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Reduction of Collection Efficiency of Charge Carriers with Increasing Cell Size in Polymer Bulk Heterojunction Solar Cells Won-Ik Jeong, Jane Lee, Sun-Young Park, Jae-Wook Kang, and Jang-Joo Kim* There are a few recent reports on cell size effects in OPVs. Analytic approaches to relate sheet resistance to cell size and regarding the employment of grid structures in OPVs have been introduced.[22,23] Those authors showed that reductions in short circuit current (Jsc) and fill factor (FF) occur with increasing active cell area and they attributed the change in cell performance to an increase in the series resistance of the indium tin oxide (ITO) conductive film. The Shockley diode equation, based on an equivalent circuit model, was proposed as a method to account for the effect of the series resistance that originated from the cell area.[24] However, to date, there is a lack of quantitative understanding of the relationship between solar cell area, series resistance, and solar cell performance. Furthermore, to our best knowledge, there are no reports of experimental work determining whether the Shockley equation is applicable when accounting for the effects of series resistance and cell area in bulk heterojunction organic solar cells. Here, we report on a systematic investigation of the effects of cell size in OPVs. We fabricated cells over a range of areas (0.09–16.0 cm2) and introduced sub-electrodes to define the geometry of the cells. The results demonstrated that the Shockley diode equation, based on the equivalent circuit model, cannot accurately describe the effects of series resistance and cell area on the performance of bulk heterojunction solar cells unless voltage dependent photocurrent collection is also considered.[25–29] We show that collection efficiency of photo-generated charges in a bulk heterojunction solar cell is not constant, but is highly dependent on the applied bias. That dependence results in a significant reduction in the performance of OPVs with increasing cell area and increasing series resistance and is assumed to arise from interfacial recombination.[28,29] An important factor when considering the effect of cell size is the geometry of the solar cells. If active areas are defined by the overlap of bottom and top electrode, which is one of the most widely used cell geometries in OPVs, then the ITO-related resistive loss is influenced by the length over which the lateral current flows to the contact finger.[25,30–33] In that situation, it is difficult to define the series resistance of ITO quantitatively. We avoided that problem by introducing sub-electrodes to define the geometry of the cell and were able to fabricate large area cells of up to 16.0 cm2. Figure 1 shows a schematic cross-section of the

Changes in solar cell performance related to active area size were investigated using polymer bulk heterojunction devices. Cell geometry was defined by introduction of a sub-electrode. The cells were uniform up to 16 cm2. The solar cells showed little change in performance up to a cell area of 1 cm2. As cell area increased above 4 cm2 the power conversion efficiency dropped significantly, mostly because of fill factor (FF) drop and short circuit current density (Jsc) suppression. The changes in FF and Jsc could not be described solely by a Shockley diode equation based on an equivalent circuit model unless photocurrent collection was also considered. As cell area increased, collection efficiency deviated from unity, which further reduced device performance. That deviation is attributed to acceleration of recombination loss at low built-in junction potentials.

1. Introduction Organic photovoltaic devices (OPVs) have attracted attention due to their potentially low production cost, ease of scale-up, and their widespread applicability. Improvements to polymerbased OPVs have been made and power conversion efficiency (PCE) of up to 7.4% have been reported.[1–6] To develop commercially attractive OPV modules, both enlargement of cell size and enhancement of cell PCE are important. To date, however, most researchers have focused on enhancing solar cell PCE by developing novel materials[5–11] and/or novel device structures,[2,4,11–16] with little attention paid to the effects of cell size on solar cell performance. Dependence of cell performance on cell size and geometry has been discussed; however, existing reports have been restricted to obtaining accurate measurements of solar cell performance by reducing the edge effect.[17–21]

W.-I. Jeong, J. Lee, Prof. J.-J. Kim OLEDs Center, Deptartment of Materials Science and Engineering Seoul National University Seoul, 151–744, Republic of Korea E-mail: [email protected] S.-Y. Park, Dr. J.-W. Kang Department of Material Processing Hybride Coating Group Korea Institute of Materials Science (KIMS) 531 Changwondaero Changwon, Gyeongnam, 641–831, Republic of Korea

