# Periodic Generation and Propagation of Traveling Fronts in DC Voltage Biased Semiconductor Superlattices

@article{Bonilla1997PeriodicGA, title={Periodic Generation and Propagation of Traveling Fronts in DC Voltage Biased Semiconductor Superlattices}, author={L. Bonilla}, journal={SIAM J. Appl. Math.}, year={1997}, volume={57}, pages={1588-1614} }

The continuum limit of a recently proposed model for charge transport in resonant-tunneling semiconductor superlattices (SLs) is analyzed. It is described by a nonlinear hyperbolic integrodifferential equation on a one-dimensional spatial support, supplemented by shock and entropy conditions. For appropriate parameter values, a time-periodic solution is found in numerical simulations of the model. An asymptotic theory shows that the time-periodic solution is due to recycling and motion of shock… Expand

#### 23 Citations

Dynamics of electric field domain walls in semiconductor superlattices

- Physics
- 2000

Abstract A self-consistent microscopic model of sequential tunneling in superlattices is employed to investigate self-sustained current oscillations. Current spikes – high-frequency modulation due to… Expand

Nonlinear Transport in Semiconductor Superlattices

- Physics
- 2002

Nonlinear electronic transport in weakly coupled superlattices results in formation of electric field domains, self-sustained current oscillations (periodic, quasiperiodic or chaotic), wave… Expand

Semiconductor superlattices: a model system for nonlinear transport

- Physics
- 2002

Abstract Electric transport in semiconductor superlattices is dominated by pronounced negative differential conductivity. In this report, the standard transport theories for superlattices, i.e.… Expand

Motion of wave fronts in semiconductor superlattices.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2001

An analysis of wave front motion in weakly coupled doped semiconductor superlattices is presented and wave fronts are described near the threshold currents J(i) (i=1,2) at which they depin and move. Expand

Wave fronts may move upstream in semiconductor superlattices

- Physics, Medicine
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000

In weakly coupled, current biased, doped semiconductor superlattices, domain walls may move upstream against the flow of electrons against a first critical current, and remains stationary between this value and a second critical current. Expand

TOPICAL REVIEW: Theory of nonlinear charge transport, wave propagation, and self-oscillations in semiconductor superlattices

- Physics
- 2001

Nonlinear charge transport in semiconductor superlattices under strong electric fields parallel to the growth direction results in rich dynamical behaviour including the formation of electric field… Expand

Non-linear dynamics of semiconductor superlattices

- Physics
- 2005

In the last decade, non-linear dynamical transport in semiconductor superlattices (SLs) has witnessed significant progress in theoretical descriptions as well as in experimentally observed non-linear… Expand

Thermal breakdown, bistability, and complex high-frequency current oscillations due to carrier heating in superlattices

- Physics
- 2000

The impact of electron heating on vertical electrical transport in superlattices is shown to cause an S-shaped current–voltage characteristic in addition to the conventional N type occurring at lower… Expand

Bifurcation Behavior of a Superlattice Model

- Computer Science, Mathematics
- SIAM J. Appl. Math.
- 2000

It is shown that the organizing centers for the long time dynamics are Takens--Bogdanov bifurcation points in a broad range of parameters and the results are cast in a $\phi$-$\nu$ phase diagram. Expand

Photon-assisted transport in semiconductor nanostructures

- Physics
- 2004

Abstract In this review we focus on electronic transport through semiconductor nanostructures which are driven by ac fields. Along the review we describe the available experimental information on… Expand

#### References

SHOWING 1-10 OF 35 REFERENCES

Solitary waves in semiconductors with finite geometry and the Gunn effect

- Mathematics
- 1991

An asymptotic analysis of the Gunn effect (oscillations of the current through a semiconductor under constant voltage bias) is given. The electric field inside the one-dimensional semiconductor is… Expand

Solitary-wave dynamics in extrinsic semiconductors under dc voltage bias.

- Materials Science, Medicine
- Physical review. B, Condensed matter
- 1993

Numerical-simulation results are presented for a simple drift-diffusion model which describes timedependent
and nonlinear electrical transport properties of extrinsic semiconductors under… Expand

Dynamics of Electric Field Domains in Superlattices

- Physics
- 1995

A discrete drift model of resonant tunneling transport in weakly-coupled GaAs quantum-well structures under laser illumination is introduced and analyzed. Results include explanations (via formation… Expand

Simple model for multistability and domain formation in semiconductor superlattices.

- Materials Science, Medicine
- Physical review. B, Condensed matter
- 1994

The model considers the lowest two subbands of the single quantum wells and includes resonant tunneling between adjacent wells, miniband conduction, and intersubband relaxation within each well, obtaining multistability of the current-voltage characteristic and various hysteretic transitions which arise upon sweeping the applied voltage. Expand

Theory of periodic and solitary space charge waves in extrinsic semiconductors

- Physics
- 1991

Abstract We present a theory of the existence and stability of traveling periodic and solitary space charge wave solutions to a standard rate equation model of electrical conduction in extrinsic… Expand

New Transport Phenomenon in a Semiconductor "Superlattice"

- Materials Science
- 1974

We report electronic transport properties in a GaAs-AlAs periodic structure known as a "superlattice" prepared by a molecular-beam epitaxy. Its differential conductance in the superlattice direction… Expand

Chaos in resonant-tunneling superlattices.

- Physics, Medicine
- Physical review. B, Condensed matter
- 1995

Chaos is the result of forcing this natural oscillation by means of an appropriate external microwave signal in n-doped semiconductor superlattices with sequential resonant tunneling as their main charge transport mechanism. Expand

Dynamics of electric-field domains and oscillations of the photocurrent in a simple superlattice model.

- Physics, Medicine
- Physical review. B, Condensed matter
- 1994

A discrete model is introduced to account for the time-periodic oscillations of the photocurrent and photoluminescence time-dependent oscillations in a superlattice observed by Kwok et al. in an undoped 40-period AlAs/GaAs superlATTice. Expand

Theory of current-voltage instabilities in superlattices.

- Physics, Medicine
- Physical review. B, Condensed matter
- 1993

The solution of the stability problems shows that near the instability threshold only long-wavelength fluctuations are unstable, and at the initial stage of the development of the instability nonlinear effects accelerate the fluctuation growth. Expand

Gunn instability in finite samples of GaAs. II: Oscillatory states in long samples

- Physics
- 1992

Abstract An asymptotic description is given of the well known phenomenon of charge density waves propagating in long samples of n-type GaAs with Ohmic contacts and voltage bias. Depending on the… Expand