Journal of Modern Physics, 2011, 2, 113-123
doi:10.4236/jmp.2011.23018 Published Online March 2011 (http://www.SciRP.org/journal/jmp)
Schottky Barrier Parameters of Pd/Ti Contacts on N-Type
InP Revealed from I-V-T And C-V-T Measurements
D. Subba Reddy1, Matli Bhaskar Reddy2, N. Nanda Kumar Reddy1, Varra Rajagopal Reddy1*
1Department of Physics, Sri Venkateswara University, Tirupati, India
2Government Degree College, Puttur, India
Received January 5, 2011; revised February 26, 2011; accepted February 27, 2011
Abstract
We report on the current-voltage (I-V) and capacitance-voltage (C-V) characteristics of the Pd/Ti/n-InP
Schottky barrier diodes (SBDs) in the temperature range 160-400 K in steps of 40 K. The barrier heights and
ideality factors of Schottky contact are found in the range 0.35 eV (I-V), 0.73 eV (C-V) at 160 K and 0.63
eV (I-V), 0.61 eV (C-V) at 400 K, respectively. It is observed that the zero-bias barrier height bo decreases
and ideality factor n increase with a decrease in temperature, this behaviour is attributed to barrier inho-
mogeneities by assuming Gaussian distribution at the interface. The calculated value of series resistance (Rs)
from the forward I-V characteristics is decreased with an increase in temperature. The homogeneous barrier
height value of approximately 0.71 eV for the Pd/Ti Schottky diode has been obtained from the linear rela-
tionship between the temperature-dependent experimentally effective barrier heights and ideality factors. The
zero-bias barrier height (bo ) versus 1/2 kT plot has been drawn to obtain evidence of a Gaussian distribu-
tion of the barrier heights and values of


0b
= 0.80 eV and 0

= 114 mV for the mean barrier height and
standard deviation have been obtained from the plot, respectively. The modified Richardson ln(I0/T2)−
(22 22
02qk
 T) versus 1000/T plot has a good linearity over the investigated temperature range and gives the
mean barrier height (0b) and Richardson constant (A*) values as 0.796 eV and 6.16 Acm-2K-2 respectively.
The discrepancy between Schottky barrier heights obtained from I-V and C-V measurements is also inter-
preted.

Keywords: Schottky Barrier Parameters, I-V-T and C-V-T Measurements, Pd/Ti Schottky Contacts, N-Type
InP, Gaussian Distribution
1. Introduction
Metal-semiconductor (MS) structures are important re-
search tools in the characterization of new semiconductor
materials, and at the same time, the fabrication of these
structures plays a vital role in constructing some useful
devices in technology [1-3]. Indium phosphide (InP) is a
promising III-V compound semiconductor material for
high-speed electrical and optoelectronic devices. Due to
its direct bandgap, high electron mobility, high saturation
velocity and breakdown voltage which are very impor-
tant in electronic devices [4-5]. But, a serious limitation
of InP Schottky barrier diodes is the low barrier height
and large leakage currents. However, low barrier height
Schottky diodes of InP seem to be a good candidate for
the application of zero-bias Schottky detector diodes [5].
Most studies of Schottky barrier diodes (SBDs) formed
on n-InP were limited to the determination of the Schottky
barrier height (SBH) at room temperature (RT) by meas-
uring either the current-voltage (I-V) characteristics or the
capacitance-voltage (C-V) characteristics of the diodes
[6-8]. Therefore, analysis of the current-voltage (I-V)
characteristics of the SBDs at room temperature only does
not give detailed information about their conduction proc-
ess or the nature of the barrier formed at the metal-semi-
conductor (M-S) interface. On the other hand, the tem-
perature dependent studies of the Schottky contacts enable
one to understand different aspects of conduction mecha-
nisms [9-11]. The observed current-voltage (I-V) charac-
teristics of the real SBDs usually deviate from the ideal
thermionic emission (TE) model. The strong dependence
of both barrier height and the ideality factor on tempera-

