Lecture #6 OUTLINE Carrier scattering mechanisms Drift current Conductivity and resistivity...
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![Page 1: Lecture #6 OUTLINE Carrier scattering mechanisms Drift current Conductivity and resistivity Relationship between band diagrams & V, Read: Section 3.1.](https://reader036.fdocuments.net/reader036/viewer/2022062421/56649d355503460f94a0c643/html5/thumbnails/1.jpg)
Lecture #6
OUTLINE
• Carrier scattering mechanisms
• Drift current
• Conductivity and resistivity
• Relationship between band diagrams & V, Read: Section 3.1
![Page 2: Lecture #6 OUTLINE Carrier scattering mechanisms Drift current Conductivity and resistivity Relationship between band diagrams & V, Read: Section 3.1.](https://reader036.fdocuments.net/reader036/viewer/2022062421/56649d355503460f94a0c643/html5/thumbnails/2.jpg)
EE130 Lecture 6, Slide 2Spring 2007
Dominant scattering mechanisms:
1. Phonon scattering (lattice scattering)
2. Impurity (dopant) ion scattering
2/32/1
1
velocityermalcarrier thdensityphonon
1
TTTphononphonon
Phonon scattering mobility decreases when T increases:
= q / m
Mechanisms of Carrier Scattering
Tvth
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EE130 Lecture 6, Slide 3Spring 2007
_+
- -Electron
Boron Ion Electron
Arsenic Ion
DADA
thimpurity NN
T
NN
v
2/33
There is less change in the electron’s direction of travel if the electron zips by the ion at a higher speed.
Impurity Ion Scattering
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EE130 Lecture 6, Slide 4Spring 2007
Matthiessen's Rule
• The probability that a carrier will be scattered by
mechanism i within a time period dt is
where i is the mean time between scattering events due to mechanism i
The probability that a carrier will be scattered within a
time period dt is
impurityphonon
impurityphonon
111
111
i i
dt
i
dt
![Page 5: Lecture #6 OUTLINE Carrier scattering mechanisms Drift current Conductivity and resistivity Relationship between band diagrams & V, Read: Section 3.1.](https://reader036.fdocuments.net/reader036/viewer/2022062421/56649d355503460f94a0c643/html5/thumbnails/5.jpg)
EE130 Lecture 6, Slide 5Spring 2007
1E14 1E15 1E16 1E17 1E18 1E19 1E20
0
200
400
600
800
1000
1200
1400
1600
Holes
Electrons
Mo
bili
ty (
cm2 V
-1 s
-1)
Total Impurity Concenration (atoms cm-3)Total Doping Concentration NA + ND (cm-3)
Mobility Dependence on Doping
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EE130 Lecture 6, Slide 6Spring 2007
Temperature Effect on Mobility
impurityphonon
impurityphonon
111
111
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EE130 Lecture 6, Slide 7Spring 2007
vd t A = volume from which all holes cross plane in time t
p vd t A = # of holes crossing plane in time t
q p vd t A = charge crossing plane in time t
q p vd A = charge crossing plane per unit time = hole current
Hole current per unit area J = q p vd
Drift Current
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EE130 Lecture 6, Slide 8Spring 2007
Jp,drift = qpvdn = qppJn,drift = –qnvdn = qnn
Jdrift = Jn,drift + Jp,drift = =(qnn+qpp)
Conductivity of a semiconductor is qnn + qpp
Resistivity 1 /
Conductivity and Resistivity
(Unit: ohm-cm)
![Page 9: Lecture #6 OUTLINE Carrier scattering mechanisms Drift current Conductivity and resistivity Relationship between band diagrams & V, Read: Section 3.1.](https://reader036.fdocuments.net/reader036/viewer/2022062421/56649d355503460f94a0c643/html5/thumbnails/9.jpg)
EE130 Lecture 6, Slide 9Spring 2007
n-type
p-type
Resistivity Dependence on Doping
For n-type material:
nqn 1
For p-type material:
pqp 1
Note: This plot does not apply for compensated material!
