1. Introduction

The efficiency of organic photovoltaic (OPV) cells and particularly bulk heterojunction (BHJ) polymer solar cells has increased steadily [1, 2] through improvements in control over donor-acceptor blend phase separation and more recently, through advances in the electronic properties of the polymer materials [3–5]. By lowering the bandgap and increasing the highest occupied molecular orbital (HOMO) level, a broader absorption spectrum and increasing open circuit voltage (V_OC) are achieved. Despite the advances mentioned above, the external quantum efficiency (EQE) in devices optimized for maximum overall power conversion efficiency (PCE), is limited by the ability of the active layer to completely absorb the incident light. This is certainly the case in spectral regions where absorption is weak, but even at peak absorption wavelengths the photon absorption probability is usually <75%. Even with internal quantum efficiencies (IQEs) >90% (i.e. the processes of exciton diffusion, charge transfer, charge pair separation and carrier collection, are all very efficient), the external quantum yield is limited by optical absorption to <70%. One possible strategy that significantly increases the probability that an incident photon is absorbed is light trapping. Without any changes in the structure or active materials used in the devices, it can result in a much more efficient device since the EQE approaches the IQE. Here, we apply such a light trapping strategy based on a V-trap [6–11] to an efficient BHJ solar cell and show a significant increase in PCE.

Several photon management schemes for OPV cells have been explored. One approach has been to apply a conductive optical spacer such as BCP or TiO_x to maximize light absorption in the active layer by engineering an optical interference effect [12, 13]. To enhance optical absorption further, micro scaled geometric light trapping was tried [14–17], however, electric shunt and morphology distortion due to the grating limit the advantage. Other geometric light trapping schemes employing micro-lenses or AR coating [18, 19] were introduced, for which focusing oblique incident of light and additional cost issue for light trapping layer should be solved. More recently, wave optics approaches to enhance optical absorption were suggested [20–24] and some success has been achieved in this area [25–30]. Here, we use a geometric scheme in which incident light enters the device active area multiple times. In particular, we use the V-shape configuration, which was shown to be effective to low performing OPV [7–11], however, has been argued whether it functions well to the optimized OPV as well. Efficient BHJ solar cell based on poly [N-9’–heptadecanyl-2,7-carbazole-alt-5,5-(4’,7’-di-2-thienyl-2’,1’,3′-benzothiadiazole)] (PCDTBT): [6,6]-phenyl C71 butyric acid methyl ester (PC₇₀BM) blend [1] was chosen and proved that the scheme is effective even on the already optimized high performance polymer cells.

2. Proposed model and simulation

Figure 1 illustrates the design and operation of the V-shaped light trap for a thin film organic cell. Figure 1(a) shows how multiple bounces of an incident light ray off the active layer results in an increase in the optical path length and does an increase in absorption. The flat (no light trap) configuration results in a single bounce. At an opening angle (2α) of 60° and 30°, 3 and 6 bounces are achieved. Normalized photon absorption as a function of position in the V-shape and wavelength is shown in Fig. 1(b). Note that incident intensity at each wavelength is also normalized, so that integrated value over the position of V-shape at each wavelength is proportional to the value of absorption quantum efficiency. Photon absorption varies spatially and depends on the position in the V-shape as the ray picture shows that light is not uniformly distributed over the surface. The absorption is larger in the regions where the number of bounces is larger. For the case of a 30° of opening angle, for instance, the number of bounces increase from 2 at edge region to 4 at the middle region and finally becomes 6 near the tip of the V, resulting in three different absorption regions. An opening angle of 30° leads to the highest concentration of light toward the tip of the V compared to the planar or opening angle of 60°. Especially, the concentrated absorption near the tip is more pronounced at the spectral regions, where a planar cell shows weak absorption, due to the multitude of reflections. This indicates that the V-trap functions more effectively for the wavelengths at which photons are absorbed weakly and thus the absorption spectrum in the tip is substantially broadened compared to the spectrum of a planar cell. This also explains the reason that V-shaped light trap performs well for high performance polymer cells as well.

 

Fig. 1 Geometry of V-shaped geometric light trap for an organic solar cell for specified folding angles (planar / 60 degrees / 30 degrees) The rays schematically show the benefits of folding the solar cell structure on the number of bounces incident sunlight makes and thus the light absorption in the cell. Jsc is defined as the photocurrent generated inside the V-trap divided by aperature size (0.15 cm²). (b) Photon absorption in the active layer for a specified folding angle (planar / 60 degrees / 30 degrees) We note that the geometric distance of the cell (x axis) is normalized to the projected distance (aperature distance) of a V-trap. (c) Fabrication steps for V-shaped PCDTBT:PC₇₀BM OPV used on the presented experiments.

