Photoexcited semiconductor superlattices as constrained excitable media: Motion of dipole domains and current self-oscillations

Abstract

A model for charge transport in undoped photoexcited semiconductor superlattices, which includes the dependence of the electron-hole recombination on the electric field and on the photoexcitation intensity through the field-dependent recombination coefficient, is proposed and analyzed. Under dc voltage bias and high photoexcitation intensities, there appear self-sustained oscillations of the current due to a repeated homogeneous nucleation of a number of charge dipole waves inside the superlattice. In contrast to the case of a constant recombination coefficient, nucleated dipole waves can split for a field-dependent recombination coefficient in two oppositely moving dipoles. The key for understanding these unusual properties is that these superlattices have a unique static electric-field domain. At the same time, their dynamical behavior is akin to the one of an extended excitable system: an appropriate finite disturbance of the unique stable fixed point may cause a large excursion in phase space before returning to the stable state and trigger pulses and wave trains. The voltage bias constraint causes new waves to be nucleated when old ones reach the contact.

Wave fronts, pulses and wave trains in photoexcited superlattices behaving as excitable or oscillatory media

“…While there are at least two stable EFDs with an almost constant value of the electric field in the case of doped SLs, there may be only one stable EFD in the case of an undoped SL under high photoexcitation. [2] This is similar to what happens in excitable media such as those described by the FitzHugh-Nagumo (FHN) model for nerve conduction. [3,4] For background information on this model and related models, see Refs.…”

“…Written in nondimensional form, the equations governing nonlinear charge transport in a weakly coupled, undoped, photoexcited GaAs/Al x Ga 1−x As SL are: [2]…”

“…The case of an oscillatory medium in which there is a single unstable spatially homogeneous state can also be realized in both the FHN model and a strongly photoexcited undoped SL. [2] However, the electric field in a voltagebiased SL with a finite number of periods is constrained to have a fixed area underneath its spatial profile, and this constraint causes it to exhibit a more complex behavior. [2] The key ingredient to the complex dynamics of electron transport in photoexcited undoped SLs is the introduction of an electron-hole recombination coefficient, which is a function of the electric field.…”

“…[2] However, the electric field in a voltagebiased SL with a finite number of periods is constrained to have a fixed area underneath its spatial profile, and this constraint causes it to exhibit a more complex behavior. [2] The key ingredient to the complex dynamics of electron transport in photoexcited undoped SLs is the introduction of an electron-hole recombination coefficient, which is a function of the electric field. Nonlinear charge transport in weakly coupled undoped type-I superlattices (SL) under photoexcitation is well described by spatially discrete drift-diffusion systems (DDDS) of equations.…”

“…[14] Introducing a field-dependent electronhole recombination coefficient in the model has striking consequences. [2] For high photoexcitation densities, it is possible to find only one stable EFD, not two as in the case of a constant recombination coefficient. [12] Then, under a dc voltage bias, periodic or chaotic SSOC may appear.…”