D. S. REDDY ET AL. 114
ture, the difference in BHs obtained from different meth-
ods and the non-linearity of the Richardson’s plot are the
factors associated with the deviation from the TE model
[9,12,13]. Explanation of the possible origin of such
anomalies has been proposed, taking into account the in-
terface state density distribution [11], quantum-mechanical
tunneling [14-16], image force lowering [14] and most
recently the lateral distribution of barrier height inho-
mogeneities [17,18]. Another way to describe the inho-
mogeneity is to assume a Gaussian distribution of the bar-
rier heights over the contact area [19].
Schottky barrier diodes (SBDs) formed by depositing
various metals on n- type InP have been studied over a
wide temperature range [20-25]. Cetin et al. [20] studied
the temperature dependent electrical characteristics of
Au/n-InP SBDs in the temperature of 80 - 320 K. They
showed that barrier heights and ideality factors varied in
the range of 0.274 - 0.516 eV and 2.32 - 1.05, respec-
tively in the measured temperature range. Bhaskar Reddy
et al. [21] investigated the current-voltage-temperature
(I-V-T) characteristics of Pd/Au/InP SBDs in the tem-
perature range of 220 - 400 K. They reported that the
barrier heights, ideality factors and series resistance were
strongly temperature dependent. Soylu et al. [22] inves-
tigated the current-voltage (I-V) and capacitance-voltage
(C-V) characteristics of the gold Schottky contacts on
moderately doped n-InP in the temperature range of
60-300 K. They found that the ideality factor n of the
diode decreases while the corresponding zero-bias SBH
increasing with an increase in the temperature. Ashok
kumar et al. [23] evaluated the Schottky barrier parame-
ters of Pd/Pt/n-InP Schottky barrier diode in the tem-
perature range of 230 - 410 K. They found that the in-
crease in ideality factor and decrease in barrier height
with a decrease in temperature and explained such be-
haviour on the basis of the thermionic emission with
Gaussian distribution of the barrier heights at the inter-
face. Cimilli et al. [24] investigated the temperature de-
pendent electrical characteristics of Ag Schottky contacts
on n-InP in the temperature range of 30 - 320 K. They
reported that the decrease in the experimental barrier
height calculated from I-V measurement and an increase
in the ideality factor with a decrease in the temperature
which was due to the barrier inhomogeneities at the
metal-semiconductor interface. More recently, Naik et al.
[25] investigated the temperature dependent current-
voltage (I-V) and capacitance-voltage (C-V) characteris-
tics of the Au/Ni/n-InP SBDs in the temperature range of
210 - 420 K. They showed that the barrier parameters
varied significantly with temperature.
The main aim of the present study is to fabricate Pd/Ti
Schottky contacts to n-type InP and measured the cur-
rent-voltage (I-V) and capacitance-voltage (C-V) char-
acteristics in the temperature range of 160 - 400 K by
steps of 40 K. In this work, titanium (Ti) is selected as a
first contact layer because it has low work function and it
provides the lowest forward voltage drop as well. The
palladium (Pd) is used as over layer on Ti contact be-
cause it reacts with InP at low temperatures and im-
proved contact morphology. The resultant temperature-
dependent barrier characteristics of the Pd/Ti/n-InP
Schottky contacts have been interpreted on the basis of the
existence of Gaussian distribution of the barrier height
around a mean value due to barrier height inhomogenei-
ties prevailing at the metal-semiconductor (M-S) interface.
2. Experimental Procedure
Liquid Encapsulated Czokralski (LEC) grown undoped
n-InP (111) samples with carrier concentration of 4.5 ×
1015 cm–3 are used in the present work. Prior to metal
deposition, the InP wafer is degreased for 5 min in warm
organic solvents like trichloroethylene, acetone and
methanol sequentially by means of ultrasonic agitation to
remove contaminants followed by rinsing in deionized
(DI) water and then the samples are dried in high purity
N2 gas. The cleaning procedure is followed by a 60 s dip
in HF (49%) and H2O (1:10) to remove the native oxides
from the front surface of the wafer. After this etching
process the wafer is immediately loaded into the deposi-
tion chamber of e-beam evaporation system. For ohmic
contact, indium (In) is evaporated on to the non-polished
side of the wafer with a thickness of 500 Å. Then the
ohmic contacts are formed by thermal annealing at 350 ˚C
for 60 s in N2 atmosphere. Finally, Ti(200 Å)/Pd(300 Å)
metals are deposited on the polished side of the InP wa-
fer as circular dots with a diameter of 0.7 mm as Schot-
tky contacts by electron beam evaporation system. All
evaporation processes are carried out in a vacuum coat-
ing unit at about 7 × 10–6 mbar. Metal layer thickness as
well as deposition rates are monitored with the help of a
digital quartz crystal thickness monitor. The deposition
rates are about 1.0 Ås–1. The current-voltage (I-V) and
capacitance-voltage (C-V) measurements are carried out
by Keithley source measure unit (Model No.2400) and
automated deep level spectrometer (SEMILAB DLS –
83D) in the temperature range 160 - 400 K by step of 40
K in the dark using temperature controller DLS 83D1
cryostat with a sensitivity of 1 K.
3. Results and Discussion
3.1. Analysis of Current-Voltage-Temperature
(I-V-T) Characteristics
Based on the thermionic emission theory, the current-

