Tight-binding methods

Abstract

The history of tight-binding theory is traced, from the corresponding band models of Bloch, to the development of universal parameters, derivable from a combination of tight-binding theory and free-electron theory. In the end, tight-binding theory becomes an independent, and in that sense ab initio, method for studying virtually all of the properties of surfaces. It is this conceptual aspect, rather than semiempirical tight-binding theory as an approximate computational method, which is emphasized here. We outline the application first to surface energy, and its dependence upon structure, for semiconductors, ionic insulators, and simple metals, finding wide differences from the rudimentary view of one bond energy per broken bond. We turn to photothresholds. work functions and electron affinities, finding direct tight-binding predictions but necessary corrections for image potentials, which also are derivable in terms of tight-binding theory. For the particular case of electron affinities there are additional corrections to the band gap, usually associated with correlation energy, but readily and generally estimated as the intra-atomic Coulomb U divided by the dielectric constant. We turn to history of the understanding of heterojunction band line-ups, which in the end can be obtained by matching “neutrality levels” in each band structure, those levels being the average sp 3-hybrid energy in tight-binding theory and in the case of metals, the Fermi energy. Alternate views are also discussed as is the bonding of individual atoms to the surface. Finally, the successes and failures of tight-binding theory in understanding semiconductor surface reconstructions are reviewed.