TIGHT-BINDING METHODS

The history of tight-binding theory is traced, from the corresponding band models of Bloch, to the development of universal parameters, deri vable from a combination of tight-binding theory and free-electron the ory. In the end, tight-binding theory becomes an independent, and in t hat sense ab initio, method for studying virtually all of the properti es of surfaces. It is this conceptual aspect, rather than semiempirica l tight-binding theory as an approximate computational method, which i s emphasized here. We outline the application first to surface energy, and its dependence upon structure, for semiconductors, ionic insulato rs, and simple metals, finding wide differences from the rudimentary v iew of one bond energy per broken bond. We turn to photothresholds, wo rk functions and electron affinities, finding direct tight-binding pre dictions but necessary corrections for image potentials, which also ar e derivable in terms of tight-binding theory. For the particular case of electron affinities there are additional corrections to the band ga p, usually associated with correlation energy, but readily and general ly estimated as the intra-atomic Coulomb U divided by the dielectric c onstant. We turn to history of the understanding of heterojunction ban d 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 F ermi energy. Alternate views are also discussed as is the bonding of i ndividual atoms to the surface. Finally, the successes and failures of tight-binding theory in understanding semiconductor surface reconstru ctions are reviewed.