Tight-binding representation of the optical matrix elements: Theory and applications

We have derived new expressions for the interband optical matrix elements of crystalline solids, applicable when the k-space Hamiltonian is known. The formalism does not require a complete knowledge of the electronic states and is hence useful for empirical band-structure calculations. We find that no additional parameters, other than those present in the Hamiltonian, are required. The accuracy of the results obtained from different tight-binding parameter sets for the GaAs/AlAs system for bulk semiconductors and heterostructures is compared.