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 Γ7, Γ8 conduction bands nonperturbatively. With appropriate approximations, the envelope functions associated with the Γ7, Γ8 bands can be expressed in terms of the two Γ6 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 Γ6 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.