Exciton binding energy in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As multiple quantum wells

We have used a variational three-dimensional trial envelope function to calculate the exciton binding energy in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As multiple quantum wells. In all the limiting cases that the barrier width ${\mathit{d}}_{\mathit{A}}$→∞ or ${\mathit{d}}_{\mathit{A}}$→0, and the well width ${\mathit{d}}_{\mathit{B}}$→∞ or ${\mathit{d}}_{\mathit{B}}$→0, the calculated binding energy approaches the respective correct value. From the computed binding energies in several experimentally studied samples, we have discovered the systematic dependence of the exciton binding energy on the well width and the barrier width.