COMPACT FORMULA FOR THE DENSITY-OF-STATES IN A QUANTUM-WELL

In this paper we derive a formula for the density of states in the pre sence of inelastic scattering in the quantum well of a double-barrier structure as a function of a characteristic time of the motion of elec trons (namely, the round-trip time in the well) and of transmission pr obabilities for the whole structure and for each barrier. In the model we use, the scattering processes due to phonons, impurities, and inte rface roughness are taken into account by a unique phenomenological pa rameter, the mean-free path, which plays the role of a relaxation leng th. We also show that, for lower rates of incoherent processes, the de rived formula reduces to the one obtained by means of the Breit-Wigner formalism.