Graphene Conversion

Carrier density, Fermi energy, and Gate voltages

Carrier Density (n)

Fermi Energy (E_F)

Fermi Wavenumber (k_F)

v_F

Gate Voltage (SiO₂)

Thickness:

Gate Voltage (hBN)

Thickness:

Constants used: ε_r(SiO₂) = 3.9, ε_r(hBN) = 3.0

E_F = &hbar; v_F √(π n)

n = (E_F / (&hbar; v_F))² / π

n = ε₀ ε_r V_g / (e d)

k = E_F / (h c)