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Carrier transport and capture paths via barriers of different dimensionality in AlGaAs/GaAs quantum wire (QWR)/quantum dot (QD) heterostructures, grown in inverted pyramids, are studied by photoluminescence (PL) spectroscopy. Evidence for thermally activated diffusion related to potential disorder in the QWR barriers and thermionic emission of carriers from the QD into the QWR barrier is observed in temperature dependent PL spectra. Similar activation energies for the thermionic emission are derived from the continuous-wave and time-resolved PL spectroscopy.