Transferability of Tight-Binding Matrix Elements
The empirical tight-binding method was initially introduced by Slater and Koster1 as an interpolation scheme for band structure calculations. Hamiltonian matrix elements determined by fitting the electronic energies at a few high symmetry points of the Brillouin zone could be used to calculate the entire energy band structure. Reasonably accurate fits to the electronic structure of many crystalline solids, e.g., for Si, have been obtained in this way.2–6 In the last decade the method has been used less frequently as an interpolation scheme and more as a convenient computational tool in studies of surface atomic and electronic structure,7–11 band lineups at interfaces,12 grain boundaries,13,14 phonons,15,16 and structural stabilities of atomic clusters17 and crystalline phases.18 The method is especially suited for studying systems with a large number of atoms. The feasibility of performing realistic total-energy calculations within the tight-binding scheme which makes it possible to do relative comparisons is an important feature of many of these studies. The tight-binding approach to structural studies of semiconductor surfaces, particularly of the prototypical group IV and III-V semiconductors Si and GaAs has been discussed in detail elsewhere.7–11 The tight-binding theory of cohesion in transition metals and their alloys is also well-developed but will not be discussed here.19
KeywordsMatrix Element Diamond Structure Atomic Coordination High Symmetry Point Hamiltonian Matrix Element
Unable to display preview. Download preview PDF.
- 11.D.J. Chadi, J. Vac. Sci. Technol. A 5, 834 (1987). In this paper the atomic structure of As-stabilized GaAs (100) surface is analyzed.Google Scholar
- 20.W.M.C. Foulkes, PhD Thesis, University of Cambridge 1987; M.W. Finnis, in “Proceedings of this Conference”; and D.G. Pettifor, in “Proceedings of the Conference”.Google Scholar
- 22.D.J. Chadi, J. Vac. Sci. Technol. A2, 948 (1984).Google Scholar