Solutions Manual for Semiconductor Physics and Devices: Basic Principles, 4th Edition by Donald A. Neamen – Complete Step-by-Step Solutions

All Chapters Covered
g g




SOLUTION MANUAL
g

, SemiconductorgPhysicsgandgDevices:gBasicgPrinciples,g3rdgedition Chapterg1
SolutionsgManual ProblemgSolutions


Chapter 1
F 4 r I
g
3g
Problem Solutions g g g




1.1
4 atoms per cell, so atom vol.  4G
g g g
H 3 JK g g g g g
gg


(a) fcc:g8gcornergatomsg g 1/8g=g1gatomg Then
6gfacegatomsg g ½ =g3gatoms F4r IJ
4G
3



H3 K  100%  Ratio  74%
g

Totalgofg4gatomsgpergunitgcell
Ratio  g g g gg g g

(b) bcc:g8gcornergatomsg g 1/8g=g1gatomg
3
16g g 2grg
1genclosedgatom =g1gatom (c) Body-centeredgcubicglattice
Totalgofg2gatomsgpergunitgcell 4
dg g 4rg g a 3 gag  r
(c)g Diamond:g8gcornergatomsg g 1/8g=g1gatom
6gfacegatomsg g ½ =g3gatoms g4
3
F I 3




3 K F 4 r I
4genclosedgatoms
Unitgcellgvol.g g ag  r
3g
=g4gatoms g
g g
3g

gTotalgofg8gatomsgpergunitgcell


H
1.2 2gatomsgpergcell,gsogatomgvol.g g2 GH 3 JK
F 4 r I
gg
(a)g 4gGagatomsgpergunitgcell
4 Then 3g
Densityg   g


2G
H 3 JK
g



b 5.65x10
8g
g
3


3
g g

DensitygofgGaggg 2.22gx10 Ratiog g68%
22g
Ratio 
F4r I  100% 
cm g g g
3

4gAsgatomsgpergunitgcell,gsogthatg
3 g
DensitygofgAsg gg2.22gx10 cm
22g

(d)g Diamondglattice
(b) 8
Bodygdiagonalg gdg g8rg g3a 3 gag 
FI
8gGegatomsgpergunitgcell r
Densityg  8 g8rg
3

b5.65x10 g g
8g 3


3
Unit cell vol.  a 
g g
H 3 K F 4 r I
g g
3g
g g
DensitygofgGeggg4.44gx10
22g 3g
cm g g




1.3
8 atoms per cell, so atom vol. 8G
g g g
H 3 JK g g g g
gg



8G 4r J
gcellgvolg g ag g 2r
g2rg8rg3 Then

HF3 K I 100% Ratio 34%
(a) Unit
Simple gcubicglattice;
3g g ag 3g 3



F 4 r I
g

3g
g g g g g


1 atom per cell, so atom vol.  1G J
Ratio
g g g
H 3 K
g g g g g g
F8r I 3g
  

H 3K
g g


Then
FG4r IJ 3g



H 3 K  100%  Ratio  52.4%
g


g
g
g
1.4
Ratio  g g g g g FromgProblemg1.3,gpercentgvolumegofgfccgatomsg
3
8rg isg74%;g Thereforegaftergcoffeegisgground,
(b) Face-centeredgcubicglattice Volumeg g0.74gcm
3

d
dg g 4rg g a 2 g g ag  g 2g g 2g r
2

Unitgcellgvolg gag g
3g
c2 2 rh  16 2 r
g g
3g
g g
3
g g




3

,SemiconductorgPhysicsgandgDevices:gBasicgPrinciples,g3rdgedition Chapterg1
SolutionsgManual ProblemgSolutions

 Thengmassgdensitygis
23
1.5  4.85x10
gg
b g
8 
(a)
ag g5.43g A
 Fromg1.3d,g ag  r 2.8x10
8g 3g

3
g g2.21ggmg/gcm
3

ag g 3 5.43g 3 
sogthatg rg   g1.18gA
8 8
Centergofgonegsilicongatomgtogcentergofgnearest 1.8
(a) a 3gg22.2gg21.8gg8g A


neighborg g 2rg  2.36g A
sogthat 
(b) Numbergdensity 
ag g4.62g A
b g
g 8  3
Densityg g5x10 cm
3g 22g
8g
5.43x10 1 22 3
DensitygofgAg   1.01x10g cm
(c) Massgdensity

b
28.09 g b4.62 x10 g g
8 3



NggAt.Wt.
22g
5x10 1
g g    1.01x10 cm
22g 3




b g 
23
NA 6.02gx10 DensitygofgBg g 8g
4.62gx10 g
g g2.33ggramsg/gcm (b) Samegasg(a)
3

