Quantum confinement in superlattice finite cylindrical wires using the transfer matrix approach

Abstract

This paper investigates the electronic states in a periodic system of two cylindrical quantum wires based on GaAs/AlGaAs semiconductors. The system is integrated between two GaAs quantum cylinders of semi-infinite length. The effect of radius variation on the confined energy states of electrons in the cylindrical quantum wires is investigated. Using the in-array transfer matrix method, we have obtained analytical expressions for the transmission coefficient of an electron wave in cylindrical quantum wires (CQW). For different regions, the solution of the Schrödinger equation for the effective mass is obtained using radial cylindrical Bessel functions and axial eigenfunctions. According to our results, we can observe a graphical representation of the variations in energy and transmission of electronic states as a function of system parameters. The system has energy levels for controlling and manipulating electronic waves, which coincide with the energy of their states. Consequently, these energy levels appear when the quantitative radius of the net exceeds the critical radius. In these energy levels, analysis of transmission spectra and band structures shows a tendency for energies to decrease with increasing wire radius. The number of crossovers between passbands that form within band gaps increases due to variations in structure parameters with increasing electron energies. The results are sensitive to various system parameters, including radius, molar proportion of aluminum, and length. A better understanding of electronic states in semiconductor materials with cylindrical heterostructures could improve the efficiency of many quantum systems.