Strong enhancements of the exciton binding energy (E(x)), compared to
bulk GaAs, are deduced from high-resolution spectroscopic studies of s
hallow GaAs-AlyGa1-yAs quantum wells, with aluminum concentrations of
(1-4.5)%. A clear increasing trend in E(x) from 5.9 meV at 1% aluminum
to 7.0 meV at 4.5% is deduced, in good agreement with the predictions
of variational calculations. Even at 1%, the value of E(x) represents
an enhancement of 40% over that in three-dimensional GaAs. The simila
rity of all the spectra supports strongly the marked two dimensionalit
y of the lowest exciton states, even for very low barrier heights.