D. S. REDDY ET AL. 115
voltage characteristics are given by the relation [1]
0exp1 exp
qV qV
II nkT kT

 

  
 



(1)
where V is the applied voltage drop across the junction
barrier, q is the electronic charge, k is the Boltzmann’s
constant, T is the absolute temperature in Kelvin, n is the
diode ideality factor and I0 is the saturation current and is
expressed [1,2] as
20
exp
*b
o
q
IAAT kT
 





(2)
where A is the diode area, A* is the effective Richard-
son’s constant (9.4 A·cm–2·K–2) based on effective mass
(m* = 0.078 mo) of n-InP [2] and bo is the apparent
barrier height. The values of the barrier height (bo


),
and ideality factor (n) for the device are determined from
the y intercepts and slopes of the forward bias lnI versus
V plot at each temperature, respectively. The barrier
height () can be obtained by rewriting Equation (2) as
bo

2
0
ln
*
bo
kTAA T
qI





(3)
The ideality factor ‘n’ is determined from the slope of
the linear region of the plot of natural log of forward
current versus forward bias voltage and is given by

d
dln
qV
nkT I






(4)
The semi-logarithmic reverse and forward bias cur-
rent-voltage characteristics of Pd/Ti/n-InP Schottky bar-
rier diode (SBDs) in the temperature range of 160-400 K
in steps of 40 K are shown in Figure 1. It is observed
that the leakage current increase with the increase in tem-
perature is in the range 2.44 × 10-7 A (at 160 K) to 1.21 ×
Figure 1. Semi-logarithmic reverse and forward bias cur-
rent-voltage characteristics of Pd/Ti/n-InP SBD in the tem-
perature range of 160 - 400 K.
10–3 A (at 400 K) at –1 V. Measurements showed that the
zero bias barrier height and the ideality factor (calculated
using Equations (3) and (4)) of Pd/Ti/n-InP SBDs with
temperature are 0.35 eV and 3.75 at 160 K to 0.63 eV
and 1.73 at 400 K respectively. It is noted that the barrier
height (BH) is increased linearly from 0.35 eV to 0.63
eV with the increase in temperature from 160 K to 400 K,
accompanied by a significant improvement of the ideal-
ity factor n from 3.75 to 1.73. Interestingly it is noted
that the experimental value of bo is found to increases
with increase in temperature as shown in Figure 2. Since
current transport across the metal-semiconductor inter-
face is controlled by temperature, electrons at low tem-
perature pass over the lower barriers and therefore cur-
rent will flow through patches of the lower SBH and
results in a larger ideality factor. In other words, as the
temperature increases, more and more electrons have
sufficient energy to overcome the higher barrier [11,26].
Figure 3 shows that the experimental values of n (repre-
sented by open circles) increased with a decrease in
temperature. The higher values of the ideality factor (n >
1) indicate that there is a deviation from TE theory for
current mechanism. Idealities greater than one can be
attributed to the presence of a thick interfacial insulator
layer between the metal and semiconductor [1,27].

As shown in the Figure 1, the forward bias I-V char-
acteristics are linear on a semi-logarithmic scale at low
forward bias voltages but deviate considerably from
linearity due to the effect of series resistance (Rs). Tem-
perature dependence of series resistance effect on the I-V
characteristics of the Pd/Ti/n-InP SBDs are investigated
Figure 2. Temperature dependence of the zero-bias appar-
ent barrier height, barrier height from C-V data and flat
band barrier height for Pd/Ti/n-InP SBD. The filled circles
represent experimentally calculated barrier heights. The
open circles represent estimated values of ap using Equa-
tion (13) with

0b

(T = 0 K) = 0.8006 eV and 0

= 0.1144
V values.

