2.1 (a)
k = 8.617 × 10
−5
eV/K
n
i
(T = 300 K) = 1.66 ×10
15
(300 K)
3/2
exp
−
0.66 eV
2 (8.617 ×10
−5
eV/K) (300 K)
cm
−3
=
2.465 ×10
13
cm
−3
n
i
(T = 600 K) = 1.66 ×10
15
(600 K)
3/2
exp
−
0.66 eV
2 (8.617 ×10
−5
eV/K) (600 K)
cm
−3
=
4.124 ×10
16
cm
−3
Compared to the values obtained in Example 2.1, we can see that the intrinsic carrier concentration
in Ge at T = 300 K is
2.465×10
13
1.08×10
10
= 2282 times higher than the intrinsic carrier concentration in
Si at T = 300 K. Similarly, at T = 600 K, the intrinsic carrier concentration in Ge is
4.124×10
16
1.54×10
15
=
26.8 times higher than that in Si.
(b) Since phosphorus is a Group V element, it is a donor, meaning N
D
= 5 × 10
16
cm
−3
. For an
n-type material, we have:
n = N
D
=
5 × 10
16
cm
−3
p(T = 300 K) =
[n
i
(T = 300 K)]
2
n
=
1.215 × 10
10
cm
−3
p(T = 600 K) =
[n
i
(T = 600 K)]
2
n
=
3.401 × 10
16
cm
−3
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