Axisymmetric pulse recycling and motion in bulk semiconductors

The Kroemer model for the Gunn effect in a circular geometry (Corbino disks) has been numerically solved. The results have been interpreted by means of asymptotic calculations. Above a certain onset dc voltage bias, axisymmetric pulses of the electric field are periodically shed by an inner circular cathode. These pulses decay as they move towards the outer anode, which they may not reach. As a pulse advances, the external current increases continuously until a new pulse is generated. Then the current abruptly decreases, in agreement with existing experimental results. Depending on the bias, more complex patterns with multiple pulse shedding are possible.Comment: 8 pages, 15 figure

Chaotic motion of space charge wavefronts in semiconductors under time-independent voltage bias

A standard drift-diffusion model of space charge wave propagation in semiconductors has been studied numerically and analytically under dc voltage bias. For sufficiently long samples, appropriate contact resistivity and applied voltage - such that the sample is biased in a regime of negative differential resistance - we find chaos in the propagation of nonlinear fronts (charge monopoles of alternating sign) of electric field. The chaos is always low-dimensional, but has a complex spatial structure; this behavior can be interpreted using a finite dimensional asymptotic model in which the front (charge monopole) positions and the electrical current are the only dynamical variables.Comment: 12 pages, 8 figure

Free boundary problems describing two-dimensional pulse recycling and motion in semiconductors

An asymptotic analysis of the Gunn effect in two-dimensional samples of bulk n-GaAs with circular contacts is presented. A moving pulse far from contacts is approximated by a moving free boundary separating regions where the electric potential solves a Laplace equation with subsidiary boundary conditions. The dynamical condition for the motion of the free boundary is a Hamilton-Jacobi equation. We obtain the exact solution of the free boundary problem (FBP) in simple one-dimensional and axisymmetric geometries. The solution of the FBP is obtained numerically in the general case and compared with the numerical solution of the full system of equations. The agreement is excellent so that the FBP can be adopted as the basis for an asymptotic study of the multi-dimensional Gunn effect.Comment: 19 pages, 9 figures, Revtex. To appear in Phys. Rev.

Universality of the Gunn effect: self-sustained oscillations mediated by solitary waves

The Gunn effect consists of time-periodic oscillations of the current flowing through an external purely resistive circuit mediated by solitary wave dynamics of the electric field on an attached appropriate semiconductor. By means of a new asymptotic analysis, it is argued that Gunn-like behavior occurs in specific classes of model equations. As an illustration, an example related to the constrained Cahn-Allen equation is analyzed.Comment: 4 pages,3 Post-Script figure

Magnetoswitching of current oscillations in diluted magnetic semiconductor nanostructures

Strongly nonlinear transport through Diluted Magnetic Semiconductor multiquantum wells occurs due to the interplay between confinement, Coulomb and exchange interaction. Nonlinear effects include the appearance of spin polarized stationary states and self-sustained current oscillations as possible stable states of the nanostructure, depending on its configuration and control parameters such as voltage bias and level splitting due to an external magnetic field. Oscillatory regions grow in size with well number and level splitting. A systematic analysis of the charge and spin response to voltage and magnetic field switching of II-VI Diluted Magnetic Semiconductor multiquantum wells is carried out. The description of stationary and time-periodic spin polarized states, the transitions between them and the responses to voltage or magnetic field switching have great importance due to the potential implementation of spintronic devices based on these nanostructures.Comment: 14 pages, 4 figures, Revtex, to appear in PR

Chaos in resonant-tunneling superlattices

Spatio-temporal chaos is predicted to occur in n-doped semiconductor superlattices with sequential resonant tunneling as their main charge transport mechanism. Under dc voltage bias, undamped time-dependent oscillations of the current (due to the motion and recycling of electric field domain walls) have been observed in recent experiments. Chaos is the result of forcing this natural oscillation by means of an appropriate external microwave signal.Comment: 3 pages, LaTex, RevTex, 3 uuencoded figures (1.2M) are available upon request from [email protected], to appear in Phys.Rev.

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

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 {\it et al} (Phys. Rev. B {\bf 64}, 041308(R) (2001)).Comment: 9 pages, 12 figures, 2 column forma

Dynamics of Electric Field Domains and Oscillations of the Photocurrent in a Simple Superlattice Model

A discrete model is introduced to account for the time-periodic oscillations of the photocurrent in a superlattice observed by Kwok et al, in an undoped 40 period AlAs/GaAs superlattice. Basic ingredients are an effective negative differential resistance due to the sequential resonant tunneling of the photoexcited carriers through the potential barriers, and a rate equation for the holes that incorporates photogeneration and recombination. The photoexciting laser acts as a damping factor ending the oscillations when its power is large enough. The model explains: (i) the known oscillatory static I-V characteristic curve through the formation of a domain wall connecting high and low electric field domains, and (ii) the photocurrent and photoluminescence time-dependent oscillations after the domain wall is formed. In our model, they arise from the combined motion of the wall and the shift of the values of the electric field at the domains. Up to a certain value of the photoexcitation, the non-uniform field profile with two domains turns out to be metastable: after the photocurrent oscillations have ceased, the field profile slowly relaxes toward the uniform stationary solution (which is reached on a much longer time scale). Multiple stability of stationary states and hysteresis are also found. An interpretation of the oscillations in the photoluminescence spectrum is also given.Comment: 34 pages, REVTeX 3.0, 10 figures upon request, MA/UC3M/07/9

Stationary states and phase diagram for a model of the Gunn effect under realistic boundary conditions

A general formulation of boundary conditions for semiconductor-metal contacts follows from a phenomenological procedure sketched here. The resulting boundary conditions, which incorporate only physically well-defined parameters, are used to study the classical unipolar drift-diffusion model for the Gunn effect. The analysis of its stationary solutions reveals the presence of bistability and hysteresis for a certain range of contact parameters. Several types of Gunn effect are predicted to occur in the model, when no stable stationary solution exists, depending on the value of the parameters of the injecting contact appearing in the boundary condition. In this way, the critical role played by contacts in the Gunn effect is clearly stablished.Comment: 10 pages, 6 Post-Script figure

Generalized drift-diffusion model for miniband superlattices

A drift-diffusion model of miniband transport in strongly coupled superlattices is derived from the single-miniband Boltzmann-Poisson transport equation with a BGK (Bhatnagar-Gross-Krook) collision term. We use a consistent Chapman-Enskog method to analyze the hyperbolic limit, at which collision and electric field terms dominate the other terms in the Boltzmann equation. The reduced equation is of the drift-diffusion type, but it includes additional terms, and diffusion and drift do not obey the Einstein relation except in the limit of high temperatures.Comment: 4 pages, 3 figures, double-column revtex. To appear as RC in PR