The stationary semiconductor device equations
The stationary semiconductor device equations
Semiconductor equations
A finite element approximation theory for the drift diffusion semiconductor model
SIAM Journal on Numerical Analysis
On the stationary quantum drift-diffusion model
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
The Stationary Current-Voltage Characteristics of the Quantum Drift-Diffusion Model
SIAM Journal on Numerical Analysis
Convex analysis and variational problems
Convex analysis and variational problems
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Quantum-corrected drift-diffusion models for transport in semiconductor devices
Journal of Computational Physics
Entropic Discretization of a Quantum Drift-Diffusion Model
SIAM Journal on Numerical Analysis
An entropic quantum drift-diffusion model for electron transport in resonant tunneling diodes
Journal of Computational Physics
Beyond the conventional transistor
IBM Journal of Research and Development
Ballistic FET modeling using QDAME: quantum device analysis by modal evaluation
IEEE Transactions on Nanotechnology
Journal of Computational Electronics
Hi-index | 31.45 |
This article deals with the analysis of the functional iteration, denoted Generalized Gummel Map (GGM), proposed in [C. de Falco, A.L. Lacaita, E. Gatti, R. Sacco, Quantum-Corrected Drift-Diffusion Models for Transport in Semiconductor Devices, J. Comp. Phys. 204 (2) (2005) 533-561] for the decoupled solution of the Quantum Drift-Diffusion (QDD) model. The solution of the problem is characterized as being a fixed point of the GGM, which permits the establishment of a close link between the theoretical existence analysis and the implementation of a numerical tool, which was lacking in previous non-constructive proofs [N.B. Abdallah, A. Unterreiter, On the stationary quantum drift-diffusion model, Z. Angew. Math. Phys. 49 (1998) 251-275, R. Pinnau, A. Unterreiter, The stationary current-voltage characteristics of the quantum drift-diffusion model, SIAM J. Numer. Anal. 37 (1) (1999) 211-245]. The finite element approximation of the GGM is illustrated, and the main properties of the numerical fixed point map (discrete maximum principle and order of convergence) are discussed. Numerical results on realistic nanoscale devices are included to support the theoretical conclusions.