An Analytical and Numerical Investigation of the Dissipative Chaos in Semiconductor Superlattices

The transport of electrons in a semiconductor superlattice miniband under the influence of electrical and magnetic fields, which are applied in different directions on the superlattice, is investigated. The time series diagrams and the Lyapunov exponent are computed using the fourth-order Runge-Kutta method. The numerical computations show that for particular values of the parameters, which depend on the superlattice characteristics and the fields applied on them, electrons show chaotic behaviors. In addition, for some other parameter values these behaviors become regular and non-chaotic. The presence of a magnetic field, perpendicular to the electrical field, is shown to reduce the chaotic areas in the motion of the electron. An alteration in electron average energy and velocity is attributed to application of the external fields, carrier scattering from other carriers, and the phonons’ and lattices’ faults. The study has important applications in computational physics and semiconductor chaotic simulations.