Tight binding for complex semiconductor systems

In this review, we illustrate multiple aspects of the application of the em pirical tight binding (ETB) approximation. We begin by summarizing the gene ral principles of ETB where the Hamiltonian matrix is written in a restrict ed atomic basis set and in terms of a relatively limited number of paramete rs. We describe how these parameters are deduced, either from so-called "un iversal rules" or from a fit to experiment or to the results of correspondi ng ab-initio calculations. We show on various examples that ETB not only ca n be viewed as a simulation tool which allows to handle complex situations but also can be used to provide quantitative values on various physical pro perties (electronic structure, optical properties, quasi-particles self-ene rgies, electron-phonon coupling,...), even if it must be done with some car e. We emphasize that ETB provides the most natural approach to understand t he formation of chemical bonds, starting from their atomic constituents. It also offers a very efficient tool to treat large non-periodic systems whic h cannot be handled by abinitio methods.