The PL spectra are dominated by one or two spectral bands, corresponding, respectively, to one or two populated electron sub-bands in the InGaAs quantum well. An enhancement of PL intensity at the Fermi level energy (EF) in the high-energy tail of the PL peak is clearly observed and associated with the Fermi edge singularity (FES). This is practically detected at the same energy for all samples, in contrast with energy transitions in the InGaAs channel, which are shifted to lower energy with increasing channel thickness. PL spectra at low temperature and low excitation density are used to optically determine the density of the two-dimensional electron gas (2DEG) in the InGaAs channel for different thicknesses. The results show an enhancement of the 2DEG density when the well width increases, in good agreement with our previous theoretical study.