Nonequilibrium Green’s function theory for transport and gain properties of quantum cascade structures

Abstract:
The transport and gain properties of quantum cascade (QC) structures

are investigated using a nonequilibrium Green's function (NGF) theory

which includes quantum effects beyond a Boltzmann transport description.

In the NGF theory, we include

interface roughness, impurity, and electron-phonon scattering

processes within a self-consistent Born approximation,

and electron-electron scattering in a mean-field approximation.

With this theory we obtain a description of the nonequilibrium

stationary state of QC structures under an applied bias,

and hence we determine transport properties, such as the current-voltage

characteristic of these structures. We define two contributions

to the current, one contribution driven by the scattering-free

part of the Hamiltonian, and the other driven by the scattering

Hamiltonian. We find that the dominant part of the current

in these structures, in contrast to simple superlattice

structures, is governed mainly by the scattering Hamiltonian.

In addition, by considering the linear response of the

stationary state of the structure to an applied optical field,

we determine the linear susceptibility, and

hence the gain or absorption spectra of the structure.

A comparison of the spectra obtained from the more rigorous

NGF theory with simpler models shows that the spectra tend to

be offset to higher values in the simpler theories.