Employing statistical design of experiments, we have performed studies on the characterization of electrodes using TiO
and process variables in the fabrication process of nanocrystalline dye sensitized solar cell. Systematic experiment to identify the effects of process variables on cell’s efficiency has based on broad-band absorption of light by tailor made organometallic dye molecules dispersed on a high surface of TiO
. Employing statistical design of experiment on TiO
photoelectrode forming process, structural characterization of electrodes and process variable have been investigated. Through the statistical analysis we have found that the particle size of TiO
and the amount of PEG/PEO are significantly affecting on the cell efficiency. In addition, a significant amount of interaction exists between the particle size and the amount of PEG/PEO.
Most photovoltaic solar cells currently produced are based on silicon p-n junctions
However, there is an increasing interest in dye-sensitized solar cells (DSC)s because only simple materials and equipment are required for their manufacture, and the production costs are potentially low. Also they, have achieved adequate and stable conversion efficiencies in small-area cells
A DSC differs from conventional semiconductor devices in that the functions of light absorption and charge carrier transport are separate. In the case of n-type materials, such as TiO
, current is generated when a photon absorbed by a dye molecule gives rise to electron injection into the conduction band of the semiconductor
In this work, the photoelectrode of a DSC consists of a 10~20 μm thick film of TiO
particles that have a monolayer of absorbed dye molecules. The TiO
layer on FTO glass plays a vital role in increasing the active surface area i and also in maximizing photon absorption. During the fabrication of a DSC, a nano-porous TiO
photoelectrode was formed with statistical methodology.
A key issue in the development of such devices is the optimization of interactions between the sensitizer dye and the nanocrystalline metal oxide, and in particular the optimization of the injection process
Most of the previous works on DSC development were focused on the relationship between certain parameters and device performance. In order to improve processing performance or to obtain a process that is robust to external sources of variability, statistical design of experiments (DOE) have been used either in process development or process troubleshooting
They can also be very useful in establishing the statistical control of a process. However, only few of the published research studies have utilized the relatively recent developed statistical testing method known as the statistical design of experiments (DOE), to assist in the study of the production of DSCs. In the present, we have characterized and predicted the process parameters in fabrications of TiO
deposited photoelectrodes with several controllable factors that affect to the final power conversion efficiency and others.
- 2.1 Fabrication of dye-sensitized solar cells
powder, P25 (Degussa, approximately 70% anatase and 30% rutile) and NT-12 (Nanoin, approximately 87% anatase and 13% rutile) were prepared from a deposition on FTO glass, respectively. FTO glass was applied to the photo and counter electrode after an organic cleaning process.
For preparation of the TiO
solution, 6 mL of D.I. water was injected into 1.2 g of colloidal TiO
powder and ground with a pestle to obtain a more porous structure. 100 μL of acetyl acetone (Sigma Aldrich) and 120 μL of acetic acid (Sigma Aldrich) were added to TiO2 powder in order to sustain TiO2 particles in a colloidal state. Furthermore, 100 μL of Triton X-100 (Junsei) were added to the precursor in order to fully disperse the TiO
nano particles. Poly ethylene glycol (PEG, Sigma Aldrich, MW 1000) and poly ethylene oxide (PEO, Sigma Aldrich, MW 10000) were employed as chemical binders to provide additional forces between molecules. With magnetic bar stirring, this colloidal TiO
was equally mixed for 6 hours followed by deposition on organic cleaned FTO glass using a doctor-blade whose dimensions were 1cm x1cm. This conductive glass was then dried at room temperature. Finally, the deposited glass was annealed for 10 minutes at 100°C and for 30 minutes at 500°C in tube type furnace
Main effect profiles for the responses of interest.
In this study, Ruthenium 535 bis-TBA (known as N719, Solaronix S.A., Switzerland), which sensitizes TiO
very efficiently was used as the dye for causing photons to be absorbed into the DSC. The dye [cis-bis(isothiocyanato) bis(2,2'- bipyridyl-4,4'-dicarbo xylato) ruthenium (II) bistetrabutylammonium, N719] was absorbed by immersing the TiO
photoelectrodes for 12 hours in a 0.5 mL ethanol solution
The highly porous oxide layer acts like a sponge and there is very efficient uptake of the dye. Iodidetriiodide couple (I- / I3-) was fully implemented as the redox mediator. The gap between the TiO
photoelectrode and carbon counter electrode is then filled with a low-volatility electrolyte of 0.5 M LiI, 0.05 MI2, and 0.5 M 4-tert-butylpyridine in 3-methoxy-propionitril which had been injected by capillary force into the inter-electrode space
Carbon blacks and activated carbon were used as counter electrodes in this research. In order to obtain a carbon paste, 0.2 g of the carbon black powder was sequentially ground in a mortar with 1 g of activated carbon, carboxy-methylcellulose (CMC) as a binder, 16 mL of D.I. water, and 5 mL of ethanol. The ground carbon paste was coated on FTO glass by a doctor blade followed by sintering for 1 hour at 150oC in a tube furnace.
