High Resolution Parameter Space from a Two Level Model on Semi-Insulating GaAs

TL;DR

This paper introduces a new two-valley model for semi-insulating GaAs that successfully reproduces negative differential conductivity and reveals complex self-organized structures in the system's parameter space.

Contribution

The paper proposes an alternative two-valley model that captures NNDC in SI-GaAs and constructs a detailed high-resolution parameter space revealing complex chaotic structures.

Findings

The two-valley model reproduces NNDC in SI-GaAs.

The parameter space shows self-organized periodic and chaotic regions.

Complex structures like 'shrimp' and 'snail shell' shapes are identified.

Abstract

Semi-insulating Gallium Arsenide (SI-GaAs) samples experimentally show, under high electric fields and even at room temperature, negative differential conductivity in N-shaped form (NNDC). Since the most consolidated model for n-GaAs, namely, "the model", proposed by E. Scholl was not capable to generate the NNDC curve for SI-GaAs, in this work we proposed an alternative model. The model proposed, "the two-valley model" is based on the minimal set of generation recombination equations for two valleys inside of the conduction band, and an equation for the drift velocity as a function of the applied electric field, that covers the physical properties of the nonlinear electrical conduction of the SI-GaAs system. The "two valley model" was capable to generate theoretically the NNDC region for the first time, and with that, we were able to build a high resolution parameter-space of the periodicity (PSP) using a Periodicity-Detection (PD) routine. In the parameter space were observed self-organized periodic structures immersed in chaotic regions. The complex regions are presented in a "shrimp" shape rotated around a focal point, which forms in large-scale a "snail shell" shape, with intricate connections between different "shrimps". The knowledge of detailed information on parameter spaces is crucial to localize wide regions of smooth and continuous chaos.