D. S. REDDY ET AL. 116
Figure 3. Temperature dependence of the ideality factor for
Pd/Ti/n-InP SBD in the range of 160 - 400 K. The open cir-
cles shows the experimental ideality factors and continuous
curve shows the estimated value of nap using Equation (14)
with 2

= 0.2504 V and3

= –0.01417 V.
Figure 4. Plot of dV/dln(I) versus I for Pd/Ti/n-InP SBD.
in the temperature range of 160 - 400 K. The resistance
of the SBD is the sum of the total resistance value of the
resistors in series and resistance in semiconductor device
in the direction of current flow. The values of series re-
sistance (Rs) are achieved from the forward bias I-V data
using the method developed by Cheung [28]. The for-
ward bias current-voltage characteristics due to thermio-
nic emission of a Schottky contact with the series resis-
tance can be expressed as [1,29]

d
dln S
V
IRn kT
I
q





(5) Figure 5. Temperature dependence of series resistance of
Pd/Ti/n-InP SBD in the temperature range of 160 - 400 K.
Figure 4 shows the plot of dV/d(lnI) versus I as a
function of temperature. Equation (5) should give
straight line for the data of downward curvature region in
the forward bias I-V characteristics. Thus the slope of the
plot of dV/d(lnI) versus I gives RS as the slope and
n(kT/q) as the y-axis intercept. The series resistance (Rs)
obtained for each temperature using Equation (5) and
corresponding values are 1836  at 160 K and 272  at
400 K. It is observed that the series resistance increases
with decrease of temperature as shown in Figure 5. As
can be seen in Figure 5, the decrease of RS with the in-
creasing of temperature is believed to be due to factors
responsible for increase in ideality factor n and lack of
free carrier concentration at low temperatures [30]. The
calculated zero-bias BH, ideality factors and series resis-
tance of the Pd/Ti Schottky contacts as a function of
temperature is given in the Table 1.
The plot of ln(I0/T2) versus 103/T is found to be non-
linear in the measured temperature range as shown in
Figure 6. The non-linearity of the conventional ln(I0/T2)
versus 103/T is caused by the temperature dependence of
the BH and ideality factor. The experimental data are
seen to fit asymptotically to a straight line at higher tem-
peratures only. According to Equation (6), the plot of
ln(I0/T2) versus 103/T yields a straight line with the slope
giving the BH at T = 0 K and the intercept giving the
Richardson constant. An activation energy value of 0.27
eV from the slope of this straight line is obtained for the
Pd/Ti Schottky contact. The values of A* obtained from
the intercept of the straight line portion at the ordinate of
the experimental ln(I0/T2) versus 1000/T plot in Figure 6
is equal to 2 × 10–3 A·cm-2·K-2, which is lower than the
known value of 9.4 A·cm-2·K-2. The deviation in the
Richardson plot may be due to the effects of the image-
force, the effect of tunneling current through the poten-
tial barrier, the effect of recombination in the space
charge region appearing at low voltage and the variation
of the charge distribution near the interface [31]. Ac-
For the evaluation of the BH, one may also make use
of the Richardson plot of the saturation current. Equation
(2) can be written as

00
2
lnln *b
I
AA kT
T





q
(6)

D. S. REDDY ET AL.117
Table 1. Ideality factors, series resistances and Schottky barrier heights of Pd/Ti Schottky contact on n-type InP in the tem-
perature range of 160-400 K.
Temperature Ideality Series Barrier heights
factor (n) resistance (Rs)
(K) (Ω) 0b

(eV) VC

(eV) bf

(eV)
160 3.75 1836 0.35 0.73 1.136
200 3.11 1255 0.40 0.71 1.074
240 2.61 1143 0.47 0.69 1.056
280 2.26 893 0.53 0.68 1.051
320 2.08 442 0.55 0.65 0.983
360 1.92 392 0.59 0.63 0.975
400 1.73 272 0.63 0.61 0.949
Figure 6. Richardson plot of ln(I0/T2) versus 103/T for
Pd/Ti/n-InP SBD.
cording to Horvath [32], the A* value obtained from the
temperature dependence of the I-V characteristics may
be affected by the lateral inhomogeneity of the barrier,
and the fact that it is different from the theoretical value
may be connected to a value of the real effective mass
that is different from the calculated one.
It is observed that ideality factor n is greater than unity
which indicates that TE is not the only operative mecha-
nism for current flow and is usually attributed to a SBH
which is bias dependent. If the current transport is con-
trolled by the thermionic field emission (TFE) theory, the
relation between current and voltage can be expressed as
[33,34]
0
exp
s
V
II E






