G. F. Koster

Bio: G. F. Koster is an academic researcher from Massachusetts Institute of Technology. The author has contributed to research in topics: Wannier function & Brillouin zone. The author has an hindex of 11, co-authored 11 publications receiving 4405 citations.

Simplified LCAO Method for the Periodic Potential Problem

Abstract: The LCAO, or Bloch, or tight binding, approximation for solids is discussed as an interpolation method, to be used in connection with more accurate calculations made by the cellular or orthogonalized plane-wave methods. It is proposed that the various integrals be obtained as disposable constants, so that the tight binding method will agree with accurate calculations at symmetry points in the Brillouin zone for which these calculations have been made, and that the LCAO method then be used for making calculations throughout the Brillouin zone. A general discussion of the method is given, including tables of matrix components of energy for simple cubic, face-centered and body-centered cubic, and diamond structures. Applications are given to the results of Fletcher and Wohlfarth on Ni, and Howarth on Cu, as illustrations of the fcc case. In discussing the bcc case, the splitting of the energy bands in chromium by an antiferromagnetic alternating potential is worked out, as well as a distribution of energy states for the case of no antiferromagnetism. For diamond, comparisons are made with the calculations of Herman, using the orthogonalized plane-wave method. The case of such crystals as InSb is discussed, and it is shown that their properties fit in with the energy band picture.

Simplified Impurity Calculation

Abstract: The methods of previous papers by the authors are applied to a simplified impurity calculation. This is the case of a localized perturbation in a simple cubic lattice. We consider the effect of the perturbation on a single band which is describable in terms of a Wannier function which only has nearest neighbor interactions. The results of this calculation are compared with some approximate treatments of impurity calculations.

Method of Treating Zeeman Splittings of Paramagnetic Ions in Crystalline Fields

Abstract: In this paper, we present an alternative method to the "spin Hamiltonian" for treating the behavior of a paramagnetic ion under the combined influence of the host crystal and an applied magnetic field. This method has the advantage of being applicable to all strengths of couplings between the paramagnetic ion and the surrounding crystal. It is applicable to free-ion $S$ states in the same way that it applies to all other states. It gives all of the constants one needs to describe the energy level structure as a function of field as restricted by symmetry and the properties of the levels considered. The method is more general and is expected to be also more accurate than the conventional spin Hamiltonian formalism. It is illustrated by the application to the problem of the $({d}^{5})^{6}S$ level in a cubic crystalline environment.

Theory of scattering in solids

Abstract: The scattering of an electron by an imperfection in a lattice is set up in terms of a linear combination of the Wannier functions associated with the lattice. The difference equations which the coefficients of the Wannier functions satisfy are discussed in the light of simple examples. A Green's function formulation of the difference equations is then introduced which leads to the proper asymptotic behavior of the scattered wave. This approach avoids many of the unwarranted assumptions usually made in the discussion of scattering in solids.

Black phosphorus field-effect transistors

Abstract: Two-dimensional crystals have emerged as a class of materials that may impact future electronic technologies. Experimentally identifying and characterizing new functional two-dimensional materials is challenging, but also potentially rewarding. Here, we fabricate field-effect transistors based on few-layer black phosphorus crystals with thickness down to a few nanometres. Reliable transistor performance is achieved at room temperature in samples thinner than 7.5 nm, with drain current modulation on the order of 10(5) and well-developed current saturation in the I-V characteristics. The charge-carrier mobility is found to be thickness-dependent, with the highest values up to ∼ 1,000 cm(2) V(-1) s(-1) obtained for a thickness of ∼ 10 nm. Our results demonstrate the potential of black phosphorus thin crystals as a new two-dimensional material for applications in nanoelectronic devices.

Band parameters for III–V compound semiconductors and their alloys

Abstract: 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.

Electronic Structure: Basic Theory and Practical Methods

Abstract: 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.