Materials Sciences and Applicatio n, 2011, 2, 1000-1006
doi:10.4236/msa.2011.28135 Published Online August 2011 (
Copyright © 2011 SciRes. MSA
Schottky Barriers on Layered Anisotropic
Semiconductor—WSe2—with 1000 Å Indium
Metal Thickness
Achamma John Mathai1*, Chalappally Kesav Sumesh2, Bharat Purushotamds Modi3
1Department of Applied Physics, Indian School of Mines, Dhanbad, India; 2Faculty of Technology and Engineering, Charotar Uni-
versity of Science and Technology, Changa, India; 3Department of Physics, Veer Narmad South Gujarat Uni.ersity, Surat, India.
Email: *
Received March 17th, 2011; revised April 28th, 2011; accepted June 22nd, 2011.
We have studied the forward I-V characteristics of In-pWSe2 Schottky barrier diode with 1000 Å indium thickness in the
temperature range 140 - 300 K well within the domain of thermionic emission theory with Gaussian distribution of bar-
rier height. However we found some anomalies in the low temperature range below 200 K. Hence we have considered a
model that incorporates thermionic emission, generation recombination and tunneling components. The low tempera-
ture anomalies observed in the diode parameters were effectively construed in terms of the contribution of these multi-
ple charge transport mechanisms across the interface of the fabricated diodes. Various Schottky diode parameters were
also extracted and compared with that of 500 Å metal thickness In-pWSe2 diode.
Keywords: Schottky Diodes, Interface, Inhomogeneities, In-pWSe2, Metal Thickness, Current-Voltage, Thermionic
Emission, Generation Recombination, Tunneling, Gaussian Distribution
1. Introduction
Tungsten diselenide (WSe2)—a member of group VI
transition metal dichalcogenides is used in such diverse
applications as batteries, catalysis and lubricants.1-4 The
high optical absorption, layered arrangement between the
cations, high resistance against photo-corrosion, inher-
ently stable nature against the electrolytic environment
and the optically matching magnitude of bandgap makes
WSe2 a prominent material in photoelectrochemical
conversion and photovoltaic solar energy conversion
[5-7]. WSe2 in their thin film forms are well known for
their self lubricating properties.[8] The lamellar structure,
consisting of W atoms sandwiched between two sheets of
Se atoms whereby weak “van der Waals” forces act be-
tween the layers is commonly believed to be responsible
for their excellent self lubricating properties. The layer
type structure also facilitates the process of intercalation
by a variety of foreign atoms, ions or molecules to form
new compounds [9,10]. WSe2 exhibit marked anisotropy
in most of their physical properties. Besides, it possess
good stability, high melting point, less sensitivity to hu-
midity and are more oxidation resistant in humid envi-
ronment than sulphides [11].
WSe2 based Schottky barrier diodes have been studied
with great interest over the years [12-17]. The chemical
inertness of the basal plane due to the lack of dangling
bonds make it an ideal material for the evolutionary
studies in Schottky barrier diodes. The focus was mostly
on understanding the contact properties as well as con-
duction properties. We have already reported the mecha-
nisms of charge transport in In-pWSe2 with 500 Å metal
thickness [18]. Here we have carried out a systematic
investigation on the temperature dependence of the elec-
trical properties of these structures with 1000 Å metal
thickness over a wide temperature range and its com-
parison with 500 Å metal thickness In-pWSe2 diode.
2. Experiment
In this investigation, p type WSe2 crystals of net acceptor
density 1016/cm3 were grown by direct vapour transport
technique. Type and carrier concentration of the grown
crystals were determined by Hall effect technique (Lake-
shore Cryotronics 7504). One side of the crystal was
cleaved with adhesive tape to get a more homogeneous
surface with large terraces of non-reactive van der
Waal’s plane for metal deposition. The surface prepara-
tion techniques were described in detail elsewere [18].
Schottky Barriers on Layered Anisotropic Semiconductor – WSe – with 1000 Å Indium Metal Thickness1001
High purity indium metal (Aldrich 99.99%) was ther-
mally evaporated at the rate of 0.2 Å/s onto the cleaved
front surface of the crystal through a shadow mask to
form circular Schottky contacts of area of 3.6 × 10–3 cm2.
