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Characterization of Semiconductors by Capacitance Methods
Háskóli Íslands
Experimental Physics
Physics department
April 21, 2006
Characterization of Semiconductors
by Capacitance Methods
Gísli Jóhann Grétarsson
Ólafur Sindri Helgason
Wing Wa Yu Contents
1 Introduction
2
2 Theoretical background
2
2.1 Schottky diode . . . . . . . . . . . . . . . . . . . . . . . . . .
2
2.2 Deep Level Transient Spectroscopy (DLTS) . . . . . . . . . .
6
3 Capacitance-Voltage Proling (CV)
9
3.1 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
3.2 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
4 Deep Level Transient Spectroscopy (DLTS)
13
4.1 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.2 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5 Conclusion
15
1 1 Introduction
The eect that semiconductor physics have had on modern technology is
immense. Devices such as the transistor and the diode are one of the most
important inventions that semiconductor physics has provided. For produc-
tive usage of the semiconductor one must know their characteristics. In this
report we are going to examine the characteristics of a Schottky diode by
the use of capacitance methods such as CV proling and DLTS. The diode
was made by combining a n-type GaAs with gold metal plate.
2 Theoretical background
2.1 Schottky diode
If one combines n-type and p-type semiconductors in a very close contact
one gets a p-n junction, which is commonly used as a diode. When one uses
a metal surface instead of the p-type semiconductor, one gets a Schottky
barrier (see gure 4),
b
, also known as Schottky diode, (see gure 3). The
largest dierences between a Schottky barrier and a p-n junction are its typ-
ically lower junction voltage, and decreased (almost nonexistent) depletion
width in the metal [2]. Since the depletion layer in the metal is so small
it can be neglected, and therefore all the depletion and potential dierence
occurs in the semiconductor.
The equivalent circuit for the diode is shown on gure 1. There one can
see that there are two resistances, R
l
nonlinear (i.e. leakage resistance) and
R
s
serial connected. The Schottky diode impedance is
Z = R
l
+ R
s
(1 +
2
c
2
R
2
l
)
(1 +
2
c
2
R
2
l
)
+ j
cR
l
(1 +
2
c
2
R
2
l
)
(1)
Figure 1: The equivalent circuit for the Schottky diode.
2 If we dene C
m
as the value measured by the capacitance meter, then
the error of the measurement is
C
m
C =
1
(1 +
R
s
R
l
)
2
+
2
c
2
R
2
s
(2)
If R
s
= 0
then
C
m
C
= 1
and therefore there is no error, but as R
s
decreases
the error decreases for the measured value of C
m
.
The diagram for the current through the diode, I, vs. the voltage applied
across it, V , i.e. I-V diagram is shown in gure 2. There one can see that
for high bias the diagram gets nearly linear because there R
l
<< R
s
and one
can assume that the resistance in the circuit depends only on R
s
.
When we apply the reverse bias then we get a small saturation current,
I
s
, since the diode is not perfect one way gate. This current is given by:
I
s
= AT
2
exp
e
b
kT
(3)
where A is the area of the metal semiconductor interface.
Figure 2: Typical diode characteristic.
3 When R
l
>> R
s
at low bias the current is given by
I = I
s
exp
eV
nkT
1
(4)
where n is the ideality factor of the diode given by
n = 1
b
V
(5)
For ideal diodes
b
does not depend on V and therefore n = 1. For non-ideal
diodes we always have n > 1.
If one applies reverse bias, V
r
, on the Schottky diode the total potential
becomes V
b
+V
r
, where V
b
(see gure 4) is the sum of the built-in potentials of
the metal and the n-type semiconductor. For uniform distribution of donors
the depletion width is
x
d
=
2
r 0
(V
b
+ V
r
)
eN
d
(6)
Here N
d
is the donor concentration, which is assumed to be constant.
Figure 3: Schottky junction, (a) before contact and (b) after contact.
The eect of increasing V
r
is that it lowers the energy levels of the semicon-
ductor, which enables the negative charges to move into the metal. Therefore
the depletion region acts like a capacitor.
