Thin Solid Films 480–481 (2005) 307 – 311
www.elsevier.com/locate/tsf
Temperature dependence of the diode ideality factor in
CuInS2-on-Cu-tape solar cells
Johan Verschraegena,*, Marc Burgelmana, Jqrgen Penndorf b
a
Gent University, Electronics and Information Systems (ELIS), Pietersnieuwstraat 41, B-9000 Gent (B), Belgium
b
Institut für Solartechnologien (IST), Im Technologiepark 7, D-15236 Frankfurt/Oder (D), Belgium
Available online 15 December 2004
Abstract
Current versus voltage measurements were done on copper indium disulphide cells fabricated on a continuous copper tape fabricated at
IST (Frankfurt/Oder, D). Temperatures were in the range of 90–370 K. We compared the measurements with an ideal diode model and
extracted parameters accordingly. The temperature dependence of the diode ideality factor can give valuable information about the main
recombination mechanism in the cell. We find a remarkable agreement of the temperature dependence with a theory derived by Padovani et
al. We conclude that tunneling currents play an important role inside the cell.
D 2004 Elsevier B.V. All rights reserved.
Keywords: CuInS2; CISCuT; Capacitance; Modelling
1. Introduction
2. Experimental
First reports on the CISCuT (CuInS2 on Cu-tape,
fabricated at IST, Frankfurt/Oder, D) cells in literature
date from 1998 [1]. Starting from a near endless copper
tape, an absorbing layer is made by deposition of In
followed by a short sulphurisation step. In this phase, the
CuInS2 is formed. The solar cell is completed by adding a
CuI buffer layer and a transparent front contact [2,3].
Since the introduction of this cell, the efficiency has
improved a lot and has now reached over 9%. Although a
very good result already, further improvements should be
possible. Interpretation of I–V measurements can give a
lot of information about the diode parameters. In
particular, the temperature dependence of the diode ideality factor and the dark saturation current gives indications
on what the main recombination paths are. In this paper,
we will discuss the I–V measurements that were done and
try to find the mechanisms which are limiting the opencircuit voltage.
The samples used were prepared at IST (D) by the
standard CISCuT roll-to-roll procedure until the absorber
layer is formed. The cells were completed by spraying a thin
CuI buffer layer and by sputtering a ZnO layer as the front
contact. The area of the buffer and contact is confined to
single dots with area between 9 and 10 mm2.
We performed dark and light I–V measurements using a
236 Keithley source measure unit with bias voltage varying
between 1 and 1 V. As a light source, an Oriel Xenon arc
lamp was used with an infrared filter (but no solar spectrum
correction filters). Through the use of neutral density filters,
a total of 16 different illumination intensities were achieved,
ranging from about 1 to 1500 W/m2. The samples were
mounted in a cryostat setup and their temperature was
varied between 90 and 370 K. At the same temperatures, we
also did I sc versus Voc measurements.
3. The I sc–Voc theory
* Corresponding author. Tel.: +32 9 264 8953; fax: +32 9 264 8961.
E-mail address: Johan.Verschraegen@elis.ugent.be (J. Verschraegen).
0040-6090/$ - see front matter D 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.tsf.2004.11.006
First, we will discuss the I sc–Voc measurement. While
this kind of measurement is well known, there are some
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J. Verschraegen et al. / Thin Solid Films 480–481 (2005) 307–311
implicit assumptions connected with its interpretation and
those will be shown here. We will start from the diode
equation, corrected for series resistance R s and parallel
conductance G sh:
qð V R s I Þ
1 þ Gsh ðV Rs I Þ IL
I ¼ I0 exp
nkT
ð1Þ
I L is the light current, I 0 is the dark saturation current and n
is the diode ideality factor, which can all be dependent on
bias voltage and temperature. For an ideal diode, n is
however constant and I 0 is only dependent on temperature.
In the case where there is no recombination in the space
charge region, n has a value of 1. If on the other hand, the
current is dominated by recombination in the space charge
region, n will be equal to 2. Usually, n has a value between
1 and 2, but values greater than 2 are also possible.
It is not straightforward to extract the diode parameters
from a measurement that is influenced by series resistance
and shunt conductance. Therefore, we measure the short
circuit current I sc=I|V=0 and the open-circuit voltage
Voc=V|I=0 for different illumination intensities. Inserting,
respectively, V=0 and I=0 in Eq. (1) gives:
qRs Isc
Isc ¼ I0 exp
ð2Þ
1 Gsh Rs Isc IL
nkT
qVoc
1 þ Gsh Voc :
IL ¼ I0 exp
nkT
ð3Þ
If R s is small compared to Voc/I sc (less than 1%) and
G shR s is much smaller than 1, then we see by Eq. (2) that
I sc=I L and by Eq. (3) that I sc and Voc satisfy the diode law
without the influence of series resistance. The influence of
the parallel conductance remains, but for high-enough light
intensities, it does not affect the open-circuit voltage. It is
now easier to extract the diode parameters. A semilogarithmic plot of I sc versus Voc will yield a straight line for
high-enough Voc. From the slope, n can be calculated if one
knows the temperature. I 0 can be found by taking the
intercept of the straight part of the plot with the I sc-axis. A
small error in the estimation for the diode ideality factor
results in a large error in I 0 due to the use of the logarithmic
scale. Therefore, the value of I 0 will generally be less
accurate than that of n.
One could also try to fit a measurement to Eq. (1) using
R s as an extra parameter, instead of making an I sc–Voc
measurement, but then there is less confidence in the
obtained values, the more because the series resistance
might be bias voltage dependent.
During the derivation of Eqs. (3) and (4), a few implicit
assumptions have been made. First, we assumed the diode
parameters to be independent of illumination intensity. This
condition has to be fulfilled to get meaningful results from
the I sc–Voc measurements; it can, however, be formulated a
little less stringent as will be shown further on. Second, we
assume I L to be independent of bias voltage. This condition
is also crucial, if it is not met, we get:
qVoc
ð4Þ
Isc ¼ I0 exp
1 þ Gsh Voc þ DIL ðVoc Þ;
nkT
with DI L(Voc) being the difference in light current for zero
voltage and open-circuit voltage. We can expand this in
terms of Voc. If only the first-order term is not negligible,
then we get an effective G sh [4], and we can still use the I sc–
Voc curve to extract the diode parameters.
4. Results
The cells that were measured have an efficiency of 5–
6%. Best efficiencies for CISCuT cells so far are around 9%.
The rather large difference is mainly caused by a much
lower short circuit current. For our cells, this is around 14
mA/cm2 (not corrected for contact pin shadowing), while
for the best cells, it is around 21 mA/cm2. Therefore, we will
focus on the mechanisms that limit the open-circuit voltage.
It will be shown further on that there is crossover
between the light and dark curves and thus the diode
parameters differ for light and dark conditions. According to
the theory given in the previous paragraph, this would mean
that the I sc–Voc technique is not applicable. However, we
will still use it, but the diode parameters thus obtained will
not give information about the cell under dark conditions.
Still to get meaningful results, the diode parameters have to
be illumination intensity independent. This supposes that
there are two current mechanisms, one for dark and one for
light conditions. In Fig. 1, a number of I–V curves for
different light intensities are plotted together with the dark
Fig. 1. I–V measurements for different illumination intensities (from 0.1 to
1.5 suns) together with the dark I–V curve. Note the crossover of the dark
curve with the others.
J. Verschraegen et al. / Thin Solid Films 480–481 (2005) 307–311
curve. The fact that even for low intensities there is already
crossover with the dark I–V curve supports the idea of two
distinct current mechanisms. This can be verified by starting
from the I sc–Voc curve, and pretending that it represents the
dark I–V characteristic of the junction, only influenced by
parallel resistance. We can then calculate the light characteristic by adding series resistance and a light current. If the
diode parameters are independent of illumination intensity
and the light current is independent of bias voltage, then this
should give a perfect fit with the measured light I–V curve.
The result can be seen in Fig. 2. For three different
illumination intensities, the I–V curve is fitted using the
explained technique. The fit is reasonable but not perfect.
Especially for the curve with the largest illumination
intensity, there is a notable difference at low bias voltages.
Looking at the slope of the I–V curve around 0 V, it seems
as if the parallel conductance were much higher. Although
this means that the conditions that allow the use of I sc–Voc
curves to extract the diode parameters are not fully met, we
will still use them and the confidence in the results will be
based on the good agreement with the recombination model
that will be proposed further on.
In Fig. 3, a number of I sc–Voc curves are presented on a
semilog scale plot for temperatures going from 90 to 370 K.
According to the ideal diode model, one would expect a
curve which only deviates from a straight line at low bias
voltages due to parallel conductance in the cell. The
CISCuT cells do not follow the ideal diode model. In fact,
in Fig. 3, there seems to be a transition from one flat region
at low bias voltages to another at high bias voltages. This
can be interpreted as two current mechanisms being present
in the cell. The first one has the weakest voltage dependence
and governs the current at low bias voltages. The second
one has a stronger bias voltage dependence and will
therefore be the main current mechanism at high-enough
voltages. It is however also possible that there are not just
two distinct mechanisms but that there is a continuous
309
Fig. 3. I sc–Voc curves for temperatures going from 90 to 370 K, in steps of
20 K. Each measurement was done for 16 illumination intensities ranging
from about 1 to 1500 W/m2.
transition. In what follows, we will determine the diode
parameters for the high bias voltage region. After all, this is
the region closest to the working condition of the cell and if
we can determine, and eventually diminish, the main
recombination paths at these voltages, then that would
result in the greatest gain in efficiency.
