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Origin of Different Dependences of Open-Circuit Voltage on the Electrodes in Layered and Bulk Heterojunction Organic Photovoltaic Cells Chunfu Zhang, Shi-Wun Tong, Chang-Yun Jiang, En-Tang Kang, Daniel S. H. Chan, Senior Member, IEEE, and Chunxiang Zhu, Member, IEEE
Abstract—Experimental results show that the VOC of layered heterojunction (HJ) organic photovoltaic (PV) cells behaves with a very weak dependence on the electrodes. However, the VOC of bulk HJ PV cells behaves with a strong dependence on the electrodes. In this paper, an explanation for the different behaviors of VOC on the electrodes is proposed. It is found that the VOC of the two types of PV cells follows the same mechanism and is mainly determined by the light-injected carriers at the donor/acceptor (D/A) interface and the electrodes. However, the distinct device structures make the boundary conditions in layered and bulk HJ PV cells different, which leads to the different dependences of VOC on the electrodes. The layered HJ PV cells have geometrically “flat” D/A and metal/organic (M/O) interfaces (the interface near the electrode), which makes the effective thickness from the D/A interface to the M/O interface large. Thus, there is a low electric field at the M/O interface and, then, a very small barrier lowering. Under this condition, the light-injected carriers at the D/A interface tend to “pin” the Fermi level of the electrodes. As a result, VOC shows only a very weak dependence on the work function of the electrodes. However, the formation of the interpenetrating network in bulk HJ PV cells greatly decreases the D and A domain dimensions and induces the ambipolar carrier distribution in the blend layer. This will cause very large barrier lowering at the M/O interface when there is a high barrier. Under this condition, the light-injected carriers at the D/A interface can no longer “pin” the electrode Fermi level. Thus, a strong dependence of VOC on the electrodes for bulk HJ PV cells is observed. Index Terms—Ambipolar carrier distribution, electrode dependence, light injection, open-circuit voltage, organic solar cells.
Manuscript received March 24, 2009; revised October 6, 2009. First published December 31, 2009; current version published January 22, 2010. The review of this paper was arranged by Editor J. Kanicki. C. Zhang is with the Silicon Nano Device Laboratory, Department of Electrical and Computer Engineering, National University of Singapore, Singapore 119260, and also with the institute of Microelectronics, A∗STAR, Singapore 117685. S.-W. Tong and C. Zhu are with the Silicon Nano Device Laboratory, Department of Electrical and Computer Engineering, National University of Singapore, Singapore 119260 (e-mail:
[email protected]). C.-Y. Jiang is with the Institute of Materials Research and Engineering, A∗STAR, Singapore 117602. E.-T. Kang is with the Department of Chemical and Bimolecular Engineering, National University of Singapore, Singapore 119260. D. S. H. Chan is with the Department Electrical and Computer Engineering, National University of Singapore, Singapore 119260. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TED.2009.2036787
I. I NTRODUCTION
S
INCE the discovery of ultrafast photo-induced charge transfer between organic donors and acceptors, great effort has been devoted to organic photovoltaic (PV) cells based on both small molecules and conjugated polymers due to their low cost, light weight, and ease of processing [1]–[7]. In the past decade, the performance of organic PV cells has steadily improved, reaching, nowadays, power conversion efficiency (PCE) of more than 6% [6]. However, this PCE is still not high enough for commercial viability. In order to further improve the device performance, much work has to be done, including better understanding of the device physics behind the organic PV cells [8]–[13]. The performance of organic PV cells is mainly determined by the short-circuit current density JSC , the open-circuit voltage VOC , and the fill factor (FF), given that η = JSC VOC FF/Pin (where η is the PCE and Pin is the incident optical power density). Here, JSC is directly related to the light-harvesting capability of organic materials. Due to the large band gap of organic materials (usually about 2 eV), there is a large spectral mismatch between the sunlight and their absorption spectrum [6], [7], [14], [15], which makes their JSC much lower than those reported for inorganic devices. Much research has been carried out to improve the device light-harvesting capability, such as using small-band-gap materials and/or combining different organic materials with complementary absorption spectra in one device [14]–[16]. JSC also depends on the active layer thickness because of the optical interference effect [17], [18]. Other factors such as the film morphology, solvent type, or deposition method can also greatly influence JSC [19], [20]. Another issue of considerable focus in organic PV cells is VOC , which has been the subject of much interest in recent years [21]–[27]. It has been shown that VOC does not follow the traditional metal–insulator–metal (MIM) model [VOC1 in Fig. 1(a)] but has a direct relationship with the offset energies between the highest occupied molecular orbital (HOMO) of the Donor (D) and the lowest unoccupied molecular orbital (LUMO) of the Acceptor (A) [VOC2 in Fig. 1(a)] in both the layered and bulk heterojunction (HJ) PV cells. For example, a recent study including a total of 26 different polymer/fullerene blend devices showed that VOC linearly varies with the HOMO of the polymer [24]. Then, the enhancement of VOC can be obtained by using new materials with larger offset energies.
