All Chapters Included
, 2.1 (a)
k = 8.617 × 10 −5 eV/K
0.66 eV
ni (T = 300 K) = 1.66 × 1015(300 — cm−3
2 (8.617 × 10−5 eV/K) (300 K)
K)3/2exp
= 2.465 × 1013 cm−3 0.66 eV
—
2 (8.617 × 10−5 eV/K) (600 K)
ni (T = 600 K) = 1.66 × 1015(600 cm−3
K)3/2exp
= 4.124 × 1016 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 21.465 × 10
13
.08×101
= 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× 1016
0
1.54×101 =
26.8 times higher than that in Si.
5
(b) Since phosphorus is a Group V element, it is a donor, meaning ND = 5 × 1016 cm− 3. For
an n-type material, we have:
16 −3
n = ND = 5 × 10 cm
2
[ni(T = 300 K)]
p(T = 300 K) = = 1.215 × 1010 cm−3
n 2
[ni(T = 600 K)]
p(T = 600 K) = = 3.401 × 1016 cm−3
n