In this paper we derive a new hybrid model for drift diffusion 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 effects 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 effects 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 different devices, by means of Colsys software.
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