The charge stored in a region of width x
d
, with N
d
constant, is
Q = eN
d
x
d
A
4 Figure 4: Energy level diagram of a Schottky diode, q
b
is the barrier height, s
is the electron anity in the semiconductor,
s
and
m
are the semicon-
ductor and the metal work functions, and V
b
is the built-in voltage.
where A is the area of the junction. Inserting for x
d
in formula 6 gives:
Q = A
2
r 0
eN
d
(V
b
+ V
r
)
(7)
and the capacitance of the Schottky junction, C, is
C = dQ
dV
r
= 1
2 A
2
r 0
eN
d
(V
b
+ V
r
) =
r 0
A
x
d
(8)
or
x
d
=
r 0
A
C
(9)
It can be shown [3] that same applies when N
d
varies with distance x
d
,
which we can write as
N
d
(x
d
) =
C
3
e
r 0
A
2
dC
dV
r
1
(10)
5 2.2 Deep Level Transient Spectroscopy (DLTS)
Deep level transient spectroscopy is unique and powerful tool for the study
of electrically active defects in semiconductors. Defects in semiconductors
usually give rise to an energy band in the band gap. Deep defects are defects
that have energy level far from the conduction band, when we have n-type
semiconductors. If we use a DLTS with Schottky diode only majority carrier
traps can be observed. The technique works by observing the capacitance
transient associated with the change in depletion region width as the diode
returns to equilibrium from an initial non-equilibrium state.
The energy level for electrons or holes in the gap between the conduction
band and valence band is called a trap. Traps can form due to the defects
in the semiconductor lattice or impurities in the crystal. When measuring
the capacitance of the Schottky diode a small sinusoidal voltage is applied
over the biased diode. Because of this voltage the Fermi level of the diode
starts to oscillate just as the voltage (see gure 5(a)). If deep level impurites
crosses the Fermi level we get a frequency dependent capacitance.
Figure 5: (a) When the capacitance is measured a sinusoidal voltage is applied
over the sample resulting in oscillation of the Fermi level. (b) The behaviour
of the capacitance as a function of frequency for a schottkey diode with one
deep level trap, and (c) with many deep level traps.
When a lled trap emerges it wants to emit its electron to the conduction
band. If the frequency is too high then the trap does not have enough time
to release the electron. This rate of emission is given by
e
n
= T
2
exp
E
a
kT
(11)
6 where E
a
is the thermal ionization energy of the defect, which is the same
as the dierence between the energy level of the traps and the energy of
the conduction band. Here is a constant dependent on the semiconductor
( = 2, 28·10
20
cm
2
s
1
K
2
for n-type GaAs and = 1, 7·10
21
cm
2
s
1
K
2
for p-type GaAs) and is the capturing cross section.
The closer the deep trap is to the conduction band, e
n
becomes higher.
If the trap level is too low it is always under the Fermi level and the traps do
not aect the capacitance measurements. Therefore we can detect shallow
defects by measuring the capacitance with dierent frequencies, see gures
5(b) and 5(c). According to [3] we can write
G/f dC
df
(12)
where G is the conductance. Therefore we would expect to see a peak at the
point(s) of inection of the capacitance on a G/f vs f graph.
We apply a constant reversed bias V
r2
on a Schottky diode. When a pulse
is added, so the bias goes to V
r1
for a short time, the majority carriers will
ow into the depletion region. When the pulse is over we return to V
r2
and
the depletion region is emptied again of free carriers. Because the emission
rate of the shallow defects is so high they get emptied almost instantly, but
deep defects have smaller emission rate and can therefore be measured. In
gure 6 this eect is shown.
Figure 6: Capacitance as a function of time when applying pulsed bias.
7 When we increase the temperature we also increase e
n
as we can see from
equation 11. Also if we x two points t
1
and t
2
we get that the dierence in
capacitance between these points is given by
S = C
0
(exp(e
n
t
2
) exp(e
n
t
1
))
(13)
If we plot S as a function of temperature we will get a maximum at T
0
and
we have also that dS/dT = 0, so we get
e
n
=
ln
t
2
t
1 (14)
where = t
2
t
1
. By changing we can deduce the values of E
a
and if
we know . From the amplitude C
0
we can deduce the concentration of
the deep defect N
t
and is given by
N
t
= 2N
d
C
0
C
0
(15)
8 3 Capacitance-Voltage Proling (CV)
3.1 Measurements
We began the experiment by putting the sample in the cryostat, which was
n-type GaAs Schottky diode with contacts made of Au (1000 Å thickness).
Then we connected the sample to a voltage source and to an ammeter. We
checked both polarities of bias by increasing the voltage, V , and found both
the forward and the reverse characteristics.
The sample was connected to a capacitance meter and a voltage source.
Both polarities were checked and the reverse bias found. After that C-V
measurements were taken for V = [0 , 30] V.
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