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Binding Energy of Quantum Bound States in X-shaped Nanowire Intersection

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Master's thesis

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The question of the possible existence of the quantum bound states localized states due to special geometries has been a long standing problem in quantum theory. Knowledge of quantum bound states in crossed nanowire system is very important in understanding the properties of spatially confined nanostructures which are promising candidates for device applications such as transistors, amplifiers, switches, biosensors, photo-detectors, solar cells, lasers and light-emitting diodes. This study focuses mainly on investigating the angular dependence of the lowest bound energy state for the model system of an electron trapped at the intersection of two identical narrow channels nanowires crossed at an arbitrary angle. When the channels are perpendicular, such a classically unbound system is known to possess a quantum bound state. We used the variational principle to obtain the general criterion to study the role of tilted geometry for the existence of bound state of an electron in such a quantum system. Using suitable trial wave functions, calculations were carried out to estimate the upper bound for the ground state energy of an electron located inside the crossed nanowire system. The results of our calculations show that the bound state energy varies as the squared sine of the intersection angle of the crossed nanowires. We have found that the system is strongly bound when the intersection angle is 90 degree and the system is unbound when the intersection angle is 00. These particular features of the crossed nanowire system can be exploited to design single electron ultra-sensitive switching devices using newly developed lithographic and etching techniques in nanotechnology. Furthermore, our model may be useful to interpret electron transport peculiarities in realistic systems such as semiconductor nanowire films, nanorods and carbon nanotube bundles.

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  • Electrical and Electronic Equipment
  • Quantum Theory and Relativity

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