The 2DEG in (iii) is patterned to produce a clean, quasi-1D channel. The current I through the channel is = Nev, where N = the number of electrons, e the electronic charge and = the electrons' group velocity. The number of electrons N(ɛ) = f(ɛ, µ)g(ɛ), where f (ɛ, u) =Fermi-Dirac distribution = 1 and g(ɛ) density of states = dn/dɛ. 1+exp() kBT (a). Write down the dispersion relation for free electrons of mass m. What is their group velocity v? (b). Find an expression for g(ɛ) involving the group velocity. Leave your answer in terms of v.
The 2DEG in (iii) is patterned to produce a clean, quasi-1D channel. The current I through the channel is = Nev, where N = the number of electrons, e the electronic charge and = the electrons' group velocity. The number of electrons N(ɛ) = f(ɛ, µ)g(ɛ), where f (ɛ, u) =Fermi-Dirac distribution = 1 and g(ɛ) density of states = dn/dɛ. 1+exp() kBT (a). Write down the dispersion relation for free electrons of mass m. What is their group velocity v? (b). Find an expression for g(ɛ) involving the group velocity. Leave your answer in terms of v.
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Transcribed Image Text:The 2DEG in (iii) is patterned to produce a clean, quasi-1D channel. The current I through
the channel is =
Nev, where N =
the number of electrons, e
the electronic charge and
= the electrons' group velocity. The number of electrons N(ɛ) = f(ɛ, µ)g(ɛ), where
f (ɛ, u) =Fermi-Dirac distribution =
1
and g(ɛ)
density of states = dn/dɛ.
1+exp()
kBT
(a).
Write down the dispersion relation for free electrons of mass m. What is their group
velocity v?
(b).
Find an expression for g(ɛ) involving the group velocity. Leave your answer in terms
of v.
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