A general analytical method for finding the quantum capacitance of graphene

The quantum capacitance of graphene has been modeled in numerous articles using approximate analytical expressions and numerical methods. However, no article shows how to analytically find the quantum capacitance of graphene for the full temperature range and for any Fermi level. This, of course, wo...

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Bibliographic Details
Published in:Journal of computational electronics 2018-09, Vol.17 (3), p.1268-1275
Main Author: Selvaggi, Jerry P.
Format: Article
Language:English
Subjects:
Approximation
Astrophysics
Bilayers
Capacitance
Electrical Engineering
Engineering
Fermi level
Graphene
Integrals
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mechanical Engineering
Numerical analysis
Numerical methods
Optical and Electronic Materials
Temperature
Theoretical
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Summary:The quantum capacitance of graphene has been modeled in numerous articles using approximate analytical expressions and numerical methods. However, no article shows how to analytically find the quantum capacitance of graphene for the full temperature range and for any Fermi level. This, of course, would require a complete analytical evaluation of Fermi–Dirac-type integrals valid for any temperature. This article will illustrate a method for finding the quantum capacitance of monolayer graphene in the presence of electron–hole puddles for any Fermi level and for any temperature. The method employed is easily generalized to find the quantum capacitance of bilayer graphene as well as any other material when the density of states is a known function of energy.
ISSN:1569-8025
1572-8137
DOI:10.1007/s10825-018-1202-0