Anomalous current transport in Au/low-doped n-GaAs Schottky
barrier diodes at low temperatures
S. Hardikar
1
, M.K. Hudait
1,2
, P. Modak
1
, S.B. Krupanidhi
2,∗
, N. Padha
3
1
Central Research Laboratory, Bharat Electronics Ltd., Bangalore - 560 013, India
2
Materials Research Center, Indian Institute of Science, Bangalore - 560 012, India
(Fax: +91-80/334-1683, E-mail: sbk@mrc.iisc.ernet.in)
3
Department of Physics and Electronics, University of Jammu, Jammu - 180 004, India
Abstract. The current–voltage characteristics of Au/low-
doped n-GaAs Schottky diodes were determined at vari-
ous temperatures in the range of 77–300 K. The estimated
zero-bias barrier height and the ideality factor assuming
thermionic emission (TE) show a temperature dependence
of these parameters. While the ideality factor was found to
show the T
0
effect, the zero-bias barrier height was found
to exhibit two different trends in the temperature ranges of
77–160 K and 160–300 K. The variation in the flat-band bar-
rier height with temperature was found to be −(4.7 ± 0.2) ×
10
4
eVK
−1
, approximately equal to that of the energy band
gap. The value of the Richardson constant, A
∗∗
, was found to
be 0.27 Acm
−2
K
−2
after considering the temperature depen-
dence of the barrier height. The estimated value of this con-
stant suggested the possibility of an interfacial oxide between
the metal and the semiconductor.Investigations suggested the
possibility of a thermionic field-emission-dominated current
transport with a higher characteristic energy than that pre-
dicted by the theory. The observed variation in the zero-bias
barrier height and the ideality factor could be explained in
terms of barrier height inhomogenities in the Schottky diode.
PACS: 72.10.-d; 73.30.+y; 73.40.GK
The current transport across a Schottky junction is of interest
to materials physicists and device physicists. Schottky bar-
rier diodes (SBD) are widely studied and many attempts have
been made to understand their behaviour. The knowledge of
the conduction mechanism across the Schottky barrier is es-
sential in order to calculate the Schottky barrier parameters
and explain the observed effects. Generally, the SBD param-
eters are determined over a wide range of temperatures in
order to understand the nature of the barrier and the con-
duction mechanism. Although the thermionic emission (TE)
theory is normally used to extract the SBD parameters, there
have been reports of certain anomalies at lower temperatures
deviating from the theory. The ideality factor and the bar-
rier height determined from the forward-bias current–voltage
∗
To whom all the correspondence should be addressed
(I–V) characteristics are found to be a strong function of tem-
perature [1–7]. The ideality factor is found to increase with
decreasing temperature. This effect, known as the T
0
, effect
was first reported by Padovani and Sumner [1] and is widely
studied. The zero-bias barrier height as determined from the
forward-bias I–V characteristics for the thermionic emission
decreases with decreasing temperature. The zero-bias barrier
height appears to be lower than the barrier height obtained
from the capacitance–voltage (C–V) measurements in the
temperature range used for the study. This implies that there
is an excess current flow in the diodes than that predicted by
the thermionic emission theory. Explanations of the possible
origin of such anomalies have been proposed taking into ac-
count the interface state density distribution [8, 9], quantum-
mechanical tunnelling including the thermionic field emis-
sion [2,10–12] and more recently the lateral distribution of
barrier height inhomogenities[5, 13–15].We have studied the
forward-bias I–V characteristics of a Au/n-GaAs Schottky
diode in the low temperature range of 77–300 K, with the
doping concentration of the n-GaAs well within the domain
of the TE theory and found some anomalies. Attempts were
made to examine the possible factors contributing to the ob-
served anomalies based on the proposed theories.