 (7)
with 00
000
coth tun
qEn kT
EE kT q



 (8)
where Eoo is the characteristic energy, which is related to
the transmission probability of the carrier through the
barrier given by
1
2
00 4
d
*
es
N h
Em




where h is the Planck constant (h = 6.626 × 10–34 J·sec), Nd
is the donor concentration, εs is the semiconductor di-
electric constant and is the electron effective mass.
*
e
m
In the case of our Pd/Ti/n-InP SBDs with Nd = 2.63 ×
1015 cm–3 (from C-V method at room temperature), =
0.077 m0 and εs = 12.4ε0 the value of E00 is found to be
about 0.9738 meV. When considering the bias coeffi-
cient of the barrier height, β = /V, Equation (8) can
be written as [32,35]
*
e
m
b


0
1
tun
E
nkT

 (10)
The theoretical temperature dependence of ideality
factor for the case when the current through Schottky
junction is dominated by the TFE is shown in Figure 7.
The solid lines in Figure 7 are obtained by fitting Equa-
tion (8) to the experimental temperature dependence
values of the ideality factor presented for different values
of the characteristic energy Eoo, without considering the
bias coefficient of the BH, β = 0, for the Pd/Ti/n-InP
SBDs. The filled circles in the Figure 7 shows the tem-
perature dependence values of ideality factor obtained
from the experimental current-voltage (I-V) characteris-
tics. From the Figure 7, it is observed that the experi-
mental temperature dependence of ideality factor is in
agreement with the curve (C) obtained with Eoo = 15
meV for the Pd/Ti/n-InP SBD studied in the temperature
range of 160 - 400 K. Hence, there is a significant con-
sistency between the theoretical and experimental char-
acteristics as shown in Figure 7 (curve C).
The characteristic energy Eoo value is much larger than
the theoretical value 0.973 meV calculated for n-InP. To
understand the possible origin of the high characteristic
energy values Eoo, it should be underlined that Eoo is
connected with the transmission probability [36,37]. The
characteristic energy has been related to several effects
such as the electric field present on the surface of the
semiconductor [38], the existence of relatively a thick
interfacial insulating layer between the deposited metal
and semiconductor and the density of states. Therefore,
any mechanism which enhances the electric field or the

(9)

D. S. REDDY ET AL. 118
Figure 7. Theoretical temperature dependence of ideality
factor for the case when the current through the junctions
is dominated by the TFE with characteristic energy values
E00 according to Equation (8) (Solid lines) for Pd/Ti/n-InP
SBD. The filled circles show the experimental temperature
dependence values of the ideality factor obtained from I-V
characteristics as shown in Figure 1.
density of states at the semiconductor surface will in-
crease the TFE, and so the apparent Eoo [32].
Another way to correlate the obtained parameters ide-
ality factor n and barrier height bo is to calculate the
flat-band BHbfThe BH decreases with decreasing
temperature which is obtained from Equation (3) is
called apparent or zero-bias BH. The BH obtained under
flat-band condition is called the flat-band BH and is con-
sidered as the real essential quantity. In contrast to the
case of the zero-bias BH, the electric field in the semi-
conductor is zero under the flat-band condition and thus
the semiconductor bands are flat, which eliminates the
effect of tunneling and image force lowering that would
affect the I-V characteristics and removes the influence
of lateral inhomogeneity [12,20]. The flat-band barrier
height () is given by [39,40]

. 
bf


01ln
c
bf b
d
N
kT
nn
qN



 

 


T 

(11)
where Nc is the effective density of states in the conduc-
tion band and Nd the carrier concentration. The tempera-
ture dependent Nc and Nd values are used in calculating
CV andbf. Figure 2 shows the variation of flat-
band barrier height bf as a function of the temperature.
However, it is observed that bf increase with de-
creasing temperature. Similar phenomenon is also re-
ported by the others [20,22]. The temperature depend-
ence of the flat-band barrier height can be expressed as





