Experimental evidence for the transition from two- to three-dimensional behavior of excitons in quantum-well structures

The transition from two- to three-dimensional behavior of excitonic recombination was investigated by optical-absorption and photoluminescence (PL) spectroscopy. By molecular-beam epitaxy, we have grown pseudomorphic ${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/Ga(Al)As multiple- and single-quantum-well structures with and without Al in the barriers and with an In content between 13% and 22%. The well width was varied from 25 nm to less than 1 nm. From absorption spectra, we have directly determined the exciton binding energy for the first heavy-hole-to-electron transition and unambiguously for the light-hole-to-electron transition in a sample with a well width of 3 nm. The exciton binding energy nearly reaches the bulk values of the barrier material for very small well widths, e.g., 4.2 ±0.5 meV for a 1-nm well width with a GaAs barrier. The dependence of the PL linewidth on the well width in single-quantum-well structures shows behavior similar to the exciton binding energy. We also reach the narrowest linewidths (0.6 meV) for the thinnest quantum well (0.75 nm) and a maximum (3 meV) at around a 5-nm well width. Samples with Al in the barriers (14%) show similar behavior, but the linewidths increase by about 30% at larger well widths and more than 100% at narrower wells in comparison to samples with a binary barrier material. These experimental results demonstrate very clearly the transition from an exciton with three-dimensional properties of the well material (at larger well widths) to an intermediate state with a maximum two-dimensional character (at around 5 nm) and once again to a three-dimensional behavior of the exciton with the properties of the barrier material (at well widths less than 4–5 nm). All PL peaks show a fine structure, which can be very accurately fitted by only two Gaussian curves. A comparison between absorption and PL spectra shows that an additional higher-energy PL peak, which can be resolved in the spectra of high-quality samples with narrow linewidths, corresponds to the onset of the exciton continuum.