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A Hybrid Drift Diffusion Model: Derivation, Weak Steady State Solutions and Simulations
- Source :
- Mathematics for Applications. 2012, 1, č. 1, s. 37-55. ISSN 1805-3629.
- Publication Year :
- 2012
- Publisher :
- Brno University of Technology, 2012.
-
Abstract
- In this paper we derive a new hybrid model for drift di usion equations. This model provides a description of the quantum phenomena in the parts of the device where they are relevant, and degenerates to a semiclassical model where quantum e ects are negligible, so that the system can be considered classically. The study of quantum correction to the equation of state of an electron gas in a semiconductor with the assumption of localized quantum e ects leads to a further condition on the classical-quantum interface. Moreover, we prove the existence of weak solutions for our hybrid model. Finally, we present numerical results for di erent devices, by means of Colsys software.
- Subjects :
- drift diffusion
Physics
Equation of state
Steady state
quantum drift diffusion
hybrid model
transmission conditions
business.industry
Applied Mathematics
Macroscopic quantum phenomena
Semiclassical physics
Mathematics (miscellaneous)
Classical mechanics
Semiconductor
Quantum correction
Statistical physics
Fermi gas
business
Quantum
Subjects
Details
- ISSN :
- 18053629 and 18053610
- Volume :
- 1
- Database :
- OpenAIRE
- Journal :
- MATHEMATICS FOR APPLICATIONS
- Accession number :
- edsair.doi.dedup.....2b63753c10e76eebd01f726675431065