Nonlinear stochastic discrete drift-diffusion theory of charge fluctuations and domain relocation times in semiconductor superlattices

Abstract

A stochastic discrete drift-diffusion model is proposed to account for the effects of shot noise in weakly coupled, highly doped semiconductor superlattices. Their current-voltage characteristics consist of a number stable multistable branches corresponding to electric field profiles displaying two domains separated by a domain wall. If the initial state corresponds to a voltage on the middle of a stable branch and a sudden voltage is switched so that the final voltage corresponds to the next branch, the domains relocate after a certain delay time. Shot noise causes the distribution of delay times to change from a Gaussian to a first passage time distribution as the final voltage approaches that of the end of the first current branch. These results agree qualitatively with experiments by Rogozia et al (Phys. Rev. B 64, 041308(R) (2001)

Noise-enhanced spontaneous chaos in semiconductor superlattices at room temperature

“…[28], and in Ref. [42] for a somewhat simpler discrete transport model. We consider current fluctuations associated to dissipation due to electron diffusion and model them by Landau-Lifshitz fluctuating hydrodynamics [29,43] adapted to SLs.…”

Vanishing Viscosity Regimes and Nonstandard Shock Relations for Semiconductor Superlattices Models

“…In spite of the existence of exact formulas for v and D, due to their complexity (see [3]), we have used the following numerical approximations inspired by the results of [2, Appendix A] and [4]: …”

Low-Field Limit for a Nonlinear Discrete Drift-Diffusion Model Arising in Semiconductor Superlattices Theory

“…There exist solutions corresponding to low voltages which are stationary and typically develop low electric fields. It is very important to understand the time evolution of the solutions toward these stationary profiles (see [5] where relocation experiments are studied).…”

“…Then, a description of charge transport in such devices has been proposed through a DDD model; see [1,4,6,15]. This model has been extended by taking into account stochastic effects by Bonilla, Sánchez, and Soler [5], in comparison with the experimental results of Rogozia et al [12].…”

“…All the coefficients v, D, W (b) , W (f ) , j (e) are supposed to be nonnegative and satisfy some regularity properties. Typical graphs for these functions can be found in [5].…”