Determination of valence-band discontinuity via optical transitions in ultrathin quantum wells

The energy separation (ΔE) between the heavy-hole and the light-hole subbands as a function of the well width for ultrathin quantum-well structures is calculated using a single-band particle-in-a-box model. It is found that the most sensitive range for the well width ($L_z$) to determine accurately the valence-band discontinuity (Δ$E_v$) is between 15 and 80 Å whereas it is insensitive for $L_z$>80 Å using optical transitions in quantum wells. A controversial issue for the determination of Δ$E_v$ can then be resolved by measuring the ΔE’s in the sensitive well-width range. Results for the GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As system are presented and compared with the available experimental data in the sensitive range yielding good agreement with Dingle’s initial work.