MSE 2620, Spring ‘09
Homework #4
Instructions:
Due
Tuesday, April 21st, 2009.
Turn in one solution per group and be sure to include the
group letter, the names of the group members, and if any group members did not participate
enough to deserve full credit along with the reasons why.
1.
Schottky and Ohmic
a.
Describe the difference between a Schottky and Ohmic contact.
In a Schottky contact there is a potential energy barrier to overcome in order for
carriers to transfer from the metal to the semiconductor.
In an ohmic contact
there is no barrier for the carriers in the metal to move to the semiconductor.
b.
If a metal makes a Schottky to ntype Si, would it more likely be an Ohmic or
Schottky contact to ptype Si.
Justify your answer.
It would more likely make an
ohmic contact to ptype Si.
(I will update with the exact reason).
c.
Consider a Schottky junction diode between Au and nSi doped with 10
16
donors
cm
3
.
The crosssectional area is 1mm
2
.
Given the work function of Au is 5.1 eV,
what is the theoretical barrier height Φ
B
from the metal to the semiconductor?
χ

Φ
=
Φ
m
B
= 5.1 – 4.01eV (table 5.1) = 1.09 eV
d.
Given that the experimental barrier height Φ
B
is about 0.8 eV, i) what is the
reverse saturation current and ii) the current when there is a forward bias of 0.3 V
across the diode?
Φ

=
kT
T
B
J
B
exp
2
0
and
3
2
0
/
4
h
k
em
B
e
π
=
,
where k is the Boltzmann constant,
e
is the elementary charge,
m
e
is the electron
mass, and
h
is Planck’s constant.
Assume T = 300K
3
2
0
/
4
h
k
em
B
e
π
=
= 1.2 x 10
6
A m
2
K
2
I
0
=
Φ

=
kT
AT
B
JA
B
exp
2
0
=(1.2x10
6
)(1e
6
)(300)
2

eV
eV
026
.
0
8
.
0
exp
I
0
= 4.68 nA
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I
f
=

1
exp
0
kT
V
I
f
=

1
026
.
0
3
.
0
exp
0
eV
eV
I
= 480 μA
2.
pn junctions
a.
Draw a band diagram for a pn junction for i) no bias ii) Forward Biased iii)
reverse biased.
The following should be clearly labeled on your diagrams:
conduction and valence bands, Fermi level, built in potential and applied bias.
Figure 6.11 Kasap.
b.
Consider a long Si diode made of an abrupt p
+
n junction which has 10
16
donors
cm
3
on the nside and 10
18
acceptors cm
3
on the pside.
The diode is kept at
27˚C.
Calculate the builtin voltage.
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 Spring '09
 MALLIARAS
 Ohmic, Pn junction, Schottky

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