Decay of metastable current states in one-dimensional resonant tunneling devices

TL;DR

This paper analyzes the decay of metastable current states in one-dimensional resonant tunneling devices, deriving exact expressions for switching times and their dependence on device length and bias voltage.

Contribution

It provides analytical formulas for switching times in resonant tunneling structures, highlighting the effects of device geometry and bias on metastable state decay.

Findings

Switching time increases exponentially as bias approaches the bistability boundary.

Long strips exhibit  au  ext{proportional to } (V_{th} - V)^{5/4}.

Short strips exhibit  au  ext{proportional to } (V_{th} - V)^{3/2}.

Abstract

Current switching in a double-barrier resonant tunneling structure is studied in the regime where the current-voltage characteristic exhibits intrinsic bistability, so that in a certain range of bias two different steady states of current are possible. Near the upper boundary V_{th} of the bistable region the upper current state is metastable, and because of the shot noise it eventually decays to the stable lower current state. We find the time of this switching process in strip-shaped devices, with the width small compared to the length. As the bias V is tuned away from the boundary value V_{th} of the bistable region, the mean switching time \tau increases exponentially. We show that in long strips \ln\tau \propto (V_{th} -V)^{5/4}, whereas in short strips \ln\tau \propto (V_{th} -V)^{3/2}. The one-dimensional geometry of the problem enables us to obtain analytically exact expressions for both the exponential and the prefactor of \tau. Furthermore, we show that, depending on the parameters of the system, the switching can be initiated either inside the strip, or at its ends.