CarrierDensity

graphenemodeling.graphene.monolayer.CarrierDensity(mu, T, model)

Computes the carrier density directly from the band structure.

Parameters:

• mu (array-like, J) – Chemical potential \(\mu\)
• T (scalar, K) – Temperature \(T\)

Returns:

Return type:

array-like

Notes

When T>0, we use the standard formula of integrating the Fermi-Dirac distribution over the density of states \(\rho\) .

\[n = \int_{-\infty}^{\infty} \frac{1}{e^{(\epsilon-\mu)/k_BT}+1}\rho(\epsilon) d\epsilon\]

For graphene at T=0, this reduces to

\[n = \frac{\mu^2}{\pi\hbar^2 v_F^2}\]