Bloch and localized electrons in semiconductor superlattices

The energy spectrum of electrons in semiconductor superlattices consists of Bloch-like miniband states and localized impurity states. Optical transitions between these states are investigated by infrared spectroscopy. The inter-miniband absorption spectrum is dominated by the van Hove singularities of the quasi one-dimensional joint density of states. The detailed shape of the absorption can be understood in terms of the relevant transition matrix elements and the electron concentration, i.e. it depends on whether the first miniband is full or half-filled. We show that this has implications for intra-miniband absorption and the optical sum rules. In addition, a transition between the states localized at the lower edge of the minibands occurs, which can be traced back to the 1s-2p_z hydrogenic donor transition in the low-doping limit. Finally, we discuss the relevance of our observations for the study of the metal-insulator transition in superlattices.