Física de Semicondutores

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Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 8 
By D. A. Neamen Problem Solutions 
______________________________________________________________________________________ 
 
8.14 
 (a) 
 
p
nop
n
pon
n
pon
pn
n
L
peD
L
neD
L
neD
JJ
J



 
 
d
i
po
p
a
i
no
n
a
i
no
n
N
nD
N
nD
N
nD
22
2





 
 










d
a
pon
nop
N
N
D
D


1
1
 
 We have 
 
4.2
1

n
p
n
p
D
D


 and 
1.0
1

po
no


 
 so 
 











d
apn
n
N
NJJ
J
1.0
1
4.2
1
1
1
 
 or 
 
  










d
apn
n
N
NJJ
J
04.21
1
 
 (b) Using Einstein's relation, we can write 
 
d
i
p
p
a
i
n
n
a
i
n
n
pn
n
N
n
L
e
N
n
L
e
N
n
L
e
JJ
J
22
2



 

 
 
ap
p
n
dn
dn
Ne
L
L
Ne
Ne



 
 We have 
 dnn Ne  and app Ne  
 Also 
 90.4
1.0
4.2

pop
non
p
n
D
D
L
L


 
 Then 
 
 
  90.4

 pn
pn
pn
n
JJ
J


 
_______________________________________ 
 
 
 
8.15 
 (a) p-side; 
 









i
a
FFi
n
N
kTEE ln 
   










10
15
105.1
105
ln0259.0 
 or 
 329.0 FFi EE eV 
 Also on the n-side; 
 









i
d
FiF
n
N
kTEE ln 
   









10
17
105.1
10
ln0259.0 
 or 
 407.0 FiF EE eV 
 (b) We can find 
    4.320259.01250 nD cm 2 /s 
    29.80259.0320 pD cm 2 /s 
 Now 
 









pO
p
dnO
n
a
iS
D
N
D
N
enJ

112 
   21019 105.1106.1   
 











 717615 10
29.8
10
1
10
4.32
105
1
 
 or 
 1110426.4 SJ A/cm 2 
 Then 
   114 10426.410   SS AJI 
 or 
 1510426.4 SI A 
 We find 
 








t
D
S
V
V
II exp 
   





 
0259.0
5.0
exp10426.4 15 
 or 
 
61007.1 I A 07.1 A 
 (c) The hole current is 
 








t
D
po
p
d
ip
V
VD
N
AenI exp
12
