Investigation of Organic Bulk Heterojunction Solar Cells from Optical Aspect

Low in cost, light in weight and flexible in mechanics, the solution-processed organic solar cells have aroused worldwide interest and have been the promising alternative to the tradi‐ tional silicon-based solar cells [1-4]. However, they are still not available for the commercial‐ ization due to their low power conversion efficiency (PCE). Therefore, many research works have focused on the employing of new materials and device structures to improve the de‐ vice performance. The milestone is the introduction and application of the bulk heterojunc‐ tion structure consisting of an interpenetrating network of electron donor and acceptor materials [5]. By using this structure, the conventional organic solar cell (OSC) with poly(3hexylthiophene)/[6,6]-phenyl C61-butyric acid methyl ester (P3HT:PCBM) blend shows a su‐ perior performance. Recently, the inverted organic solar cell (IOSC, in which the polarities of the two electrodes are exchanged) has also been introduced as the possible candidate for OSC to remedy the low air stability of OSC [6]. Both OSC and IOSC are now attracting the research interest. However, most of the previous works are mainly done for OSC or IOSC separately, and almost no researches are reported about the systemic comparison between OSC and IOSC for their different performances besides the air stability. Since the reported PCE of IOSC is relatively lower than that of OSC in many researches, one may doubt that which structure is better, the conventional one or the inverted one? As a result, one section of this chapter aims to investigate the performance differences of OSC and IOSC.


Introduction
Low in cost, light in weight and flexible in mechanics, the solution-processed organic solar cells have aroused worldwide interest and have been the promising alternative to the traditional silicon-based solar cells [1][2][3][4]. However, they are still not available for the commercialization due to their low power conversion efficiency (PCE). Therefore, many research works have focused on the employing of new materials and device structures to improve the device performance. The milestone is the introduction and application of the bulk heterojunction structure consisting of an interpenetrating network of electron donor and acceptor materials [5]. By using this structure, the conventional organic solar cell (OSC) with poly(3hexylthiophene)/ [6,6]-phenyl C61-butyric acid methyl ester (P3HT:PCBM) blend shows a superior performance. Recently, the inverted organic solar cell (IOSC, in which the polarities of the two electrodes are exchanged) has also been introduced as the possible candidate for OSC to remedy the low air stability of OSC [6]. Both OSC and IOSC are now attracting the research interest. However, most of the previous works are mainly done for OSC or IOSC separately, and almost no researches are reported about the systemic comparison between OSC and IOSC for their different performances besides the air stability. Since the reported PCE of IOSC is relatively lower than that of OSC in many researches, one may doubt that which structure is better, the conventional one or the inverted one? As a result, one section of this chapter aims to investigate the performance differences of OSC and IOSC. charge mobility, and these factors limit the maximum thickness of the active layer for light absorption. Second, most organic semiconducting materials show discrete absorption behaviour and cover only a fraction of the solar spectrum, leading to inefficient light harvest. To overcome these drawbacks, the realization of the tandem structure based on complementary thin absorber materials provides a reasonable solution to the above obstacles. As a promising concept to achieve high PCE, the tandem solar cell can reduce the loss via subbandgap transmission of photons, the major loss mechanism in solar cells [7]. For an ideal tandem solar cell, it requires current matching of the subcells, a lossless recombination contact and a complementary absorption of the subcells. Among them, current matching of the subcells is a leading design criterion for improving the tandem device performance. Then, the organic tandem solar cell optimization by considering the current matching is also involved in this chapter.
As is well known, the working principle of organic photovoltaic devices can be simply described as a process of "light in-current out". This process consists of seven parts: 1. in-coupling of photon,
The first two parts are the optical mechanisms of the device and the other parts constitute the electrical aspect. The optical aspect plays a significant role because more incident photons and absorbed photons are the baseline for the better device performance. It has been reported that the internal quantum efficiency (IQE) of organic bulk heterojunction solar cells can reach 100% [8]. Thus the external quantum efficiency (EQE) can be approximately described as the product of IQE and the ratio of the number of absorbed photons in active layer to the number of incoming photons. As a result, the optimization of organic solar cells from the optical aspect is seriously important. This is why we investigate the device performance of standalone and tandem organic solar cells mainly from the optical aspect in this work.
The contents of this chapter are arranged as the following: Section 2 investigates the performance of the standalone conventional and inverted organic solar cells, especially the performance differences between the two types of devices. Section 3 discusses the optimization of the organic tandem solar cell from the optical aspect by considering the current matching. At last, a short conclusion is given in Section 4.

