The Analysis of the Open Circuit Voltage of Dye Sensitized Solar ...

2012 International Conference on Environmental Engineering and Technology
Advances in Biomedical Engineering, Vol.8
The Analysis of the Open Circuit Voltage of Dye Sensitized Solar Cells
and its Influencing Factors
Tian Hanmin a ,Liu shoubin b
a Department of Electronic Science and Technology,School of Information, Hebei University of
Technology,Tianjin, China
b Nanjing College of Information Technology ,Nanjing, China
tianhanmin@hebut.edu.cn, liushoubin@hotmail.com
Keywords: Solar cells; Open circuit voltage;Dye sensitized
Abstract. Based on the mechanism of charge transport within the solar cell, the open circuit voltage
of Dye sensitized solar cells and its influencing factors are analysised. According to the measured I-
V curve of a DSSC and its estimated parameter values, the influencing factors of the open circuit
voltage of Dye sensitized solar cells were obtained by mathematical interpolation and further
discussed.
1. Introduction
Dye sensitized solar cells (DSSCs) have been intensively studied in the last decade as one of the
most promising future energy resource due to their high energy efficiency, low produce cost, and
simple manufacture process compared with conventional Si solar cell.
However, the open circuit voltage(V oc ) of Dye-sensitized solar cells is relatively low (typically
less than 1V), so that further increasment of the open circuit voltage will greatly increase the overall
light efficiency of dye-sensitized solar cell. Till current, the nature of V oc and its influencing factors
are little reported [1,2].
M. Grätzel and his research group considered that the maximum open circuit voltage of DSSC, in
theory, depends on the TiO 2 Fermi level and electrolyte redox potential difference [1]. However, in
the presence of load conditions, the electrode potential is lower than the theorical open cases. This is
because the current loss in the electrolyte (that is, a large number of current transfer overpotential,
Mass-transfer overpotential (η mt ), and electrolyte-electrode interface loss (kinetic overpotential(η ct )).
For example, Hoshikawa found the electrolyte with LiI led to the addition of V oc reduction, and t-
BuPy concomitting the V oc decreasation [3]. Another experimental finding to significantly improve
the open circuit voltage was depositing fine TiO 2 laryer on the semiconductor-FTO interface[4].
These experimental results led us to consider what mechanism led to the change in V oc . In this
paper, based on the mechanism of charge transport within the solar cell, the open circuit voltage of
Dye sensitized solar cells and its influencing factors are analysised.
2. Theoretical analysis
As shown in Figure 1, N-type semiconductor and the electrolyte will change the band before and
after contact, and there is a surface recombination current. The surface recombination current J r
depends on electron back-propagation constant K et , the concentration of redox C ox , light
semiconductor light-free electron concentration n and the difference between the concentration of
semiconductor n 0 , in which the redox reaction rate, the electron transfer rate and the reaction rate is
the exponential function, with coefficients of magnitude m, u, a, as shown in equition 1
978-1-61275-026-2/10/$25.00 ©2012 IERI ICEET 2012
59

m uα
uα
Jr = qk
etCox
( n −n0
)
(1)
The light of current density J ph is obtained by the following formula:
Jph = Jinj − Jr
(2)
in which, J inj : the current density of dye injected into the semiconductor; J r : the surface
recombination current. J inj is proportional incident photon flux I 0 (cm -2 s -1 ) of the DSSC, as shown
equition 3. q is the electron charge, A is the optical absorption coefficient of I 0
J = qAI
(3)
The photoelectron density n in the titanium dioxide semiconductor films is the exponential
function of voltage V = E f - E f0 . E f and E f0 are the corresponding Fermi level of titanium dioxide in
the light and dark conditions. Because of the macro-homogeneous nanocrystalline thin films, the
porous membrane ion diffusion effect is not affected by internal differences in the impact of nanocrystalline,
so the nanocrystalline thin films are ideal as a homogeneous block proliferation of
materials [4].
= exp( qV
n n )
0
kT
Where K is the Boltzmann constant, T is absolute temperature.
so, forumla 5 is got by formula 1 to 4:
inj
m uα
uα
J
ph
= qAI0 − qKetCox
( n − n0
)
(5)
So, the ideal dye-sensitized solar cell current - voltage relationship is derived by the formula 4
and 5 as formula 6.
m ⎧ qV ua ua ⎫
J
ph
= qAI0 − qKetcox
⎨[ n0 exp( )] − n0
⎬
⎩ kT ⎭
(6)
m ua ⎧ uaqV ⎫
= qAI0 − qKetcox
n0
⎨exp( ) −1
⎬
⎩ kT ⎭
Taking into account the contact resistances between gate line, conductive substrate and
semiconductor electrode, and the recombinations of charge carriers in the electrolyte and in the
interfaces of electrolyte and electrodes, the actual DSSC current J can be derived with the
consideration of series resistance (R s ) and parallel resistance (R sh ) as formula 7.
m ua ⎧ ua( V + JRs
)
J = qAI0 − qKetcoxn0
⎨exp( q )
⎩ KT
(7)
⎫ V + JRs
-1 ⎬ −
⎭ Rsh
0
(4)
Conduction Band
E F
O x
V B
O x
E g
Red
Valence Band
helmholtz
Depletion
Layer
Layer
Semiconductor Electrolyte Semiconductor Electrolyte
a
b
E g
Figure. 1 Energy band change of N semiconductor and electrolyte
contractions. (a). before contact. (b). after contact.
E F
Red
60

