Organic solar cells (OSCs), offers tremendous promise as an alternative to conventional Si-based solar photovoltaics (PV) technology as it requires less production cost and effort because organic semiconductors are simple to process than the inorganic cells due to much lower processing temperatures [1] -[11] . Although it is in early stage of technology, the vision is mass production of these devices with less stringent and less thermal budget requirements than those needed for traditional silicon solar cells. The production potential may possibly exceed 1000 m² per hour [5] . Because of the development of newer materials, new designs and interfacial layers it can exhibit very high power conversion efficiency (PCEs).

The most promising designs are a combination of electron-accepting and electron-donation molecular materials, so as to develop a p-n heterojunction. Efficient charge carrier extraction from the active layer to the respective electrodes is essential for optimal functioning of OSCs and depends on the character of the interface of each layer. One way to obtain efficient charge extraction is to match the work function of anode and cathode with the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies of the active layer [12] [13] . The introduction of self-assembled mono-layers of molecules on ITO substrates with appropriate direction and magnitude of dipole moment, improves the performance of organic solar cells [14] [15] . This method decreases the injection barrier between the HOMO level and the ITO and it also effectively changes the work function of ITO. Another way to increase the efficiency is the formation of an interfacial energy step [16] [17] .

One particular interest is that the donor-acceptor heterojunction is formed from a blend of conjugated polymer with a fullerene derivative [18] - [23] . An example of promising OSCs, is a blend of the fullerene derivative [6, 6]-phenyl-C61 butyric acid methyl ester (PCBM) and regioregular poly (3-hexylthiophene) (P3HT) heterojunction, which has been experimentally studied earlier [24] . A phase-separated bulk heterojunction (BHJ) nanostructure of large interfacial area is formed from this blend [25] . A thin poly (3, 4-ethylenedionythiophene): poly (styrenesulfonate) (PEDOT:PSS) layer is used as an anode contact because the work function of PEDOT:PSS matches with the HOMO of P3HT and this allows for effective extraction of holes from the active layer [26] . The PEDOT:PSS layer planarizes the ITO surface without affecting the light absorption by the active layer significantly. PEDOT:PSS has high electrical conductivity and low temperature solution processability, which makes it an ideal hole transport material. Though it is used as a hole transport layer, its electrical inhomogeneity property prevents it to be an electron blocking layer [27] . Moreover, the hygroscopic and acidic nature of PEDOT:PSS can degrade the device performance. Metal oxides like VO_x, NiO_x and MnO_x have been used as a replacement of PEDOT:PSS but the rough interfaces formed by metal oxides can also degrade device performances [28] [29] . The future of P3HT:PCBM organic solar cells will depend on the improvement of their conversion efficiency. Currently organic solar cells shows relatively lower efficiency (3.5% or lower) when compared to the inorganic solar cells. Therefore, more studies are needed to enhance and understand the conversion efficiency of these devices. In addition, the traditional equivalent OSC circuit used to describe OSC does not accurately describe devices that have incorporated novel interfacial layers [30] .

The goal of this work is to investigate the properties of OSC devices with an added AgO_x interfacial layer between the PEDOT:PSS and ITO and to develop a model that best describes this device. The added AgO_x layer increases the fill-factor (FF), power conversion efficiency (PCE) and reduces the physical contact of PEDOT:PSS with ITO. While developing a revised model, we also revisit some earlier models for different solar cells. This methodology will correlate between theoretically constructed current-voltage (I-V) plots and experimental I-V plots. Then based on the I-V correlation results a model will be suggested that bests describes the P3HT:PCBM organic solar cell.

The fabrication of the device consists of five layers. Figure 1 shows the device structure of the organic solar cell.

Patterned ITO coated glass substrates were cleaned in ultrasonic baths of methanol, acetone and isopropanol, followed by 15 min ultraviolet ozone (UVO) treatment. On top of the ITO, 1 nm of Ag metal was deposited by thermal evaporation at a pressure of ~10^?7 Torr followed by 1 min UVO treatment. Using Ocean Optics double channel spectrometer (model DS200) optical transmittance of bare ITO and ITO with AgO_x layer, were measured in 300 - 800 nm wavelength range. Electron acceptor material PCBM and electron donor P3HT were weighed (1:1 w/w) and dissolved in 1, 2-dichlorobenzene (DCB). PEDOT:PSS solution was spin coated at 5000 rpm for 60 s. After that photoactive layers were spin-coated at 600 rpm for 1 min. It was then annealed at 120˚C on a hot plate for 30 mins, which corresponds to a layer thickness of 250 nm. Finally, 0.7 nm of LiF was thermally deposited followed by 80 nm Al cathodes in vacuum. During thermal evaporation a shadow mask was used to define 0.2 cm² of active area. Under simulated AM 1.5 global solar irradiation photo current density-voltage (J-V) measurements were performed using a xenon-lamp solar simulator.

