Dr.
Nasim
Zafar
Electronics 1
EEE 231
–
BS Electrical Engineering
Fall Semester
–
2012
COMSATS Institute of Information Technology
Virtual campus
Islamabad
Semiconductor device lab.
Kwangwoon
Un i v er 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
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.
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.
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.
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.
Carrier Diffusion
:
How can we produce
a concentration 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
carriers
.
Photo Generation and Diffusion:
Current mechanisms
Drift
Current
Diffusion
Current
photons
Contact with a metal
Photo Generation and Diffusion:
By shining light,
electron

hole pairs
can be produced when
the photon
energy>
E
g
.
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
unit time
, which is called
flux
.
Units:
[
Flux
]
= m

2
–
S

1
Diffusion Flux :
Fick’s
first law
Diffusion Flux
∞
Concentration Gradient
dn
/
dx
[
Flux
]
= m

2
–
S

1
D =
v
th
l ,
[
D
]
= m
2
/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.
Diffusion Flux :
For Electrons:
F
n
=

D
n
dn
/
dx
For Holes:
F
p
=

D
p
dp
/
dx
D
n
= electron diffusion coefficient
D
p
= hole diffusion coefficient
Einstein Relationship:
Einstein relation relates the two independent current mechanicms of
mobility
m
with
diffusion
D
.
m
n
=
q
t
n
/
m
n
*
D
n
=
kT
t
n
/
m
n
*
½ m*v
2
= ½
kT
D
n
= v
2
t
n
= l
2
/
t
n
Einstein Relation
:
Constant value at a fixed temperature
Diffusion Current Density:
J
Diffusion current density = charge
x
carrier flux
Total Current:
Diffusion Current within a semiconductor consists of:
i.
hole component and
ii.
electron component
Total Current flowing in a semiconductor is the sum of:
i.
drift current and
ii.
diffusion current:
Diffusion Current Densities:
Total
Current Density
:
When both
electric field
and
the
concentration gradient
are
present,
the total current density
, for the electron, is given as:
Summary
Current flowing in a semiconductor consists of
drift
and
diffusion
components:
Mobility and Conductivity are highly temperature dependent.
Generation and Recombination processes were discussed.
Nasim Zafar
18
19
Resistivity formula
J
=
J
n
+
J
p
Drift current density
Diffusion current density
Total hole and electron
current density
Total current density
Summary
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