Biexcitons in semiconductor quantum wires

We report on spectrally resolved four-wave mixing experiments on ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ 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 mixing spectrum can be clearly attributed to biexcitons. We find that the biexciton binding energy depends on both the vertical and lateral dimensions of the wires. For quantum wires with a large vertical confinement we observe an enhancement of the binding energy of about 40% as compared to a two-dimensional reference sample whereas the biexciton binding energy is found to be wire width independent in wires with shallow vertical confinement.