Energy-gap discontinuities and effective masses forGaAs−AlxGa1−xAsquantum wells

For the first time a single set of quantum-well parameters that describes the energies of the observed exciton transitions has been determined for both parabolic and square GaAs quantum wells grown with the $\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}\ensuremath{-}{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ system. With the new set of parameters one can fit both the energies of the allowed ($\ensuremath{\Delta}n=0$) heavy- and light-hole transitions, and the forbidden ($\ensuremath{\Delta}n\ensuremath{\ne}0$) heavy-hole transitions, for both types of quantum wells. For square wells, the GaAs well widths range from 51 to 521 \AA{}. The new parameters include a conduction-band energy-gap discontinuity equal to \ensuremath{\sim} 57% of the total gap discontinuity and the following effective masses: $\frac{{m}_{e}^{*}}{{m}_{0}}=0.0665$, $\frac{{m}_{h}^{*}}{{m}_{0}}=0.34$, and $\frac{{m}_{l}}{{m}_{0}}=0.094$.