How can we calculate the Fermi velocity of doped graphene? Usually the inter atomic distance is used in the calculations, however, the inter atomic distance in doped graphene varies between C-C atoms and dopants-C atoms. In this case, how can we calculate Fermi velocity?
Is there any reference for the calculation of Fermi velocity/carrier mobility and effective masses in silicon carbide?
Thank you.
Fermi velocity is defined as (3*pi*Rho0)^1/3 = 1.917/rw-s. in atomic units (1a.u = 2.18 10^6 m/s), where rw-s=1.389*[A /(N*density)]. rw-s is Wigner-Seitz radius, A is atomic weight in g, and N is valence electrons number.
Graphene rw-s~1.53 a.u., resulting vF= 2.73 10^6 m/s. In order to find the value of doped graphene you need to determine rw-s, i.e, find the value of A and density.
Thank you for your comment. In case of band gap, we cannot calculate Fermi velocity anymore, as it is related to Fermi energy. We generally use an equation for parabolic band structure by taking double derivative of energy with respect to momentum space to calculate the effective mass of electron or hole. But in case of linear dispersion band, it is no any more valid. Could you please suggest any method to calculate the mobility of the material through its linear dispersion of band structure with band gap or mobility of carriers at Dirac point?
Aguiar is, I think, assuming free electron mass. But there is no effective mass in graphene! The ration between energy and momentum is constant, like a photon. So the electron just goes with a constant velocity of 1/300th the speed of light.
See this paper:
doi:10.1038/nature04233
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