Abstract
If a constant voltage above a certain threshold is applied to a piece of semiconductor material with negative differential resistance periodic current oscillations are observed in certain parameter regimes. The current peaks are due to dipole waves which are generated periodically at one contact of the device and leave at the other contact. We give a refined analysis of the classical explanation of the Gunn effect as traveling waves on an infinite domain. We show that under appropriate boundary conditions multiple steady state solutions exist and that periodic solutions are generated by a Hopf bifurcation. A singular perturbation analysis of a steady moving dipole wave on a finite domain is given.
The work of this second author has been supported by the Fonds zur Förderung der wissenschaftlichen Forschung, Autria and by the Insitute for Mathematics and its Applications with funds provided by the National Science Foundation.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
L.L. Bonilla, Solitary waves in semiconductors with finite geometry and the Gunn effect, SIAM J.Appl.Math 51, Nr.3, (1991).
B.G. Bosch, R.W.H. Engelmann, Gunn Effect Electronics, Halsted Press, (1975).
M. Crandall and P. Rabinowitz, Bifurcation, perturbation of simple eigenvalues and linearized stability, Arch. Rat. Mech. Anal. 52, (1972), pp.161–181.
N. Fenichel, Geometric singular perturbation theory, Journal of Differential Equations 31, (1979), pp. 53–98.
J.B. Gunn, Microwave oscillations of current in III-V semiconductors, Solid State Comm.1, (1963), pp.88–91.
H. Kroemer, Nonlinear space-charge domain dynamics in a semiconductor with negative differential mobility, IEEE Trans. Electron Devices, Vol. Ed.-13, (1966), pp.27–40.
J.E. Marsden and M. McCracken, The Hopf Bifurcation and Its Applications, Springer, New York (1976).
P.A. Markowich, C.A. Ringhofer, and C. Schmeiser, Semiconductor Equations Springer, New York (1990).
B.K. Ridley, The inhibition of negative resistance dipole waves and domains in n-GaAs, IEEE Trans. Electron Devices, Vol. Ed.-13, (1966), pp.41–43.
M.P. Shaw, H.L. Grubin, and P.R. Solomon, The Gunn-Hilsum Effect, Academic Press, New York (1979).
S.M. Sze, Physics of semiconductor devices, 2nd. Ed., Wiley, New York (1981).
P. Szmolyan, Traveling waves in GaAs-semiconductors, Physica D 39, (1989), pp.393–404.
P. Szmolyan, Analysis of a singularly perturbed traveling wave problem, IMA-preprint 649 (1990), to appear SIAM J.Appl.Math.
P. Szmolyan, Transversal heteroclinic and homoclinic orbits in singular perturbation problems, J.Differential Equations 92, Nr.2, (1991), pp.252–281.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag New York, Inc.
About this paper
Cite this paper
Steinrück, H., Szmolyan, P. (1994). Analysis of the Gunn Effect. In: Coughran, W.M., Cole, J., Lloyd, P., White, J.K. (eds) Semiconductors. The IMA Volumes in Mathematics and its Applications, vol 59. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8410-6_22
Download citation
DOI: https://doi.org/10.1007/978-1-4613-8410-6_22
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-8412-0
Online ISBN: 978-1-4613-8410-6
eBook Packages: Springer Book Archive