Methology
In order to investigate the standalone organic solar cell, we have performed optical simulations based on the Transfer Matrix Formalism with two subsets of 2×2 matrices (layer matrix and interface matrix), which was firstly introduced into organic solar cells by Pettersson et al [9] and now has been used widely. In this method, the cell is treated as a one-dimensional stack of homogeneous and isotropic layers with flat interfaces, and the number of photons absorbed in the active layer is obtained by calculating the time average of the energy dissipated per second in it. The detailed calculation processes are not presented here since the transfer matrix method is widely applied [10].
In the calculation, we assume that one absorbed photon produces one exciton in the active layer and one exciton divides into two free charges (one electron and one hole), and one electron (or hole) is collected by cathode (or anode). As a result, the number of photons absorbed in the active layer can be used as the substitute for the maximum possible short circuit current density and the EQE can be simplified as the ratio of the number of photons absorbed in the active layer to the number of incident photons.  [11][12][13].
It should be noted that, the reflection of the glass substrate is taken into account to revise the initial intensity of optical electric field at glass/ITO interface and can be described as where R* represents the reflectance of air/glass interface, R the reflectance for the stack structure, n g the refraction coefficient of glass and |E 0 | 2 (modulus squared of the optical electric filed) the initial intensity of optical electric field when light arrives at air/ glass interface.
To calculate the number of absorbed photons (or excitons) in the active layer, the energy flow dissipation per second for single wavelength in active layer, Q is given as where c is the speed of light, ε 0 the permittivity of vacuum, α the absorption coefficient, n the real index of refraction, and |E| 2 the total optical electric field intensity in the multilayer stack at single wavelength. Then the number of photons absorbed in the active layer can be expressed as where N represents the number of photons absorbed in the active layer, hc/λ the photon energy at a specified wavelength λ, h the Planck constant and c the speed of light. The devices are illuminated with AM 1.5G solar spectra.

Results and discussion
The number of photons absorbed in the active layer as a function of the active layer thickness is obtained for OSC and IOSC, as well the EQE as a function of the wavelength or the active layer thickness. The optical modulation effect is investigated by inserting a ZnO layer between P3HT: PCBM and Al for OSC, and changing the thickness of MoO 3 layer for ISOC, respectively.

Comparison of photons absorbed in the active layer
The results of the number of photons absorbed in the active layer as a function of the active layer thickness for OSC are shown in Fig. 2(a). It is clear that the number of absorbed photons increases with the active layer thickness and one can see a notable behavior of oscillation which is due to the optical interference effect induced by the incident light and the reflected light from the mirror metal electrode. The inserting of a ZnO layer leads to the shift of interference maxima to lower thicknesses and the remarkable increase of absorbed photons especially for the relatively thin active layer. However, the insertion of a ZnO layer makes no improvement near the active layer thicknesses where the interference maxima are obtained. This variation of the number of absorbed photons with the active layer thickness is the same as that of maximum possible short circuit current density in other researches [14].
For IOSC, Fig. 2(b) shows the same tendency as OSC. It is obvious that the influence of optical modulation effect is more slightly when the active layer is relatively thick (about 150 nm). Comparing OSC with IOSC, as shown in Fig. 2 (c), it is clear that the number of absorbed photons in IOSC is larger at any active layer thicknesses except for the thicknesses around which the interference maxima of OSC are obtained. In other words, for most active layer thicknesses, the light absorption in IOSC is more effective, hence the larger contribution to photocurrent. It has been reported that the refractive index of TiO x is very similar to that of PEDOT:PSS, therefore the light loss induced by the reflection at the ITO/TiO x interface and that at the ITO/PEDOT:PSS interface is nearly equivalent. However, light absorption loss in the TiOx layer is smaller than that in the PEDOT:PSS layer [15].In addition, the layer of MoO 3 in IOSC can act as an optical spacer layer. As a result, one can say the better light absorption in IOSC is attributed to the nearly equal amount of entering light and the smaller absorption loss in TiO x layer, as well as the optical modulation effect caused by MoO 3 layer. Although IOSC shows a better performance than OSC at most of the active layer thicknesses, it is noted that the performance of IOSC is slightly lower than that of OSC around the interference peaks as shown in Fig. 2(c). One possible reason is the parasitic absorption in the MoO 3 layer, because not only the the optical modulation effect but also the absorption loss could be caused by the MoO 3 layer, which produces a tradeoff.
To well understand the difference between OSC and IOSC, the distribution of optical electric field is investigated at different active layer thicknesses. According to the absorption coefficient of P3HT:PCBM calculated by α=4πk/λ, the maximum absorption coefficient is obtained at the incident light wavelength of around 512 nm, which agrees to the range of maximum absorption coefficient from 500 nm to 550 nm for P3HT:PCBM active material. As a result, the incident light of 512 nm is chosen to calculate the optical electric field distribution. The distributions of normalized modulus squared optical electric field at three different active layer thicknesses (45, 85, and 150 nm) for OSC and IOSC are shown in Fig. 3. The thickness of TiO x is specified as 50 nm to make the active layer region at same position in Fig.  3 for a clear comparison since its thickness has no significant influence on the photons absorbed in the active layer. Fig. 3(a) and (c) illustrate that the area below the curve of IOSC is larger than that below the curve of OSC for both thin and thick devices, which is consistent with the more absorbed photons in IOSC. And from Fig. 3(b), the opposite result can be seen when the active layer is 85 nm where the interference maximum of OSC is obtained, which agrees to the situation in Fig. 2(c). The similar results will also be shown in next part where the different performances of EQE for OSC and IOSC are discussed.