 
0
bf bf
TT   (12)
where and

0
bf T
 

are the flat-band barrier
height extrapolated to the absolute zero and the tempera-
ture coefficient of the flat-band barrier height, respec-
tively. The fit of Equation (12) to the experimental data
(filled triangles) in Figure 2 yields (T = 0) = 1.24
eV and bf


= –7.4285 × 10–4 eVK–1.
The ideality factor is simply a manifestation of the
barrier uniformity and it increases for an inhomogeneous
barrier [41]. A significant increase in the ideality factor
and decrease in the SBH at low temperatures are possibly
originated by inhomogeneities of thickness, and compo-
sition of the layer, non-uniformity of the interfacial
charges or the presence of a thin insulating layer between
the metal and the semiconductor [9,10,26,39]. Schmits-
dorf [42] used Tung’s theoretical approach and they
found a linear correlation between the experimental zero-
bias SBHs and ideality factors. Figure 8 shows a plot of
experimental BHs versus ideality factor with temperature
for the Pd/Ti/n-InP Schottky diode. The solid line in the
Figure 8 is the least-squares fit to the experimental data.
As can be seen from the Figure 8, there is a linear rela-
tionship between the experimental effective SBHs and
the ideality factors of the Schottky contact. The extrapo-
lation of the experimental BHs versus ideality factor plot
to n = 1 has given a homogeneous BH (hom ) of ap-
proximately 0.71 eV. The other BH values deviate from
this value due to local inhomogeneities. A homogeneous
BH of approximately 0.71 eV obtained from the ex-
trapolation of the least-square linear fitting to data to n =
1 (Figure 8) is in agreement with the value obtained by
Ashok et al. [23] for the Pd/Pt/n-InP Schottky barrier
diodes.

The decrease in the BH with a decrease in temperature
can also be explained by the lateral distribution of BH if
the BH has a Gaussian distribution of the BH values over
the Schottky contact area with the mean BH (0b

) and
standard deviation (0

). The standard deviation is a
measure of the barrier homogeneity. The Gaussian dis-
tribution of the BHs yields the following expression for
Figure 8. The zero-bias barrier height versus ideality factor
for the Pd/Ti/n-InP SBD at different temperatures.

D. S. REDDY ET AL. 119
the BH [9,10,12,20,22]

2
0
002 b
ap
q
T kT

 
(13)
where ap is the apparent BH measured experimentally.
The same expression (Equation (13)) is used already by
Song et al. [9] and also by Werner and Guttler [10] for
the apparent BH construction. Usually the temperature
dependence of 0


is small and it can be neglected. The
observed variation of ideality factor with temperature in
the model is given by [10]
3
2
112
ap
q
nkT







(14)
where nap is apparent ideality factor (experimental data),
and the coefficients 2

and 3

quantify the voltage
deformation of the BH distribution, that is, the voltage
dependencies of the mean BH and the barrier distribution
widths are given by coefficients 2

and3

, respec-
tively. The experimental bo versus 1/2 kT and nap ver-
sus 1/2 kT plots are shown in Figure 9. The linearity in
the apparent barrier height or ideality factor versus 1/2
kT curves is in agreement with the recent model which is
related to thermionic emission over a Gaussian distribu-
tion. The plot of bo versus 1/2 kT is a straight line with
the intercept on the ordinate determining the zero mean
BH


0b (T = 0 K) and the slope gives the standard de-
viation (0


). The corresponding values are 0.80 eV and
114 mV for 0b
 ( 0) and 0 T =

respectively. More-
over, as can be seen in the Figure 2, the experimental
results ofap
 fit ve well with the theoretical Equation
(13) with
ry
0b
 (T == 0.80 eV and 0 0)

= 114 .
The open circles in Figure 2 indicates the data estimated
with these parameters in using Equation (13) and filled
circles indicates the experimental barrier heights meas-
ured from I-V characteristics. The observed standard
deviation is 14.3% of the mean barrier height. The lower
value of standard deviation shows the better rectifying
performance with barrier homogeneity.
mV
Figure 9 shows the experimental ideality factor versus
1/2 kT plot is a straight line. The values obtained for 2

and 3

from the intercept and the slopes of the straight
line are 0.2504 V and −0.0141 V, respectively. The linear
behavior of this plot reveals that the ideality factor does
indeed express the voltage deformation of the Gaussian
distribution of the SBH. Furthermore, the experimental
results of nap fit very well with theoretical Equation (14)
with 2

