1.13 Boron atoms are added to a Si film resulting in an impurity density of 4 × 1016 cm³. (a) What is the conductivity type (N-type or P-type) of this film? (b) What are the equilibrium electron and hole densities at 300 K and 600 K? (c) Why does the mobile carrier concentration increase at high temperatures? (d) Where is the Fermi level located if T = 600 K? (b) At T = 300 K, since the intrinsic carrier density is negligible compared to the dopant concentration, p=N=4×10¹6 cm³³, and n = (n=10¹0 cm³)²/p = 2500 cm³. At T = 600 K, n₁ = √N (600K)N,(600K)e˜¯ -(E)/(2kT) =1.16×10¹5 cm³ where 3/2 3/2 N¸(T = 600 K) = 2 2π mankT T 'dn h² = 2.8×1019 × ст -³ = 7.92×10¹⁹ cm³ ст 300K and 3/2 N,(T = 600K)=2 2π mapkT h² = 1.04×1019 × 3/2 -3 ст = 2.94×1019 cm³. ст -3 2 300K The intrinsic carrier concentration is no more negligible compared to the dopant concentration. Thus, we have -3 ст = 4.12×10¹6 cm³, and p = Nã +n₁ = (4×10¹ +1.16×10¹³) cr a -3 n = n² / p = (1.16×10¹³ cm³ ³)²/4.12×10¹6 cm³ = 3.27×10¹³ cm³. ст The electron concentration has increased by many orders of magnitude.
1.13 Boron atoms are added to a Si film resulting in an impurity density of 4 × 1016 cm³. (a) What is the conductivity type (N-type or P-type) of this film? (b) What are the equilibrium electron and hole densities at 300 K and 600 K? (c) Why does the mobile carrier concentration increase at high temperatures? (d) Where is the Fermi level located if T = 600 K? (b) At T = 300 K, since the intrinsic carrier density is negligible compared to the dopant concentration, p=N=4×10¹6 cm³³, and n = (n=10¹0 cm³)²/p = 2500 cm³. At T = 600 K, n₁ = √N (600K)N,(600K)e˜¯ -(E)/(2kT) =1.16×10¹5 cm³ where 3/2 3/2 N¸(T = 600 K) = 2 2π mankT T 'dn h² = 2.8×1019 × ст -³ = 7.92×10¹⁹ cm³ ст 300K and 3/2 N,(T = 600K)=2 2π mapkT h² = 1.04×1019 × 3/2 -3 ст = 2.94×1019 cm³. ст -3 2 300K The intrinsic carrier concentration is no more negligible compared to the dopant concentration. Thus, we have -3 ст = 4.12×10¹6 cm³, and p = Nã +n₁ = (4×10¹ +1.16×10¹³) cr a -3 n = n² / p = (1.16×10¹³ cm³ ³)²/4.12×10¹6 cm³ = 3.27×10¹³ cm³. ст The electron concentration has increased by many orders of magnitude.
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question and solution to part be is shown. Im confused on that K equals too when solving for ni.
Transcribed Image Text:1.13 Boron atoms are added to a Si film resulting in an impurity density of 4 × 1016 cm³.
(a) What is the conductivity type (N-type or P-type) of this film?
(b) What are the equilibrium electron and hole densities at 300 K and 600 K?
(c) Why does the mobile carrier concentration increase at high temperatures?
(d) Where is the Fermi level located if T = 600 K?
Transcribed Image Text:(b) At T = 300 K, since the intrinsic carrier density is negligible compared to the dopant
concentration, p=N=4×10¹6 cm³³, and n = (n=10¹0 cm³)²/p = 2500 cm³.
At T = 600 K,
n₁ = √N (600K)N,(600K)e˜¯
-(E)/(2kT)
=1.16×10¹5 cm³
where
3/2
3/2
N¸(T = 600 K) = 2
2π mankT
T
'dn
h²
= 2.8×1019 ×
ст -³ = 7.92×10¹⁹ cm³
ст
300K
and
3/2
N,(T = 600K)=2
2π mapkT
h²
= 1.04×1019 ×
3/2
-3
ст
= 2.94×1019 cm³.
ст
-3
2
300K
The intrinsic carrier concentration is no more negligible compared to the dopant
concentration. Thus, we have
-3
ст = 4.12×10¹6 cm³, and
p = Nã +n₁ = (4×10¹ +1.16×10¹³) cr
a
-3
n = n² / p = (1.16×10¹³ cm³ ³)²/4.12×10¹6 cm³ = 3.27×10¹³ cm³.
ст
The electron concentration has increased by many orders of magnitude.
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