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SemiconductorPhysicsandDevices:BasicPrinciples,4theditionChapter4
ByD.A.NeamenProblemSolutions
______________________________________________________________________________________
Chapter4
4.1
whereandarethevaluesat300K.
(a)Silicon
(K)
(eV)
(cm)
(b)Germanium(c)GaAs
(K)
(cm)
(cm)
_______________________________________
4.2
Plot
_______________________________________
4.3
Bytrialanderror,K
(b)
Bytrialanderror,K
_______________________________________
4.4
AtK,
eV
AtK,
eV
or
oreV
Now
socm
_______________________________________
4.5
ForK,eV
ForK,eV
ForK,eV
ForK,
ForK,
ForK,
_______________________________________
4.6
Let
Then
Tofindthemaximumvalue:
whichyields
Themaximumvalueoccursat
(b)
Let
Then
Tofindthemaximumvalue
Sameaspart(a).Maximumoccursat
or
Theionizationenergyis
or
eV
_______________________________________
4.17
eV
eV
cm
Holes
eV
_______________________________________
4.18
eV
eV
cm
eV
_______________________________________
4.19
eV
eV
cm
p-type
_______________________________________
4.20
eV
cm
eV
cm
eV
eV
cm
_______________________________________
4.21
eV
cm
eV
cm
eV
eV
cm
_______________________________________
4.22
p-type
eV
cm
eV
cm
_______________________________________
4.23
cm
cm
cm
cm
_______________________________________
4.24
eV
eV
cm
Holes
eV
_______________________________________
4.25
eV
cm
cm
cm
eV
eV
cm
Holes
eV
_______________________________________
4.26
cm
eV
cm
eV
cm
cm
eV
eV
cm
_____________________________________
4.27
cm
eV
cm
eV
cm
cm
eV
eV
cm
_______________________________________
4.28
(a)
For,
Then
cm
(b)
cm
_______________________________________
4.29
So
Wefind
eV
_______________________________________
4.30
(a)
Then
cm
(b)
cm
_______________________________________
4.31
Fortheelectronconcentration
TheBoltzmannapproximationapplies,so
or
Define
Then
Tofindmaximum,set
or
whichyields
Fortheholeconcentration
UsingtheBoltzmannapproximation
or
Define
Then
Tofindmaximumvalueof,set
Usingtheresultsfromabove,
wefindthemaximumat
_______________________________________
4.32
Silicon:Wehave
Wecanwrite
For
eVandeV
wecanwrite
or
cm
Wealsohave
Again,wecanwrite
For
andeV
Then
or
cm
GaAs:assumeeV
Then
or
cm
AssumeeV
Then
or
cm
_______________________________________
4.33
Plot
_______________________________________
4.34
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
_______________________________________
4.35
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
_______________________________________
4.36
Ge:cm
(i)
or
cm
cm
(ii)
cm
cm
GaAs:cm
(i)cm
cm
(ii)cm
cm
(c)Theresultimpliesthatthereisonlyoneminoritycarrierinavolumeofcm.
_______________________________________
4.37
(a)Forthedonorlevel
or
(b)Wehave
Now
or
Then
or
_______________________________________
4.38
p-type
Silicon:
or
cm
Then
cm
Germanium:
or
cm
Then
cm
GalliumArsenide:
cm
and
cm
_______________________________________
4.39
n-type
cm
cm
cm
cm
_______________________________________
4.40
cm
n-type
_______________________________________
4.41
cm
Socm,
Thencm
sothatcm
_______________________________________
4.42
Plot
_______________________________________
4.43
Plot
_______________________________________
4.44
Plot
_______________________________________
4.45
socm
cm
_______________________________________
4.46
p-type
Majoritycarriersareholes
cm
Minoritycarriersareelectrons
cm
Boronatomsmustbeadded
Socm
cm
_______________________________________
4.47
n-type
cm
electronsaremajoritycarriers
cm
holesareminoritycarriers
socm
_______________________________________
4.48
ForGermanium
(K)
(eV)
(cm)
and
cm
(K)
(cm)
(eV)
_______________________________________
4.49
Forcm,eV
cm,eV
cm,eV
cm,eV
Forcm,eV
cm,eV
cm,eV
cm,eV
_______________________________________
4.50
cm
so
Now
Bytrialanderror,K
AtK,
eV
AtK,
eV
cm
eV
theneV
Closertotheintrinsicenergylevel.
_______________________________________
4.51
AtK,eV
K,eV
K,eV
AtK,
cm
AtK,
cm
AtK,
cm
AtKandK,
cm
AtK,
cm
Then,K,eV
K,eV
K,eV
_______________________________________
4.52
(a)
Forcm,eV
cm,eV
cm,eV
cm,eV
(b)
Forcm,eV
cm,eV
cm,eV
cm,eV
_______________________________________
4.53
or
eV
Impurityatomstobeaddedso
eV
(i)p-type,soaddacceptoratoms
(ii)eV
Then
or
cm
_______________________________________
4.54
so
or
cm
_______________________________________
4.55
Silicon
(i)
eV
(ii)eV
cm
cmAdditional
donoratoms
GaAs
(i)
eV
(ii)eV
cm
cmAdditional
donoratoms
_______________________________________
4.56
eV
eV
Forpart(a);
cm
cm
Forpart(b):
cm
cm
_______________________________________
4.57
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