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Chapter 15 1
OutlineReading: Livingston, Chapter 15.1-15.3
A Review of Semiconductors Intrinsic Semiconductors
Electrons in Conduction Band and Holes in Valence Band Intrinsic
carrier concentration Fermi Energy
Extrinsic Semiconductors Dopants Complete ionization NeNh
product
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Chapter 15 2
Semiconductors: Review
Semiconductors have electrical and optical properties between
metals and insulators.
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Chapter 15 3
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Chapter 15 4
Intrinsic Semiconductors
Chapter 15
Ze(E)
Zh(E)
2/1)()( gee EECEZ =Amend equations used for metals
2/1)()( ECEZ hh =
3
2/3*)2(4hmC ee
= 3
2/3* )2(4hmC hh
=
TkEE BFeEF /)(1
1)(+
=
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Chapter 15 5
Total # of Electrons in Conduction Band
=g
BF
E
TkEEgee dEeEECN
/)(2/1)(
=
0
)](1)[( dEEFEZN hh
Total # of Hole in Valence Band
TkEECe
BFgeNN /)( =
TkEVh
BFeNN /=
3
2/3* )2(2h
TkmN BeC
=
3
2/3* )2(2h
TkmN BhV
=
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Chapter 15 6
Eliminate EF from the Equation
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Chapter 15 7
Intrinsic Carrier Concentration Bandgap and Temperature
7
( ) TkEVCi BgeNNN 2/2/1 =
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Chapter 15 8
Example: Fermi Level in Intrinsic Semiconductor
Chapter 15 8
Where is the Fermi level in intrinsic GaAs? How far is it from
midgap? The bandgap of GaAs is 1.42 eV.
Material me*/mo mh*/moSi 0.26 0.39Ge 0.55 0.37
GaAs 0.068 0.54
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Chapter 15 9
Example: Intrinsic Carrier Concentration and Bandgap
Which semiconductor has the largest intrinsic carrier
concentration?
Ec
Ev
Ec
EvEg = 5 eV
Eg = 1 eV
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Chapter 15 10
Example: Conductivity in Intrinsic Semiconductor
Calculate the conductivity of intrinsic silicon at room
temperature for e = 0.15 m2V-1s-1 and h = 0.05 m2V-1s-1. Assume me*
= 0.26mo, mh* = 0.39mo, and Eg = 1.1 eV.
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Chapter 15 11
Extrinsic Semiconductors
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Chapter 15 12
Extrinsic Semiconductors (cont.)
Ze(E)
Zh(E)
Ze(E)
Zh(E)
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Chapter 15 13
Extrinsic Semiconductors (cont.)For extrinsic semiconductors
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Chapter 15 14
Example: Carriers in an Extrinsic SemiconductorIf you add 1017
donor atoms/cm3 to a semiconductor with a 0.6 eV bandgap, what will
be the charge carrier concentrations in the valence and conduction
bands at T = 300K? Where is the Fermi level before and after
doping? Assume that the donors are fully ionized and that both the
hole effective mass and electron effective mass have the mass of a
free electron.
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Chapter 15 15
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Chapter 15 16
Example: Conductivity in Extrinsic SemiconductorWhat is the
conductivity of a silicon crystal doped with 5 x 1013 cm-3 atoms of
As? ni = 1010 cm-3, e = 1350 cm2V-1s-1, and h = 450 cm2V-1s-1.
Assume all dopants are ionized.
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Chapter 15 17
Semiconductors: How to Get Electrons into Conduction Band (and
Holes in the Valence Band)
1. Thermal Excitation
2. Optical Excitation
3. Dopants
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Chapter 15 18
Review Questions
1. Define intrinsic and extrinsic semiconductor.2. What is a
hole?3. Where is the Fermi energy in an intrinsic semiconductor?4.
If an intrinsic semiconductor has 1010 cm-3 holes, how many
electrons does it have?5. What is the majority carrier in n-type
material?6. What is the minority carrier in p-type material?7.
Donors are added to ________ type material?8. Where, in general, is
the Fermi energy in a p-type semiconductor ,
above or below Eg/2? And a n-type semiconductor?9. Assuming
complete ionization, what is the electron concentration in
an n-type semiconductor with 1010 cm-3 donor atoms?10. What does
the product of NeNh equal? Does this apply to intrinsic
or extrinsic semiconductors?11. List 3 ways to excite electrons
into the conduction band.
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Chapter 15 19
Important Equations2/1)()( gee EECEZ =
3
2/3*)2(4hmC ee
=
2/1)()( ECEZ hh =
3
2/3* )2(4hmC hh
=
TkEE BFeEF /)(1
1)(+
=
TkEECe
BFgeNN /)( =
3
2/3* )2(2h
TkmN BeC
=
TkEVh
BFeNN /=
3
2/3* )2(2h
TkmN BhV
=
( ) TkEVCi BgeNNN 2/2/1 =hei NNN =
2
*
*
ln4
32 e
hBgF m
mTkEE += hhee eNeN +=