1 Experimental
The Schottky diodes were fabricated on epitaxial undoped
GaAs film, grown on silicon-doped (2× 10
18
cm
−3
) n
+
-
GaAs substrates (100) 2
◦
off-oriented towards the h110i
direction, using the metal organic chemical vapor deposition
(MOCVD) technique, by evaporating gold under vacuum.
The back ohmic contact was made using Au−Ge eutectic
with an overlayer of gold. The growth procedure used yields
an epitaxial film of n-type conductivity with an unintentional
doping concentration of the order of 10
15
cm
−3
[16].
Room temperature I–V characteristics of the diodes
were measured using an automated arrangement consist-
ing of a Keithley source measure unit SMU236, a PC486
and a probe station. Diodes amongst several diodes show-
ing similar I–V characteristics at room temperature were
50
mounted and bonded on TO-39 headers. Low-temperature I–
V characteristics were obtained in the temperature range of
77–300 K using the automated setup mentioned above and
a cryostat. The temperature was within ±1Kduring the data
acquisition.
The carrier concentration of the epitaxial layer, 2.5×
10
15
cm
−3
, was determined using the reverse-bias C–V
characteristics at 1MHz on a HP4194A LCR bridge and
was further confirmed by means of electrochemical C–V
characteristics.
2 Method of analysis
2.1 Forward I–V characteristics
The current density vs. voltage (J–V) characteristics of the
Schottky diode are plotted as a function of temperature in
Fig. 1. The plot exhibits a linear portion over 3–4 decades of
magnitude of current density. The diode ideality factor, n,the
saturation current density, J
s
, and the barrier height, Φ
b
were
measured by using the TE theory. According to the TE theory
the current transport across a Schottky diode is governed by
the relation [17]
J = A
∗∗
T
2
exp
(
−qΦ
b
/kT
)
exp
(
qV/nkT
)
for V > 3kT/q ,
(1)
J
s
= A
∗∗
T
2
exp
(
−qΦ
b
/kT
)
, (2)
where A
∗∗
is the Richardson constant for GaAs.
The linear portion of the J–V characteristics was plotted
on a semi-log plot to extract the Schottky diode parameters
viz. the ideality factor, n, and the zero-bias barrier height, Φ
b
.
The value of A
∗∗
= 8Acm
−2
K
−2
was used to calculate the
value of the zero-bias barrier height.
Fig.1. The current density vs. voltage characteristics of the Au/n-GaAs
Schottky diode at various temperatures
The ideality factor and the zero-bias barrier height, are
plotted as a function of temperature in Fig. 2. The plot shows
that the ideality factor exhibits an increasing trend with de-
creasing temperature, the change being more pronounced be-
low 150 K, whereas the zero-barrier height first increases with
decreasing temperature upto 160 K and then decreases. This
apparent decrease in the zero-bias barrier height below 160K
is consistent with the observations made by others on dif-
ferent Schottky diodes [3–7]. They found that the zero-bias
barrier height decreases with decreasing temperature. The
increase in the zero-bias barrier height with decreasing tem-
perature in the 160–300 K range is similar to the variation in
the barrier height measured by C–V measurements and has
not been reported in the literature.
2.1.1 Flat-band barrier height. The barrier height as obtained
from the TE theory decreases with decreasing temperature.
The barrier height obtained from (1) is called the appar-
ent barrier height or the zero-bias barrier height. The barrier
height obtained under flat-band condition is called the flat-
band barrier height and is considered the real fundamental
quantity. Unlike the case of the zero-bias barrier height, the
electric field in the semiconductor is zero under the flat-band
conditions. The flat-band barrier height is given by [18].
Φ
f
b
= nΦ
b
− (n − 1)kT ln
(
N
C
/N
D
)
, (3)
where Φ
b
is the zero-bias barrier height, N
C
is the density of
states in the conduction band, and N
D
is the doping concen-
tration in the semiconductor.
The variation in Φ
f
b
as a function of temperature is shown
in Fig. 3. Φ
f
b
increases with decreasing temperature in the
150–300 K range and, anomalously, decreases below 150 K.
