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Gunn effect: Instability of the steady state and stability of the solitary wave in long extrinsic semiconductors

Publication ,  Journal Article
Bonilla, LL; Higuera, FJ; Venakides, S
Published in: SIAM Journal on Applied Mathematics
January 1, 1994

A linear stability analysis of the stationary solution of a one-dimensional drift-diffusion model used to describe the Gunn effect in GaAs is performed. It is shown that for long semiconductor samples under dc voltage bias conditions, and small diffusivity, the steady state may lose stability via a Hopf bifurcation. In the limit of infinitely long samples, there is a quasicontinuum of oscillatory modes of the equation linearized about the steady state that a acquire positive real part for voltages larger than a certain critical value. The linear stability of the solitary wave characteristic of the Gunn effect is proved for an idealized electron velocity curve in the zero diffusion limit.

Duke Scholars

Published In

SIAM Journal on Applied Mathematics

DOI

ISSN

0036-1399

Publication Date

January 1, 1994

Volume

54

Issue

6

Start / End Page

1521 / 1541

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

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Bonilla, L. L., Higuera, F. J., & Venakides, S. (1994). Gunn effect: Instability of the steady state and stability of the solitary wave in long extrinsic semiconductors. SIAM Journal on Applied Mathematics, 54(6), 1521–1541. https://doi.org/10.1137/S0036139992236554
Bonilla, L. L., F. J. Higuera, and S. Venakides. “Gunn effect: Instability of the steady state and stability of the solitary wave in long extrinsic semiconductors.” SIAM Journal on Applied Mathematics 54, no. 6 (January 1, 1994): 1521–41. https://doi.org/10.1137/S0036139992236554.
Bonilla LL, Higuera FJ, Venakides S. Gunn effect: Instability of the steady state and stability of the solitary wave in long extrinsic semiconductors. SIAM Journal on Applied Mathematics. 1994 Jan 1;54(6):1521–41.
Bonilla, L. L., et al. “Gunn effect: Instability of the steady state and stability of the solitary wave in long extrinsic semiconductors.” SIAM Journal on Applied Mathematics, vol. 54, no. 6, Jan. 1994, pp. 1521–41. Scopus, doi:10.1137/S0036139992236554.
Bonilla LL, Higuera FJ, Venakides S. Gunn effect: Instability of the steady state and stability of the solitary wave in long extrinsic semiconductors. SIAM Journal on Applied Mathematics. 1994 Jan 1;54(6):1521–1541.

Published In

SIAM Journal on Applied Mathematics

DOI

ISSN

0036-1399

Publication Date

January 1, 1994

Volume

54

Issue

6

Start / End Page

1521 / 1541

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics