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Related Concept Videos

Continuous Charge Distributions01:17

Continuous Charge Distributions

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Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
The electric charge can also be subjected to an analogical...
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Charging Conductors By Induction01:15

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The Earth is a good conductor of electricity, and it is so big that it can be considered an infinite source or sink of charges. It can easily exchange charges with any matter.
Generally, conductors like metals do not allow any excess charge to be present on them. Any excess charge added to metals easily flows away, for example, when a metal is placed on the Earth. This process is called earthing.
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Electric Field of a Charged Disk01:23

Electric Field of a Charged Disk

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The simplest case of a surface charge distribution is the uniformly charged disk. Calculating its electric field also helps us calculate the electric field of a large plane of charge.
The system's symmetry is in the cylindrical directions across the plane of the charge. As a result, the electric fields created by various surface charge elements nullify each other in the direction parallel to the surface. Thereby, the resulting electric field is perpendicular to the plane. Since the disk is...
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Carrier Transport01:21

Carrier Transport

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The generation of electrical current in semiconductors is fundamentally driven by two mechanisms: drift and diffusion. These processes are essential for the functionality and performance of semiconductor-based devices.
Drift Current:
The drift of charge carriers is started by an external electric field (E). Charged particles, such as electrons and holes, experience an acceleration between collisions with lattice atoms. For electrons, this results in a drift velocity (vd) given by:
557
Charge on a Conductor01:26

Charge on a Conductor

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An interesting property of a conductor in static equilibrium is that extra charges on the conductor end up on its outer surface, regardless of where they originate. Consider a hollow metallic conductor with a uniform surface charge density. Since the conductor itself is in electrostatic equilibrium, there should not be any electric field inside the conductor. Now, assume a Gaussian surface enclosing the hollow portion. Applying Gauss's law, the inner surface of the hollow conductor will not...
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Electric Field of a Non Uniformly Charged Sphere01:22

Electric Field of a Non Uniformly Charged Sphere

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Gauss's law states that the electric flux through any closed surface equals the net charge enclosed within the surface. This law is beneficial for determining the expressions for the electric field for a particular charge distribution if the electric flux is known.
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...
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Fabrication of Gate-tunable Graphene Devices for Scanning Tunneling Microscopy Studies with Coulomb Impurities
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Modeling Hydrodynamic Charge Transport in Graphene.

Arif Can Gungor1, Stefan M Koepfli1, Michael Baumann1

  • 1Institute of Electromagnetic Fields (IEF), 8092 Zurich, Switzerland.

Materials (Basel, Switzerland)
|June 24, 2022
PubMed
Summary

New mathematical models accurately simulate graphene devices by addressing limitations in traditional solvers. These models capture unique electronic properties crucial for future graphene technology development.

Keywords:
Tesla valvecomputational semiconductorsdiscontinuous Galerkinfinite element methodgraphenehydrodynamic modelnonlinear modeling

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Nanotechnology

Background:

  • Graphene exhibits unique electronic properties like zero band gap and high carrier mobility.
  • Traditional drift-diffusion models fail to accurately simulate graphene's charge distribution and transport due to inherent simplifications.
  • Graphene's exotic carrier dynamics, including inertia and viscosity, are not captured by conventional semiconductor solvers.

Purpose of the Study:

  • To propose novel mathematical models for simulating graphene-based devices.
  • To overcome the limitations of traditional drift-diffusion models in accurately representing graphene's unique electronic behavior.
  • To enable the design and development of advanced graphene devices by providing accurate simulation tools.

Main Methods:

  • Developed a modified nonlinear Poisson's equation to solve for electrostatic charge distribution and Fermi level, incorporating gating and contact doping.
  • Implemented a hydrodynamic model to simulate carrier transport, accounting for effects like charge inertia and viscosity.
  • Applied the hydrodynamic model to a graphene Tesla-valve structure to demonstrate its capability in simulating rectification effects.

Main Results:

  • The modified Poisson's equation accurately models electrostatic behavior in graphene devices.
  • The hydrodynamic model successfully simulates carrier transport, including viscosity and collective motion effects.
  • Demonstrated rectification in a graphene Tesla-valve structure, validating the hydrodynamic model's predictive power.

Conclusions:

  • The proposed mathematical models provide accurate simulation capabilities for graphene devices.
  • These models capture unique graphene properties not addressed by conventional methods.
  • The developed simulation tools are essential for advancing the design and application of future graphene-based electronic devices.