Electronic properties and optical-absorption spectra of graded-gap GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As quantum wells

A study of the electronic and optical properties of GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As graded-gap quantum wells is presented using a formalism which takes into account the valence-subband mixing effects. The system considered in this investigation consists of two semi-infinite slabs of ${\mathrm{Al}}_{\mathrm{y}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{y}}$As barrier material having aluminum concentration y surrounding a graded-gap region of ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As whose aluminum concentration x is a linear function of z (the direction of growth) such that x=($x_0$/w)(z +w/2). Here w is the width of the graded region. At z=-w/2, x=0 and at z=+w/2, x=$x_0$, where $x_0$ varies between 0 and y. Conduction- and valence-subband structure, exciton binding energies, exciton oscillator strengths, and the total absorption spectra are calculated as a function of well size and aluminum concentration $x_0$. Optical transitions associated with several conduction and valence subbands are considered. Computed electronic and optical properties are found to be the result of an interplay between the effects of the overlap of electron and hole envelope functions and the valence-subband mixing. Valence-subband mixing leads to the removal of Kramers degeneracy in the quantum-well system when $x_0$ is different from zero, as in this case the system does not possess inversion symmetry.