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) = K₂T \n [exp (™ 7 In nëħ² mkgT || mº πη
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) = K₂T \n [exp (™ 7 In nëħ² mkgT || mº πη
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92b098b1-776e-4b52-a881-73cea01a37f4%2F71eba833-1e6a-459d-a7b5-968874843d36%2Fe3scprc_processed.png&w=3840&q=75)
Transcribed Image Text: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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