Summary
A nonlocal (quantum) drift-diffusion equation for the electric field and the electron density is derived from a Wigner-Poisson equation modelling quantum vertical transport in strongly coupled semiconductor superlattices, by using a consistent Chapman-Enskog procedure. Numerical solutions for a device consisting of a n-doped superlattice placed in a n+-n-n+ diode under a constant voltage bias are presented and compared with those obtained by using a semiclassical approximation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
L. L. Bonilla and. Theory of nonlinear charge transport, wave propagation, and self-oscillations in semiconductor superlattices. J. Phys.: Condens. Matter, 14(R341–R381), 2002.
P.L. Bhatnagar, E.P. Gross, and M. Krook. A model for collision processes in gases. i. Small amplitude processes in charged and neutral one-component systems. Phys. Rev., 94:511–525, 1954.
V.L. Bonch-Bruevich, I.P. Zvyagin, and A.G. Mironov. Domain electrical instabilities in semiconductors. Consultants Bureau, New York, 1975.
L.L. Bonilla, R. Escobedo, and Á. Perales. Generalized drift-diffusion model for miniband superlattices. Phys. Rev. B, 68(241304):241304-1–241304-4, 2003.
A.A. Ignatov and V.I. Shashkin. Bloch oscillations of electrons and instability of space-charge waves in superconductor superlattices. Sov Phys. JETP, 66:526–530, 1987. [Zh. Eksp. Teor. Fiz. 93, 935 (1987)].
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bonilla, L., Escobedo, R. (2006). Quantum Kinetic and Drift-Diffusion Equations for Semiconductor Superlattices. In: Di Bucchianico, A., Mattheij, R., Peletier, M. (eds) Progress in Industrial Mathematics at ECMI 2004. Mathematics in Industry, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28073-1_10
Download citation
DOI: https://doi.org/10.1007/3-540-28073-1_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28072-9
Online ISBN: 978-3-540-28073-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)