A combined model for miniband and hopping transport in superlattices

We compare the description of electronic transport in a semiclassical miniband model and within the hopping transport model. While the miniband theory is correct at low fields, quantum mechanical corrections to the Bloch oscillation picture due to the formation of the Wannier-Stark ladder at high fields have to be treated within the hopping theory. This model cannot reproduce an ohmic drift velocity regime, but we can show that the hopping relaxation time becomes field independent at low fields. Using this time within the relaxation time approximation of the Boltzmann equation we are able to combine the two transport theories to cover the whole range of electric fields. The results obtained from this combined model agree very well with those of a k-space Monte-Carlo simulation for the range from low to moderately high fields. At very high fields, however, only the hopping picture provides the correct results. (C) 1998 Elsevier Science B.V. All rights reserved.