We simulate the low temperature confinement of electrons in quantum wires formed at the corners of periodic saw-tooth structures consisting of layers of AlxGa1−xAs and GaAs materials. A very efficient self-consistent procedure for the solution of Schrödinger’s and Poisson’s equations, including shifted periodic boundary conditions, is used to obtain the wave functions and energy levels in the quantum well. Self-consistency is very important to obtain an accurate result; in particular, the precise details of the potential at the corners must be resolved. The formation of a quantum wire at the corners of the GaAs layer is found to be very sensitive to the physical parameters of the neighboring AlxGa1−xAs layers. We find that to avoid sizeable electron population in the GaAs region between the corners, asymmetric doping is necessary, which normally results in electron confinement only at every other corner.
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