Nonlinear Electronic Transport in Semiconductor Superlattices

Abstract

Nonlinear charge transport in strongly coupled semiconductor superlattices is described by single or two-miniband Wigner-Poisson kinetic equations with BGK collision terms. Balance equations for miniband populations and electric field are derived using the Chapman-Enskog method. Numerical solutions show stable self-oscillations of the current through a voltage biased superlattice.

Maximum Entropy Closure of Balance Equations for Miniband Semiconductor Superlattices

“…A simple Boltzmann-Poisson model containing these ingredients evolved from the work of Ktitorov et al [17], Ignatov and Shashkin [18], and later authors. In the limit of strong electric fields for which the Bloch frequency has the same order as collision frequencies, it is possible to derive balance equations for the electron and current densities and the electric field by a systematic Chapman-Enskog perturbation method [14,16,19]. In this situation of a SL very far even from local equilibrium, the performance of a maximum entropy closure can be ascertained by comparison to the perturbation results.…”

“…In certain regimes, electronic transport can be described by Boltzmann-type kinetic equations, from which one can derive balance equations for electron density, current density and electric field in a controlled way. In this paper, we derive balance equations using the maximum entropy principle in the hyperbolic limit of large electric field and large collision frequencies, and compare it with existing derivations that use systematic perturbation methods [14,16]. In this limit, transport coefficients appearing in the balance equations depend on the electric field, a feature that is also captured by the maximum entropy closure as we shall see below.…”

“…Quasi one dimensional semiconductor superlattices are among the simplest. There is a large literature on nonlinear electronic transport in semiconductor superlattices (SLs); see [14][15][16]. On the one hand, these materials have many interesting properties as they exhibit nonlinear periodic and chaotic time-dependent oscillations, multistability, pinning effects due to the lattice, etc.…”

“…On the one hand, these materials have many interesting properties as they exhibit nonlinear periodic and chaotic time-dependent oscillations, multistability, pinning effects due to the lattice, etc. Applications include fast oscillator devices, infrared detectors, quantum cascade lasers [16]. On the other hand, their quasi one dimensional character makes theoretical study of SLs easier.…”

Photopolarization Effect and Photoelectric Phenomena in Layered GaAs Semiconductors

“…One of the typical findings observed in nonlinear semiconductors is the dynamics of propagating electrical solitary waves which could be periodic or chaotic. Many of these phenomena have been studied in bulk semiconductors as well as superlattices, and can be successfully explained by means of theoretical as well as numerical approaches (Amann & Schöll, 2005;Bonilla & Grahn, 2005;Cantalapiedra et al, 2001;Gaa & Schöll, 1996;Wack, 2002). Of particular interest is that GaAs semiconductors have been shown to generate microwave radiation.…”