1 (99)

Prévia do material em texto

Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 8 
By D. A. Neamen Problem Solutions 
______________________________________________________________________________________ 
 
 (a) 3.0aV V, 
41051.1 pN 
 (b) 4.0aV V, 
51017.7 pN 
 (c) 5.0aV V, 
71040.3 pN 
 
 Similarly, the total number of excess holes in 
 the n-region is found to be 
 
















 1exp
t
a
nopn
V
V
pALP 
 We find that 
 0.10pD cm 2 /s and 0.10pL m 
 Also 
 
  4
16
2102
1025.2
10
105.1



d
i
no
N
n
p cm 3 
 Then 
  
















  1exp1025.2 2
t
a
n
V
V
P 
 So 
 (a) 3.0aV V, 31041.2 nP 
 (b) 4.0aV V, 51015.1 nP 
 (c) 5.0aV V, 61045.5 nP 
_______________________________________ 
 
8.20 
 













 









kT
eV
kT
E
V
V
nI ag
t
a
i expexpexp2 
 Then 
 







 

kT
EeV
I
ga
exp 
 so 
 







 







 

kT
EeV
kT
EeV
I
I
ga
ga
22
11
2
1
exp
exp
 
 or 
 







 

kT
EEeVeV
I
I ggaa 2121
2
1 exp 
 We then have 
 







 





0259.0
525.032.0255.0
exp
1010
1010 2
6
3
gE
 
 or 
 
 
 
 
 







 

0259.0
59.0
exp10
23 gE
 
 Then 
    3
2 10ln0259.059.0 gE 
 or 
 769.02 gE eV 
_______________________________________ 
 
8.21 
 (a) We have 
 









pO
p
dnO
n
a
iS
D
N
D
N
AenI

112 
 which can be written in the form 
 2
iS nCI  
 







 







kT
ET
NNC
g
OcO exp
300
3
 
 or 
 







 

kT
E
CTI
g
S exp3 
 (b) Taking the ratio 
 







 







 









1
2
3
1
2
1
2
exp
exp
kT
E
kT
E
T
T
I
I
g
g
S
S 
 

























21
3
1
2 11
exp
kTkT
E
T
T
g 
 For 3001 T K, 0259.01 kT , 61.38
1
1

kT
 
 For 4002 T K, 03453.02 kT , 96.28
1
2

kT
 
 (i) Germanium: 66.0gE eV 
    96.2861.3866.0exp
300
400
3
1
2 






S
S
I
I
 
 or 1383
1
2 
S
S
I
I
 
 (ii) Silicon: 12.1gE eV 
    96.2861.3812.1exp
300
400
3
1
2







S
S
I
I
 
 or 
5
1
2 1017.1 
S
S
I
I
 
_______________________________________