Application of analytical k.p model with envelope function approximation to intersubband transitions in n-type III-V semiconductor Γ quantum wells

Abstract

A 14-band k.p model combined with an envelope function approximation has been developed for the analysis of III-V semiconductor quantum wells by including the six Γ 7, Γ 8 conduction bands nonperturbatively. With appropriate approximations, the envelope functions associated with the Γ 7, Γ 8 bands can be expressed in terms of the two Γ 6 conduction band envelope functions, which are the most important components in the electron wave function of an n-type direct-gap III-V compound semiconductor quantum well of zincblende structure. The Schrödinger-type equations for the Γ 6 conduction band envelope functions are derived, together with the energy-dependent effective mass that includes the effect of band nonparabolicity, as well as the eigenenergy-dependent effective potential for the envelope wave functions. The Schrödinger-type equations and the boundary conditions for the conservation of probability flux in the 14-band k.p model are found to be different from those of the conventional effective mass model. The 14-band model is then applied to the study of intersubband transitions due to transverse magnetic (TM) and transverse electric (TE) mode infrared radiation in n-type Γ quantum wells, and the calculated absorption spectra are compared with those computed using an equivalent 8-band k.p model. It is found that the TM absorption spectra calculated using the two models are very similar, but the TE absorption spectra calculated using the 14-band model is up to 6 times higher than that calculated using the 8-band model. A design of the quantum well structure for enhancing TE absorption is also discussed. © 2002 American Institute of Physics.