DOI: 10.1002/adfm.201001578

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+

Current Density [mA/cm ]

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Cathode

-

Rc 1

Organic layer Cr/Al ITO

Rc 2

Cr/Al

RI T O

Glass Active area

10 5 0

2

0.09 cm 2 0.38 cm 2 0.5 cm 2 1.02 cm 2 4 cm 2 9 cm 2 16 cm

-5 -10 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

Voltage [V]

Figure 2. Current density versus voltage (J–V) curves for different cell sizes under AM 1.5G solar simulator illumination (open symbols) and in the dark (solid line). Different cell areas are indicated by different symbols.

Figure 1. (a) Schematic cross-sectional diagram of the tested solar cell structure showing possible resistive sources (Rx) in the device. (b) Images of 0.09 cm2, 0.5 cm2 and 16.0 cm2 devices. The purple areas in (b) indicate the active area while the grey colored areas correspond to the sub-electrodes formed by Cr/Al on ITO.

cell structure (a) and images of three different-sized fabricated cells (b). The sub-electrode defines the cell’s active area and also functions as a conducting electrode with low resistance to the finger point. The series resistance of the ITO (RITO) in the active area of the cell was well defined (see Experimental section) and the fabricated devices had square active areas with sizes of 0.09, 0.38, 0.5, 1.0, 4.0, 9.0, and 16.0 cm2. The fabricated solar cells had the structure of ITO/PEDOT:PSS(40 nm)/P3HT:PCM(200 nm) /LiF(1nm)/Al(100 nm). The P3HT:PCBM (1:1) was dissolved in o-dichlorobenzene (DCB). The ITO coated glass had a sheet resistance of 8 Ω/square.

2. Results and Discussion Figure 2 shows the current density-voltage (J–V) characteristics of the six different cell sizes tested. Solar cell parameters, such as PCEs, Jsc, open circuit voltages (Voc), FF, series (Rs) and parallel (Rp) resistances, and ideality factors of the diodes (n) for each of the different cell sizes are summarized in Table 1. Cells with areas of 0.09 cm2 to 1.0 cm2 had PCEs of ∼3.4% and Jsc values of between 8.9 mA/cm2and 9.5 mA/cm2, Voc of between 0.57 V and 0.58 V and FF of between 0.64 and 0.65. The Rs, Rp, and the dark- saturation current density (Js) were estimated by fitting the dark J–V curves with the following Shockley diode equation     V − J Rs V − J Rs (1) −1 + J = J s exp nkT)q Rp

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where q and k are the charge of one electron and the Boltzmann constant, respectively. The values were obtained by averaging the measurements from more than four devices. The devices showed reproducible results with measurement variation of less than 5%. As expected, device efficiency was lower in the larger cells (Table 1). The reduction in PCE in the larger cells is mainly related to the lowering of FF and Jsc. The results indicate that Voc does not change with cell area. Voc is related to the junction properties of the donor and acceptor layers, or to the work functions of the cathode and anodes;[34–36] both of which influence vertical current flow between two electrodes. Because an increase in cell size simply extends the length of the current flow in the lateral direction, Voc should not change with cell area; thus supporting our experimental results. The absence of a change in Voc with changes in cell area also confirms that the physical properties of the cells were independent of cell area and were uniform over the range of cell sizes tested. Such cell uniformity was also indicated by the small changes observed in Js and n, both of which are related to the junction properties of the active layer.[25,36] Rp is indicative of a leakage factor in the flow of current and, as cell areas increased, Rp fluctuated. However, the values were all more than 10 kΩcm2, a level that is high enough to not significantly affect device performance. Figure 3 presents a plot of the Rs obtained from the inverse slope at J = 0 in Figure 2 versus cell area. Rs shows a linear dependence upon cell area with the slope of 2.77 Ω and intercept of 1.29 Ωcm2. Such linear dependence is consistent with theoretical predictions.[23,30] The intercept value corresponds to the vertical components of Rs, which is not influenced by cell area. The slope is related to a combination of ITO sheet resistance and cell geometry. This linear dependence of Rs on cell area indicates that defining cell geometry through the use of sub-electrodes is adequate for the study of the effects of cell area and Rs on OPV performance. Furthermore, it demonstrates that the fabricated OPVs were uniform up to an area of 16 cm2. The variations of Jsc and FF with changes in both cell area and series resistance are displayed in Figure 4a and b,

