Practical solar cells require larger active areas than ones in the R&D stage in laboratories. However, the enlargement lowers conversion efficiency because of the following two reasons: (1) increase of resistive loss in the transparent conductive electrode caused by the longer distance for the photogenerated carriers to pass and (2) active area loss caused by shadows of collector electrodes laid on to reduce the previous resistive loss. In the present study, we have constructed an advisable modeling method to calculate output power of medium-sized solar cells and optimized geometry of the collector electrodes. Results of the modeling taught us a possible improvement of the output power by over 10%. These simulated results were reproduced by electrochemical experiments.
Practical solar cells require large active areas than ones in the R&D stage. Scaleup of solar cells from laboratory samples to practical modules usually decreases conversion efficiency, as evidently displayed by Green et al. [
Although some radial patterns of collector electrode have been proposed in place of conventional parallel type to reduce the shadowing loss [
The adverse influence of collector electrodes on dye-sensitized solar cells (DSSCs) is more remarkable than that on Si solar cells, because protection layers such as a glass flit passivation or a bismuth borosilicate-based thick film passivation [
Therefore, here, we developed the modeling of the geometry of the collector electrode to give the highest output power of medium-sized solar cells with a special attention to features of DSSCs.
In the present study, we have constructed an advisable modeling method for calculation of output power of medium-sized solar cells to optimize the geometry of the collector electrodes. We carried out electrochemical experiments to verify the effect of the optimized geometries.
Figure
Schematic diagram of a dye-sensitized solar cell: (a) a side view, (b) an enlarged top view of a collector electrode portion.
We evaluated the performance of solar cells with various collector electrode geometries using a newly devised 2-dimensional model. Solar cells are approximated to consist of elements referred to as “nodes” and “links” that connect the neighboring nodes. There are two kinds of nodes: active nodes and collector nodes representing the active areas and the collector electrodes, respectively.
The method to divide the whole cell into the elements is a great issue for compatibility of accuracy and reasonable computation time. Figure
Division methods. Active nodes are indicated with closed circles and collector nodes indicated with open circles. Lines indicate links. (a) Equal division and (b) unequal division for collector electrodes.
Let
The assumption that all the active nodes work at the MPP allows us to deal with them as independently working ones. Therefore, as shown in Figure
Schematic diagram of calculation of trajectories of
The output power of the cell,
The value of the resistance of the
The
We used the
The first term in (
Therefore,
We verified the validity of (
As for voltage, we have also confirmed that the voltage drops in the links between the collector nodes are negligibly small, experimentally. The estimated voltage drop was at most 10 mV, that is, around 2% of
The present method to calculate
In contrast, the present method can be applied to complicated geometries like being examined here with sufficiently high accuracy. The computational complexity of the present method, however, is not suitable for calculation on extreme conditions such as solar cells of very low photovoltaic performance or high resistance as written later.
At the start of the series of simulations, we calculated output power of a 2-dimensional “Standard geometry” of the collector electrode generally used for DSSCs as shown in Figure
Geometries of standard collector electrodes and their relative power: (a) Standard geometry, (b) relative power changing with the number of vertical electrodes.
Geometries of poorer performance than the Standard geometry in Figure
As an exception, the geometry in Figure
Examples of geometries of good performance with problem in fabrication. (a) The pattern produced by a genetic algorithm. (b) The pattern that has an output terminal in the center.
Figure
(a) A finger electrode geometry. (b) Current density in the electrodes. Thickness of line is proportional to the current density.
Devised geometries (a) Standard geometry, (b) Geometry 2, (c) Geometry 3, and (d) Geometry 4. The output terminal is supposed to be located at the same position as in Figure
Figures
The optimized geometries and the dependence of the output power on the number of the vertical electrode for (a) Geometry 2, (b) Geometry 3, and (c) Geometry 4.
