# ECE 340

Semiconductor

Nov 1, 2013 (4 years and 6 months ago)

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Chapter 5

Part 5

Metal
-
Semi Junctions

-
n junction lets try using a metal
semiconductor junction. It turns out that many of the
things that we have studied translate with little trouble.

In a metal the average energy of all electrons is
assumed to be at the metal Fermi
-
Level
Φ
m
. There are
no bands as in a semiconductor.

The energy required to remove an electron from the
metal in a vacuum is called the work function of the
metal = q
Φ
m
.

Charges near the surface of a metal will cause some +
charge to accumulate on that surface (called image
charge). In the presence of an electric field this effect will
change any barrier height slightly (neglect for now).

Metal
-
Semi Junctions

If we bring a metal into contact with a semiconductor, the
semiconductor has a work function =q
Φ
s

and we will get
charge transfer until the Fermi
-
Levels align establishing
an equilibrium.

Lets assume we have an n
-
type semiconductor and we
also have
Φ
m
>
Φ
s
. To raise electron potentials we have
to lower their energy.

When we do this electrons in the n
-
type semiconductor
conduction band will move to the metal (a lower energy
state) creating the slope in the energy band and causing
an equilibrium to be established (as well as an
Σ

field).

Moving charge leaves uncovered donor dopants N
d
+
.

Rectifying
-
Separate

Metal
-
Semi Junctions

Φ
m
>
Φ
s

E
Fs

E
C

E
V

E
0

E
Fm

Metal

Semiconductor

q
Φ
m

q
Φ
s

q
Χ

n
-
type

Increasing electron energy

Increasing potential

Metal
-
Semi Junctions

Rectifying
-
Equilibrium

E
Fs

E
C

E
V

E
Fm

q
Φ
B
=q(
Φ
m
-
Χ
)

q(
Φ
m
-
Φ
s
)=qV
0

W

n

-

-

-

+

+

+

never changes

changes w.r.t.
Φ
B

Metal
-
Semi Junctions

This self correcting mechanism stops at equilibrium.

The fact that we have uncompensated charge that is +
means that we have a depletion region like we did in the
p
-
n junction (essentially 1
-
sided). There is still excess

charge in a thin layer on the metal side.

We also have a built in potential V
0

which can be
calculated as the movement in energy of E
s

to get to E
m
.

To aid in this we define an electron affinity =q
Χ

as the
energy between the semiconductor conduction band and
vacuum.

Metal
-
Semi Junctions

A potential barrier in the metal
-
semiconductor interface
of
Φ
B
=
Φ
m
-
Χ

is established. Since there is only a Fermi
-
Level in the metal there must necessarily be a
discontinuity between it and the conduction band energy
of the semiconductor

Recall that all energy diagrams are for electrons and that
the lower an electrons potential the higher its energy.

For electrons the smaller the voltage gets the larger the

electron energy gets.

Metal
-
Semi Junctions

In the semiconductor when equilibrium is established,
bands will bend in the semi in the amount of q(
Φ
m
-
Φ
s
).

The bands are bent down from the discontinuous barrier at
the junction forming a built in potential V
0
.

Lets now redo things for a p
-
type semiconductor.

Here we will try
Φ
m
<
Φ
s
. The energies in the semi have to
be raised (lower potentials of electrons or raise potentials
of holes) for the Fermi
-
Levels to align.

Metal
-
Semi Junctions

Rectifying
-
Separate

E
Fs

E
C

E
V

E
0

E
Fm

Metal

Semiconductor

q
Φ
m

q
Φ
s

q
Χ

Φ
m
<
Φ
s

p
-
type

Metal
-
Semi Junctions

Rectifying
-
Equilibrium

E
Fs

E
C

E
V

E
Fm

Metal

Semiconductor

q(
Φ
s
-
Φ
m
)=qV
0

W

p

-

-

-

+

+

+

Metal
-
Semi Junctions

Again a built in potential of q(
Φ
s
-
Φ
m
) is present

We see we can also view this as diffusion of holes into
the metal (surface). This will lower the energy of the
metal.

