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Electron Energy in Rectangular and Cylindrical Quantum Wires

The influence of the cross-sectional shape of a quantum filament on the energy spectrum of electrons is studied. The calculation of energy levels of electrons in a quantum wire is performed. For the AlxGa1 – xAs quantum wire with infinite and finite depths, energy level spectra were obtained. The dispersion dependence with a parabolic law in a quantum wire with finite and infinite height of the potential barrier based on Al0.25Ga0.75As and Al0.75Ga0.25As was calculated, and graphs of dispersion dependences were obtained. The results are obtained for the linear sizes of a quantum wire from 5 nm to 15 nm. The transverse dimensions of cylindrical and rectangular quantum wires with close energy levels are found. The analysis of energy levels in cylindrical and rectangular quantum wires is carried out, and their similarities are revealed. It is shown that the energy levels are close to each other when the cross-sectional areas of rectangular and cylindrical quantum wires become equal. The solutions of the Schrödinger equation are presented, when the solution for a cylindrical wire can be replaced by the solution for a rectangular wire.