Quantum models for two-band dynamics in semiconductor devices

In the most bipolar electrons-holes models, there is no coupling mechanism between energy bands which are always decoupled in the effective-mass approximation and the coupling is heuristically inserted by a "generation-recombination" term. However in some nanometric semiconductor devices, like Interband Resonant Tunneling Diodes, the transport due to tunneling effects becomes important and it is essential to incorporate quantum mechanical phenomena. A starting point to take into account this purely quantum mechanism is given by different approximations of the Schrodinger equation. In this talk we review two Schrodinger-like models, the first one well-known in literature as Kane model, the second recently derived within the usual Bloch-Wannier formalism. Such model is formulated in terms of a set of coupled equations for the electron envelope functions by an expansion in terms of the crystal wave vector k. >From the point of view of practical applications, the approaches based on microscopic models are not completely satisfactory. Hence, it is useful to formulate semi-classical models in terms of macroscopic variables. Using the WKB method, we obtain a system for densities and currents in the two bands. In this context zero and nonzero temperatures drift diffusion models are derived