Comparison the Photoluminescence and Magneto-transport Techniques for Measuring 2D Electron Density in GaAs Quantum Wells

We compare photoluminescence (PL) and transport measurements as a measure of the electron density in clean, two-dimensional (2D) systems confined to GaAs quantum wells (QWs), grown via molecular beam epitaxy. We explore the PL shape evolution across a number of samples with different QWs and as-grown electron densities and study its correspondence with the density obtained in transport measurements. We also measure the 2D density in a top-gated quantum well sample in both PL and transport and find that they are in agreement to within a few percent. The PL measurements are sensitive to gate-induced 2D density changes as small as 10$^{\mathrm{9}}$ electrons/cm$^{\mathrm{2}}$. The spatial resolution of the PL 2D density measurement is 40$\mu $m, which is already substantially better than is possible in spatial maps with magneto-transport. Our results establish that PL could be used as a reliable technique for non-invasive measurements of small density variations with high spatial resolution.