Abstract
The present work aims at formulating quantum energy-transport and drift-diffusion equations for charge transport in graphene from a quantum hydrodynamic model proposed in Luca and Romano (Ann. Phys. 406:30–53, 2019), obtained from the Wigner-Boltzmann equation via the moment method. Here, we only sketch the main ideas and show the most relevant formulas. Further developments are under current investigation by the authors. The interested reader can find the omitted details in the references. In analogy with the semiclassical case, we are confident that the energy-transport and drift-diffusion models have mathematical properties which allow an easier numerical treatment.
Highlights
Graphene, a monolayer of sp2-bonded carbon atoms, is the basis for graphite and a new material with immense potential in microelectronics for its exceptional electrical transport properties, like high conductivity and high charge mobility
If the length of the active area is of the order of few nanometers, quantum phenomena must be taken into account and a semiclassical description of charge transport is no longer adequate
The present work aims at formulating quantum energytransport and drift-diffusion models for a proper description of charge transport in
Summary
A monolayer of sp2-bonded carbon atoms, is the basis for graphite and a new material with immense potential in microelectronics for its exceptional electrical transport properties, like high conductivity and high charge mobility. The present work aims at formulating quantum energytransport and drift-diffusion models for a proper description of charge transport in. In [1] a quantum hydrodynamic model for charge transport in graphene is derived from a moment expansion of the Wigner-Boltzmann equation and the needed closure relations are obtained by adding quantum corrections based on the equilibrium Wigner function to the semiclassical model formulated in [2,3,4,5,6] by exploiting the Maximum Entropy Principle. From this hydrodynamic model, a quantum energy-transport and a quantum drift-diffusion model are deduced in the long time asymptotic limit. The last section is devoted to the deduction of a quantum energy-transport and a quantum drift-diffusion model
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