Tight binding for complex semiconductor systems

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