The photoelectrode and counter electrode were sandwiched with a 50 μm thick spacer made from thermobonding tape and heated for several seconds to seal it on three sides except leaving one side unsealed. The unsealed side allowed the injection of liquid electrolyte between the two electrodes. After sealing, the liquid electrolyte was injected into the space between the two electrodes using a syringe.
- 2.2 Design of experiments
Experiments in this study were designed and analyzed statistically based on the method of the statistical design of experiments (DOE) with the aid of a statistical analysis program. For more systematic design and analysis, the full
Interaction profiles for efficiency.
factorial design method was performed with three controllable factors, each with two possible levels, in this study. Application of this technique to the current experiments was useful in determining the factors(s) (TiO
particle size (21 and 30 nm diameter), PEG/PEO wt% (20 and 40 wt%), the amount of Triton X-100 (10 and 30 μL)) that has the greatest influence on the performance characteristics of DSC and the process results. It was considered that the performance characteristics were the open- circuit voltage (V
, mV), short-circuit current (I
, mA), fill factor (FF), and energy conversion efficiency (Eff., %).
A set of experimental data was acquired from 23 full factorial designs with 2 center points followed by 1 repetition process to characterize process variations with three controllable input factors, those contained in each of two levels. Thus, the number of total experiments was 20. Using statistical analysis performed with a custom statistical package, the statistical design of experiments based on full factorial design was achieved.
3. RESULTS AND DISCUSSION
- 3.1 Statistical analysis
Most of the statistical analysis methods depend on the assumption that the data sets are sampled from a normal (or Gaussian) distribution. However, most actual data from experiments unfortunately do not follow the normal distribution
It is necessary that data sets not following to normal distribution should be transformed using an appropriate technique.
With the four interesting performance characteristics (I
, FF, and efficiency), the normality test was fully employed before the analysis. The results for I
and FF fell below the normal distribution. However the others data sets involving V
and the efficiency, did not fit to the normality test. So The Box-Cox transformation (BCT) was followed to make them the normal distribution. This transformation can be used to attempt to impose linearity, reduce skewness or stabilize the residual variance
After the normality test, a full model was first investigated to check the main effect and 2-way interactions. The main effect plots are for individual effects of each input parameter. If the slope is zero or lies
ANOVA table for efficiency.
ANOVA table for efficiency.
horizontal in the main effect plots, the corresponding parameter has no effect on the response of interest. The Main effect profiles for the responses of interest are provided in
As shown by the main effect plot provided in
, the main effect of the particle size is the most significant factor that affects I
and FF; thus, the efficiency is also affected by the size of TiO
particle. Even though the main effect of Triton X-100 on I
was less significant than the other main effects, this term could not be eliminated. This kind of otherwise insignificant factor can influence the interaction profiles.
The purpose of 2-way interaction plots is to check the interactions between two input parameters. Cell efficiency is derived from the other responses. For this reason, interaction plots for the efficiency were only investigated. Interaction profilers for efficiency are provided in
The crosslink between TiO
particle size and PEG/PEO wt% was distinguishable from other relationships. In the interaction profiles, the lines showing the dependence of a number of properties of interest, including efficiency, on the amount of Triton X-100 and the TiO
particle size, were almost parallel. To the axes for these latter quantities, showing an The interaction turned out to be the most insignificant interaction between the amount of Triton X-100 and PEG/PEO wt %.
Regression analysis is a statistical technique for investigating and modeling the relationship between variables. An important objective of the regression analysis is to estimate the unknown parameters in the regression model
In general, the response variable y may be related to k the predictor variable, x1, x2… xk, so that
This is called a multiple linear regression model because more than one predictor variable is involved. In order to make a model of the interaction between PEG/PEO wt% and Triton X-100 and between TiO
particle size and Triton X- 100, three interaction terms were excluded due to the somewhat high p-value. The required predictions are given by Equation (2).
Process conditions and photoelectric performances of cells.
Process conditions and photoelectric performances of cells.
There are two other ways to assess the overall adequacy of the model. These are the use of R2 and adjusted R
. In this test of the model, the values of R2 and adjusted R
are 0.635 and 0.537, respectively. The coefficient of multiple determinations, R
may be used as a global statistic to access the fit of the model. The model accounts for about 63% of the variability in the efficiency response. The R
statistic is somewhat problematic as a measure of the quality of the fit for a multiple regression model because it always increases when a variable is added to a model
The value of R
and adjusted R
was somewhat low. This means that above prediction equation does not fit perfectly to real data. It will be the subject of future experiments to make uncontrollable factors such as the processes of TiO
paste deposition and sealing more controllable and also the amount of electrolyte to be more precisely controlled. The analysis of variance is presented in
- 3.2 Process characterization
Transmittance is one of the most important parameters in the evaluation of solar cells. Amongst various process conditions, two were chosen for comparison with each other because they showed the highest and lowest efficiency. The transmittance comparison is illustrated in
. The highest transmittance is approximately twice the lowest transmittance. It was assumed that the decreased transmittance came from thickness augmentations of the TiO
layer according to different process conditions.
