Soluções de Problemas de Física de Semicondutores

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Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 6 
By D. A. Neamen Problem Solutions 
______________________________________________________________________________________ 
6.16 
 1515 102108  ado NNn 
 15106 cm 3 
 
  4
15
262
104.5
106
108.1 



o
i
o
n
n
p cm 3 
(a) 
0
4
4
0
104.5
104
pp
o
o
p
R


 
 so 
8
0 1035.1 p s 
(b)   821
0 1035.1102  pgp  
 13107.2  cm 3 
(c) 8
0 1035.1  p s 
_______________________________________ 
 
6.17 
(a) (i)For 
71050  t s 
    0/
0 1 pt
p egtp



 
    0/720 1105105 pt
e
  
  0/14 1105.2 pt
e

 cm 3 
 At 7105 t s, 
  1/114 1105.2  ep 
 
141058.1  cm 3 
 For 
7105 t s 
     pOt
etp


/10514
7
1058.1

 cm 3 
 (ii)   147 1058.1105  p cm 3 
(b) (i) For 
61020  t s 
    0/14 1105.2 pt
etp



 cm 3 
 At 
6102 t s, 
 
    76 105/10214 1105.2
  ep 
 
1410454.2  cm 3 
 For 
6102 t s, 
     pOt
etp


/10214
6
10454.2

 cm 3 
 (ii)   146 10454.2102  p cm 3 
_______________________________________ 
 
6.18 
(a) For 
61020  t s 
   0/
0
nt
n egtn
  
    0/721 10510 nt
e
 
 0/14105 nt
e

 cm 3 
 
 
 
 At 6102 t s, 
 
   76 105/10214
1 105
  en 
 121016.9  cm 3 
 For 6102 t s 
   0/1214 11016.9105 nt
en
 
 
 121016.9  
   12/14 1016.9110908.4 0 
 nt
e

cm 3 
(b) (i)   141050 n cm 3 
(ii)   126 1016.9102  n cm 3 
(iii)   14105n cm 3 
_______________________________________ 
 
6.19 
 p-type; minority carriers - electrons 
   12000259.0





 nn
e
kT
D  
 08.31 cm 2 /s 
     2/16
0 1008.31  nnn DL  
 
310575.5  cm 
(a)     nLx
expxn
/14102

  cm 3 
(b) 
   nLx
nnn e
dx
d
eD
dx
nd
eDJ
/14102



 
   nLx
n
n e
L
eD /14102



 
 
   
 
nLx
e
/
3
1419
10575.5
10208.31106.1 




 
 nLx
n eJ
/
1784.0

 A/cm 2 
 Holes diffuse at same rate as minority carrier 
electrons, so 
 nLx
p eJ
/
1784.0

 A/cm 2 
_______________________________________ 
 
6.20 
(a) p-type; 
1410pOp cm 3 
 and 
 
  6
14
2102
1025.2
10
105.1



pO
i
pO
p
n
n cm 3 
(b) Excess minority carrier concentration 
 pOp nnn  
 At 0x , 0pn so that 
   61025.200  pOnn cm 3