Comparison of EQE
The EQE as a function of incident light wavelength for OSC and IOSC is shown in Fig. 4, and the thicknesses of the active layer are specified as 40, 80, 160 and 220 nm. For OSC in Fig. 4(a), the EQE trends to increase with the thickness of the P3HT:PCBM layer in the range of wavelength from 450 to 650 nm. It should be noted that, the lower EQE at 160 nm than 80 nm can be explained by the fact that 80 nm is closed to the thickness where the first interference maximum of OSC is obtained (Fig. 2(c)). At the same time, the wavelength range possessing higher EQE is also expanded especially at the wavelength near 600 nm, where the shoulders are generally changed into peaks with the increasing of the active layer thickness. Of course, for the light over 650 nm, it prefers thicker active layer to achieve better absorption of light, and for the light near 400 nm, the variation of EQE with the active layer thickness displays a behavior of increase and decrease in turn. The similar results can be obtained from Fig.4 (b) for IOSC. For the thicker active layer beyond 220 nm, the same simulation results can be obtained (not presented here) and the results are agreed to the measured EQE of OSC and IOSC with 250 nm thick active layer. In short, the thick active layer brings higher EQE for both OSC and IOSC, and the main absorption range from 400 to 650 nm can be observed from Fig. 4. The comparison of EQE varying with the wavelength for OSC and IOSC is presented in Fig.  5. It is evident that IOSC with 40 and 160 nm active layer has better performance in EQE in the main absorption range. However, for the 80 and 220 nm active layer, the EQE of OSC is closed to or even higher than that of IOSC, which is due to the fact that these two thicknesses nearly equal the thicknesses where the interference maxima of OSC are obtained. In other words, IOSC is super to OSC in EQE in the main absorption range for both thin and thick active layers except for thicknesses around which the interference maxima of OSC are obtained, which agrees to the analysis of the number of photons absorbed in active layer in Fig. 2. Hence the explanation is the same for this result.    To verify the above conclusion, the EQE as a function of the active layer thickness at different wavelengths of incident light is investigated. For the EQE of OSC and IOSC depicted in Fig. 6, a remarkable increase and oscillation behavior with the increase of the active layer thickness can be observed. From Fig. 6, a conclusion may be obtained that IOSC performs better than OSC at any thickness of active layer for the light ranging from 400 to 650 nm. However, at the active layer thicknesses around which the interference maxima of OSC are obtained, the EQE of OSC is close to or even higher than that of IOSC. To well investigate the difference between OSC and IOSC, the positions and amplitudes of the first maximum EQE at different wavelengths are shown in Table 1. The clear oscillation behavior of the positions and amplitudes of the maximum EQE can be seen for both OSC and IOSC, and OSC exhibits more slight thickness oscillation behavior than IOSC. It is evident that the slight oscillation of maxima at single wavelength is beneficial to the final maximum in the range including all wavelengths. Therefore, the results from Table 1 can also be used to explain the results shown in Fig. 2(c) and Fig. 5.
In summary, from pure optical aspect, OSC and IOSC have the same tendency in the number of photons absorbed in the active layer, EQE, and the optical electric field distribution as well as the similar influence of optical modulation effect. However, IOSC performs better than OSC except for the case wherein the interference maxima of OSC are obtained, which is due to the better light absorption of ISOC possible absorption loss caused by MoO3 layer.

