The temperature and density dependencies of the exciton dephasing time in I
n0.18Ga0.82As/GaAs single quantum wells with different thicknesses have bee
n measured by degenerate four-wave mixing; The exciton-phonon scattering co
ntribution to the dephasing is isolated by extrapolating the dephasing rate
to zero-exciton density. From the temperature dependence of this rate we h
ave deduced the linewidth broadening coefficients for acoustic and optical
phonons. We find acoustic-phonon coefficients that increase from 1.6 to 3 m
u eV/K when increasing the well width from 1 to 4 nm. This is in quantitati
ve agreement with theoretical predictions when the spatial extension of the
exciton wave function, strongly penetrating into the GaAs barrier in thin
InxGa1-xAs quantum wells, is taken into account. The optical-phonon coeffic
ient does not show a systematic dependence on well thickness, and is compar
able with the value for bulk GaAs. [S0163-1829(99)02103-7].