We report on spectrally resolved four-wave mixing experiments on InxGa
1-xAs/GaAs quantum wires for a wide range of lateral sizes. Due to the
polarization dependence of the four-wave mixing signal, beats in the
decay of the signal and an additional emission line in the four-wave m
ixing spectrum can be clearly attributed to biexcitons. We find that t
he biexciton binding energy depends on both the vertical and lateral d
imensions of the wires. For quantum wires with a large vertical confin
ement we observe an enhancement of the binding energy of about 40% as
compared to a two-dimensional reference sample whereas the biexciton b
inding energy is found to be wire.width independent in wires with shal
low vertical confinement.