EE471 Course Notes: Week 2
Tewksbury
2. Transport in Semiconductors
Chapter 3 of the textbook covers carrier transport (current) in semiconductors.
Two equations
were developed  the current equation
and the current continuity equation
.
These two equations
capture the relationships between currents and carrier densities for all semiconductors and all
electrical devices made using semiconductors.
2.1 Current Equation
The current is the rate of flow of charge across the device area.
In particular,
I
=
q
!
R
Q
=
Q
t
where
Q
is the total charge passing through the area in time
t
.
The electrons and holes contribute
separate currents
I
n
and
I
p
, respectively and the total current is the sum of these two currents,
I
=
I
n
+
I
p
.
As the cross sectional area
A
increases, more charge flows across the larger area,
with the current being proportional to the cross sectional area.
To obtain general equations
independent of this area, the current density
(represented by
J
) is used.
The current
(amps) and
current density
(
amps/cm
2
) are related by
J
=
I
/
A
.
The current due to a given carrier type (electron or hole) has two contributions  one due to
electric fields (and called the drift current
) and the other due to a gradient in the carrier density
(which causes diffusion of carriers into lower density region) and called the diffusion current
.
2.1A Drift Current
To obtain the drift current, it was necessary to obtain the velocity of carriers due to an electric
field
E
.
We discussed the "cloud" of carriers (moving at high velocities in random directions and
scattering from scattering points caused by deviations of the silicon crystal from a perfect
crystal).
When an electric field is applied, this "cloud" of carriers moves (drifts), with the cloud
of holes drifting in the direction of the electric field and the "cloud" of electrons drifting in the
direction opposite to the electric field direction.
From this, we established that carriers have a
"drift velocity" proportional to the electric field, with the mobility of the carriers being the
proportionality constant.
In particular (using vector notation to capture the drift direction), the
electron and hole drift velocities, respectively, are
r
v
n
=
!
μ
n
r
E
and
r
v
p
= +
p
r
E
.
Here, the electron and hole mobilities are, for silicon at 300K
n
=
1450 cm
2
/volt  sec
and
p
=
505 cm
2
/volt  sec
.
The electron, hole and total drift current
densities
(J) and the corresponding currents
(I) are
J
n
=
q
n
nE
J
p
=
q
p
pE
J
=
J
n
+
J
p
I
n
=
J
n
!
A
=
q
n
( )
A
I
p
=
J
p
!
A
=
q
p
( )
A
I
=
I
n
+
I
p
.
(3A)
Here, we have left off the sign and eliminated the vector notation (the two currents simply add
and, when considering currents in electrical circuits, we represent electrons flowing in one
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Don't worry about these details  just use
the equations above.
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 Spring '09
 chavez
 Electron, Semiconductors, Electric charge, Condensed matter physics

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