![Page 10: Lecture #6 OUTLINE Carrier scattering mechanisms Drift current Conductivity and resistivity Relationship between band diagrams & V, Read: Section 3.1.](https://reader036.fdocuments.net/reader036/viewer/2022062421/56649d355503460f94a0c643/html5/thumbnails/10.jpg)
EE130 Lecture 6, Slide 10Spring 2007
Electrical Resistance
where is the resistivity
Resistance Wt
L
I
VR (Unit: ohms)
V
+_
L
tW
I
homogeneously doped sample
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EE130 Lecture 6, Slide 11Spring 2007
Consider a Si sample doped with 1016/cm3 Boron.What is its resistivity?
Answer:
NA = 1016/cm3 , ND = 0 (NA >> ND p-type)
p 1016/cm3 and n 104/cm3
Example
cm 4.1)450)(10)(106.1(
11
11619
ppn qpqpqn
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EE130 Lecture 6, Slide 12Spring 2007
Example: Dopant Compensation
Consider the same Si sample, doped additionallywith 1017/cm3 Arsenic. What is its resistivity?
Answer:
NA = 1016/cm3, ND = 1017/cm3 (ND>>NA n-type)
n 9x1016/cm3 and p 1.1x103/cm3
cm 12.0)600)(109)(106.1(
11
11619
npn qnqpqn
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EE130 Lecture 6, Slide 13Spring 2007
Consider a Si sample doped with 1017cm-3 As.How will its resistivity change when the temperature is increased from T=300K to T=400K?
Solution:
The temperature dependent factor in (and therefore ) is n. From the mobility vs. temperature curve for 1017cm-3, we find that n decreases from 770 at 300K to 400 at 400K. As a result, increases by
Example: Temperature Dependence of
93.1400
770
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EE130 Lecture 6, Slide 14Spring 2007
Potential vs. Kinetic Energy
electron kinetic energyin
crea
sing
ele
ctro
n en
ergy
Ec
Evhole kinetic energy
incr
easi
ng h
ole
ener
gy
referencecP.E. EE Ec represents the electron potential energy:
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EE130 Lecture 6, Slide 15Spring 2007
N-+ –
0 .7 V
Si
E
x
Ec(x)
Ef(x)
Ev(x)
E
0.7 V
-
+
V(x)
0.7 V
x0
(a)
(b )
(c)
+ –
0 .7 V
Si
E
x
Ec(x)
Ef(x)
Ev(x)
E
0.7 V
-
+
V(x)
0.7 V
x0
(a)
(b )
(c)
Electrostatic Potential, V
• The potential energy of a particle with charge -q is related to the electrostatic potential V(x):
)(1
creference EEq
V
qVP.E.
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EE130 Lecture 6, Slide 16Spring 2007
N-+ –
0 .7 V
Si
E
x
Ec(x)
Ef(x)
Ev(x)
E
0.7 V
-
+
V(x)
0.7 V
x0
(a)
(b )
(c)
+ –
0 .7 V
Si
E
x
Ec(x)
Ef(x)
Ev(x)
E
0.7 V
-
+
V(x)
0.7 V
x0
(a)
(b )
(c)
Electric Field,
dx
dE
qdx
dV c1
• Variation of Ec with position is called “band bending.”
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EE130 Lecture 6, Slide 17Spring 2007
Carrier Drift (Band Diagram Visualization)
Ec
Ev
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EE130 Lecture 6, Slide 18Spring 2007
Summary• Carrier mobility varies with doping
– decreases w/ increasing total concentration of ionized dopants
• Carrier mobility varies with temperature– decreases w/ increasing T if lattice scattering is dominant– decreases w/ decreasing T if impurity scattering is dominant
• The conductivity of a semiconductor is dependent on the carrier concentrations and mobilities
• Ec represents the electron potential energy
Variation in Ec(x) variation in electric potential V
Electric field
• E - Ec represents the electron kinetic energy
= qnn + qpp
dx
dE
dx
dE vc