(c) Samegmaterial

1.6 1.9
(a) ag g2rA g21.02gg2.04g A

(a) Surfacegdensity
Now 1 1
 2  
2rg g2rg g a 3 g2rg g 2.04 3 g2.04 ag 2 g
g g
A B B

sogthatg g rgB g0.747g A 3.31x10 cm
14g 2


(b) A-type;g1gatomgpergunitgcell SamegforgAgatomsgandgBgatoms
1
Densityg  (b) Samegasg(a)
b g

8g 3g (c) g Samegmaterial
2.04gx10
23g 3
Density(A)g=g1.18x10 cm 1.10
B- 1
(a) Volgdensity 
type:g1gatomgpergunitgcell,gs ao
3

23g
ogDensity(B)g=g1.18x10 cm 1
3
2

1.7  Surfacegdensityg  ago 2

(b) 
 (b)g Samegasg(a)
agg1.8gg1.0g ag g2.8g A





(c) 1.11
 1 g2g Sketch
3
Na:gDensityg  g 2.28x10
22g
cm
g

1.12
3
Cl:gDensityg(samegasgNa)g g2.28x10
22g
cm (a)
(d) FH1 , 1 ,1IK  (313)
g
g
g
g g
Na:gAt.Wt.g=g22.99gC 1 3 1
g g g




F1 1 1 I 121
l:gAt.gWt.g=g35.45 (b)
So,gmassgpergunitgcell g g g g

1 1
g22.99gg g35.45 H 4 , 2 , 4 K 
gg
g
g g
g
gg





g g2 2 23
g
g4.85x10
23
6.02gx10

4

, SemiconductorgPhysicsgandgDevices:gBasicgPrinciples,g3rdgedition Chapterg1
SolutionsgManual ProblemgSolutions



b g
1.13 g 2gatoms
2g
 14g 2
(a) Distancegbetweengnearestg(100)gplanesgis: 4.50x10
8g 9.88x10 cm

dg gag g5.63g A
(b) Distancegbetweengnearestg(110)gplanesgis: (ii) (110)gplane,gsurfacegdensity,
2gatoms 2
1 a 5.63  g 6.99gx10 cm
14g

dg g ga 2   g
2 2 2
or (iii) (111)gplane,gsurfacegdensity,
dg g3.98g A

FH31
g gg  3 1
g g gg g IK 4
(c) Distancegbetweengnearestg(111)gplanesgis: 6 2g
g 
g

1 a 5.63 3 2
g

dg g ga 3   a
3 3 3 2
15g 2
or or 1.14gx10 cm

dg g3.25g A
1.15
1.14 (a)
(a) (100)gplanegofgsilicong–gsimilargtogagfcc,
Simplegcubic:g ag g4.50g A
 2gatoms
surfacegdensity g
b g

8g 2g
(i) (100)gplane,gsurfacegdensity, 5.43x10
1 atom 2 2


b g
g  4.94gx10 cm
14g 14g
6.78x10 cm
8g 2g
4.50x10 (b)
(ii) (110)gplane,gsurfacegdensity, (110)gplane,gsurfacegdensity,
2 2
g 3.49gx10 cm  g g 9.59gx10 cm
14g 14g
= 1gatom 4gatoms

b4.50x10 g
2g
8g 2
g



(iii) (111) plane, surface density, (c)

3 F Iatoms
g g g

(111)gplane,gsurfacegdensity,
HK
1 1
4gatoms 2
 g g 7.83x10g g cm
14
g g
6g  2  1

ca 2 hx
1 2 g 2
1 ag 3 3ag
g g g
gag g 2g
2 2 2
1 1.16
2
  2.85x10 cm
14g

g dg g 4rg g a 2
 then
(b) 4r 42.25

Body-centeredg cubic ag   g6.364g A
(i) (100)gplane,gsurfacegdensity, 2 2
14g 2 (a)
Samegasg(a),(i);gsurfacegdensityg 4.94x10 cm
4gatoms
VolumegDensityg 
b g
(ii) (110)gplane,gsurfacegdensity, 8 
6.364gx10 3
2 atoms 2


b g
  6.99gx10 cm
14

8g 2g 22g 3
2g 4.50x10 1.55x10 cm
(iii) (111)gplane,gsurfacegdensity, (b)
14g 2 Distancegbetweeng(110)gplanes,
Samegasg(a),(iii),gsurfacegdensityg 2.85x10 cm
1 a 6.364
(c) g ga 2   
Facegcenteredgcubic 2 2 2
(i) (100)gplane,gsurfacegdensity or




5