Density of electrons and holes The density of occupied states per unit volume and unit energy, n(E), is the product of the density of states in the conduction band g.(E) and the Fermi function f(E): n(E) = g(E)f(E) E E. EA Conduction band Ec Eg Correspondingly for the density for holes p(E) is: p(E) = g(E)[1 − ƒ (E)] Ev о Valence band n = n₁ Ec EF EF Ev p = n₁ 0 0.5 1.0 N(E) F(E) n(E) and p(E) The total density of charge carriers (concentration) is obtained by integrating the product of the density of states and the Fermi/Boltzmann function over all possible energies. For electrons, the integral is taken from the bottom of the conduction band Ę up to the positive infinity. For holes - from the top of the valence band down to negative infinity. no = ཆུ 4π(2m)³/2 h³ E- Ec exp - (E — EF) | dE kT n-electron concentration, p - hole concentration. A common unit is [cm³]. Electron and hole concentrations n = Ne -(E-E₁)/KT 13/2 2лm,kT N = 2 h² N is the effective density of states of the conduction. p = N₁e¯(Eƒ—E₁)/kT 13/2 N₁ = 2 2πmpkT h² ༡ N, is the effective density of states of the valence band. The closer Fermi level to Ę, the greater n. The closer Fermi level to E,, the larger p. At room temperature: for silicon N = 2.8×1019 cm³ and N₁ = 1.04×1019 cm-3 for germanium N = 1×1019 cm³ and N, = 5×1018 cm³ Effective density of states 1. Calculate effective density of states of the conduction and valance bands in GaAs at temperature 100°C. 2. Calculate effective density of states of the conduction and valance bands in Si and Ge at temperature 150°C. 3. Compare your calculations in Problem 2 with N and N, in silicon and germanium at room temperature.
Density of electrons and holes The density of occupied states per unit volume and unit energy, n(E), is the product of the density of states in the conduction band g.(E) and the Fermi function f(E): n(E) = g(E)f(E) E E. EA Conduction band Ec Eg Correspondingly for the density for holes p(E) is: p(E) = g(E)[1 − ƒ (E)] Ev о Valence band n = n₁ Ec EF EF Ev p = n₁ 0 0.5 1.0 N(E) F(E) n(E) and p(E) The total density of charge carriers (concentration) is obtained by integrating the product of the density of states and the Fermi/Boltzmann function over all possible energies. For electrons, the integral is taken from the bottom of the conduction band Ę up to the positive infinity. For holes - from the top of the valence band down to negative infinity. no = ཆུ 4π(2m)³/2 h³ E- Ec exp - (E — EF) | dE kT n-electron concentration, p - hole concentration. A common unit is [cm³]. Electron and hole concentrations n = Ne -(E-E₁)/KT 13/2 2лm,kT N = 2 h² N is the effective density of states of the conduction. p = N₁e¯(Eƒ—E₁)/kT 13/2 N₁ = 2 2πmpkT h² ༡ N, is the effective density of states of the valence band. The closer Fermi level to Ę, the greater n. The closer Fermi level to E,, the larger p. At room temperature: for silicon N = 2.8×1019 cm³ and N₁ = 1.04×1019 cm-3 for germanium N = 1×1019 cm³ and N, = 5×1018 cm³ Effective density of states 1. Calculate effective density of states of the conduction and valance bands in GaAs at temperature 100°C. 2. Calculate effective density of states of the conduction and valance bands in Si and Ge at temperature 150°C. 3. Compare your calculations in Problem 2 with N and N, in silicon and germanium at room temperature.
Physical Chemistry
2nd Edition
ISBN:9781133958437
Author:Ball, David W. (david Warren), BAER, Tomas
Publisher:Ball, David W. (david Warren), BAER, Tomas
Chapter12: Atoms And Molecules
Section: Chapter Questions
Problem 12.22E: Write a Slater determinant for the lithide ion, Li.
