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How does the electronic band structure of graphene change with varying levels of doping using density functional theory calculations?

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The electronic band structure of graphene is known for its unique properties, such as high electron mobility and a linear energy dispersion relation near the Dirac points. Doping graphene can significantly alter its electronic properties, making it a material of interest for various applications. Density functional theory  DFT  calculations can be used to study the changes in the electronic band structure of graphene upon doping.When graphene is doped, either by introducing impurities  substitutional doping  or by adsorbing atoms/molecules on its surface  adsorption doping , the electronic band structure changes in the following ways:1. Shift in Fermi level: Doping introduces additional charge carriers  electrons or holes  into the graphene lattice, which causes a shift in the Fermi level. For n-type doping  electron doping , the Fermi level moves upwards, while for p-type doping  hole doping , it moves downwards. This shift in the Fermi level can be observed in the DFT calculations as a change in the position of the Fermi energy relative to the valence and conduction bands.2. Modification of the bandgap: Pristine graphene is a zero-bandgap semiconductor, which limits its use in some electronic applications. Doping can open up a bandgap in graphene, making it a more suitable material for electronic devices. DFT calculations can be used to determine the size of the bandgap upon doping and to study its dependence on the doping concentration and the type of dopant.3. Changes in the band dispersion: The linear energy dispersion relation near the Dirac points in pristine graphene gives rise to its high electron mobility. Doping can modify the band dispersion, leading to changes in the electronic properties, such as carrier mobility and effective mass. DFT calculations can provide insights into these changes by analyzing the shape of the energy bands near the Dirac points.4. Localized states: In some cases, doping can introduce localized states in the band structure, which can affect the electronic properties of graphene. These localized states can be observed in the DFT calculations as peaks or dips in the density of states  DOS  plot.In summary, density functional theory calculations can be used to study the changes in the electronic band structure of graphene upon doping, providing valuable insights into the effects of doping on the electronic properties of this material. These insights can guide the design of graphene-based devices with tailored properties for specific applications.
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