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Semiconductor Physics and Devices: Basic Principles, 4
th
 edition Chapter 3 
By D. A. Neamen Problem Solutions 
______________________________________________________________________________________ 
 
3.16 
 For A: 2kCE i 
 At 101008.0 k m 1 , 05.0E eV 
 Or    2119 108106.105.0  E J 
 So  210
1
21 1008.0108   C 
 38
1 1025.1 C 
 Now 
 
 38
234
1
2
1025.12
10054.1
2 





C
m

 
 311044.4  kg 
 or omm 






31
31
1011.9
104437.4
 
 omm 488.0 
 For B: 2kCE i 
 At 
101008.0 k m 1 , 5.0E eV 
 Or    2019 108106.15.0  E J 
 So  210
1
20 1008.0108   C 
 37
1 1025.1 C 
 Now 
 
 37
234
1
2
1025.12
10054.1
2 





C
m

 
 
321044.4  kg 
 or omm 






31
32
1011.9
104437.4
 
 omm 0488.0 
_______________________________________ 
 
3.17 
 For A: 2
2kCEE   
     210
2
19 1008.0106.1025.0   C 
 39
2 1025.6 C 
 
 
 39
234
2
2
1025.62
10054.1
2 







C
m

 
 
31108873.8  kg 
 or omm 






31
31
1011.9
108873.8
 
 omm 976.0 
 For B: 2
2kCEE   
     210
2
19 1008.0106.13.0   C 
 38
2 105.7 C 
 
 
 
 
 
 38
234
2
2
105.72
10054.1
2 







C
m

 
 
3210406.7  kg 
 or omm 






31
32
1011.9
10406.7
 
 omm 0813.0 
_______________________________________ 
 
3.18 
(a) (i) hE  
 or 
  
34
19
10625.6
106.142.1





h
E
 
 
1410429.3  Hz 
 (ii) 
14
10
10429.3
103





c
E
hc
 
 
51075.8  cm 875 nm 
(b) (i) 
  
34
19
10625.6
106.112.1





h
E
 
 
1410705.2  Hz 
 (ii) 
14
10
10705.2
103





c
 
 
410109.1  cm 1109 nm 
_______________________________________ 
 
3.19 
(c) Curve A: Effective mass is a constant 
Curve B: Effective mass is positive 
 around 0k , and is negative 
 around 
2

k . 
_______________________________________ 
 
3.20 
   OO kkEEE  cos1 
 Then 
      OkkE
dk
dE
  sin1 
   OkkE   sin1 
 and 
   OkkE
dk
Ed
  cos2
12
2