Energy-gap discontinuities and effective masses for $\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}-{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum 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 $\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}-{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ system. With the new set of parameters one can fit both the energies of the allowed ($\Delta n=0\mathrm{}$) heavy- and light-hole transitions, and the forbidden ($\Delta n\ne 0$) heavy-hole transitions, for both types of quantum wells. For square wells, the GaAs well widths range from 51 to 521 Å. The new parameters include a conduction-band energy-gap discontinuity equal to ∼ 57% of the total gap discontinuity and the following effective masses: $\frac{m_e^{*}}{m_0}=0.0665\mathrm{}$, $\frac{m_h^{*}}{m_0}=0.34\mathrm{}$, and $\frac{m_l}{m_0}=0.094\mathrm{}$.