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We have developed a scanning photoluminescence technique that can directlymap out the local two-dimensional electron density with a relative accuracy of$\sim2.2\times10^8$ cm$^{-2}$. The validity of this approach is confirmed bythe observation of the expected density gradient in a high-quality GaAs quantumwell sample that was not rotated during the molecular beam epitaxy of itsspacer layer. In addition to this global variation in electron density, weobserve local density fluctuations across the sample. These random densityfluctuations are also seen in samples that were continuously rotated duringgrowth, and we attribute them to residual space charges at thesubstrate-epitaxy interface. This is corroborated by the fact that the averagemagnitude of density fluctuations is increased to $\sim9\times10^{9}$ cm$^{-2}$from $\sim1.2\times10^9$ cm$^{-2}$ when the buffer layer between the substrateand the quantum well is decreased by a factor of seven. Our data provide directevidence for local density inhomogeneities even in very high-qualitytwo-dimensional carrier systems.

Spatial Mapping of Local Density Variations in Two-dimensional Electron Systems Using Scanning Photoluminescence