Investigation of the Organic Tandem Solar Cell
Although PCE of the organic solar cell is improved continuously, there are still some drawbacks for standalone devices: First, the organic solar cell is dominated by the excitonic effect, the relatively short lifetime and the low charge mobility. All of these limit the maximum thickness of the active layer for light absorption. Second, most organic semiconducting materials show discrete absorption behavior and cover only a fraction of the solar spectrum, leading to inefficient light harvest. The realization of the organic tandem solar cell based on complementary thin absorber materials provides a reasonable solution to improve device performance further.
In the existing views, matching the photocurrents of the subcells leads to the maximum PCE in the corresponding tandem cell, making it a crucial design criterion for optimum perform-Solar Cells -Research and Application Perspectives ance. Then to achieve a better device performance, the tandem cell should be optimized by considering current matching.  Fig. 7 (a)). It is necessary to carefully optimize the thicknesses of the front and back cells for different layer sequences to deeply exploit the opportunity provided by this tandem solar cell. Therefore, detailed optical simulations of tandem cells based on P3HT:PCBM and pBBTDPP2:PCBM have been carried out in this chapter.

Methodology
As in previous section, the calculation is still based on the Transfer Matrix Formalism. The basic structure of the tandem solar cell is shown in Fig. 7(b). On top of the glass, a 100 nm indium-tin-oxide (ITO) layer is used as the anode, followed by a 50 nm layer of PEDOT:PSS and a front active layer with variable thicknesses. The recombination contact consists of a 30 nm ZnO layer and a 15 nm PEDOT:PSS layer, followed by a back active layer with variable thicknesses. Finally, 100 nm Al is deposited to realize the cathode. In conventional tandem solar cells, materials mainly absorbing light of shorter wavelengths act as the front active layer to provide a window for the back cell while materials mostly absorbing light of longer wavelengths work as the back active layer. Thus the device with P3HT:PCBM in the front cell and pBBTDPP2:PCBM in the back cell is defined as"Normal Tandem Solar Cell" or "NTSC", the device with pBBTDPP2:PCBM in the front cell and P3HT:PCBM in the back cell as "Reverse Tandem Solar Cell" or "RTSC".
Before starting our work, three assumptions should be stated. First, an electron-hole pair is generated in the solar cell with every photon absorbed. Second, Ohmic losses in the recombination contact and the spacer are negligible. In consequence, the open circuit voltage of the tandem solar cell is a summation of those of both subcells. Thus, the performance of the tandem solar cell is mainly determined by its short circuit current density (J SC ). Three, the glass substrate is thicker than the coherence length of light, so optical interference in it can be neglected.
Considering current matching, we optimize the thicknesses of the front and back cells for NTSC and RTSC respectively. All the calculations are carried out under AM 1.5G radiation.

