Empirical study of the characteristics of organic solar cells

We compare the reported characteristics of 36 different bulk heterojunction organic solar cells fabricated and characterized by different research institutes. By comparing our results with our similar empirical study from 2006, we chart the technological progress for organic solar cells. Among others, we find an empirical threshold of 0.3 eV between the LUMOs of donor and acceptor, necessary for exciton dissociation. This work was performed by one of my students Tom Vandecaveye as part of his (excellent) master thesis, titled "A simulation program for and empirical study of photovoltaic organic multi-junction solar cells".

1. Introduction

In 2006, we compared the reported characteristics of 22 different bulk heterojunction organic solar cells fabricated and characterized by different research institutes [1]. Now (begin 2014), we repeat this study but now for the organic solar cells fabricated today.
More specifically:

We compare the improvements of the characteristics between the 2006 study [1] and the current state-of-the-art.
In the 2006 study, we concluded that the current was the bottleneck for efficiency improvements for organic solar cells. We analyze whether this is still the case.

Table 1. The efficiency and year of publication of the 36 organic solar cells considered in this study. The second-to-last column refers to the considered photovoltaic cell. The last column refers to the energy levels of the materials.

We determine an empirical threshold between the energy levels necessary for exciton dissociation.
We search for a relationship between the interface bandgap and the open circuit voltage.
We study the relation between the voltage factor and open circuit voltage for the organic solar cells.
We compare the photovoltaic cells with the two most frequently used acceptors.

For this empirical research, we studied and compared the reported characteristics of 36 different organic solar cells fabricated and characterized by different research institutes (Table 1). We only considered solar cells where both the donor and the acceptor are organic solid state materials. Organic-inorganic hybrid cells, liquid dye sensitized solar cells and multi-junction cells were omitted for this study. For each donor-acceptor material combination, only the cell with the highest reported efficiency was taken into account. The cells were characterized under illumination with the standard A.M. 1.5 spectrum and an intensity of 100 mW/cm². Two cells [23] were characterized with a lower intensity (95 mW/cm²) and one [4] at a higher intensity (128 mW/m²). We adapted the Jsc linearly of those cells to compare them with the cells characterized at 100 mW/cm². No corrections were made for the Voc or FF.

This resulted in experimental data of 36 bulk heterojunction organic solar cells, published within the time frame 2009 - 2013. In a bulk heterojunction solar cell, the active layer consists of a nanoporous interpenetrating network of the donor and the acceptor. As expected, no bilayer cells were found with a higher efficiency as their bulk heterojunction counterpart. All 36 cells use as transparent hole-contact Indium Tin Oxide (ITO) cathode. As electron contact, different materials can be used. Al is used in most cases (26 cells), Ag is used in 9 cells [7,8,15,30,32].

The highest standard efficiency published for organic solar cells is at this time 9.214 % for an ITO / PFN interlayer / PTB7:PC71BM / MoO3 / Al – cell [36]. This cell has an active area of 8 mm², and is characterized at 100 mW/cm² by an open circuit voltage Voc of 0.754 V, a short circuit current density Jsc of 17.46 mA/cm², and a fill factor FF of 69.99 %. We want to remark that the world record efficiency reported for an organic solar cell is 12.0 %, fabricated by the company Heliatek. But since they don’t disclose the used materials, we could not include this cell in this study.

2. Results

The power conversion efficiency η of a solar cell is given by the formula:

where Voc is the open circuit voltage, Jsc the short circuit current density, FF the fill factor and Pin the incident solar light power. When we plot the measured characteristics of the different cells versus the efficiency (Figure 1 and 2), we see a clear linear correlation for the short circuit current density Jsc (and to a lesser extend for the fill factor FF). An increase of 1 mA/cm² results roughly in an efficiency gain of 1/2 of a percent absolute. In our 2006 study, this was 1/3 of a percent absolute. However, this linear correlation is not seen for the efficiency versus the open circuit voltage Voc (Figure 3). This empirical result indicates that, with the current state of the technology, the current is the limiting factor for reaching higher efficiencies, and not the Voc. The average Voc of the cells (0.81 V) is already satisfyingly high. Where there is no clear relationship between the Voc and the efficiency, this relation is present for the Jsc. Of course, reaching higher voltages will increase the efficiency of the solar cells, but a higher efficiency gain can be obtained by focusing on reaching higher currents, which is an important bottleneck for the breakthrough of organic solar cells. These conclusions are the same as our 2006 study. Also then, the Voc was already satisfyingly high (with an average of 0.75 V). The average Voc hardly increased (+ 8 % relative) whereas the average Jsc more than doubled (from 5.5 to 11.5 mA/cm²). Figure 1 indicates the progress during the last 8 years in Jsc. This proves the conclusion from the 2006 study that the current (and not the voltage) was (and still is) the limiting factor. Also the average fill factor FF increased from 45 % in 2006 to 59 % now (a relative increase of 31 %).

Figure 1. The efficiency η of the studied solar cells versus the short circuit current density Jsc. The crosses represent the cells from the 2006 study. The circles and squares represent respectively cells from the current study where PC70BM and PC60BM are the acceptor material. The triangles represent cells with other acceptor materials. The straight line is the linear fit through the origin for the cells of the current study. The dashed line is the linear fit through the origin for the 2006 study.

