Complutense University Library

Motion of wave fronts in semiconductor superlattices


Carpio Rodríguez, Ana María and Bonilla , L.L. and Dell’Acqua, G. (2001) Motion of wave fronts in semiconductor superlattices. Physical Review E, 64 (3). ISSN 1539-3755

[img] PDF
Restringido a Repository staff only hasta 2020.


Official URL:


An analysis of wave front motion in weakly coupled doped semiconductor superlattices is presented. If a dimensionless doping is sufficiently large, the superlattice behaves as a discrete system presenting front propagation failure and the wave fronts can be described near the threshold currents J(i) (i= 1,2) at which they depin and move. The wave front velocity scales with current as \J-J(i)\(1/2). If the dimensionless doping is low enough, the superlattice behaves as a continuum system and wave fronts are essentially shock waves whose velocity obeys an equal area rule.

Item Type:Article
Uncontrolled Keywords:Gaas-alas superlattices; Electrtic-field domains; Charge-density waves; Boundary-conditions; Propagation; Oscillations; Dynamics; Systems; Chaos
Subjects:Sciences > Physics > Mathematical physics
ID Code:15056

H. T. Grahn, R. J. Haug, W. M¨uller and K. Ploog, Phys.

Rev. Lett. 67, 1618 (1991); J. Kastrup, H. T. Grahn,

K. Ploog, F. Prengel, A. Wacker and E. Sch¨oll, Appl.

Phys. Lett. 65, 1808 (1994); J. Kastrup, F. Prengel, H.

T. Grahn, K. Ploog and E. Sch¨oll, Phys. Rev. B 53, 1502


J. Kastrup, R. Klann, H.T. Grahn, K. Ploog, L.L.

Bonilla, J. Gal´an, M. Kindelan, M. Moscoso, and R.

Merlin, Phys. Rev. B 52, 13761 (1995); J. Kastrup, R.

Hey, K.H. Ploog, H.T. Grahn, L. L. Bonilla, M. Kindelan,

M. Moscoso, A. Wacker and J. Gal´an, Phys. Rev. B

55, 2476 (1997); E. Schomburg, K. Hofbeck, J. Grenzer,

T. Blomeier, A. A. Ignatov, K. F. Renk, D.G. Pavel’ev,

Yu. Koschurinov, V. Ustinov, A. Zukhov, S. Ivanov and

P.S. Kop’ev, Appl. Phys. Lett. 71, (1997); Y. Zhang, J.

Kastrup, R. Klann, K.H. Ploog and H. T. Grahn, Phys.

Rev. Lett. 77, 3001 (1996); K. J. Luo, H. T. Grahn, K.

H. Ploog and L. L. Bonilla, Phys. Rev. Lett. 81, 1290

(1998); J. C. Cao and X.L. Lei, Phys. Rev. B 60, 1871


L.L. Bonilla, J. Gal´an, J.A. Cuesta, F.C. Mart´ınez and J.

M. Molera, Phys. Rev. B 50, 8644 (1994); A. Wacker, in

Theory and transport properties of semiconductor nanostructures,

edited by E. Sch¨oll (Chapman and Hall, New

York, 1998). Chapter 10.

M. B¨uttiker and H. Thomas, Phys. Rev. Lett. 38, 78

(1977); A. Sibille, J. F. Palmier, F. Mollot, H. Wang and

J.C. Esnault, Phys. Rev. B 39, 6272 (1989).

L. L. Bonilla, M. Kindelan, M. Moscoso and S. Venakides,

SIAM J. Appl. Math. 57, 1588 (1997).

A. Carpio, L. L. Bonilla, A. Wacker and E. Sch¨oll, Phys.

Rev. E 61, 4866 (2000).

J. P. Keener, SIAM J. Appl. Math. 47, 556 (1987).

J.P. Keener and J. Sneyd, Mathematical Physiology

(Springer, New York, 1998). Chapter 9.

A. E. Bugrim, A.M. Zhabotinsky and I.R. Epstein, Biophys.

J. 73, 2897 (1997).

G Gr¨uner, Rev. Mod. Phys. 60, 1129 (1988); A.A. Middleton,

Phys. Rev. Lett. 68, 670 (1992).

H. S. J. van der Zant, T. P. Orlando, S. Watanabe and

S. H. Strogatz, Phys. Rev. Lett. 74, 174 (1995); S. Flach

and M. Spicci, J. Phys. C 11, 321 (1999).

M. L¨ocher, G.A. Johnson and E.R. Hunt, Phys. Rev.

Lett. 77, 4698 (1996).

F.R.N. Nabarro, Theory of Crystal Dislocations (Oxford

University Press, Oxford, 1967).

P. M. Chaikin and T. C. Lubensky, Principles of condensed

matter physics (Cambridge University Press,

Cambridge, 1995). Chapter 10.

A. Carpio and L.L. Bonilla, Phys. Rev. Lett. (2001), to


L. L. Bonilla, G. Platero and D. S´anchez, Phys. Rev. B

62, 2786 (2000).

L. L. Bonilla, in Nonlinear Dynamics and Pattern Formation

in Semiconductors and Devices, edited by F.-J.

Niedernostheide (Springer-Verlag, Berlin, 1995), page 1.

F. J. Higuera and L. L. Bonilla, Physica D 57, 161 (1992);

L. L. Bonilla, I. R. Cantalapiedra, G. Gomila and J. M.

Rub´ı, Phys. Rev. E 56, 1500 (1997).

Refs. [5] and [18] consider current self-oscillations mediated

by monopoles in SL with D = 0 or by dipoles in the

hiperbolic limit of the Gunn effect, respectively. We can

use these studies to describe self-oscillations in SL with

D 6= 0. The only thing we need to change is to substitute

our equal-area formulas (23) or (B2) instead of the

equal-area formulas considered in those papers.

If we have ln(0) ≤ un(0) such that u˙n ≥ D(un) (un+1 −

2un+un−1)/−v(un) (un−un−1)/+J−v(un), and ˙ ln ≤

D(ln) (ln+1−2ln+ln−1)−v(ln) (ln−ln−1)/+J −v(ln),

then ln(t) ≤ un(t) for all later times. ln(t) and un(t)

are called sub and supersolutions, respectively. See Ref.

[6]. The use of comparison principles is restricted to spatially

discrete or continuous differential equations which

are first order in time. For applications to parabolic partial

differential equations, see M.H. Protter and H.F.

Weinberger, Maximum principles in differential equations

(Springer, New York, 1984).

A. Carpio, S.J. Chapman, S. Hastings, J.B. McLeod, Eur.

J. Appl. Math. 11, 399 (2000).

S. Flach, Y. Zolotaryuk and K. Kladko, Phys. Rev. E 59,

6105 (1999). See paragraph below Eq. (27).

B. Zinner, J. Diff. Eqs. 96, 1 (1992); A.-M. Filip and S.

Venakides, Comm. Pure Appl. Math. 52, 693 (1999).

L. L. Bonilla, J. Statist. Phys. 46, 659 (1987).

B. W. Knight and G. A. Peterson, Phys. Rev. 147, 617

(1966); J. D. Murray, J. Fluid Mech. 44, 315 (1970).

Deposited On:03 May 2012 09:30
Last Modified:06 Feb 2014 10:15

Repository Staff Only: item control page