3. Experimental analysis and discussion
It is difficult to get the explicit expression of V or V oc by J and also difficult to get its numerical
solution, for equation 7 of DSSCs is a complicated exponential-type implicit function. However, we
can obtain the influencing factors of the open circuit voltage of Dye sensitized solar cells by
mathematical interpolation based on the experimental measured I-V data and formula 7.
According to the measured I-V curve of a DSSC and its estimated parameter values, which the
fabriaction method was same as literature [5], by stepwise changing the value of each parameter in
formula 7 and fixing the values of the other equivalent circuit parameters, the influence of this
parameter on the I-V curve is therefore quantificational revealed by ranking these curves together.
m ua
With more calculation and comparation, it was found qKetcoxn0
significantly influences the V oc of
the I-V curve, as shown in figure 2, which is co-directionally moved following the variety of
m ua
m ua
qKetcoxn 0
. However when qKetcoxn0
increases, no obvious change is observed in I sc , FF and the
shape of I-V curve.
Further analysis showed that the exponential function magnitude coefficients, of electron transfer
rate of the reaction rate, u, a , influenced V oc more significantly, as shown in figure 3.
While, other parameters, such R s ,R sh , A and I 0 , do not affect the open circuit voltage, but to
change short circuit current and fill factor of DSSC.
Therefore, we believe that, improving the electron back-propagation constant K et , the electrolyte
redox concentration C ox , the semiconductor light-free concentration n 0 , or decreasing the exponential
function magnitude coefficients of electron transfer rate of the reaction rate , u, a, will enhance the
open circuit voltage of DSSC.
12
10
8
Current[mA]
6
4
128M
M
2
0.008M
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Vol tage[V]
Figure. 2 the calculated influence of
m ua
qK c n to the open circuit voltage and the I-V curve.M=
m ua
0
qK c n in the figure
0
et ox
et ox
61

12
10
8
Current[mA]
6
1.8/ua
4
1/ua
2
0.4/ua
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Vol tage[V]
Figure. 3 the calculated influence of u,a to the open circuit voltage and the I-V curve.
Some studies have shown a great impact of the electrolyte redox concentration C ox on DSSC
performance. For example, Hoshikawa found additional LiI in the electrolyte led to the addition of
V oc reduction, t-BuPy with the V oc decreased [3]. Liu and Zaban belived that the electrolyte in the
DSSC roles not only in the hole transport between the positive and negative, but also through the
shielding effect promote electrons which has been injected into the TiO 2 electrode move smoothly in
the TiO 2 porous membrane [6]. In short, both Hoshikawa and we showed that by increasing the
electrolyte concentration of redox C ox will help to enhance the open circuit voltage of DSSC.
Although we derived the current - voltage formula for V oc according to solid state physics to
enhance the expression (formulas 7), but it is also noted that there exists controversy in the current
DSSC researchers on the source of open circuit voltage. Some scholars believe that the voltage
comes from the chemistry of chemical potential gradient [2], who pointed out that the DSSC were
significantly different with the traditional pn-junction cells, while most of others, such as Grätzel,
discusses that DSSC has the similarities and differences with traditional pn junction cell but
essentially similar, as derived in this paper [7,8].
4. Conclusions
The influencing factors of the open circuit voltage of Dye sensitized solar cells were obtained
according to the measured I-V curve by mathematical interpolation and was further discussed.
Improving the electron back-propagation constant K et , the electrolyte redox concentration C ox , the
semiconductor light-free concentration n 0 , or decreasing the exponential function magnitude
coefficients of electron transfer rate of the reaction rate , u, a, will enhance the open circuit voltage of
DSSC.
5. Acknowledgment
The authors would like to acknowledge financial support from Start Fund of Hebei University of
technology, as well as to thank Mr. Tianxuemin and Mr. Wangxiaoqi for their helpful discussions.
References
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