Electronic transport in quantum cascade structures
  The transport in complex multiple quantum well heterostructures is theoretically described. The model is focused on quantum cascade detectors, which represent an exciting challenge due to the complexity of the structure containing 7 or 8 quantum wells of different widths. Electronic transport can be fully described without any adjustable parameter. Diffusion from one subband to another is calculated with a standard electron-optical phonon hamiltonian, and the electronic transport results from a parallel flow of electrons using all the possible paths through the different subbands. Finally, the resistance of such a complex device is given by a simple expression, with an excellent agreement with experimental results. This relation involves the sum of transitions rates between subbands, from one period of the device to the next one. This relation appears as an Einstein relation adapted to the case of complex multiple quantum structures. 
C. Koeniguer, G. Dubois, A. Gomez and V. Berger