Microelectronics Solutions Manual (3rd Edition, Razavi) | Step‑by‑Step Problem Explanations PDF

, 2.1 (a)

k= 8.617 × 10−5 eV/K
0.66 eV
— cm−3
n (T = 300 K) = 1.66 × 1015(300
2 (8.617 × 10−5 eV/K) (300 K)
K)3/2exp
0.66 eV
= 2.465 × 1013 cm−3 —
2 (8.617 × 10−5 eV/K) (600 K)
cm−3
n (T = 600 K) = 1.66 × 1015(600
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 2.465 ×10
13

1.08×101
= 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
1.54×101
=
26.8 times higher than that in Si.
(b) Since phosphorus is a Group V element, it is a donor, meaning ND = 5 × 10 16 cm −3. For
an n-type material, we have:

n= ND = 5 × 1016 cm−3
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