Mathematical modelling of charge transport in graphene heterojunctions

Barletti, Luigi; Nastasi, Giovanni; Negulescu, Claudia; Romano, Vittorio

doi:10.3934/krm.2021010

“…A phase-space formulation can also be considered thanks to the Wigner formalism as proposed for instance in [25]. Finally, we mention that different description levels can be spatially coupled deriving quantum interface conditions as done in [3,2] in the case of graphene. In this work, since our aim is to focus on the numerical resolution of the Poisson equation and to present the efficiency of the proposed interface approach, we have chosen not to enrich the transport description and to perform (non realistic) self-consistent computations using (56).…”

Section: Drift-diffusion Poisson Couplingmentioning

confidence: 99%

An interface formulation for the Poisson equation in the presence of a semiconducting single-layer material

Jourdana¹,

Pietra²

2023

Preprint

0

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In this paper, we consider a semiconducting device with an active zone made of a single-layer material. The associated Poisson equation for the electrostatic potential (to be solved in order to perform self-consistent computations) is characterized by a surface particle density and an out-of-plane dielectric permittivity in the region surrounding the single-layer. To avoid mesh refinements in such a region, we propose an interface problem based on the natural domain decomposition suggested by the physical device. Two different interface continuity conditions are discussed. Then, we write the corresponding variational formulations adapting the so called three-fields formulation for domain decomposition and we approximate them using a proper finite element method. Finally, numerical experiments are performed to illustrate some specific features of this interface approach.

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“…Barletti et al derived a mathematical model describing a general graphene heterojunction device consisting of two classical regions (diffusive transport) and one middle active region (quantum transport) [251]. Where the first are modelled by a conventional drift-diffusion modeling approach, the latter is modelled by an interface where suitable transmission conditions are imposed, which take the quantum scattering process into account.…”

Section: D Materialsmentioning

confidence: 99%

Computational perspective on recent advances in quantum electronics: from electron quantum optics to nanoelectronic devices and systems

Weinbub

¹

,

Kosik

²

2022

J. Phys.: Condens. Matter

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Quantum electronics has significantly evolved over the last decades. Where initially the clear focus was on light-matter interactions, nowadays approaches based on the electron's wave nature have solidified themselves as additional focus areas. This development is largely driven by continuous advances in electron quantum optics, electron based quantum information processing, electronic materials, and nanoelectronic devices and systems. The pace of research in all of these areas is astonishing and is accompanied by substantial theoretical and experimental advancements. What is particularly exciting is the fact that the computational methods, together with broadly available large-scale computing resources, have matured to such a degree so as to be essential enabling technologies themselves. These methods allow to predict, analyze, and design not only individual physical processes but also entire devices and systems, which would otherwise be very challenging or sometimes even out of reach with conventional experimental capabilities. This review is thus a testament to the increasingly towering importance of computational methods for advancing the expanding field of quantum electronics. To that end, computational aspects of a representative selection of recent research in quantum electronics are highlighted where a major focus is on the electron's wave nature. By categorizing the research into concrete technological applications, researchers and engineers will be able to use this review as a source for inspiration regarding problem-specific computational methods.

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An interface formulation for the poisson equation in the presence of a semiconducting single-layer material

Jourdana,

Pietra

2024

ESAIM: M2AN

0

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In this paper, we consider a semiconducting device with an active zone made of a single-layer material. The associated Poisson equation for the electrostatic potential (to be solved in order to perform self-consistent computations) is characterized by a surface particle density and an out-of-plane dielectric permittivity in the region surrounding the single-layer. To avoid mesh refinements in such a region, we propose an interface problem based on the natural domain decomposition suggested by the physical device. Two different interface continuity conditions are discussed. Then, we write the corresponding variational formulations adapting the so called three-fields formulation for domain decomposition and we approximate them using a proper finite element method. Finally, numerical experiments are performed to illustrate some specific features of this interface approach.

show abstract

Mathematical modelling of charge transport in graphene heterojunctions

Cited by 5 publications

References 32 publications

An interface formulation for the Poisson equation in the presence of a semiconducting single-layer material

An interface formulation for the Poisson equation in the presence of a semiconducting single-layer material

Computational perspective on recent advances in quantum electronics: from electron quantum optics to nanoelectronic devices and systems

An interface formulation for the poisson equation in the presence of a semiconducting single-layer material

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