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Question
Please answer 1, 2 and 3 on the end
![Density of electrons and holes
The density of occupied states per
unit volume and unit energy, n(E), is
the product of the density of states in
the conduction band g.(E) and the
Fermi function f(E):
n(E) = g(E)f(E)
E
E.
EA
Conduction
band
Ec
Eg
Correspondingly for the density for
holes p(E) is:
p(E) = g(E)[1 − ƒ (E)]
Ev
о
Valence
band
n = n₁
Ec
EF
EF
Ev
p = n₁
0
0.5 1.0
N(E)
F(E)
n(E) and p(E)
The total density of charge carriers (concentration) is obtained by integrating the product of the density of states and the
Fermi/Boltzmann function over all possible energies. For electrons, the integral is taken from the bottom of the
conduction band Ę up to the positive infinity. For holes - from the top of the valence band down to negative infinity.
no =
ཆུ
4π(2m)³/2
h³
E- Ec exp
- (E — EF) |
dE
kT
n-electron concentration, p - hole concentration. A common unit is [cm³].
Electron and hole concentrations
n = Ne
-(E-E₁)/KT
13/2
2лm,kT
N = 2
h²
N is the effective density of states
of the conduction.
p = N₁e¯(Eƒ—E₁)/kT
13/2
N₁ = 2
2πmpkT
h²
༡
N, is the effective density of states
of the valence band.
The closer Fermi level to Ę, the greater n.
The closer Fermi level to E,, the larger p.
At room temperature:
for silicon N = 2.8×1019 cm³ and N₁ = 1.04×1019 cm-3
for germanium N = 1×1019 cm³ and N, = 5×1018 cm³
Effective density of states
1. Calculate effective density of states of the conduction and valance bands in
GaAs at temperature 100°C.
2. Calculate effective density of states of the conduction and valance bands in Si
and Ge at temperature 150°C.
3. Compare your calculations in Problem 2 with N and N, in silicon and
germanium at room temperature.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce0afc3b-3e57-4487-b673-cf6f07e8890b%2F3a92cf1e-2a1c-4302-962a-4f5212806ffe%2F6mul47w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Density of electrons and holes
The density of occupied states per
unit volume and unit energy, n(E), is
the product of the density of states in
the conduction band g.(E) and the
Fermi function f(E):
n(E) = g(E)f(E)
E
E.
EA
Conduction
band
Ec
Eg
Correspondingly for the density for
holes p(E) is:
p(E) = g(E)[1 − ƒ (E)]
Ev
о
Valence
band
n = n₁
Ec
EF
EF
Ev
p = n₁
0
0.5 1.0
N(E)
F(E)
n(E) and p(E)
The total density of charge carriers (concentration) is obtained by integrating the product of the density of states and the
Fermi/Boltzmann function over all possible energies. For electrons, the integral is taken from the bottom of the
conduction band Ę up to the positive infinity. For holes - from the top of the valence band down to negative infinity.
no =
ཆུ
4π(2m)³/2
h³
E- Ec exp
- (E — EF) |
dE
kT
n-electron concentration, p - hole concentration. A common unit is [cm³].
Electron and hole concentrations
n = Ne
-(E-E₁)/KT
13/2
2лm,kT
N = 2
h²
N is the effective density of states
of the conduction.
p = N₁e¯(Eƒ—E₁)/kT
13/2
N₁ = 2
2πmpkT
h²
༡
N, is the effective density of states
of the valence band.
The closer Fermi level to Ę, the greater n.
The closer Fermi level to E,, the larger p.
At room temperature:
for silicon N = 2.8×1019 cm³ and N₁ = 1.04×1019 cm-3
for germanium N = 1×1019 cm³ and N, = 5×1018 cm³
Effective density of states
1. Calculate effective density of states of the conduction and valance bands in
GaAs at temperature 100°C.
2. Calculate effective density of states of the conduction and valance bands in Si
and Ge at temperature 150°C.
3. Compare your calculations in Problem 2 with N and N, in silicon and
germanium at room temperature.
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