SEM images of photoelectrode: (a) for highest efficiency cell and(b) for lowest efficiency cell.
Thus the building up of both adequate pore size and porosity inside the TiO
photoelectrode led to a higher transmittance. This situation was related to a better energy conversion efficiency i.e. the higher the transmittance the higher is the photovoltaic effect that can be generated. The process conditions having the highest and lowest efficiency can be seen in
In the wavelength range between 380 and 720 nm, the transmittance never exceeded 60%. The reason was that the dispersion of the TiO
paste was not enough. Comparatively larger and less dispersed TiO
particle caused injected light to be more highly reflected and dispersed. The surface morphology comparison of the TiO
photoelectrodes with the highest and lowest energy conversion efficiencies was accomplished using FE-SEM images. The surface images were shown in
. With reference to
, the different average TiO
particle sizes and the porosity structure on the photoelectrode surfaces can also be observed in this Figure.
Well-formed porosity structures lead to high surface areas of TiO
particles followed by plentiful dye absorption. In other words, the dispersion of TiO
particles can affect the porosity, the surface states for recombination, the surface area which eventually affects the photocurrent, the voltage and also the fill factor of the DSC. From
, it seems that the dispersion of nano-sized particles is not fully satisfactory, and we postulate that poor dispersion may affect the efficiency of the sample. However, dispersion is not a controllable factor in DOE, but an intermediate material state parameter. For this reason, the amount of dispersion is omitted from the list of controllable input parameters in our experiment.
A large amount of dye around the TiO
particles made cell efficiency more competitive. Energy conversion efficiency is positively proportional to I
, and fill factor. Moreover, photoelectric performances of the cells are also listed in
. The performances in terms of high efficiency were remarkably different from another one in terms of I
and fill factor. There was almost no difference in the V
response. However, it was presumed that a higher sheet resistance of the TiO
surface layer caused a lower I
. Also it had an impacted on the fill factor. The total cell efficiency was affected by all the factors considered above except V
There are numerous of controllable and uncontrollable factors arising during fabrication which can affect the energy conversion efficiency of TiO
photoelectrode fabrications in dye-sensitized solar cells. This research was intended as an investigation of TiO
layer fabrication through the statistical design of experiments. Using 23 full factorial and 2 center points with 1 repetition, more precise experiments can be obtained with 3 controllable factors such as TiO
particle size, PEG/PEO wt%, and Triton X-100.
The modeling and its analysis were done by statistical method. The use of DOE allowed quantification and ranking of the importance of the factors relative to one another for each property studied. In this work, the key points were discovered to be the TiO
porosity, the uniformity of structures inside the TiO
layer, and the accurate dispersion of TiO
paste. However, the dispersion process needs to be improved in order to achieve for a high efficiency. Further research on the dispersion process is now on going. The cell efficiency can be improved by using DOE within the limits defined by the finite controllable parameters and this result is applicable to other process methods of DSC.
Further experiments on materials characterization, including study of the content of WO
powder mixtures and process conditions, may lead to a substantial improvement on fabrication technology in this type of research.
This work was supported by Korean Ministry of Economy and Knowledge (Grant ID: 10031812-2008-11), and authors are grateful to the members of IMNP Lab and Mr. Hyunseok Lee, currently pursuing his Ph.D. degree in PSU in the US, for the meaningful discussion to overcome limited experimental apparatus.
Multicrystalline silicon for solar cells
Thin Solid Films
DOI : 10.1016/j.tsf.2005.01.061
Nanocrystalline dye-sensitized solar cells having maximum performance
Progress in Photovoltaics: Research and Applications
DOI : 10.1002/pip.707
O Regan Brian
A low-cost high-efficiency solar cell based on dye-sensitized colloidal CO2films
DOI : 10.1038/353737a0
Acc Chem Res
DOI : 10.1021/ar980112j
Introduction to Statistical Quality Control
J Chem Educ
Bilayer nanoporous electrodes for dye sensitized solar cells
DOI : 10.1039/b005921h
High efficiency dye-sensitized nanocrystalline solar cells based on sputter deposited Ti oxide films
Solar Energy Materials and Solar Cells
DOI : 10.1016/S0927-0248(00)00231-2
Journal of the Royal Statistical Society: Series B
Introduction to Linear Regression Analysis
Applied Statistics and Probability for Engineers