A Hybrid Drift Diffusion Model: Derivation, Weak Steady State Solutions and Simulations
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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.
Document typePeer reviewed
Document versionFinal PDF
SourceMathematics for Applications. 2012, 1, č. 1, s. 37-55. ISSN 1805-3629.
- 2012/1