The thickness of the metal film was 1000 Å and the
pressure inside the chamber was 10–6 Torr. Silver paste
(Eltec-1228 C) was brushed on the uncleaved side of the
WSe2 crystal to form back ohmic contact.
The current-voltage-temperature (I-V-T) characteris-
tics were measured in the temperature range 140 - 300 K
using Keithley 2400 Sourcemeter and Lakeshore Closed
Cycle Refrigerator (CCR 75014) at an interval of 20 K.
The sample temperature was controlled with Lakeshore
Model 340 autotuning temperature controller with sensi-
tivity better than ± 0.1 K. The measurement and sourcing
activities were done by Keithley Lab-Tracer software.
3. Results and Discussion
The current ‘I’ through the junction of a Schottky barrier
diode with series resistance ‘Rs’ can be expressed by the
thermionic emission (TE) theory as:[19,20]
exp 1
II nkT
provided, V 3kT/q. Here q is the electronic charge, V
is the applied voltage across the diode, k is the Boltz-
mann’s constant, T is the absolute temperature in k, n is
the ideality factor and IRs term is the voltage drop across
the junction. I0 is the reverse saturation current, which
can be expressed as:
*2 0
0exp b
where A is the diode contact area, A* is the effective
Richardson constant which is 27.6 A/cm2/K2 for WSe2
[5], and
bo is the zero bias barrier height, expressed as:
The current vs. voltage (I-V) characteristics of the
Schottky diode are plotted as a function of temperature in
Figure 1. The least square fitting is carried out by a com-
puter program using I0, n and Rs as adjustable parameters.
Here we assume that A* is equal to its known value of 27.6
A/cm2/K2 at any temperature. The fitting curves are also
shown in Figure 1 as continuous lines. They match the
experimental data quite well at high temperature or in the
large bias region at low temperature. The
b0 values were
calculated from Equation (3). The barrier height obtained
from Equation (1) is called the zero bias barrier height
whereas the barrier height obtained under flat band condi-
tion is called the flat band barrier height
bf. Flat band bar-
rier height is considered as the real fundamental quantity
Figure 1. Experimental and simulated I–V curve of
In-pWSe2 (1000 Ǻ) Schottky diode at different tempera-
since the electric field in the semiconductor is zero under
flat band conditions unlike in the case of zero bias barrier
height. The
bf were calculated by the following Equation:
bf b
where NV is the effective density of states in the valance
band and NA is the carrier concentration of the semicon-
ductor used.
Figure 2 shows the variation of Rs with temperature.
The values of Rs are found to be around several hundred
ohms at 300 K and slowly increase with decreasing tem-
perature initially but are more rapid below 200 K. The
values of
bf and n are plotted as a function of tem-
perature in Figure 3. The plot shows a decreasing trend
b0 and an increasing trend for n values with the fall
in temperature; the changes being more pronounced be-
low 200 K. The
bf values first decreases with decreasing
temperature upto 200 K and below this temperature,
these value shows a steady nature. Normally, the Richar-
dson constant A* is determined from the intercept of
ln(I0/T2) vs 1000/T plot. Figure 4 shows the Richardson
plot of the diode under investigation. This should be a
straight line with slope giving
b0 and the intercept at the
ordinate giving A*. Here the experimental data display
linearity in the temperature regime 200 K to 300 K only.
The low temperature points are bent upwards. Consider-
ing the linear region, the Richardson constants obtained
is 65.7 A/cm2/K2, which is away from the known value
of 27.6 A/cm2/K2. Moreover, the activation energy value
is determined to be 0.03 eV, which is quite low.
The decrease in the barrier height and the increase in
the ideality factor with the decrease in the operating
temperature along with anomalies in the Richardson plot-
and other diode parameters are indicative of a deviation
Copyright © 2011 SciRes. MSA
Schottky Barriers on Layered Anisotropic Semiconductor – WSe2 – with 1000 Å Indium Metal Thickness
Copyright © 2011 SciRes. MSA
3.1. Barrier Height Inhomogeneities and Low
Temperature Anomalies
A model that physically justifies the temperature de-
pendence of Schottky barriers is that proposed by Werner
and Guttler [23]. This model assumes a spatial distribu-
tion of the barrier height as described by a Gaussian
function due to the inhomogeneous nature of the inter-
face. The current across the interface depends exponen-
tially on the detailed barrier distribution at the interface.