A linear fit is used to fit the points in the range of 150–300 K
in order to determine the slope and the y-axis intercept, which
Fig. 2. The variation in the zero-bias barrier height and the ideality factor
with temperature, calculated using (1) and (2), for the Au/n-GaAs Schottky
diode. The zero-bias barrier height increases with decreasing temperature
up to 160 K and then decreases in the 77–160 K range
51
Fig.3. The flat-band barrier height, calculated using (3), as a function of
temperature. The continuous line represents the best fit to the points in the
150–300 K range. The slope and the barrier height at 0Kare shown in the
figure
give the valueof dΦ
f
b
/dT and the value of barrier height at ab-
solute zero, Φ
f
b
(0), respectively. The linear fit yields a slope,
dΦ
f
b
/dT equal to −(4.7± 0.2) × 10
−4
eVK
−1
and an inter-
cept, Φ
f
b
(0) equal to 1.083 eV.ThevalueofdΦ
f
b
/dT is close
to the value obtained by assuming that the variation in the
value of Φ
f
b
(0) is entirely due to the variation in the band
gap [3, 19,20].
2.1.2 Effect of image force. In order to understand the factors
influencing the lowering of the barrier height with decreasing
temperature, the effect of image-force lowering was first con-
sidered. The barrier lowering due to the image-force effect is
given by [21].
∆Φ
imf
=
q
3
N
D
/8π
2
ε
3
s
(
Φ
b
− V − Φ
n
− kT/q
)
1/4
, (4)
where Φ
n
= kT/q ln(N
C
/N
D
) and V is the applied bias.
The value of ∆Φ
imf
found by using (4) is 13.8meV at
77 K for a Φ
b
of 0.89 V and a typical forward bias voltage
of 0.45 V in the present work. This value of ∆Φ
imf
is much
lower than the observed barrier height lowering of 126 meV
(Fig. 2). Therefore, the image-forcelowering alone cannot ac-
count for the lowering of the barrier height.
The decrease in the barrier height and the increase in the
ideality factor with a decrease in the operating temperature
is indicative of a deviation from the pure thermionic emis-
sion theory and possibly the thermionic-field-emission (TFE)
mechanism warrants consideration. The parameter that de-
termines the relative importance of the TE, TFE and field
emission (FE) is given by [22].
E
00
= h/4π
N
D
/m
∗
e
ε
s
= 18.5× 10
−15
N
D
/m
∗
r
ε
r
1/2eV
(5)
In the case of our diode, with N
D
= 2.5× 10
21
m
−3
, m
∗
e
=
0.067m
e
and ε
r
= 12.8, this value turns out to be 1.056meV.
According to the theory TFE dominates only when E
00
≈ kT
and the value of E
00
calculated from (6) is less than kT by
a factor of six, even at 77 K. The barrier-height lowering ac-
counting for the TFE and using the theoretically calculated
value of E
00
is given by [23].
∆Φ
TFE
= (3/2)
2/3
(E
00
)
2/3
V
1/3
d
, (6)
where V
d
is the built-in potential.
For the E
00
value of 1.056 meV and a V
d
of 0.91 V this
value is 13.3meV, which again cannot account for the ob-
served barrier-height lowering.
2.1.3 Barrier-height inhomogenity. More recently it has been
proposed that the barrier height has a lateral Gaussian distri-
bution with a mean barrier height [5]. The reduction in the
barrier height with temperature has been explained by the lat-
eral distribution of the barrier height. The assumption of the
Gaussian distribution of the barrier height yields the follow-
ing equation for the barrier height.
Φ
b
= Φ
bmean
− σ
2
S
/
(
2kT/q
)
, (7)
where Φ
b
is the zero-bias barrier height, Φ
bmean
is the mean
barrier height, and σ
S
is the standard deviation of the barrier
distribution.