In order to understand the electrical behavior and observe how the device parameters changes with any kind of applied treatment (bias, illumination, etc.) to the device, it is modeled with discreet electrical components such as voltage or current sources, diodes and resistors. It provides a scientific and realistic physical explanation for the OPV behavior.

According to Equation (6), both the ideal diode D and R_SH are now the components that determine V_OC. This assumes that R_SH is not very high and the device is in the dark and by applying a positive voltage across the cell electrodes a voltage drop can be created across R_SH which equal to the voltage V_D across the ideal diode D. The current that can pass through the diode D at V_D is determined by its I-V characteristic. The sum of the currents through D and R_SH yields the current through the electrodes of the solar cell for a given applied voltage. Upon illumination, the current source generates the current I_L some of which passes through the diode where a voltage drop is generated that is big enough to allow the rest of I_L to go through R_SH if the electrodes are open. The same voltage can be measured with a voltmeter with high internal resistor across the device electrodes and is then termed open circuit voltage V_OC.

Figure 4 shows that the I-V characteristics changes if the shunt resistance varies between 100 ohm and 3000 Ohm assuming the shown values for R_S, I_L, and I₀. If R_SH > 1500 Ohm the shape (FF, V_OC) of the IV curves remains virtually unchanged and the current shows no significant field dependence for negative bias.

However, clearly smaller R_SH values have detrimental effects on the IV curve. The slope (field dependence) in the third quadrant increases considerably, V_OC approaches zero and the FF reaches its theoretical minimum of 0.25 very quickly. However, the short circuit current is not affected since the current through the shunt can be neglected if R_S = R_SH.

Figure 5 shows the I-V characteristics with increasing series resistance, assuming the same parameters as above. While the slope in the third quadrant remains unchanged the slope in the first quadrant starts to decrease considerably when R_S reaches the same order of magnitude as R_SH. The effect of the large R_S even extends into the third quadrant thereby decreasing FF to its minimum.

Moreover, if the two resistors have similar values, the I-V curve is dominated by their Ohmic characteristics (the inverse slope in the 1 quadrant is equal to R_S) and the ideality factor or voltage dependence of D may then have little influence. Note that in contrast to the effect of R_SH the short circuit current can decrease but the open circuit voltage cannot be affected at all―since there is no current through R_S at V_OC.

Once all the parameters for the equivalent circuit are determined, using the raw data we have constructed simulated I-V plot in order to develop a model that best describe this particular OSC. Considering the effect of R_SH and R_S as discussed above, a resistor R_S1 in series with one diode is added. R_S1 accounts for the recombination of the carriers. Figure 6 shows the proposed model. The ideality factor n for both of the diodes was assumed equal with an approximation corresponding to the Shockley-Read-Hall recombination current density in the space-charge region [32] . The current equation for the proposed two diode model is given by Equation (7).

Figure 7 shows the I-V plots for experimental data and simulated plots for the proposed model, single and two diode models under 100 mW/cm² illumination intensity. It is observed that the I-V characteristics generated from our proposed model fits well with the experimental result. The average percentage variation is 2.38%. Using a AgO_x interfacial layer between PEDOT:PSS and ITO increases the power conversion efficiency by 28%.

The device with added AgO_x interfacial layer showed 3.5% PCE and 33% increase of FF. Earlier single diode and two diode models were unable to describe the device behavior; hence, a two diode model was developed. Based on the experimental values and the simulated result under same illuminated intensity, the two diode models correlated with the experimental result showed only a 2.4% variation.

This research was partially supported by the National Science Foundation (C. Ying, Grant No. DMR-0902277).

NazmulHossain,SayantanDas,Terry L.Alford, (2015) Equivalent Circuit Modification for Organic Solar Cells. Circuits and Systems,06,153-160. doi: 10.4236/cs.2015.66016