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Table 1. Solar cell parameters of devices with different cell sizes. Rs, Rp, Js and n represent series resistance, parallel resistance, dark saturation current density, and diode ideality factor, respectively, which were obtained by fitting the dark J–V curves with the Shockley diode equation. Parameters

Values

Area [cm2]

0.09

0.38

0.5

1.02

4.0

9.0

PCE [%]

3.38

3.44 ± 0.07

3.43 ± 0.18

3.35 ± 0.12

2.81 ± 0.15

2.04

1.13

16.0

9.12

9.25 ± 0.46

9.51 ± 0.23

8.92 ± 0.21

9.18 ± 0.6

8.45

6.69

Voc [V]

0.57

0.57 ± 0.001

0.57 ± 0.01

0.58 ± 0.01

0.55 ± 0.01

0.56

0.59

FF

0.65

0.65 ± 0.02

0.65 ± 0.007

0.64 ± 0.01

0.56 ± 0.06

0.43

0.29

Jsc

[mA/cm2]

1.8

3.0 ± 0.15

2.2 ± 1.1

4.4 ± 1.4

12.1 ± 0.24

Rp [kΩcm2]

5.9

1900

22

28

88

10

24

Js [μA/cm2]

0.002

0.001

0.001

0.002

0.01

0.009

0.002

n

1.57

1.55

1.56

1.56

1.55

1.56

1.56

Rs

[Ωcm2]

2

Series Resistance [Ωcm ]

respectively. The experimentally obtained Jsc values do not significantly change up to cell areas of 4 cm2. However, there is a marked reduction in Jsc when the cell area is 9 cm2 and larger. The Jsc in the 16 cm2 cell with an Rs of 45 Ωcm2 is more than 25% lower than that in the smaller cells. The non-uniformity of the cells can also contribute to the reduction of the Jsc especially for large area cells. This contribution is apparent from the reduction of |J| for larger area cells at V < −0.3V. Figure 4(a) includes the |Jsc/Jph0| as another y axis to remove the effect of non-uniformity of the cells on Jsc, where Jph0 is defined as the J obtained at V = −0.5 V for each cell with a different area. The |Jsc/Jph0| in the 16 cm2 cell was still reduced by 14% from the smaller cells. In contrast, FF reduces almost linearly with increasing cell area and series resistance. The FF of the 16 cm2 cells was more than 50% lower than that in the 1 cm2 cells. Even in the 4.0 cm2 cells, where Jsc shows negligible change, the FF was reduced by about 15% from the level in the 0.09–1.0 cm2 cells. These results confirm that a reduction in FF is the main factor in the lowering of PCE of the OPVs when Rs increases.

50 40 30 20 10 0 0

3

6

9

12

15

18

2

Active Area [cm ]

Figure 3. Device series resistances versus active areas. Solid line represent a linear fit of the data.

