Theory of traveling filaments in bistable semiconductor structures

TL;DR

This paper develops a nonlinear model explaining how Joule self-heating induces traveling current filaments in bistable semiconductor structures, revealing bifurcation conditions and filament velocity.

Contribution

It introduces an analytical theory for traveling filaments caused by self-heating, linking temperature effects to filament motion in bistable semiconductors.

Findings

Self-heating causes bifurcation from static to traveling filaments.

Traveling filaments occur when increased temperature negatively impacts transport.

The model predicts filament velocity and bifurcation conditions.

Abstract

We present a generic nonlinear model for current filamentation in semiconductor structures with S-shaped current-voltage characteristics. The model accounts for Joule self-heating of a current density filament. It is shown that the self-heating leads to a bifurcation from static to traveling filament. Filaments start to travel when increase of the lattice temperature has negative impact on the cathode-anode transport. Since the impact ionization rate decreases with temperature, this occurs for a wide class of semiconductor systems whose bistability is due to the avalanche impact ionization. We develop an analytical theory of traveling filaments which reveals the mechanism of filament motion, find the condition for bifurcation to traveling filament, and determine the filament velocity.