Carrier Density and Quantum Capacitance Model for Doped Graphene

A complete all-region quantum capacitance model and carrier density for doped graphene is analytically derived. The proposed model is predicting the predominant quantities of interest such as individual electron/hole concentration (n/p), total sheet charge density
$(\mathbf{Q}_{sh})$
, and quantum capacitance
$(\mathbf{C}_{q})$
for both doped and undoped graphene once the positions of minimum conduction band edge
$(\mathbf{E}_{C})$
and maximum valence band edge
$(\mathbf{E}_{V})$
are known. The proposed analytical model is compatible for both doped (n-type and p-type) and undoped graphene. Accuracy of the proposed model is proved by comparing with both existing experimental and theoretical data. An excellent agreement with theoretical model in all-region and significantly acceptable agreement with experimental data in the outer region of Dirac point is observed. Both enhancement and reduction in
$\mathbf{C}_{q}$
for doped graphene is noticed while comparing with undoped graphene based on the positions of Dirac point. The carrier density and quantum capacitance are the starting point of nanoscale device modeling and hence, the proposed model discloses insight into the device modeling of doped graphene.