Adv. Funct. Mater. 2011, 21, 343–347

22.9

44.7

The observed variations in Jsc and FF with Rs or cell area were simulated using the Shockley equation under illumination as follows     V − J Rs −1 J = J s exp nkT)q (2) V − J Rs + − J ph Rp where Jph is the photo-generated current density. Jph is assumed to be constant and is the same as Jph0 in the small area devices. We take the value of Jph from the average of Jph0 of small area devices (<1.02 cm2). Even though the definition of Jph is different from the definition of Jph0 in the experimental plot, the values become same if the non-uniformity factor is gotten rid of. The simulated |Jsc/Jph| and FF values are plotted against cell areas in Figure 4a and b, respectively, where they are compared with the experimental results. Discrepancies between the experimental data and the theoretical ones are apparent in both |Jsc/Jph| and FF values over the assessed range of cell areas and series resistances. In contrast to the experimental results, the calculated |Jsc/Jph| is not significantly reduced by an increase in Rs or cell area. Even though Rs approaches 50 Ωcm2 in the 16 cm2 cells, the reduction of |Jsc/Jph| is calculated to be less than 1.5% in the Shockley equation, whereas the experimental |Jsc/Jph| value was reduced by 14% in the 16 cm2 cell. The Shockley equation’s prediction of FF shows a similar trend to that in the experimental results, but the absolute values in the experimental results were smaller than the Shockley results by about 0.1. The failure of the Shockley diode equation to describe area dependence accurately in the devices’ J–V characteristics indicates that there are other factors that produce a loss of photogenerated current during charge collection as cell area increases. The lost photo-generated current can be described by a collection function, H(λ,V), which depends on both wavelength and voltage. The Shockley diode equation can then be modified by replacing Jph with H(λ,V)Jph0 as follows     V − J Rs −1 J = J s exp nkT)q (3) V − J Rs + − J ph0 H(8 , V ) Rp

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Series resistance [Ωcm ] 10

20

30

40

50

2

Jsc [mA/cm ]

0.9

8

0.8 7 0.7 6 5 0

Jsc, Experiment |Jsc/Jph0|, Experiment

0.6

|Jsc/Jph| and Jsc, Simulation

2

4

6

8

10

12

14

16

Normalized Jsc

1.0

9

0.5 18

2

Active Area [cm ] 2

Series resistance [Ωcm ] 0.8

10

20

30

40

50

0.7

FF

0.6 0.5 0.4 0.3 0.2 0

Experiment Simulation

3

6

9

12

15

18

2

Active Area [cm ] Figure 4. Changes in Jsc (a) and FF (b) with cell size and series resistance. Normalized Jsc is represented in the right scale of (a). Normalization constants are Jph0(J at V = −0.5 V) of experimental data and Jph(Jph0 of small area device) of calculated one. Open squares represents experimental data while solid lines represent the results from Shockley diode equation calculation.

where Jph0 is the photocurrent at a large reverse bias. This kind of equation modification has been applied previously in inorganic thin film solar cells, including Cu2S,[37] CdTe,[38] CuInSe2,[39] and amorphous-Si based solar cells.[29] Also in OPVs, voltage dependent collection function has been investigated to evaluate exciton dissociation rate and recombination loss by modeling J–V curve or photocurrent generation in bilayer[40–42] and bulk-heterojunction structure devices.[43–45] Figure 5 shows the bias-dependent collection functions for the OPVs with different active areas. One needs to note that the collection function was obtained after removing the nonuniformity effect of the cells by using the Jph0 as the normalization factor. The collection functions deviate from unity as the applied voltage increases above 0.4 V, even in the small area cells (0.09 cm2). The deviation from unity takes place at progressively lower bias levels with increasing cell area, once the active area is 4 cm2 or larger. The bias dependent collection function is reported to originate from interfacial recombination.[29,37–39,41–45]

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Collection Function, H(V)

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1.0

0.5

0.0

-0.5 -1.0 -0.4

2

0.09 cm 2 0.38 cm 2 0.5 cm 2 1.02 cm 2 4.0 cm 2 9.0 cm 2 16.0 cm

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Voltage [V]

Figure 5. Bias dependence of collection function, H(V) in devices with different cell areas.

