We report photoluminescence measurements made on free‐standing, lattice‐matched GaAs/AlGaAs and pseudomorphic InGaAs/GaAs quantum boxes fabricated by laterally patterning quantum wells using electron‐beam lithography and either reactive ion etching or ion beam milling. At temperatures below 10–20 K the luminescence efficiency of most of the GaAs quantum‐box arrays tends to scale with the volume of quantum‐well material remaining after processing even for the smallest boxes which have lateral dimensions of only 40–50 nm. These observations indicate that the surface recombination rate in GaAs submicron structures can be small relative to the radiative recombination rate at low temperatures. In contrast, radiative recombination in the InGaAs/GaAs quantum boxes is strongly quenched for lateral dimensions less than 500 nm. We suggest that this is because photoexcited carriers are laterally localized in the GaAs boxes by potentials of the order of a few meV, possibly associated with interface disorder or strain relaxation, and that such localization effects are smaller in the InGaAs boxes.