The mean barrier height is the same as the barrier height
measured by capacitance measurements. Capacitance meas-
urements yield a barrier height which is essentially at zero
electric field. Since the flat-band barrier height is also ob-
tained at zero electric field, both the quantities are the
same [18]. Using this relation and Φ
f
b
= Φ
bmean
,avalue
of σ
S
= 53.3meV and Φ
b
= 1.012eV were obtained. Using
these values in (7), a continuous curve was generated as
a function of the operating temperature, which is plotted in
Fig. 2. It can be observed from the figure that although the
curve obtained by using (7) agrees well with the values of
the zero-bias barrier height in the 77–210 K range, it de-
viates appreciably from the experimental points at higher
temperatures.
Another approach to the lateral inhomogenities in the
Schottky barrier heights was proposed by Sullivan et al. [13]
and Tung [14]. They proposed that the Schottky barrier con-
sists of laterally inhomogenous patches of different barrier
heights. The patches with lower barrier height have a larger
ideality factor and vice versa. Schmitsdorf et al. [15] found
a linear correlation between the zero-bias barrier height and
the ideality factors using Tung’s theoretical approach. The ex-
trapolation of the linear fit to the these data yields the homo-
geneous barrier height at an ideality factor of 1.01. A similar
analysis of our data to this effect is presented in Fig. 4.
It is observed that the barrier height correlates linearly
with the ideality factors measured at temperatures below
200 K. The homogeneousbarrier height determined from this
analysis yields a value of 0.97 eV.
2.1.4 The ideality factor and T
0
effect. The variation in the
ideality factor with temperature is shown in Fig. 2, and is
52
Fig.4. The variation of the zero-bias barrier height with temperature. The
continuous curve is calculated using (7) with σ
0
= 53.3meV.Thecontinu-
ous curve matches well with the points in the 77–210 K range and shows
considerable deviation at higher temperatures
called the T
0
effect [1]. The ideality factor of the diodes show-
ing this behaviour varies with temperature as
n = 1+ T
0
/T , (8)
where T
0
is a constant.
This implies that a plot of nT vs. T is a straight line with
a slope of unity and the intercept T
0
at the ordinate. Figure 5
shows such a plot with the slope equal to 1.002, which is
close to unity as predicted by the empirical relation and the
intercept T
0
= 17.1± 1.2K.ThevalueofT
0
can vary between
10–100 K for diodes on the same slice of GaAs [2]. The
T
0
effect could be due to generation recombination current
in the depletion region or due to the TFE. The C–V char-
acteristics of the diode under study at different frequencies
in the range of 1kHz–1MHz were independent of the fre-
quency within this range. This indicates that the diode does
not contain a measurable amount of deep levels within the
space-charge region and therefore the influence of the minor-
ity carriers on current transport can be neglected [24,25].
2.1.5 Effect of image force. The possibility of the image-force
lowering influencing the observed variation of the ideality
factor was checked using the relation [21].
[
n
imf
]
−1
= 1− 1/4
q
3
N
D
/8π
2
ε
3
s
1/4
×
(
Φ
b
− V − Φ
n
− kT/q
)
−3/4
. (9)
This equation yields a value of 1.011 at a typical bias value of
0.45 V at 300K and a value of 1.008 at a temperature of 77 K.
This shows that the image-force lowering cannot account for
the observed variation in the ideality factor.
Fig. 5. Plot shows nT vs. T. The linear behaviour of the experimental values
is determined by (8). The value of the slope and the T
0
are shown in the
figure
2.1.6 Effect of thermionic field emission. The ideality factor is
further analyzed by considering the variation in the ideality
factor n caused by a tunnelling current. The relation for the
variation in the ideality factor is given by [22].