Any spatial variation in the barriers causes the current to
flow preferentially through the barrier maxima. A quan-
titative expression for the effective barrier height is given
by the following Equations: [23-25]
Figure 2. Series resistance of In-pWSe2 (1000 Ǻ) Schottky
diode at different temperatures.
() exp1
** 2
0exp ap
ap b
 (7)
ap is the apparent barrier height, nap is the ap-
parent ideality factor, A** is the modified Richardson
constant, 0b
is the mean barrier height under zero bias
condition and
0 is the standard deviation.
2 and
3 are
the voltage deformation on the barrier height distribution.
Figure 3. Zero bias barrier height, flat band barrier height
and ideality factor of In-pWSe2 (1000 Ǻ) Schottky diode at
different temperatures.
Equation (5) is similar to Equation (1) and hence the fit-
ting of experimental data to Equation (1) should indeed
obey Equation (7) and would give the values of
ap and
nap. The
ap vs q/2kT and (1/nap-1) vs q/2kT plots to-
gether are shown in Figure 5. Figure 6 shows the modi-
fied Richardson plot of the diode. Eventhough good lin-
ear fit is obtained in the high temperature range, it is ob-
vious that the points below 200 K show discrepancy.
These discrepancies even after applying the Gaussian
distribution model for inhomogeneous interfaces imply
that the current transport is not purely thermionic at low
temperature regime. The misfit in the I-V curve at small
bias in the low temperature region (Figure 1) is also in-
dicative of the previous statement. Hence we consider a
combined effect model, consisting of thermionic emis-
sion, tunneling and generation-recombination which is
expressed as [26]:
Figure 4. Richardson plot of In-pWSe2 (1000 Ǻ) Schottky
from the pure thermionic emission theory. Several mod-
els have been proposed to explain the low temperature
anomalies of Schottky barriers [22].
00 0
() ()()()
expexp1exp1 exp
n kTEkTkT
 
 
 S
 
Schottky Barriers on Layered Anisotropic Semiconductor – WSe – with 1000 Å Indium Metal Thickness 1003
Figure 5.
ap and (1/nap1) vs q/2kT plot of In-pWSe2 (1000
Ǻ) Schottky diode.
Figure 6. Modified Richardson plot of In-pWSe2 (1000 Ǻ)
Schottky diode.
where I0TN and I0GR are the tunneling and generation re-
combination saturation current respectively. E
0 is the
tunneling parameter described elsewere [19,20]. All the
other terms have their usual meaning.
Now the low temperature I-V curve for 140, 160 and
180 K is simulated with Equation (9) and is shown in
Figure 7, which seems to be excellent with Equation (9).
New values of I0 and nap were extracted from Equation (9)
ap were recalculated for these temperatures. Now
using the new values of
ap and nap, Figure 5 gives a
straight line over the whole temperature range. Likewise,
by the new I0 values, the modified Richardson plot also is
a straight line over the entire temperature range (Figure
The values of 0b
and 0
were determined as 0.87 eV
and 0.128 eV respectively from the linear fit of
ap vs
q/2kT plot .By the linear fit of nap vs q/2kT plot, 2
were obtained as 0.114 eV and -0.019 eV respectively.
Similarly, the modified Richardson constant A** and the
mean barrier height 0b
were extracted from the linear
fit of the modified Richardson plot. The A** value of 22.8
Figure 7. Experimental and simulated forward I–V curve of
In-pWSe2 (1000 Ǻ) Schottky diode at 180, 160 and 140 K
A/cm2/K2 is in a closer agreement with the known value
of 27.6 A/cm2/K2. Moreover, 0b
value was found to
be 0.87 eV, which matches exactly with that of
ap vs
q/2kT plot. The inhomogeneity calculated for this diode
is 14.7% which is rather high. Due to the specific nature
of WSe2 surface [27-29] inhomogeneities in various
forms can be readily expected at the In-pWSe2 interface.
This may be one of the reasons for the large values of n.
High values of n also indicate the voltage dependence of
barrier height. Such behaviors occur when the barrier
heights vary laterally and the dimensions of these inho-
mogeneities are in the order of the depletion layer width.
ap and nap vs T were plotted according to Equa-
tions (7) and (8) in the whole temperature range with
their new values at temperatures 140, 160 & 180 K
(Figure 8). We can see that the theoretical curve closely
follows the experimental data.
