Semiconductor Bloch equations for quantum-cascade structures

To predict output optical characteristics of quantum-cascade lasers, it is necessary to model dynamics of electrons, holes and photons including into consideration non-equilibrium regime. There are several approaches to modeling of the dynamics of the carrierspsila distribution: one method is based on non-equilibrium Greenpsilas functions [C.S. Lee and A. Wacker, Phys. Rev. B, 66, 245314 (2002)], another one is based on density matrix formalism which has own advantages in numerical costs and simplicity. In this paper, the second approach have been developed and the semiconductor Bloch equations for quantum-cascade structures have been obtained. Here we present new form of semiconductor Bloch equations for quantum cascade structures, which in contrast to previous works takes into account inter-quantum-well tunneling. These equations include non-equilibrium dynamics of carriers, polarization and inter-quantum-well tunneling currents.