n = qE
00
/kT coth
(
qE
00
/kT
)
, (10a)
n = qE
0
/kT , (10b)
where
E
0
= E
00
coth
(
qE
00
/kT
)
. (10c)
Figure 6 shows a plot of E
0
vs. kT/q. The intercept on the
E
0
axis of such a plot yields the value of E
00
for the Schot-
tky diode under study. It can be seen from the figure that
the experimental points are linear with temperature up to the
kT value corresponding to the temperature of 92 K. A care-
ful examination of the plot reveals a slight curvature near
77 K. This can be confirmed only by determining the ideal-
ity factors from the I–V characteristics recorded below this
temperature. Since our experimental setup is limited to an op-
erating temperature of 77 K, this could not be confirmed. If it
is assumed that the curvature near 77 K is indeed present, then
it reveals a higher characteristic energy, which cannot be ex-
plained by the above theories. In order to confirm the higher
value of the characteristic energy, another method was used
which requires plotting of the theoretically determined values
of n vs. temperature on a 1/n vs. 1000/T plot [26]. The fol-
lowing relation was used to generate such theoretical plots
with E
00
as the parameter.
1/n = kT/q
[
E
0
/
(
1− β
)]
, (11)
where β indicates the bias dependence of the barrier height.
Since the values of 1/n are sensitive to changes near unity
such a plot provides a good check to determine whether the
53
Fig.6. Plot of E
0
vs. T using (10c) assuming TFE. The slight curvature
near 92 K indicates the possibility of a higher characteristic energy than is
predicted by the theory and estimated using (5)
dominating mechanism is TE or TFE. The experimentally
determined values of the ideality factor are superimposed
on such a plot to determine the values of E
00
and β ap-
proximately. Figure 7 shows such a plot. It can be observed
that the experimental points match closely to the curve with
E
00
= 6.5meVand β = 0.032. Therefore, the diode under test
certainly exhibitshigh characteristic energiesnot expectedfor
the doping concentration range used in our GaAs film, imply-
ing a conduction mechanism dominated by TFE.
2.1.7 Influence of barrier height inhomogenity. Using the po-
tential fluctuations model [5], the ideality factor is given by
the relation
1/n = 1− γ + σ
s
qζ/kT . (12)
Using the experimentally determined values of n at different
temperatures and the value of σ
0
obtained from (7), the values
of γ = 0.006 and ζ = 0.0236 were obtained. The experimen-
tally determined values and the continuouscurve representing
a fit to these values using the parameters obtained by using
(12) are shown in Fig. 2.
2.1.8 Richardson constant. The Richardson constant is usu-
ally determined from the intercept of ln( J
s
/T
2
) vs. 1000/T
plot. Figure 8a shows the plot obtained by the usual method.
This plot yields a Richardson constant of 0.32 Acm
−2
K
−2
and a Φ
b
of 0.85 eV. The value of the Richardson constant is
about one order magnitude lower compared to the theoretical
value of 3Acm
−2
K
−2
[27]. A careful observation of the ex-
perimental points shows that the points up to a temperature
of 160 K exhibit a better linearity. A best fit to the points in
the 160–300 K range yields an A
∗∗
value of 43.2Acm
−2
K
−2
Fig. 7. Plot showing 1/n vs. 1/T curves (solid lines) with E
00
as the pa-
rameter ranging from 2–20 meV in steps of 2meVgenerated using (11) and
β = 0. The experimental points are also superimposed on the theoretically
generated plot. The dotted line shown on the plot represents a curve with
the value of E
00
= 6.5meVand β = 0.032
Fig. 8. The activation energy plots of (a) ln(J
s
/T
2
) vs. 1000/T and (b)
ln(J
s
/T
2
) vs. 1000/nT. The values using (a) show deviation from lin-
earity below the operating temperature of 160 K. The values of A
∗∗
and the barrier height, Φ
b
using (a) and (b) are A
∗∗
= 43.2Acm
−2
K
−2
,
Φ
b
= 0.94 eV using a linear fit to the values in the 160–300 K range and
A
∗∗
= 64.7Acm
−2
K
−2
, Φ
b
= 1.02 eV, respectively