Results and discussion
According to the existing views, the optimized PCE can be obtained when the photocurrents of the subcells are matched. Thus, we vary the thicknesses of both the front (d front between 10 and 250 nm) and back (d back between 10 and 200 nm) active layers to investigate J SC of both subcells. Because the front cell is much far from the mirror Al electrode, J SC(front) scarcely shows any interference oscillation in the variation range of d back . Thus, this 8% loss is J SC(front) not induced by the interference effect but the reduction of the amount of light reflected from the Al surface (and arriving at the front cell a second time) as the thickness of the back cell increases. The variation of J SC(back) is more strongly affected by d front than vice versa. While for d front =10 nm, J SC(back) goes up to 15.76 mA/cm 2 . However, when d front =250 nm, J SC(back) reduces to 10.29 mA/cm 2 . This is obviously caused by the absorption spectra overlap of the two active layer materials (see Fig.  7(a)), which reduces photons arriving at the back cell. Because the back cell is much nearer to the Al electrode than the front cell, the interference behavior of J SC(back) is very obvious as shown in Fig. 9(a). Because of the same reason, the same tendency can be observed in RTSC (see Figs. 8(b) and 9(b)). In RTSC, while for d back =10 and 200 nm, J SC(front) goes up to 18.93 and 16.04 mA/cm 2 , respectively. With the increase of d front from 10 to 250 nm, J SC(back) decreases from 10.97 to 5.53 mA/cm 2 . A obvious increase of J SC of pBBTDPP2:PCBM layer and a strong decrease of J SC of P3HT:PCBM layer can be observed in RTSC, compared with NTSC. This is caused by the absorption difference of two blends. As shown in Fig. 7(a), the spectral range of pBBTDPP2:PCBM is much wider than that of P3HT:PCBM (the former absorbs photons in the nearly entire wavelength range discussed while the latter hardly absorbs photons of wavelengths beyond 650 nm). Therefore, when acting as the front active layer, pBBTDPP2:PCBM hinders the harvest of photons in P3HT:PCBM more strongly than that in P3HT:PCBM with pBBTDPP2:PCBM as the back active layer.  Table 2 for NTSC and RTSC, respectively. It can be observed from Table 2 that RTSC shows its superiority in matching J SC when the active layers of both subcells are relatively thin. We note that RTSC can provides a larger matching J SC with a smaller d front when the device is relatively thin (d back is usually less than 100 nm). But NTSC is better as the thicknesses of both active layers increase, in agreement with the general view presented. In order to well understand this amazing phenomenon, optical electric field distributions of tandem solar cells should be taken into account. Four current matching points listed in Table  2 are used here: a 58-40-nm NTSC, a 21-40-nm RTSC, a 238-150-nm NTSC and a 77-150-nm RTSC. The reason why we choose these points is that the matching J SC differences between the corresponding NTSC and RTSC reach the maxima in positive and negative, respectively (see Δ, the last column in Table 2). The distributions of normalized modulus squared of optical electric filed |E| 2 for the above tandem solar cells are calculated and shown in Fig. 10 (the shadow area indicates the active layers of the front (left) and back (right) cells). As shown in Fig. 7(a) Table 2. It can be explained by the properties of the materials and device structures. As shown in Figs. 10 (a) and (b), no matter with which structure, the peaks of optical electric field for light of wavelengths of 727 and 809 nm are usually near or in the front active layer. Since pBBTDPP2:PCBM mainly absorbs light of longer wavelengths and P3HT:PCBM absorbs light of shorter wavelengths, RTSC (place pBBTDPP2:PCBM in the front and P3HT:PCBM in the back) has a better performance when the active layers are thin. However, things become different when the device becomes thicker and thicker. For a very thick RTSC, the first interference peaks for wavelengths of 727 and 809 nm begin to leave the front active layer and then the pBBTDPP2:PCBM subcell is no longer an effective device. At the same time, owing to the much wider spectral range of pBBTDPP2:PCBM, it hinders the harvest of photons in P3HT:PCBM with pBBTDPP2:PCBM as the front active layer. Thus, when the active layers become thicker (d back is usually over 100 nm), RTSC only allows a smaller matching J SC with a smaller d front compared with NTSC and NTSC shows its superiority. This is in good agreement with the results in Table 2.
In conclusion, it is observed that RTSC takes over the lead in matching J SC when the active layers are relatively thin; but NTSC allows a larger matching J SC as the active layers are relatively thick. The similar results are also found in the tandem solar cell based on P3HT:PC 70 BM and PCPDTBT:PC 60 BM [19]. The results are very interesting since we can choose the thinner RTSC to achieve matching J SC , which can alleviate the carrier transport problem and save the material cost.

Conclusion
The application of the bulk heterojunction structure consisting of an interpenetrating network of electron donor and acceptor materials greatly improves the standalone organic solar cells. Now there are mainly two types of standalone organic solar cells: OSC and IOSC. IOSC is introduced as the possible candidate for OSC to remedy the low air stability of OSC. However, most of the previous works reported that PCE of IOSC is relatively lower than that of OSC. As a result, the performance differences of OSC and IOSC are discussed in this work. It is concluded that in the optical aspect, OSC and IOSC have the same tendency in the number of photons absorbed in the active layer, EQE, and the optical electric field distribution as well as the similar influence of optical modulation effect. Normally, IOSC performs better due to the better light absorption of IOSC because the absorption loss in TiO x layer for IOSC is smaller than that in PEDOT:PSS layer for OSC and the hole transporting layer (MoO 3 layer in this work) can play the role of optical layer. However, around the interference maxima of OSC, OSC shows better performance because the optical electric field has been optimized under this condition and there is no room for further improvement.
Although PCE of the standalone organic solar cell is improved continuously, there are still some drawbacks for this type of devices: First, the organic solar cell is dominated by the excitonic effect, the relatively short lifetime and the low carrier mobility. And these limit the maximum thickness of the active layer for light absorption. Second, most organic semiconducting materials show discrete absorption behavior and cover only a fraction of the solar spectrum, leading to inefficient light harvest. The realization of organic tandem solar cells based on complementary thin absorber materials provides a reasonable solution to improve PCE further. In a tandem cell, to achieve the maximum PCE, it is necessary to ensure current matching of both subcells, which leads to detailed optical simulations in this work. At first, active layer thicknesses of the tandem cell are optimized by considering current matching for normal and reverse structures (see Fig. 7), respectively. Owing to the different spectral ranges of two blend materials (P3HT:PCBM and pBBTDPP2:PCBM) and device structures, it is noted that the reverse tandem cell allows a larger matching J SC when the total device is relatively thin. When the thicknesses of the active layers increase, the normal tandem solar cell begins to present its superiority in the performance. This makes senses in the aspect of application that we can choose a thinner reverse tandem cell to achieve J SC needed in some cases, which saves cost and increases the profit to an extent.