Quantum Capacitance — Graphene DOS

Dirac cone band structure, quantum capacitance C_Q = e²·D(E_F)

Parameters

DOS graphene: D(E) = g_s g_v|E|/(2π(ℏv_F)²)
g_s=2 (spin), g_v=2 (valley)
C_Q = e²·D(E_F) [F/m²]
Dirac point: D(0) = 0 (linear bands)
Fermi energy: E_F = ℏv_F√(πn)
Fermi energy E_F:
C_Q (μF/cm²):
Carrier density n:
Regime: