We have designed a high efficiency organic solar cell with light trapping structure on transference cylindrical substrate. An electrical and optical simulation of the light trapping structure has been performed on the basis of finite element and transfer matrix formalism methods. Absorption spectrum, internal quantum efficiency, external quantum efficiency, maximum power output and efficiency of the organic solar cell are simulated and presented in terms of three variables: the height, diameter of the glass substrate and the thickness of the organic active layer. The efficiency of the proposed organic solar cell with light trapping structure is enhanced by a factor of 2 than the similar structure on the flat plain glass substrate. The optimum organic active layer thickness to achieve the highest efficiency is shifted from 65 to 20 nm. Finally, we have investigated the effect of light incident angle on the performance of the proposed cell structure.
© 2012 OSA
Organic photovoltaic (OPV) has attracted much attention in recent years due to the rapid increasing of its power conversion efficiency (PCE) and the potential benefits of low cost production methods . The highest reported PCE of an OPV device is ~8.0% , which is approaching to the required efficiency for commercialization . At present, OPV devices with the highest performance are based on the bulk heterojunction (BHJ) type in which an electron-donor polymer material and an electron-acceptor fullerene material are blended to form an active photovoltaic layer. The most commonly studied polymer-fullerene system is based on a blend of donor poly (3-hexylthiophene-2,5-diyl) and acceptor [6,6]-phenyl-C61 butyric acid methyl ester(P3HT: PCBM), in which the highest reported PCE values are in the range of 4 to 6% [4–6]. The theoretical PCE limits of BHJ are over 23% . The difference between the theory and experimental PCE can be explained by five reasons: namely the energy level misalignment at the donor/acceptor interfaces, insufficient light trapping, low exciton diffusion lengths, nonradiative recombination and low charge carrier mobilities. The OPV device structure needs a thin active layer due to the low exciton diffusion length (~10 nm) for the high efficiency device , but the thin active layer is insufficient to absorb most of the incident light.
The light trapping structure is one of the potential ways to improve the PCE of BHJ by increasing the effective optical length within the active layer without the need of altering its physical thickness. The conventional light trapping structures for inorganic solar cells can’t be used on the OPV due to their larger size typically in a micrometer scale, compared to the thickness of OPV active layer in nanometer scale. Some light trapping structures for OPV, have been proposed such as submicron or micron structures, buried Nano-electrodes, multi-reflection structures and distributed Bragg reflectors [9–12]. However, light trapping structures in direct contact with thin active layer is most likely to introduce defects and contamination into the organic solar cell. Other light trapping structures like micro-lenses structure can avoid direct contact with the active layer, but it is only valid for the normally incident light . Some researchers have also proposed the light trapping structure based on the tube-like geometries . However, the bottom of the structure is closed in a hemispherical cap rather than a proposed back diffuse reflector. Besides, all the parameters associated with the light trapping structure, such as the height of the tube, the thickness of the OPV cell and etc, have not been optimized due to the lack of the detailed theoretical analysis. Finally, the effect of the different incident angles on the efficiency of OPV has not been fully discussed. Other geometries based on horizontal tube-like structure requires very complicated structure and it is still lack of fully theoretical analysis on the effect of all parameters [15–18].
The concept of the proposed structure of OPV device with light trapping on cylindrical glass substrate is shown in Fig. 1 and Fig. 2 . The proposed OPV device structure has consisted a columnar glass substrate, indium tin oxide (ITO) layer, Poly (3,4-ethylenedioxythiophene) -poly (styrenesulfonate) (PEDOT:PSS) layer, Copper phthalocyanine (CuPc) donor, thiophene-C60 acceptor, bathocuproine (BCP) layer, aluminum (Al) layer as electron collecting electrode (100 nm thick) and lambertian diffuse reflector. The incident light on the columnar glass substrate passes through the glass and is scattered in all directions in the upper hemisphere by the back diffuse reflector (96% lambertian reflector). The scattered lights bounce left and right through the active layer of the device. The unabsorbed photons in the first pass have additional opportunities to be absorbed in the subsequent passes. In this way, the effective optical length is dramatically increased.
In order to compare the performance of the proposed OPV device structure with light trapping structure, a similar OPV device cell on flat plain glass substrate without any light trapping structure is also simulated and analyzed in the similar way. The OPV device without light trapping is shown in Fig. 3 . It contains same structure of the proposed device such as an Al electrode, BCP layer, C60 acceptor, CuPc donor, PEDOT: PSS layer, ITO layer and plain glass substrate.
The proposed OPV device structure described above involves an optical modeling of the light path within the light trapping structure and a comprehensive electrical modeling of the exciton generation and transfer, exciton dissociation and charge transport and collection. After the modeling of optical and electrical properties of the proposed device, we could derive the mathematical expressions for optical absorption curve, external quantum efficiency (EQE), internal quantum efficiency (IQE), short circuit current and power conversion efficiency. The needed assumptions for the model are: (1) the glass substrate and all other layers are considered as homogeneous and isotropic; (2) interfaces are flat and parallel compared to the wavelength of the light ; (3) exciton diffusion conforms to the diffusion equation; (4) excitons contribute to the photocurrent are dissociated at the D-A interfaces; (5) the surface of the organic solar cell acts as the exciton sink with large recombination velocity; (6) all the simulations are carried out in the standard test conditions: AM1.5 spectrum, 1000 W/m2 irradiance at 25 C cell temperature; (7) The open circuit voltage of this organic solar cell is 0.5 V and fill factor (FF) is 0.6.
2.1 Optical modeling
2.1.1 Energy dissipation and diffuse reflector
It is considering a plane light wave incident from top on a glass substrate with an incident angle θ. Part of the incident light would be reflected by the air/glass interface and the reflection loss could be expressed by
When the incident light is normal to the air/glass interface, the reflection loss is reduced to:
The light absorption by the glass substrate is considered to be negligible. Incident light scattered into different directions after reflection from the bottom of glass substrate. The scattering light follow the Lambert's cosine law. The differential radiant flux at any point could be described by the Lambertian distribution :
The total radiant flux from the diffuse reflector for a specific wavelength is equal to the incident radiant flux, which is expressed as:Eq. (1), (2), (3) into Eq. (4), one can get the radiant flux contained within a differential solid angle for a particular wavelength as follow:
At this stage, the s and p polarized lights have the equal intensities, thus one can get the following expressions:
2.1.2 The distribution of exciton generation
The modeling of the exciton generation distribution in principle is following the method described by Pettersson , however, this treatment is modified and expanded for non-normal incidence case considering the effect of increasing polarization of light after each reflection. When the light with specific solid angle is incident on the multilayer, the propagation of light is generally described by the matrices. Since the tangential component of the electric field is continuous according to the theory of electromagnetic, the interface property could be expressed by:
According to the transfer matrix method listed in the reference . The total electrical field in the layer j can be expressed as follows:Eq. (12) are available in the reference . Where is absorption coefficient, T is internal intensity transmittance, is the intensity of the incident light, is the absolute value of the complex reflection coefficient.
2.2 Electrical modeling
2.2.1 Exciton transport
The electrical modeling is carried out in linear coordinates as opposed to cylindrical coordinates, since the active layer thickness, 20 nm, is orders of magnitude smaller than mm diameter cylindrical glass substrate. The exciton transport is dominated by the diffusion equation. At steady state condition if n is the exciton density, the continuity equation is:Eq. (12).
The boundary conditions for Eq. (13) are: (i) the surfaces of the active layer have infinite recombination velocity and act as perfect excitons’ sinks; (ii) all excitons can either recombine or dissociate into free charge carriers at the donor-accepter interface. By applying two boundary conditions into the general solution, one could get the exciton distribution as follows:Eq. (15).
2.2.2 Absorption spectrum, EQE, IQE and efficiency
The absorption spectrum, external quantum efficiency (EQE), internal quantum efficiency (IQE) and efficiency are the primary parameters reflecting the fundamental performance of the light trapping system. In this Section, we would derive the expressions for these significant parameters on the basis of the model described in the Section 2.1.2 and Section 2.2.1.
The absorption spectrum is generally defined as the ratio of the number of the photons absorbed at the active layer to the number of photons incident on the system. For this light trapping system, the number of photons absorbed could be estimated by:Eq. (12), stands for the total sum of the exciton generation rate in the acceptor because the light will bounce left and right in the light trapping structure until the light emits out from the system.
The number of incident photons can be defined as:
Since we have already derived the EQE and absorption spectrum, the IQE is easily defined as:
The efficiency of the whole system is defined as:
3. Results and discussions
Figure 1 shows the three dimensional (3-D) image of the proposed OPV device structure on cylindrical substrate which we have discussed above. Figure 2 is the cross sectional view of the proposed OPV device structure. An example of perpendicular incident light and the reflected light are shown in Fig. 2. Some reflected light would escape the OPV structure directly, some light would pass the organic solar cell layers several times and some light would be totally trapped by this structure. Figure 3 shows the 3-D view of an OPV structure with similar materials layers on a conventional flat plain glass substrate for comparison with the proposed structure.
Figure 4 shows the simulated absorption spectrums of the proposed OPV structure and the conventional OPV on flat plain substrate without light trapping for active layer thicknesses of 20, 40 and 80 nm (d = dD + dA). The equal layer thicknesses of donor dD and acceptor dA are considered. The light absorption in the proposed OPV structure is significantly enhanced due to the cylindrical substrate structure, especially when the organic active layer is thin enough such as 20 nm. The effect of light trapping is greatly reduced for the thicker active layers as thick layer itself can absorb much more light than the thin layers. When the active layer thickness reaches 80 nm, the conventional OPV structure on plain substrate can absorb more light in the wavelength between 300 nm to 450 nm than the proposed structure due to the more reflection loss at the interfaces. The proposed OPV structure could greatly enhance the absorption of light and the performance of device for the ultra-thin organic active layer.
Figure 5 illustrates absorption spectrum of the proposed OPV cell for height 1, 3, 5 and 7 cm of the cylindrical glass substrate with an active layer thickness 20 nm. The absorption spectrum of the OPV structure on flat plain substrate is also compared with 20 nm thick active layer. The light absorption increases with the increase of cylindrical substrate height. As the substrate height increases, the absorption spectrum starts to saturate due to the inevitable reflection losses at the multi-interfaces. However, the increased height would definitely enhance the total cost of the proposed OPV system. Figure 6 shows the absorption spectrum of the proposed OPV cell for various diameters 1, 3, 4 and 6 mm of the glass substrate with an active layer thickness 20 nm. The light absorption increases with the decrease of cylindrical glass substrate for the proposed OPV structure.
The EQE is the comprehensive indicator of both the efficiency of the exciton absorption and collection. The IQE is the inherent property of the OPV solar cell and is therefore independent of the light trapping system. With perfect light trapping system, the EQE will approach to the IQE with almost complete absorption. We present the EQE and IQE curve of the proposed system to check its performance. From the Fig. 7 , it is clear that the thinner active layer (20 nm) has the higher IQE of the proposed OPV device structure. The generated exciton in thin active layer has the highest rate of dissociation at the D-A interfaces as the distance of D-A interface within the exciton diffusion length. The charge collection probability will increase for thin active layer. The EQE depends on both light absorption ability and IQE. The highest EQE occurs for the active layer thickness 20 nm. The light trapping structure could effectively enhance the light absorption in the proposed OPV structure for thin active layer close to the diffusion length of exciton. The light trapping structure is not very effective for thicker active layer such as 80 nm as active layer itself absorb most of the incident light.
Figure 8 shows the EQE and IQE curve for different height of the glass substrate of diameter 3 mm cm with active layer thickness 20 nm. Figure 9 shows the EQE and IQE curves for different diameter of the glass substrate with 5 cm height and active layer thickness 20 nm. Similar to the absorption curve, the EQE increases with the higher substrate height and lower diameter. However, when the height reaches 7 cm and the diameter decreases to 1 mm, the EQE begins to saturate due to the limitation of IQE. The highest EQE is far below IQE because of the inevitable reflection loss at the interfaces and the absorption loss by ITO and BCP.
The effective conversion efficiency, considering the effect of the different packing densities, of proposed OPV device versus active layer thickness curves for the different heights of glass substrate is shown in Fig. 10 . The light trapping device improves the efficiency of OPV by a factor of 2 compared to the conventional OPV device structure on flat plain substrate. As expected, longer glass substrate could have the higher conversion efficiency of the proposed OPV structure, although the efficiency would saturate after the height increased to 9 cm. The active layer thickness 20 nm shows the highest efficiency of the OPV devices. The efficiency curves for different diameters of glass substrate as shown in Fig. 11 are similar to Fig. 10. It is very obvious that there is a discontinuity in the slope of the Figs. 10 and 11, due to the active layer thickness is equal to or less than 20 nm. Most of the excitens generated by photons absorption would be collected and dissociated at the D-A interface as the active layer thickness is nearly equal to the sum of the diffusion length of excitons in donor and acceptor materials. The diffusion probability of excitons to the D-A interface are almost equal to 1. When the active layer thickness is more than 20 nm, the collection probability of excitons to the D-A interface is sharply decreased. Figure 12 shows the effect of incident angle of light on the efficiency of proposed OPV device structure. The incident angle of light has a little effect on the performance of device. Most of the incident light on OPV device could be trapped by the cylindrical structure of substrate.
From the above analysis one can make the best efficiency OPV cells if it is fabricated on 5 cms long and 5 mm diameter cylindrical glass substrate with 20 nm thick active layers. For the same cross sectional areas of intersections light, cylindrical rods will have more surface area and more than double cell efficiency compare to flat surface cells. Cost effects of using long cylindrical rods will be much better than the flat substrate cells because of high efficiency cells.
We have designed and analyzed a proposed OPV device structure on cylindrical glass substrate to enhance the power conversion efficiency of organic solar cell. An optical and electrical analysis has been carried out for the proposed light trapping structure. Optical interference effects, increased polarization and non-normal incident light are considered for the analysis of the proposed device by expending the Pettersson’s method. Some significant device parameters such as IQE, EQE, efficiency and absorption spectrum are derived. The light absorption curve, EQE and efficiency are significantly enhanced by the proposed light trapping structure. The efficiency of proposed device has the potential to increase by a factor of 2 compared to the OPV device on flat plain glass substrate. The incident angle of light has a little effect on the performance of proposed OPV structure. The proposed OPV device structure can operate efficiently for all incident angle of light. The simulation program is developed in MATLAB by the author.
The authors would like to thank the School of Photovoltaic and Renewable Energy for its support. We are all grateful for Dr. Patrick Campbell, Dr. Ivan Perez-Wurfl and all the members in PV school for their suggestions and support.
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