In both cases an electric field in the direction
-
> causes
the bands to bend in the proper direction. Uncovered
charge in the semi. N
a
-

again demands a space charge
region formation.

Both the above situations cause are called rectifying
contacts. The barriers formed are consistent with p
-
n
junctions and barrier lowering or raising can be
accomplished by applying a potential across the junction.

Metal
-
Semi Junctions

Rectifying
-
Forward Bias

E
Fs

E
C

E
V

E
Fm

q
Φ
B
=q(
Φ
m
-
Χ
)

q(V
0
-
V)

qV

+

-

V

Metal
-
Semi Junctions

Rectifying
-
Reverse Bias

E
Fs

E
C

E
V

E
Fm

q
Φ
B
=q(
Φ
m
-
Χ
)

q(V
0
+V
r
)

-

+

V
r

Metal
-
Semi Junctions

Not surprisingly the current flow for the above junctions
is the same as that for the diode. That is in both cases
above semiconductor majority carriers are injected into
the metal.

Here however since a metal is involved I
0

from the theory of Thermionic emission.

Thermionic emission

is the heat
-
induced flow of charge
carriers from a surface or over a potential
-
energy barrier.
This occurs because the thermal energy given to the
carrier overcomes the binding potential, also known as
work function of the metal. The work function is also
important in the theory of thermionic emission.

Metal
-
Semi Junctions

According to the Richardson
-
Dushman

equation the
emitted electron current density, J (A/m
2
), is related to
the absolute temperature T by the equation:

Where

B

is known as
Richardson's constant
. In all we
have from the theory, with A, another constant

and in forward bias

Metal
-
Semi Junctions

We still have 2 cases to consider

one for each of the
-
rectifying or ohmic type contacts.

We would like the charge induced in the semiconductor to
be provided by
majority carriers
in aligning the Fermi
-
Levels.

Consider an n
-
type semi with
Φ
m
<
Φ
s
. We need to raise
the energies of the electrons in the semiconductor (lower
their potential). This is done from transfer of electrons to
the semi. With electrons being transferred into an n
-
type
material no space charge region is present but there is an
n+ region next on the semi. side making it more

than
the metal side which is more + because of the transfer.

Metal
-
Semi Junctions

ohmic
-
Separate

Φ
m
<
Φ
s

E
Fs

E
C

E
V

E
0

E
Fm

Metal

Semiconductor

q
Φ
m

q
Φ
s

q
Χ

n
-
type

ohmic
-
Equilibrium

Metal
-
Semi Junctions

E
Fs

E
C

E
V

E
Fm

q
Φ
B
=q(
Χ
-
Φ
m)

q(
Φ
s
-
Φ
m
)

n

-

-

-

+

+

+

Metal
-
Semi Junctions

Again there is an electric field from +
-
>
-

causing the
band bending but this barrier is small an easy to cross.

The transfer process is self correcting (stopping).

We have the same situation if we consider a p
-
type
semiconductor with
Φ
m
>
Φ
s
.

Here the electron energies of the metal are raised by
accumulating

charge near the junction. This looks like
a transfer of holes to the semiconductor which then has
a p+ region near its side of the interface.

The electric field and band bending are as before but the
barrier is much smaller.

Metal
-
Semi Junctions

ohmic
-
Separate

E
Fs

E
C

E
V

E
0

E
Fm

Metal

Semiconductor

q
Φ
m

q
Φ
s

q
Χ

Φ
m
>
Φ
s

p
-
type

Metal
-
Semi Junctions

ohmic
-
Equilibrium

E
Fs

E
C

E
V

E
Fm

q(
Φ
m
-
Φ
s
)

p

-

-

-

+

+

+

Metal
-
Semi Junctions

A practical method for forming ohmic contacts is by
doping the semiconductor heavily in the contact region.
Thus if a barrier exists at the interface, the depletion
width is small enough to allow carriers to tunnel through
the barrier.

Barriers are on the order of 0.85V and the I
-
V
characteristic approaches linear.

END