Simple theory of the interband optical absorption in an external electric field for optoelectronic materials
We study theoretically the interband optical-absorption coefficient (OAC) of optoelectronic materials within the framework of the three-band model of Kane [J. Phys. Chem. Solids 12, 181 (1959)] in the presence of an external electric field for modified photon energy (ℏω1) below and above the band gap (Eg), respectively. The optical matrix element depends on the electron wave vector k and this practical aspect has been incorporated in the present analysis. It has been found, taking InAs, InSb, Hg1-xCdxTe, and In1-xGaxAsyP1-y lattice matched to InP as examples of optoelectronic compounds for numerical computations, that for modified photon energies below the band gap, the OAC exhibits an exponential fall off with the electric field and the photon energy, respectively. For the opposite inequality, the OAC oscillates with the modified photon energy without the consideration of the Wannier-Stark levels, which generally exist in a band due to the presence of an external electric field. In both cases, the OAC exhibits the singularity when the incident photon energy (ℏω0) tends to Eg and the magnitude of the OAC depends to a large extent on the numerical values of the energy-band constants of the said compounds. In addition, the simplified results of the OAC for materials having parabolic energy bands have also been obtained from the present generalized analysis under certain limiting conditions.