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To predict the merit of the V-shape light trapping configuration on the performance of PCDTBT:PC₇₀BM cells, the absorption quantum efficiency (AQE, i.e. the probability that an incident photon is absorbed in the active layer) was modeled. Ray tracing was used for ray propagation and the transfer matrix method [7, 31] was used to model reflection, transmission and absorption at each ray bounce. Every passage of light in the V-trap as well as the wave interference effects in the thin solar films are taken into account in the calculations. For modeling simplicity, we assumed isotropic optical characteristics and optically flat interfaces between layers. Reflections within the glass substrate were treated incoherently. Using the AQE, the EQE was estimated based on reported experimentally measured IQE data for an 80nm thickness of the PCDTBT:PC₇₀BM system, which was experimentally verified to be the optimal thickness for a planar cell. Integration with the AM1.5G solar spectrum then yields modeled photocurrent densities.

The modeled AQE and parasitic absorption in the electrode materials are shown in Fig. 2 for V-shape opening angles of 180° (no light trap), 60° and 30° with the 80nm thickness of active layer. Compared to the no light trap-case, V-shaped configurations exhibit a flattened AQE. The AQE near λ = 450 nm and λ > 600 nm is substantially increased due to the light trapping effect. The benefits going from 60° to 30° stems primarily from an extension of the AQE spectrum to longer wavelengths as the AQE for shorter wavelengths has already saturated. This effect is limited because the absorption from the PEDOT:PSS HTL and cathode metal layers starts to play an important role for spectral region between λ = 650 - 700 nm. In Fig. 3 , the modeled photocurrent density (J_SC) is shown as a function of the V-shape opening angle (blue solid line). We note that J_SC is calculated as the current produced divided by the aperture that is illuminated, as defined in Fig. 1(a). Since the device area increases as the opening angle decreases, the current per unit device area (as measured along the semiconductor surface) actually decreases, but the current per unit illuminated aperture (which defines efficiency) increases. The broadening and flattening of the AQE spectrum results in an increase in the predicted J_SC from 11.3mA/cm² to 14.6mA/cm². The increase in J_SC between opening angles of 120° and 90° degrees is due to multiple ray bounces. At angles >120°, a slight increase in J_SC is observed due to a slight increase in optical path length [32]. For angles <70°, the number of bounces increases further, resulting in a further increase in J_SC. Saturation of the AQE results in diminishing returns and a saturation of the theoretically achievable J_SC at 2α = 16°. A further decrease in opening angle results in a decreasing J_SC due to the increased parasitic absorption in layers other than the active layer, especially for longer wavelength. Consequently, the ratio of photon absorption in the active layer at each single bounce is lowered and this results in decreasing Jsc.

 

Fig. 2 Absorption quantum efficiency for a specified folding angle. (a) Planar (b) 60 degrees (c) 30 degrees.

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Fig. 3 Short circuit current as a function of a V-folding angle. Blue line indicates theoretical results and red dots show the experimental result.

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3. Experimental study

Figure 1(c) describes a possible way to practically implement the V-trap for an organic cell. It shows how planar glass substrates, precoated with indium-tin-oxide (ITO), are beveled at an angle of β = 90°-α to produce a V-shaped opening angle of 2α. This beveling is crucial such that the glass substrates can make intimate contact and prevent significant photons loss through the tip region, at which the enhancement is maximized. On these modified glass substrates, a 30 nm-thick PEDOT:PSS was spin-coated, followed by a 80 nm-thick PCDTBT:PC₇₀BM 1:4 blend layer from a 1.9% solution in dichlorobenzene (DCB). Subsequently, a cathode consisting of a 8 nm-thick Ca layer and 200 nm-thick Ag layer was vacuum deposited. The cathode area of each cell is 0.075 cm² and the area between cells is also coated by the same cathode layers to reflect photons as much as possible. Two substrates are attached at their beveled edges using an epoxy glue and the cell parameters were measured under top illumination by 100 mW/cm² 1 sun AM1.5 simulated solar spectrum.

The experimentally measured J_SC, shown in Fig. 3 (red square markers), increases from 11 mA/cm² for the planar case (without the light trap) to 14.2 mA/cm², for a V-shaped light trap with an opening angle of 30°, a 29% increase. At an opening angle of 60°, J_SC = 13.7 mA/cm². It is worth noting that an equivalent thickness of a planar cell that could generate a 29% increase in J_SC is 430nm. This is based on the assumption that the IQE of thicker planar cell is same as that of thin film used for V-shaped cell. Based on the short exciton diffusion length, it is expected that it is advantageous to utilize a thinner cell and capitalize on the V-grooves to trap light. While the dependence of the experimentally measured J_SC agrees with that predicted using model calculations, the model systematically predicts a higher J_SC. This discrepancy is due to photon leakage at the gap area between separated cathodes in the substrate surface and degradation by significant light concentration to the tip regions of V-trap. Additionally the assumption that the sharp corners of V-shaped cells perform the same as planar regions need to be verified in scalable designs of the presented cells.

V_OC (Red dot) and the FF (Blue dot) were measured for devices on both sides of a V-shaped cell, as shown in Fig. 4(a) . The total short circuit current (I_SC) for a device active area of 0.15cm² is also shown in Fig. 4(a). An average value of Voc is 0.83V and 0.84V for each side, though a small fluctuation of about 0.01V is observed as a function of opening angles. A slight decrease in the Voc is observed at a folding angle of 30 degrees due to the reduced light intensity at the overall surface area of the V-shaped cell as well as an increase of dark current proportional to the surface area of the V-shaped cell [7, 33]. An average fill factor (FF) of 0.58 over the folding angles measured is obtained at both sides, where one side shows an almost constant value and the other side shows deviation from 0.01 to 0.02 as the folding angle changes. Isc increases up to 2.13mA for the V-shaped cell with the folding angle of 30 degrees over 1.65mA for the planar cell.

 

Fig. 4 (a) Open circuit voltage (Red dot) and Fill factor (blue dot) measured separately at each side, and total short circuit current (green line) as a function of the folding angle for the V-shape configuration. (b) Power conversion efficiency as a function of a folding angle of the V-shape configuration.

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By measuring the generated power at both sides, the PCE is calculated from the planar cell to the V-shaped cell for a specific folding angle, as shown in Fig. 4(b). At an angle of 30 degrees, an enhanced efficiency of 7.2% is obtained, whereas the planar cell shows an efficiency of 5.3%. It should be noted that the increased FF compensates for the reduced Voc for narrower folding angles and thereby slightly contributes to the improvement in the efficiency.

4. Effect of the oblique incident of light

To evaluate the performance of V-shaped cell under practical solar illumination conditions, the current generation with respect to the oblique incident of light is theoretically analyzed. Photocurrent is generated under the illumination of AM 1.5G solar spectrum and θ _i is defined as the angle from the normal axis of projected area of V-shaped cell. A detailed analysis of full day modeling of OPV is presented in other publication [11] and this paper focuses on the comparison of planar and V-shaped cell using PCDTBT:PC₇₀BM materials. Although the oblique incident of light into the V-shape configuration results in decreasing bounces of a ray for a given folding angle, light absorption of the V-shaped cell is still larger than that of the planar cell due to reduced Fresnel reflection. Consequently, the V-shaped PCDTBT:PC₇₀BM cell shows superior performance over the planar cell for all angles of incidence light as shown in Fig. 5 .

 

Fig. 5 Effect of the incident angle of the illumination (θ_i) on the short circuit current density (Jsc). Blue line shows the current generation at 30 degrees of the V-shaped cell and the red line shows the same for a planar cell.

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5. Conclusion

In summary, V-shaped light trap, which has shown to be efficient light trapping for low performing OPV, also enhances the performance of already optimized thin film polymer solar cells further by increasing the optical path length of low absorbing spectrum substantially. Here, both theoretical and experimental improvements were demonstrated by applying the V-shaped light trapping scheme to a PCDTBT:PC₇₀BM BHJ polymer solar cell. Theoretically, an increase of the AQE for a weakly absorbing spectral regions of a cell is expected and experimentally, 29% increase of Jsc under 100mW/cm² AM1.5G illumination is demonstrated through the intimate contact at tip region. PCE of 7.2% is attained in the V-shaped cell with folding angle of 30 degrees, whereas PCE of 5.3% is obtained in the planar cell. Also, we found that the V-shaped PCDTBT:PC₇₀BM cell is always superior to the planar cell for all angles of incident light. Furthermore, we anticipate that more practical fabrication is possible by using a plastic substrate with sharp tip or millimeter scaled prism substrate with uniform thermal evaporation.