Journal of Computational Electronics

, Volume 12, Issue 2, pp 188–202 | Cite as

Gate-induced carrier density modulation in bulk graphene: theories and electrostatic simulation using Matlab pdetool

  • Ming-Hao Liu


This article aims at providing a self-contained introduction to theoretical modeling of gate-induced carrier density in graphene sheets. For this, relevant theories are introduced, namely, classical capacitance model (CCM), self-consistent Poisson-Dirac method (PDM), and quantum capacitance model (QCM). The usage of Matlab pdetool is also briefly introduced, pointing out the least knowledge required for using this tool to solve the present electrostatic problem. Results based on the three approaches are compared, showing that the quantum correction, which is not considered by the CCM but by the other two, plays a role only when the metal gate is exceedingly close to the graphene sheet, and that the exactly solvable QCM works equally well as the self-consistent PDM. Practical examples corresponding to realistic experimental conditions for generating graphene pnp junctions and superlattices, as well as how a background potential linear in position can be achieved in graphene, are shown to illustrate the applicability of the introduced methods. Furthermore, by treating metal contacts in the same way, the last example shows that the PDM and the QCM are able to resolve the contact-induced doping and screening potential, well agreeing with the previous first-principles studies.


Graphene Carrier density Quantum capacitance Self-consistent Poisson-Dirac method Superlattice pnp junction Bloch-Zener oscillation Contact doping 



The author thanks T. Fang and D. Jena for their illuminating suggestions, F.-X. Schrettenbrunner, J. Eroms, P. Rickhaus, and R. Maurand for sharing their experimental viewpoints, and V. Krueckl and K. Richter for valuable discussions. Financial supports from Alexander von Humboldt Foundation (former part of the work) and Deutsche Forschungsgemeinschaft within SFB 689 (present) are gratefully acknowledged.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikUniversität RegensburgRegensburgGermany

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