Mathematical Advances and Horizons for Classical and Quantum-Perturbed
Drift-Diffusion Systems: Solid State Devices and Beyond
By: Joseph W. Jerome
The classical drift-diffusion model employed in semi-conductor simulation
is now seen as part of a hierarchy of mathematical models designed to
capture the intricate patterns of current flow in solid-state devices.
These models include those incorporating quantum mechanical effects.
Scientific computation has vastly outpaced our mathematical understanding
of these models.
This article is restricted in its focus,
and describes mathematical
understanding achieved during the last few decades primarily
in terms of Gummel decomposition, as applied to drift-diffusion models
and the closely related family of quantum corrected
Drift-diffusion models are being
employed once again in organic devices, and in bio-chip devices,
and a re-examination is now seen as timely, as such studies proceed
beyond solid state devices.
This review article has now appeared: Journal of
Computational Electronics 8 (2009), 132--141.
Access is provided by Springerlink.com;
DOI information is: doi:10.1016/j.na.2009.05.047.