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6c.2. The integrate the electron density n is the integral of the density state using the 2D density of
states and the Fermi-Dirac distribution,
EF
= [ƒ¥D(E) · 9(E) de
·
n =
Fermi - Dirac
distribution
density of state in 2D
per unit area
→ fFD(E): =
g²D (E)
1
eß(ε-μ) + 1
1 dN (2D)
A dE
To show that the chemical potential of a Fermi gas in two dimensions is,
H(T) = k¸T \n [exp (™
47 In [exp (m²) - 1]
mkgT
||
mº
πη

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