Electronic band structure of ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/${\mathrm{Al}}_{\mathit{y}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{y}}$As/GaAs double-barrier superlattices

The results of a semiempirical tight-binding calculation of conduction bands in (001) ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/${\mathrm{Al}}_{\mathit{y}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{y}}$As/GaAs double-barrier superlattices are described. The parameters chosen are appropriate to the design of an ${\mathrm{Al}}_{0.3}$ ${\mathrm{Ga}}_{0.7}$As/AlAs/GaAs structure for quantum-well infrared-photodetector (QWIP) applications in the 3–5-μm band. The dependence of the superlattice conduction-band energy levels on slab thicknesses, alloy compositions, and wave vector are examined. The tight-binding method has the ability to describe states far away from the center of the Brillouin zone and band mixing is shown in the characteristic energy-dependence curves. States can be identified as Γ-valley-like or X-valley-like, due to Γ or X electron localization in the wells formed by the GaAs, ${\mathrm{Al}}_{\mathit{y}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{y}}$As, or ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As slabs. The Γ-valley-like states of GaAs wells in the ${\mathrm{Al}}_{0.3}$ ${\mathrm{Ga}}_{0.7}$As/ AlAs/GaAs structure (the transition states for QWIP applications) have energies close to those of a simple AlAs/GaAs square superlattice when the number of AlAs layers is greater than 4. In addition to the GaAs well states, the results show that the X-valley-like bound states from the surrounding AlAs slabs consist of two closely spaced energy eigenvalues, the doublet splits when the two AlAs slabs become closer as the thickness of the intervening GaAs (or ${\mathrm{Al}}_{0.3}$ ${\mathrm{Ga}}_{0.7}$As) slab is reduced.