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We measure the time-resolved photoluminescence characteristics of a novel type of lithographically patterned quantum dot fabricated by electron beam lithography, wet chemical etching, and overgrowth of the barrier layers by metalorganic chemical vapor deposition.We find that the quantum dot (QD) photoluminescence exhibits a bi-exponential decay that we explain in terms of the fast capture of carriers by defect states followed by a slower radiative relaxation process. We also perform a systematic investigation of the rise time and decay time as a function of the QD density, size, and temperature. These measurements indicate that the carrier capture process in this type of QD is limited by carrier drift within the GaAs barrier material.