Subband structures of GaAs/AlxGa1−xAs multiple quantum wells

We solve the one-dimensional Schrödinger equation with a periodic potential and a kinetic-energy operator -(1/${2\mathrm{m}}^{\mathrm{\alpha }}$[ħ(d/dz)]${\mathit{m}}^{\mathrm{\beta }}$[ħ(d/dz)]${\mathit{m}}^{\mathrm{\alpha }}$, where 2α+β=-1 and the mass m depends on z. With the effective-mass theory, we have derived the subband structures of several GaAs/${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As multiple-quantum-well samples. When we fit our calculated intersubband transition energies to optical data by adjusting the β and the conduction-band offset coefficient Q, the fit is not sensitive to β, which can be explained from our analytical formula. However, the results depend on the value of Q. We obtain best fits around 0.82≤Q≤0.89 without exciton correction. With the exciton binding energy properly deduced, good fits are also obtained when we set Q≊0.65. .AE