The voltage sensitivity of the barrier height distribu-
tion and standard deviation was investigated for two bi-
Figure 8. Measured and simulated barrier height and ideal-
ity factor of In-pWSe2 (1000 Ǻ) Schottky diode based on
Equations (7) and (8).
Copyright © 2011 SciRes. MSA
Schottky Barriers on Layered Anisotropic Semiconductor – WSe – with 1000 Å Indium Metal Thickness
1004 2
Table 1. A comparative table of In-pWSe2 Schottky diode parameters with different metal thicknesses.
b0(0) (eV)
by R. plot
ap vs.
1/T plot
R. plot
σ0(eV) ρ2(eV) ρ3(eV) % of
500 Å Uncl18 0.09 16.2 35.6 0.89 0.89 0.129 0.345 –0.011 14.5
500 Å Cl18
1000 Å Cl
ases namely 0.0 V and 0.4 V using the equation:
 
ap b
 (10)
which is the general form of Equation (7). The values
of comes out to be 0.87 eV and 0.92 eV respec-
tively whereas the S
ap V
values were found as 0.128 eV
and 0.120 eV respectively for the biases 0.0 eV and 0.4
eV. It shows that the value increases whereas
ap V
value decreases with the increase of bias voltage,
which shows that an increase in bias can homogenize the
barrier height fluctuation.
3.2. Effect of Metal Thickness on the Schottky
Barrier Height Inhomogeneity
The diode parameters of the presently studied 1000 Å
In-pWSe2 diode is compared with the previously reported
diode parameters of 500 Å In-pWSe2 diodes prepared on
both cleaved and uncleaved WSe2 surface by the same
authors. The details are given in Table 1. The 500 Å
cleaved In-pWSe2 diode (Cl-500 Å) shows the highest
value. This is followed by 500 Å uncleaved
In-pWSe2 diode (Uncl-500 Å) and finally comes the
1000 Å cleaved In-pWSe2 diode (Cl-1000 Å). The higher
value of 0b
indicates a more homogeneous diode,
which is supported by the percentage of inhomogeneity
values. Similar results on metal thickness studies were
reported in Au/n-GaAs Schottky diodes also [30].
4. Conclusions
The semiconducting crystals of p type WSe2 were grown
by direct vapor transport technique. Using these crystals,
In-pWSe2 Schottky barrier diodes with 1000 Å metal
thickness were fabricated by thermal evaporation method.
The forward I-V characteristics were studied over a wide
temperature range of 140 - 300 K. The estimated zero
bias barrier height, the ideality factor and the Richardson
plot were found to exhibit two different trends; one in the
140 - 180 K regime and the other in the 200 - 300 K.
The conduction properties from 200 - 300 K regions are
successfully explained on the basis of thermionic emis-
sion mechanism with a Gaussian barrier height distribu-
tion. Investigations at temperatures below 200 K sug-
gested the possibility of multiple conduction mechanisms
along with thermionic emission. Hence a model has been
considered, which incorporates thermionic emission, gen-
eration recombination and tunneling effects. The low
temperature anomalies observed in the diode parameters
were well explained in terms of the contribution of these
combined charge transport mechanisms across the inter-
face. The value of the Richardson constant A** from the
modified Richardson plot is found to be 22.8 A/cm2/K2
which is quite close to the known value of 27.6 A/cm2/K2
for WSe2. The mean barrier height 0b
of this diode
comes to be 0.87 eV with a standard deviation of 0.128
eV. The percentage value of inhomogeneity in the pre-
sent diode even after cleavage is 14.7%. The characteris-
tics of the present diode were compared with that of 500
Å In-pWSe2 diodes and were found that the surface was
more homogeneous in the case of 500 Å In-pWSe2 diode.
In brief, when the thickness of the metal film was small,
the surfaces exhibited more homogeneity. Over and
above, an increase in the bias voltage makes the barrier
of these diodes more homogeneous. In conclusion, we
can say that the anomalies in the I-V characteristics of
the In-pWSe2 Schottky barrier diodes at low tempera-
tures are due to the multiple charge conduction mecha-
nisms of thermionic emission, generation recombination
and tunneling currents.
5. Acknowledgements
This work was financially supported by the University
Grants Commission, New Delhi, India (No. F.10-75/2001).
AJM is grateful for the many discussions with Dr. John
Mathai and Prof. R Srivastava.
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