310
5 Solid State Physics
5.39 The number of silicon atoms/m
3
n =
N 0 d
A
=
6.02 × 10
26
× 2,420
28
= 0.52 × 10
29
Let x be the fraction of impurity atom (donor). The general expression for the
conductivity is
σ = n n eμ n + n p eμ p
where n n and n p are the densities of the negative and positive charge carriers.
Because n n n p ,
σ ∼ = n n eμ n = xn p eμ n
x =
σ
n p eμ n
=
1.08
0.52 × 10 29 × 1.6 × 10 −19 × 0.13
=
9.985
10 10
or 1 part in 10
9 .
Note that in normal silicon the conductivity is of the order of 10
−4 (Ω− m)
−1 .
A small fraction of doping (10
−9 ) has dramatically increased the value by four
orders of magnitude.
5.40 n e = (4.83 × 10
21 )T
3/2 e
−Eg/2kT e/m
3
n Ge
n Si
= e
(ESi−EGe)/2kT
kT =
1.38 × 10
−23
× 400
1.6 × 10 −19
= 0.0345 eV
n Ge
n Si
= e
(1.14−0.7)/(2×0.0345)
= 588
5.41 kT =
1.38 × 10
−23
× 300
1.6 × 10 −19
= 0.0259 eV
n C
n Ge
= e
−(EGe−EC )/2K T
= e
−(5.33−07)/0.052
= e
−89
≈ 2.2 × 10
−39
5.42 I = I 0 [exp(eV/kT ) − 1]
where I 0 is the forward bias saturation current.
I = 8×10
−11
exp
0.5 × 1.6 × 10
−19
1.38 × 10 −23 × 300
− 1
= 19.7×10
−3 A = 19.7 mA
5.43 W =
2 0 r
e
(V 0 − V b )
1
N a
+
1
N d
1/2
where r is the relative permittivity, V b is the bias voltage applied to the junction (here V b = 0), N a and N d are carrier concentrations in n-type and p-type
respectively.
W =
2 × 8.85 × 10
−12
× 16 × 0.8
1.6 × 10 −19
1
1 × 10 23 +
1
2 × 10 22
1/2
= 0.29 μm