In this thesis we used the atomic force microscope (AFM) for the creation of complex mesoscopic devices with various geometries. The basis for our experiments were GaAs/AlGaAs-heterostructures with twodimensional electron gases (2DEG) 57 nm, 40 nm, and 34 nm below the surface. We studied in detail controlled mechanical nanomachining and local oxidation.
We fabricated ballistic quantum point contacts by engraving a constriction into a GaAs/AlGaAs-heterostructure with the tip of an AFM. The devices were nanomachined using both a silicon tip and a diamond tip to study the influence of the tip material. It turned out that a diamond tip is almost perfect not only for a fast and simple processing but also in forming proper potential profiles to observe ballistic electron transport. The appearance of the 0.7 (2e2/h) conductance anomaly confirms the high quality of diamond-engraved devices. We deduced the depletion lengths induced by the different tips, yielding ~ 200 nm for diamond-engraved samples, which is roughly two times smaller than typical depletion lengths in devices patterned with a Silicon tip.
A detailed study of the local oxidation with an AFM proved the importance of the oxidation current for the controlled fabrication of tunnelling barriers in 2DEGs. We found a linear dependence of the barrier height on the oxidation current which is related to the depth of the oxide lines. With these tunnelling barriers we fabricated a single-electron transistor containing several hundred electrons well described by the constant interaction model.
Further we demonstrated that the AFM-based nanolithography provides a relatively easy and controlled approach to create parallel quantum dots. The double dot was stepwise fabricated with a combination of controlled nanomachining and local oxidation. The dots were defined by splitting a quasi-one-dimensional resonant tunnelling diode in two separate zero-dimensional regions. Analysing of the transport measurements of the two quantum dots allowed the identification of the specific Coulomb-blockade oscillations of each dot. We showed that the current could be directed through both quantum dots separately by applying high negative gate voltages to the respective in-plane gates. These experiments proved that the combination of controlled nanomachining and local oxidation with an atomic force microscope is a straightforward approach to fabricate robust mesoscopic devices.
In the remaining part of the thesis we investigated the transport characteristic of a quantum ring defined by local oxidation in great detail. We discussed the Aharonov-Bohm effect in this asymmetric quantum ring with a diameter of below 450 nm. The analysis of the data with Fourier transformation indicated only one interfering subband in the ring. This led to a modulation of the conductance of more than 50%. The electron orbit extracted from the periodicity of the Aharonov-Bohm effects fits perfectly to the ring geometry. The attached in-plane gates allow to tune the phase of the Aharonov-Bohm effect at zero magnetic field and we observed the typical sharp phase jumps by π that are related to the asymmetry of our device. Finally, we showed that the line-shape of the resonances in the quantum ring is controlled by an outer gate voltage and the magnetic field. This fact was explained by interference between a resonant bound state and directly submitted electrons. This led to a Fano like characteristic.
The attached in-plane gates of the quantum ring allowed to study the same device in the Coulomb-blockade regime. With the observation of spin flips in the addition spectrum in a perpendicular magnetic field we determined the number of electrons to below ten in this voltage range. The observation of a Kondo effect enabled to study the spin structure of the measured quantum ring. The Kondo resonances vanished and broadened with increasing temperature. The peak conductance follows the universal curve and was used to estimate the Kondo temperature of the device. Non-linear transport measurements showed an even-odd behaviour of the Kondo effect. This result together with a Zeeman splitting in a perpendicular magnetic field led to the conclusion that the Kondo effect was induced by a single spin on the ring. The magnetic field dependence of the conductance in the Kondo valley could be interpreted as ballistic transport of as few as five electrons.
At low magnetic fields we observed oscillations in the ground state of the device with a periodicity related to the number of electrons on the ring. This effect caused by strong electron-electron interactions was attributed to the small number of electrons.We found Aharonov-Bohm oscillations of the conductance in the Kondo regime as well. The finite conductance due to the Kondo effect was used for an analysis of the phase evolution of this Aharonov-Bohm effect in the Coulomb-blockade valley. The measurement yielded phase jumps by π at the Coulomb-blockade resonances and a smooth shift of the Aharonov-Bohm maxima in between.
The observation of the Kondo and Aharonov-Bohm effect shows the wide range of possible research topics for these kind of devices. Due to their smallness together with the few electrons and the exact control of the sample parameters these devices are ideal systems to compare the experimental results with theoretical predictions. With the AFM-based lithography it should be possible to design novel geometries for mesoscopic systems, which may show an unexpected variety of new effects in transport experiments.
Keywords:
nano fabrication, Kondo effect, Aharonov-Bohm effect
Nanolithography with an atomic force microscope:
quantum point contacts, quantum dots, and quantum rings. Electronic publication, Universitätsbibliothek
und technische Informationsbibliothek,
Hannover (2002)
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