Tunneling in Periodic and Quasi‐Periodic Superlattices

Abstract

AbstractA comparative study of electron tunneling in periodic and quasi‐periodic systems is made. The quasi‐periodic systems considered are Fibonacci and Thue‐Morse superlattices. The transfer matrix method and Landauer formula are used to calculate the electron transmission coefficient and tunneling conductance, respectively. For the numerical calculation the superlattices are considered to be made from GaAs and GaAlAs semiconductors. Numerical calculations are performed for the tunneling conductance for different values of potential barrier height and width. The present calculations show that the peak positions of the tunneling conductance are at different energies for periodic, Fibonacci, and Thue‐Morse superlattices with equal number of layers. The height of peaks changes from one system to another. We also investigated the effect of temperature, damping, and magnetic field on the tunneling conductance in simple approximations. It is found that the peak height of the tunneling conductance decreases as the temperature increases and peak width increases at the same time. As magnetic field increases, the position of peaks of the tunneling conductance shifts to higher energy. The tunneling conductance decreases as the damping increases. Theses calculations can be extended to hole tunneling in these systems.