The absorption of a photon leads to the creation of an exciton in the donor of a bulk heterojunction solar cell. For the charge carriers to contribute to the current, the exciton needs to be dissociated into an electron and a hole before recombination occurs. The exciton is dissociated at the discontinuous potential drop at the interface between donor and acceptor. The electron is transferred to the electron acceptor due to its high electron affinity.

Figure 2. The efficiency η of the studied solar cells versus the fill factor FF. The circles and squares represent respectively cells where PC70BM and PC60BM are the acceptor material. The triangles represent cells with other acceptor materials. The straight line is the linear fit through the origin.

Figure 3. The efficiency η of the studied solar cells versus the open circuit voltage Voc. The circles and squares represent respectively cells where PC70BM and PC60BM are the acceptor material. The triangles represent cells with other acceptor materials.

Figure 4. The efficiency η of the studied solar cells versus the energy difference between the LUMOs of donor and acceptor. The circles and squares represent respectively cells where PC70BM and PC60BM are the acceptor material. The triangles represent cells with other acceptor materials. The dashed line represents the empirical threshold of 0.3 eV.

A necessary condition for exciton dissociation is that the difference between the LUMOs of the donor and acceptor (ΔLUMO) is higher than the exciton binding energy. Although the value of the exciton binding energy in different materials is often a subject of discussion, values between 0.1 eV and 2 eV are published [37]. Figure 4 shows the efficiency as a function of the energy difference between the LUMOs of the donor and the acceptor of the studied solar cells. Most energy differences are lying between 0.3 eV and 0.8 eV, although some even reach 1 eV and higher. If ΔLUMO is higher than necessary for the exciton dissociation, the electron loses useful energy that can’t contribute any more to the output power, although this is not clear from Figure 4. An empirical threshold of 0.3 eV is found between the LUMOs of the donor and acceptor. Because no working cells were found below that threshold, a minimal difference of 0.3 eV between the LUMOs can be considered as necessary for exciton dissociation. This is in accordance with the threshold found by others [38,39] and 0.1 eV higher than the 2006 study. A possible explanation for the 0.1 eV discrepancy between the current and the 2006 study could be the error margin in determining the energy levels of organic materials [40,41].

The distance between the HOMO of the donor and the LUMO of the acceptor is considered as the thermodynamic limitation of the useful energy [42]. We call this value the interface bandgap Ei. For an organic solar cell with ohmic contacts, the open circuit voltage Voc is linearly dependent on the interface bandgap Ei. This linear relationship was proven for the variation of the HOMO level of the donor [38,43,44] and of the LUMO-level of the acceptor [45-47]. For a cell with non-ohmic contacts, the Voc is dependent on the work function difference of the electrodes [48].
Figure 5 shows the Voc as a function of the interface bandgap Ei for the studied solar cells. We would expect a linear relationship, but as in the 2006 study, this relationship can not be found. Possible explanations could be the influence of bad ohmic contacts, the difference in the state of the production technology for each cell or the influence of intermediate layers [49].

Figure 5. The open circuit voltage Voc of the studied solar cells versus the interface bandgap Ei. The circles and squares represent respectively cells where PC70BM and PC60BM are the acceptor material. The triangles represent cells with other acceptor materials. The dashed line indicates the limit for the Voc.

If we consider the interface bandgap Ei as the limit for the open circuit voltage Voc, the voltage factor f is given by f = (q. Voc / Ei) (equation 2).

Because of loss factors (e.g. recombination), f can not reach 1. Figure 6 shows a linear relationship between f and Voc, meaning that the higher the Voc, the more efficiently energy of the bandgap is used. These conclusions are the same as our 2006 study. The average voltage factor f increased from 53 % in 2006 to 65 % now (a relative increase of 23 %).

Finally, we compare the two most frequently used acceptors. Of the 36 solar cells, 18 cells use PC70BM as acceptor and 9 use PC60BM. The cells with PC70BM have an average efficiency of 5.9 %, with 9.2% as maximum. This is higher than the cells with PC60BM which have an average efficiency of 5.1 % (with 6.2 % as maximum). If we only consider the cells that use the same donor, but differ in acceptor, we find 5 pairs [10,16,19,20,23,25,28,31]. The cells with PC70BM as acceptor perform on average 21 % better than the same cells with PC60BM as acceptor (6.3 % average efficiency versus 5.2 %). The Voc and FF of both members of each pair don’t differ much. It is mainly the Jsc that improves by using PC70BM as acceptor. Taken into account that both acceptors have similar HOMO and LUMO energy levels, this difference can not be explained by the location of the energy levels. A possible explanation is the fact that PC60BM is a worse absorber than PC70BM, especially in the ultraviolet and visible light region [3].

Figure 6. The voltage factor f of the studied solar cells versus the open circuit voltage Voc. The circles and squares represent respectively cells where PC70BM and PC60BM are the acceptor material. The triangles represent cells with other acceptor materials. The straight line is the linear fit through the origin.

3. Conclusions

We compared the reported characteristics of 36 different bulk heterojunction organic solar cells fabricated and characterized by different research institutes. We confirmed the results from our 2006 study that not the Voc, but the Jsc is the limiting factor for efficiency improvements for the current generation of organic solar cells. Also, an empirical threshold of 0.3 eV was found between the LUMOs of donor and acceptor, necessary for exciton dissociation. A relation between the Voc and the interface bandgap was not found. The linear relationship between the voltage factor f and Voc indicates that the higher the Voc, the more efficiently energy of the bandgap is used. Finally, the cells in our study with PC70BM as acceptor perform significantly better than the same cells with PC60BM as acceptor.

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