We study the thermal and electronic transport through epitaxial GaAs nanopillars that are about 10 nm long and 100 nm in diameter. The pillars are epitaxially embedded between three-dimensional GaAs contact reservoirs on their front and back ends and in an AlGaAs matrix along their circumference. They can be considered as very short nanowires that are lattice matched to the contacts. The pillars represent quantum point contacts between two three-dimensional GaAs charge and heat reservoirs. The AlGaAs barrier can be removed in a selective wet etching process. In this way thin GaAs membranes arise that are supported by the pillars . In such gap structures temperature gradients in the range of 107 K/m are realizable along the pillars [2,3]. Here we will report about thermal transport through pillars in such gap structures, as well as about first electronic transport experiments on pillars that are still embedded in an AlGaAs matrix.
The thermal transport along the pillars is ballistic in a wide temperature range as has been shown in previous studies [2-4]. This is given, because of short pillar length, the high crystalline quality and the epitaxial connection of the pillars to the phonon reservoirs. Here we will focus on first electronic transport studies with pillars that are still embedded in an AlGaAs matrix. Reference measurements on samples that contain just the AlGaAs matrix layer without pillars show that tunneling transport through the AlGaAs barrier is negligible at a layer thickness of 16 nm. Current-voltage characteristics of samples with pillars show distinctive asymmetries  that we associate with the conical shape of the pillars. Although contact reservoirs and pillars are made from the same material, the transport through the pillars is dominated by tunneling across shallow barriers. This is explained by the quantum size effect on the electronic states within the pillars. Thus the transport in our pillars is similar to the transport of planar quantum point contacts in two-dimensional electron systems at gate voltages close to the threshold . Molenkamp et al. reported relatively large thermo-voltages in this transport regime, which are caused by a hot electron filtering effect . Due to the good thermal conductivity of their structures Molenkamp et al. were not able to apply large temperature gradients. In our structures large temperature gradients can be established if the AlGaAs matrix is removed [2,3]. Such experiments to the electron and thermo-electric transport through pillars in structures with removed AlGaAs matrix are plant for the near future.
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