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

The energy separation ({Δ}E) 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 (Lz) to determine accurately the valence-band discontinuity ({Δ}Eᵥ) is between 15 and 80 A{} whereas it is insensitive for Lz>80 A{} using optical transitions in quantum wells. A controversial issue for the determination of {Δ}Eᵥ can then be resolved by measuring the {Δ}E's in the sensitive well-width range. Results for the GaAs-Alₓ{Ga}_{1{{-}}x}$As system are presented and compared with the available experimental data in the sensitive range yielding good agreement with Dingle's initial work.