Scaling behavior of stochastically varying current switching times in semiconductor superlattices

The stochastic switching process from a metastable state of electronic transport in a semiconductor superlattice with $N$ periods ($N\gg 1)$ is simulated using a discrete drift-diffusion model that also includes shot noise in the tunneling currents. Sequential resonant tunneling between quantum wells is the primary conduction mechanism and noise terms are treated as delta-correlated in space and time. This is a high-dimensional, non-gradient system; furthermore, the metastable state possesses stability eigenvalues with non-zero imaginary part. The distribution of metastable lifetimes is studied as a function of bias voltage $V$, in a regime for which the current-voltage characteristics exhibit bistability. The mean lifetime \textit{$\tau $} is fitted to an expression of the form $\ln \tau \propto \left| {V-V_{th} } \right|^\alpha $, where $V_{th}$ denotes the voltage for which the metastable state disappears in a saddle-node bifurcation. We find that the exponent \textit{$\alpha $} is sensitive to the initial state preparation. Starting from the exact metastable state, the exponent is $\alpha =1.67\pm 0.06$. In contrast, a pulsed initial condition, of the type that is readily achievable in experimental measurements, yields larger \textit{$\alpha $} values. In both cases, the determined \textit{$\alpha $} values exceed 3/2, which is the exponent value for a typical one-dimensional system.