= 0.2504 V and 3

= –0.0141 V as shown in
Figure 3. The continuous solid line in the Figure 3 indi-
cates data estimated with these parameters using Equa-
tion (14) and open circles indicates experimental ideality
factor values. The lower value of 0

corresponds to
more homogeneous barrier heights. According to Cavlet
Figure 9. The zero-bias barrier height and ideality factor
versus 1/2 kT plots and their linear fits for the Pd/Ti/n-InP
SBD according to Gaussian distribution of the barrier
heights.
et al. [43], the value of 0

(114 mV) is not small com-
pared to the mean value of 0b (T = 0) = 0.80 eV
which indicates the greater inhomogeneities at the inter-
face and thus potential fluctuation. The inhomogeneity
and the potential fluctuation only affect low temperature
current-voltage characteristics.

Due to the barrier inhomogeneity at low temperatures,
the conventional Richardson plot deviates from linearity.
It can be modified by combining Equations (2) and (13)
as follows

22
00
222
ln ln
2
*bo
Iq q
AA kT
TkT








 (15)
A modified ln(I0/T2) – ( 22 22
0) versus 1000/T
plot can be obtained according to Equation (15). The plot
should give a straight line with the slope directly yielding
the mean barrier height
2qkT 
0b

(T = 0) and the intercept (=
lnAA*) at the ordinate, determining A* for a given diode
area A. Figure 10 shows the modified ln(I0/T2) –
(22 22
0) versus 1000/T plot gives
2qkT 
0b (T = 0),
and A* as 0.796 eV and 6.16 A·cm–2·K–2, respectively,
without using the temperature coefficient of the barrier
height α. Mean while, this value of

0b= 0.796 eV is
approximately the same as the value of

0b= 0.80 eV
from the plot of Φap versus 1/2 kT given in Figure 9. The
modified Richardson constant A* = 6.16 A· cm–2· K–2 is in
close agreement with the theoretical value of A* = 9.4
A·cm–2·K–2.

3.2. Analysis of Capactance-Voltage-
Temperature (C-V-T) Characteristics
The experimental reverse bias C-2-V characteristics of
the Pd/Ti/n-InP SBD in the temperature range of 160 -
400 K in steps of 40 K are shown in Figure 11. The

D. S. REDDY ET AL. 120
Figure 10. Modified Richardson ln(I0/T2)-()
versus 1000/T plot for the Pd/Ti/n-InP SBD according to
the Gaussian distribution of barrier heights.
222
0
22/Tkq

Figure 11. The reverse bias C-2-V characteristics of the
Pd/Ti/n-InP SBD in the temperature range of 160 - 400 K.
junction capacitance has been performed at a frequency
of 1 MHz. The C-V relationship for Schottky diode is
[1,29]
22
2
bi
sd
1
V
q
CqNA 







kT
V



(16)
where s is the permittivity of the semiconductor (s =
12.4 0) [24], V is the applied voltage. The x-intercept of
the plot of (1/C2) versus V gives V0 and it is related to the
built in potential Vbi by the equation Vbi = V0 + kT/q,
where T is the absolute temperature. The BH is given by
the equation CV = V0 + Vn + kT/q, here Vn = (kT/q) ln
(Nc/Nd). The density of states in the conduction band
edge is given by Nc = 2 (2 m*kT/h2)3/2, where m* =
0.078mo and its value is 5.7  1017 cm–3 for InP at room
temperature [2]. The temperature dependence of the ex-
perimental carrier concentration (Nd) is calculated from
the slope of reverse bias C–2-V characteristics from Fig-
ure 11 and the values of Nd varied from 1.96 × 1015 to
3.11 × 1015 cm–3 in the temperature range of 160 - 400 K.
The values of Nc varied from 2.06 × 1017 to 8.22 × 1017
cm–3 as temperature varied between 160 K and 400 K,
respectively. It is observed that carrier concentration for
n-InP increased with increase in temperature. The esti-
mated Schottky barrier height of Pd/Ti Schottky contact
is in the range of 0.73 eV at 160 K to 0.61 eV at 400 K
respectively. It is noted that the barrier height CV