From the curves from Fig. 3, we can calculate the ideality
factor n and these are plotted in Fig. 4 as a function of
temperature. The first thing that strikes is that the values are
much greater than 2. This means that the current is not limited
by drift and diffusion or by recombination in the space charge
region. A number of models have been proposed to explain
ideality factors greater than 2. Padovani and Stratton [5]
calculated the current for a Schottky diode in the case of
tunneling through the contact barrier (thermionic field
emission). They found for the ideality factor:
E00
E00
n¼
coth
ð5Þ
kT
kT
E 00 is a characteristic tunneling energy depending on doping
concentration. In Fig. 4, a calculation of n for E 00=50 meV
(or E 00/k=580 K) is shown. The fit with the measurement data
is remarkable, the more if one realizes that this is a oneparameter fit. From this, we can conclude that tunneling plays
an important role in the cell. Konovalov and Tober [6] came
to the same conclusion on the basis of open-circuit voltage
measurements as a function of temperature and illumination
intensity. Their estimation for E 00/k was around 200 K, which
corresponds with E 00 equal to 17 meV, a much lower value
than what we find. It is interesting to note that they use an
approximation of Eq. (5) for the ideality factor [7]:
Fig. 2. Comparison of the measured light I–V characteristics (symbols) for
different light intensities with the measured I sc–Voc curve of Fig. 3, shifted
downward over the light current I L and corrected for a series resistance of 4
V cm2 (line).
1
2
E00
n¼ 1 2 2
:
3k T
ð6Þ
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J. Verschraegen et al. / Thin Solid Films 480–481 (2005) 307–311
temperature is there a reasonable fit. The fact that the
accuracy on I 0 is lower than that for the ideality factor n
might be a reason for this, but a satisfying explanation is not
found yet.
Another tunneling model which can explain ideality
factors larger than 2 was presented by Riben and Feucht [9].
They considered tunneling enhanced bulk recombination in
which electrons/holes first tunnel to a trap and then fall in
the valence/conductance band, or first fall into a trap and
then tunnel to the appropriate band. The expression for the
ideality factor reads
n¼
Fig. 4. Ideality factor n versus temperature (symbols). The full line is a fit
with Eq. (5), with E 00/k=580 K. The dotted line is a fit with Eq. (7), with
T*=580 K.
TT
;
T
ð7Þ
The approximation (Eq. (6)) has a negligible error
(b2.5%) only for E 00/kTb2/3, corresponding to nb1.15. In
our case, n is much higher and the exact expression (Eq. (5))
should be used.
From the I sc–Voc measurements, not only the ideality
factor can be calculated but also the dark saturation current.
The result as a function of temperature is shown in Fig. 5.
The two curves are calculations from one measurement
cycle with dropping temperature (290–90 K) and another
one with rising temperature (90–370 K). A kind of
hysteresis is apparent for temperatures below room temperature. This behavior is also apparent in capacitance versus
temperature measurements [8], but has not been explained
so far. It is important to note that the diode ideality factor is
not dependent on temperature history (not shown in Fig. 4).
The model from Padovani and Stratton [5] which gives us
an expression for n, also gives an expression for I 0. The
calculated dark saturation currents from Fig. 5, however,
cannot be fitted to that expression, at least not for the whole
temperature range. Only for temperatures above room
with T* a constant which plays the same role as E 00/k. If we
try to fit our calculated ideality factors to this expression, we
also get a reasonable fit (see Fig. 4). This is not surprising at
all, since Eq. (5) can be simplified to Eq. (7) for T much
lower then E 00/k. Fitting the dark saturation current to the
expression derived by Riben and Feucht is again not
possible. Nonetheless, this gives again a strong indication
that tunneling currents are dominating the recombination.
In Fig. 6, a band diagram is drawn for the CISCuT cell
junction. The band offsets are calculated with the Anderson
model by the use of SCAPS [10]. The large spike in the
valence band is most likely less pronounced. The current
mechanism is possibly tunneling from electrons from the
CuInS2 side of the junction to the CuI/CuInS2 interface. As
it is drawn in Fig. 6, this seems very unlikely due to the
large tunneling distance to the interface. In Ref. [6], it is
proposed that, near the interface, there is a larger space
charge density due to compensating defects. This would
result in a smaller barrier near the interface. Another
possibility is tunneling into defect states in the forbidden
zone of the CuInS2, followed by hopping from defect to
defect in the direction of the interface. Further investigations
will be necessary to determine the precise origin of the
tunneling currents and to find ways to reduce them.
Fig. 5. Saturation current I 0 versus temperature. One branch is for a
measurement cycle with dropping temperature, the other is for rising
temperatures.
Fig. 6. Schematic band diagram for the CuI/CuInS2 junction. The possible
tunneling path is indicated.
J. Verschraegen et al. / Thin Solid Films 480–481 (2005) 307–311
311
5. Conclusion
References
From I sc–Voc measurements, we have calculated the
diode parameters as a function of temperature. The diode
ideality factor n is much greater than 2 and has a strong
temperature dependence. It can be fitted remarkably well to
an interface tunneling model, from which we conclude that
tunneling plays an important role in the cell. This is
confirmed by work from other authors. However, fitting
the dark saturation current to the same model is problematic.
More accurate information about the band diagram is
needed to fully characterise and locate these tunneling
recombination currents.
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[9] A.R. Riben, D.L. Feucht, Solid State Electron. 9 (1966) 1055.
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Acknowledgements
The European CISLINE project (ENK6-CT-2001-00519)
(J.V.). The Research Fund of the University of Gent (BOFGOA) (M.B.).