From the experiences mentioned previously in chapters 2.3 and 2.4, we have learned the possibilities that the radial (c.f. Figure
Geometries of collector electrodes used for actual experiments. (a) Standard geometry for experiments (Standard′), (b) Geometry 2′, (c) Geometry 3′, and (d) Geometry 4′.
We fabricated collector electrode samples of the Standard geometry and the optimized ones based on the simulation, for experimental proof, although adjustment was added in production. The numbers of the vertical collector electrodes optimized as shown in Figure
An automatic printing machine was used for printing silver paste to form silver wires of typically 10
The samples consisting of TCO-covered glasses, silver wires, and protection layers were evaluated using a setup schematically illustrated in Figure
Schematic diagram of the electrochemistry experiments.
The protection layers prevented leak current from flowing out of the silver wires to the electrolyte, which takes place also in real DSSCs.
We used resin TB2249G (ThreeBond Co., Ltd.) for protection layer with the thickness of 500
In order to prevent adhesion of hydrogen and oxygen bubbles generated by water splitting to the electrodes, surfactant was added in the solution at a concentration of 1 mL/L; ultrasonic vibration was applied during the measurements.
Figure
Current
Just after an external voltage was applied, the current rapidly decreases, because the combination of an anode and a cathode with an electrolyte between them performs as a capacitor, as shown in Figure
Temporal change in the current of the Standard geometry at 2.4 V.
Figure
Experimental results for the four geometries at (a)
In the present experiments, a larger active area generates a larger current value. However, when the resistance is larger, the voltage applied between the TCO and the copper plate more remarkably falls on an average, resulting in more significant lowering in the current value. Thus, the measured current value is equivalent to the performance of each geometry. Therefore, we can conclude that Geometries 2′–4′ provide superior performance compared with the Standard geometry′. The gain achieved by the optimization of the collector electrode geometry was as high as 10–30%.
Taking additional protrusion in experimental geometry of the collector electrodes into consideration, we carried out simulations on geometries reproducing the experimental geometries more precisely which were necessary for the experimental proof. Figure
Comparison of the simulated and experimental results.
In contrast, the output power decreases for Geometry 2′ because of an increase in the resistive loss. However, the experimental result for Geometry 2′ showed over 20% gain contrary to the expectation.
The measured current values at 2.4 V are compared with the simulated output power values in Figure
Here, we must pay attention to the difference in the operating conditions. The simulation was carried out under the condition of 1 sun solar irradiation, with the resultant output currents being around 500 mA. In contrast, the experiments were carried out with the current values of around 10 mA which corresponds to very low irradiation intensity so as not to yield bubbles on the surface of the electrodes.
In the simulation, the output power goes up in the case of Geometry 2 in Figure
The reason for the difference between the results of experiment and those of simulation in Figure
The feature of large active area of Geometry 2′ efficiently contributed to an increase in the current value. This geometry has a larger resistivity in comparison with other geometries. Since the resistive loss is proportional to the square of the output current, the impact of the resistive loss is less significant at lower irradiation intensity and a lower output current.
Therefore, under the experimental condition equivalent to weak irradiation, it is conjectured that the feature of large active area of Geometry 2′ efficiently contributed to an increase in the current value, whereas the other contributions such as of the relatively large resistance was small. According to this balance between the active area and resistive loss, it is conjectured that Geometry 2′ had higher output power in experiment. These features of Geometry 2′ are more suitable for indoor use, transparent cells with low absorbance, and so forth.
The present 2-dimensional simulation is applicable to the other types of solar cells with a transparent conductive electrode layer such as amorphous Si solar cells and other thin film solar cells. As for bulk silicon solar cells whether it is single crystalline or polycrystalline ones, it is better to use 3-dimensional simulation.
We have optimized geometry of collector electrodes for DSSCs using a newly constructed modeling to calculate output power of medium-sized solar cells. The simulation predicted that significant improvements in the output power over 10% are possible, relative to the Standard geometry. These results were reproduced by electrochemical experiments.
The authors thank Ms. Y. Uchiyama for her technical support in the fabrication of collector electrode samples.