in-
creased with decrease in temperature. Furthermore, as
can be seen from Figure 2 it was observed that the
CV

values are higher than the bo values in the inves-
tigated temperature range. This discrepancy could be
explained by the existence of an interfacial layer or of
trap states in the semiconductor and the existence of
Schottky barrier height inhomogeneity [10,11,26]. Due
to the square dependence of CV on 1/C, compared to
the logarithmic dependence of ΦI-V on the current, CV



is more sensitive to the experimental error of the meas-
urement data than
I
V

[19]. Moreover, it is clearly seen
from the Figure 2 that CV

is obtained to increase with
decreasing temperature. The temperature dependence of
CV

is expressed as


0KTT
CV CV

    (17)
where CV

(T = 0 K) is the barrier height extrapolated
to zero temperature and

is the temperature coeffi-
cient of the barrier height. The linear fit of Equation (17)
to the experimental data (filled squares) in Figure 2 yiel-
ds CV

(T = 0 K) = 0.8114 eV and

= –5.1 × 10-4
eVK-1 which is the temperature coefficient of the InP
band gap [44].
Furthermore, it can be seen that the apparent barrier
height from the experimental forward bias I-V plot is
also related to the mean barrier height 0b
 =CV

from
the experimental reverse bias C-2-V plot [10,40]. The
capacitance depends only on the mean band bending and
is insensitive to the standard deviation 0

of the barrier
distribution [10,40]. The relationship between Φap and
ΦCV is given by [10,40]

2
00
22
CV ap
q
k
qT
kT






 (18)
where


is attributed to the temperature dependence of
0.

Figure 12 shows the experimental (ΦCV-ΦIV) versus
1/T plot according to Equation (18). The plot should give
a straight line of the slope 2
02k
 and a y-axis intercept
k2


from which the parameters 0

and


can be
determined. The slope and y-axis intercept of the plot
given the values of 0

= 149 mV and


= 5.59 ×
10–5 V2·K–1, respectively. The value of 0

in the inves-
tigated temperature region is in close agreement with the
value of 0

114 mV from the plot of Φap versus 1/2 =

D. S. REDDY ET AL. 121
Figure 12. Barrier height difference between values as de-
rived from the conventional evaluation of I-V and C-V data
as a function of inverse temperature.
kT given in Figure 9 which is not small when compared to
the mean BH value of 0.796 eV. Therefore, these signifi-
cantly large potential fluctuations drastically affect low
temperature I-V data and, in particular, they could be
responsible for the curved behaviour of the conventional
Richardson plot as shown in Figure 6.
4. Conclusions
In this paper, the current-voltage (I-V) and capaci-
tance-voltage (C-V) characteristics of Pd/Ti/n-InP SBDs
have been investigated in the temperature range 160 -
400 K. The electrical parameters such as ideality factor
(n) and zero-bias BH (bo ) are found to be strongly tem-
perature dependent. It is found that the ideality factor (n)
of the diode decreases while the corresponding zero-bias
SBH increasing with an increase in temperature. The
values of series resistance (Rs) estimated from Cheung’s
method were strongly temperature dependent. The
flat-band barrier height values are obtained from the
temperature dependence of the I-V characteristics and
the values are in the range 1.13 - 0.94 eV. The laterally
homogeneous SBH value is approximately 0.71 eV for
the Pd/Ti/n-InP SBD which is deduced from the linear
relationship between the experimental BHs and ideality
factors. The mean BH (

0b
 ) and effective Richardson
constant A* are found as 0.796 eV and 6.16 Acm-2K-2,
respectively, from a modified ln(I0/T2) – ()
versus 1000/T plot. The experimental results of ap
22 22
02q/kT


and
nap fit very well with the theoretical equations related to
the Gaussian distribution of ap

and nap. It can be con-
cluded that the temperature dependent current-voltage
(I-V) and capacitance-voltage (C-V) characteristic of the
Pd/Ti/n-InP Schottky barrier diodes over a wide tem-
perature range have been explained on the basis of
thermionic emission mechanism by assuming the pres-
ence of Gaussian distribution of barrier heights.
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