# COMSATS Institute of Information Technology

Dr.
Nasim

Zafar

Electronics 1

EEE 231

BS Electrical Engineering

Fall Semester

2012

COMSATS Institute of Information Technology

Virtual campus

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

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

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
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

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
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