Electronic Structures of T-Shaped Quantum Wires

In this paper, we propose the periodic boundary condition which can be applied to a variety of semiconductor nanostructures to overcome the difficulty of solving Schrödinger equation under the natural boundary condition. When the barrier width is large enough, the average of the maximum and minimum of energy band under the periodic boundary condition is very close to the energy level obtained under the natural boundary condition. As an example, we take the GaAs/Ga_1-xAl_xAs system. If the width of the Ga_1-xAl_xAs barrier is 200Å , the average of the maximum and minimum of energy band of the GaAs/Ga_1-xAl_xAs superlattices is very close to the energy level of the GaAs/Ga_1-xAl_xAs quantum wells (QWs). We give the electronic structure effective mass calculation of T-shaped quantum wires (T-QWRs) under the periodic boundary condition. The lateral confinement energies E_1D-2D of electrons and holes, the energy difference between T-QWRs and QWs, are precisely determined.