Electronics -1, Lecture 05
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Transcript of Electronics -1, Lecture 05
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8/13/2019 Electronics -1, Lecture 05
1/19
Dr. Nasim Zafar
Electronics 1
EEE 231 BS Electrical EngineeringFall Semester 2012
COMSATS Institute of Information Technology
Virtual campus
Islamabad
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8/13/2019 Electronics -1, Lecture 05
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Semiconductor device lab.Kwangwoon
U n i v e r s i t y
Semiconductor Devices.
Carrier Transport in Semiconductors
Lecture No: 5
Diffusion of Carriers
Diffusion Processes
Diffusion and Recombination
Continuity Equations
Einstein Relation
Nasim Zafar
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Carrier Diffusion:
Introduction: When excess carriers are created non-uniformly in a semiconductor,
a concentration gradientresults due to this non-uniformity of the carrier
densities in the sample. This concentration gradient, for electrons and holes, will
cause a net motion of the charge carriers from the regions of high density to theregions of low carrier density. This type of carrier motion is called Diffusion and
represents an important charge transport process in semiconductors.
Thus, the charge carriers in a semiconductor diffuse, due to the concentration
gradient by random thermal motion and under going scattering from: The lattice vibrations and
Ionized Impurity atoms.
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Carrier Diffusion:
Introduction:
When excess carriers are created non-uniformly in a semiconductor,
a concentration gradient results due to this non-uniformity of the carrier
densities in the sample. This concentration gradient, for electrons and holes,
will cause a net motion of the charge carriers from the regions of high density
to the regions of low carrier density.
This type of carrier motion is called Diffusion and represents an important
charge transport process in semiconductors.
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Carrier Diffusion:
Introduction:
Thus, the charge carriers in a semiconductor diffuse, due to
the concentration gradient by random thermal motion and
under going scattering from:
The lattice vibrations and
Ionized Impurity atoms.
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Carrier Diffusion:
How can we produce a concentr ation gradient in a semiconductor?
By making a semiconductor or metal contact.
By illuminating a portion of the semiconductor with light, (next slide).
As the carriers diffuse, a diffusion current flows. The force behind the
diffusion current is due to the random thermal motion of the carr iers.
1dn dP
dx kT dx
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Photo Generation and Diffusion:
By shining light, electron-hole pairscan be produced when the photon
energy>Eg.
The increased number of electron-hole pairs will move toward the lower
concentration region, until they reach their equilibrium values.
So there is a net number of the charge carriers crossing per unit area per
uni t time, which is called flux.
Units: [Flux]= m-2S-1
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Diffusion Flux :
Ficksfirst law
Dif fusion Flux Concentration Gradient dn/dx
ndnFlux Ddx
[Flux]= m-2S-1 D = vthl ,[ D]= m2/S
D measures the ease of carrier diffusion in
response to a concentration gradient.
D limited by vibrations of lattice atoms and
ionized dopant impurities.
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Diffusion Flux :
For Electrons:
Fn= - Dn dn/dx
For Holes:
Fp= - Dp dp/dx
Dn= electron diffusion coefficient
Dp = hole diffusion coefficient
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Einstein Relationship:
Einstein relation relates the two independent current mechanicms of
mobility with diffusion D.
mn= qtn/mn*Dn= kTtn/mn* m*v2= kTDn= v2tn= l2/tn
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Einstein Relation:pn
n p
DD kT kT and for electrons and holes
q qm m
Constant value at a fixed temperature
2
2
/sec
sec
J K Kcm kT volt volt
cm V q C
25kT
mV at room temperatureq
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Diffusion Current Density: J
Diffusion cur rent density = chargexcarr ier flux
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Total Current:
Diffusion Current within a semiconductor consists of:
i . hole component and
i i . electron component
Total Current flowing in a semiconductor is the sum of:
i . dri f t cur rent andi i . diff usion current:
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Diffusion Current Densities:
2 1
2
2
,
,th
n n n
p p p
n p
Flux m s
D l D m s
The current densities for electrons and holes
dn dnJ q D qD for electronsdx dx
dp dpJ q D qD for holesdx dx
J A m
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Total Current Density:
When both electric field and the concentration gradient are
present, the total current density, for the electron, is given as:
n n n
p p p
total n p
dnJ q nE qD
dx
dpJ q pE qD
dx
J J J
m
m
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Summary
Current flowing in a semiconductor consists of driftand
diffusioncomponents:
Mobility and Conductivity are highly temperature dependent.
Generation and Recombination processes were discussed.
Nasim Zafar 18
dx
dpqD
dx
dnqDEqnEqpJ
pnnptot
mm
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Resistivity formula
x
nqDqnJJJ
x
pqDqpJJJ
d
d
d
d)(
ndiff|ndrift|nn
pdiff|pdrift|pp
E
E
J= Jn+ Jp
np
1
mm
qnqp
EpnqJJJ pndrift|pdrift|ndrift mm
x
pqDJ
x
nqDJ
d
dand
d
d
pdiff|pndiff|n
Dr if t curr ent density
Di ff usion current density
Total hole and electron
current density
Total current density
Summary