Asymptotic analysis of the Gunn effect with realistic boundary conditions

TL;DR

This paper provides a comprehensive asymptotic analysis of the Gunn effect in n-GaAs, revealing how different boundary conditions influence wave types and current oscillation shapes, and suggesting contact parameter measurement methods.

Contribution

It introduces a general asymptotic framework for the Gunn effect with realistic boundary conditions, identifying new instabilities and detailed relationships between current features and contact parameters.

Findings

Different wave types mediate the Gunn effect depending on boundary parameters.

A new instability due to multiple shedding of dipole waves is discovered.

The shape of current oscillations relates directly to contact parameters.

Abstract

A general asymptotic analysis of the Gunn effect in n-GaAs under general boundary conditions for metal-semiconductor contacts is presented. Depending on the parameter values in the boundary condition of the injecting contact, different types of waves mediate the Gunn effect. The periodic current oscillation typical of the Gunn effect may be caused by moving charge-monopole accumulation or depletion layers, or by low or high-field charge-dipole solitary waves. A new instability caused by multiple shedding of (low field) dipole waves is found. In all cases the shape of the current oscillation is described in detail: we show the direct relationship between its major features (maxima, minima, plateau's, ...) and several critical currents (which depend on the values of the contact parameters). Our results open the possibility of measuring contact parameters from the analysis of the shape of the current oscillation.