Such recombination in OPVs can occur at the organic/electrode interface or at the bulk heterojunction of the active layer, and is apparently accelerated by the increasing cell area in our OPVs. The cause of the reduction of the collection function is not clear, but one plausible reason for accelerated photocurrent loss with increasing cell area is an increase in the potential drop across the ITO electrode to the collection point. Because of that potential drop, the built-in potential in the donor acceptor junction would become smaller and acceleration in recombination at a lowered built-in potential would be dependent upon defect levels in the bandgap of the P3HT crystals.[46] Detailed investigations into the origin of the cell area dependent loss of photogenerated current are underway.

3. Conclusion The effect of enlargement of active area on OPV performance is described. Geometry of the fabricated cells was defined through the introduction of a subelectrode. Physical properties of the cells were uniform at active areas of up to 16 cm2 resulting in large parallel resistances. The parameters influencing vertical current flow were maintained constant for all of the different active area devices. The fabricated solar cells with areas of 1.0 cm2 or less showed PCEs of 3.4% with Jsc of 9.1 mA/cm2, Voc of 0.58 V, and FF of 0.65 with little change in overall performance. As cell area increased above 4 cm2, PCE dropped significantly, mainly from a drop of FF and suppression of the photocurrent. The drop of FF and Jsc with increasing area could not be explained solely by the Shockley diode equation based on the equivalent circuit model, which relates Jsc and FF with series resistances, suggesting that there must be other factors accelerating electron and hole recombination at low built-in junction potentials. The origin of the accelerated recombination is not clear, but one plausible reason is that recombination is affected by the defect states in bandgap of the polymers used to fabricate the OPVs. Our proposed modification of the Shockley equation may be useful for optimum cell design and to investigate material systems that would increase the fill factor.

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Polymer-based OPVs were fabricated using a 1:1 blend of regioregular poly(3-hexylthiophene) and 6,6-phenyl C61-butyric acid methyl ester (P3HT:PCBM) obtained from Rieke Metals (Lincoln, NE, USA) and Aldrich Chemicals (St Louis, MO, USA), respectively. P3HT and PCBM were dissolved together with 1:1 weight ratio in o-dichlorobenzene to give an overall 40 mg/ml solution. ITO coated glass having the sheet resistance of 8 Ω/square was used as the substrate. On the pre-cleaned ITO coated glass, Cr and Al were successively deposited by e-beam evaporation through a shadow mask to thicknesses of 10 nm and 100 nm, respectively. A Cr/Al layer was used to define the cell area and was also used as a sub-electrode. On the patterned substrates, 40 nm thick PEDOT:PSS films were spin-coated and were baked for 1 min at 140 °C on a hot plate in the air. Then, the blended P3HT:PCBM films were spincoated to a thickness of 200 nm on the PEDOT:PSS layers in a glove box. After spinning the blended P3HT:PCBM solution, the samples were dried at room temperature for more than 2 h and annealed on a hot plate at 150 °C for 20 min. Finally LiF (1 nm) and Al layers (10 nm) were thermally evaporated onto the P3HT:PCBM successively to complete the sample. The photovoltaic properties of the devices were measured with an AM1.5G solar simulator (Oriel, 69911; Newport, Stratford, CT, USA) light source and a Keithley237 source measurement unit (Keithley, Cleveland, OH, USA). The measurement unit was calibrated with a National Renewable Energy Laboratory-certified reference Si-solar cell covered with a KG-5 filter before every measurement.

Acknowledgements This work was supported by Korea’s New & Renewable Energy R&D program (20093020010040) under the Ministry of Knowledge Economy and by a Korea Research Foundation NCRC grant (R15–2008-006– 01001-1) and by the WCU (R31–2008-000- 10075–0) program funded by Korea’s Ministry of Education, Science and Technology. Received: July 31, 2010 Published online: November 9, 2010

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4. Experimental Section

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Nov 9, 2010 - Won-Ik Jeong , Jane Lee , Sun-Young Park , Jae-Wook Kang , and Jang-Joo Kim *. 1. Introduction. Organic photovoltaic devices (OPVs) have attracted attention due to their potentially low production cost, ease of scale-up, and their widespread applicability. Improvements to polymer- based OPVs have ...

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