Effect of interfaces and the spin-orbit band on the band gaps of InAs/GaSb superlattices beyond the standard envelope-function approximation

Abstract

We develop a modified $8\ifmmode\times\else\texttimes\fi{}8$ envelope-function approximation (EFA) formalism for the noncommon-atom (NCA) superlattices (SL's), incorporating the effect of anisotropic and other interface (IF) interactions that go beyond the standard EFA. The boundary conditions in the presence of IF interactions are used to set up a secular equation (including a transfer matrix derivation) whose physical transparency makes possible a number of valuable insights (possibility of IF bound states, analytic solutions, indirect gaps, etc.). We show that the heavy-hole--spin-orbit IF coupling is very important due to the IF localization of the SO wave function components and the ability of the IF potential to potentially bind a hole at the IF's, all of which pose convergence problems for perturbative solutions. With two adjustable parameter for the two possible IF's, we find a very good agreement between experiment and theory for the band gaps of several sets of very long-infrared and midinfrared InAs/GaSb SL's grown at several laboratories and by us. The band gaps as a function of GaSb and InAs widths are explained in terms of variations of the HH and conduction (C) band bandwidths. We show that the cut-off wavelengths can be reduced by increasing the GaSb layer width. Thus, a consistent application of the EFA method with the inclusion of well established IF effects can provide useful physical insights and possesses good predictive capacity in the design of NCA SL's.