will produce a nearly direct band-gap superlattice (indirect only by 0.01 eV).

New optical transitions in strained Si-Ge superlattices.

Structural and electronic properties of epitaxial thin-layer SinGen superlattices.

We discuss the susceptibility of zinc-blende semiconductors to band-structure modification by insertion of small atoms at their tetrahedral interstitial states. GaP is found to become a direct-gap semiconductor with two He atoms present at its interstitial sites; Si does not. Analysis of the factors controlling these filling-induced electronic modifications allows us to predict that LiZnP [viewed as a zinc-blende-like (ZnP)– lattice partially filled with He-like Li+ interstitials], as well as other members of the Nowotny-Juza compounds AIBIICV, are likely to be a novel group of direct-gap semiconductors.

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Electronic structure of filled tetrahedral semiconductors

LiZnN, like other Nowotny-Juza filled tetrahedral A/sup I/B/sup II/C/sup V/ compounds, consists of a B/sup II/C/sup V/ zinc-blende lattice with the A/sup I/ atoms filling half of the available tetrahedral interstitial sites. Using band calculations we deduce an ''interstitial insertion rule'' which shows, following an earlier argument of Wood, Zunger, and de Groot, how the electronic structures of such ternary compounds constitute recognizable distortions of those of the underlying zinc-blende B/sup II/C/sup V/ material. The s,p, and d components of the electronic charge density at the tetrahedral interstitial sites of the zinc-blende structure are shown to play a decisive role in understanding quantitatively these distortions.

D. M. Wood

Papers

A new method for diagonalising large matrices

New optical transitions in strained Si-Ge superlattices.

Structural and electronic properties of epitaxial thin-layer SinGen superlattices.

Electronic structure of filled tetrahedral semiconductors

Electronic structure of LiZnN: Interstitial insertion rule