can we say these two velocities are equal, just in a degeneracy state?
VD=VthF1/2(η)/F0(η)
when : Vth=(2kBT/m*)1/2 Γ(3/2)/Γ(1)
then : VD=(2kBT/m*)1/2 Γ(3/2)F1/2(η)/Γ(1)F0(η) is for a 2D material.
is this equation correct? and why?
note that
VD=j/nq : is drift velocity
F1/2 : fermi-dirac integral of order 1/2
Γ : Gamma function
The drift velocity of electrons in a metal is given by the equation
I=enAvD4000
where I is the electric current in the metal wire, n is the number of electron density, A is the cross sectional area of the metal wire and vD is the drift velocity.
From this we get
vD=IenA
The thermal velocity is given by
12mev2T=32kBT
where T is the temperature of the metal, kB is Boltzmann’s constant, me is electron mass and vT is the thermal velocity. From the last equation we get
vT=3kBTme
Equating vD and vT gives the following
Condition for the two speeds to be equal:
IenA=3kBTme
this is classical thermal velocity whereas the velocities which I mentioned here are quantized velocities.
Dear Sabah
Yes there is relation between the drift velocity and the saturation velocity.
Please see this thesis it will help you very much
[The MOBILITY AND SATURATION VELOCITY IN GRAPHENE ON SILICON DIOXIDE
BY VINCENT E. DORGAN
THESIS
University of Illinois at Urbana-Champaign, 2010}
In this website (https://www.ideals.illinois.edu/bitstream/handle/2142/16801/dorgan_vincent.pdf?sequence=2)
Hope this what you look for.
Best wishes
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