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Fig. 1. (a) Schematic representation of the maximum VOC of organic PV cells. VOC1 represents the difference of the anode and cathode work functions. VOC2 represents the difference of the HOMO of the donor and the LUMO of the acceptor. (b) Gaussian DOS for organic materials. Δ represents that the transport level in a Gaussian DOS lays below its center. (c) and (d) Energy diagram of materials and device structure for the layered and HJ PV cells.
However, enhancing VOC by increasing the offset energies usually decreases JSC , because a high-band-gap absorber is required, which leads to a large mismatch with the solar spectrum. Thus, increase in the VOC of the PV cells based on the given organic materials has special significance for further performance improvement of the present devices. This makes it absolutely necessary to better understand the factors that affect VOC beyond the D and A offset energies, e.g., to well understand the influence of the electrodes. It has been observed that, in layered devices, VOC shows a very weak dependence on the electrode work function [13], [26]. However, an obvious dependence of VOC on the electrodes was reported in bulk HJ PV cells [22], [23]. Since both the layered and bulk HJ PV cells are based on organic materials and have the same operation mechanisms (light absorption, exciton production, exciton dissociation, and charge transport), their VOC should also follow the same mechanism. However, until now, the reasons for the different dependences of VOC on the electrodes in the two types of PV cells are still not well understood. It is of great importance to understand the mechanism behind this phenomenon, because it will give us a guideline on enhancing VOC by electrode modification and then further improving the performance. The aim in this paper is to investigate the factors that determine the VOC of organic HJ PV cells for the given materials beyond the D and A offset energies. Based on the experiments and theoretical analysis, an explanation for the different dependences of VOC on the electrodes in layered and bulk HJ PV cells is proposed. It is found that, although the VOC of both types of PV cells are determined by the electrodes and the light-injected carriers at the donor/acceptor (D/A) interface, the distinct device structures make the boundary conditions in layered and bulk HJ PV cells very different, which lead to the different dependences of VOC on the electrodes.
II. E XPERIMENTAL The device structures are shown in Fig. 1(c) and (d). Briefly, after routine solvent cleaning (sequentially treated with detergent, deionized water, acetone, and isopropanol in an ultrasonic bath for about 15 min), the dried indium tin oxide (ITO) glass substrates were treated with oxygen plasma for about 3 min. Then, the filtered PEDOT:PSS suspension (through a 0.45-μm filter) was spin coated on top of the ITO surface to form an ∼50-nm layer under ambient condition, before drying the substrates at 120 ◦ C in an oven for more than 1 h. For the layered HJ PV cells, an ∼20-nm copper phthalocyanine (CuPc) layer was deposited by thermal evaporation under a pressure of about 5.4 × 10−5 Pa and then followed by spin coating ∼40-nm [6,6]-phenyl-C61 -butyric acid methyl ester (PCBM) to finish the active layer. For the bulk HJ PV cells, P3HT:PCBM with different weight ratios was dissolved in dichlorobenzene and stirred in the glove box before spin casting to form an ∼100-nm blend layer. Finally, various metal electrodes were deposited through a shadow mask. The device current–voltage (J–V ) characteristics were measured as fabricated by using a Keithley 2400 parameter analyzer under a simulated light intensity (AM 1.5G) with various light intensities. The light intensity was calibrated by a Thorlabs optical power meter.
III. R ESULTS Fig. 2(a) shows the typical J–V characteristics of the layered devices with the structure configuration of ITO/PEDOT: PSS/CuPc/PCBM/cathode (cathode = Ag, Au, and Mg). The devices with Ag, Mg, and Au cathodes exhibit VOC values of 605, 608, and 589 mV, respectively. The fact of only a slightly lower VOC for devices with Au cathode than those made with the Mg and Ag cathodes suggests a severe deviation from the
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transport are also the same, it is not possible for the VOC of the two types of PV cell to follow different mechanisms. Considering the differences of the two types of devices, the essential difference is that they have distinct structures. Compared with the layered HJ PV cell, there are no geometrically “flat” D/A and metal/organic (M/O) interfaces in the bulk HJ PV cell due to the formation of the interpenetrating network. It is supposed that the different dependences of VOC on the metal electrodes should have relations with their distinct structures. In the following, how the different structures affect the behaviors of VOC will be discussed. IV. D ISCUSSIONS A. Theory
Fig. 2. (a) Characteristics of the layered HJ PV cells with different metal electrodes. (Inset) Statistical properties of VOC . (b) Characteristics of the bulk HJ PV cells with different metals. (Inset) Dark current. The structure is ITO/PEDOT: PSS/1:0.8 P3HT:PCBM/cathode. The light intensity is 100 mW/cm2 .
prediction of the classic MIM model where VOC is limited by the difference of the anode and cathode work functions [VOC1 in Fig. 1(a)]. Rand et al. [13] and Cheyns et al. [26] also reported that only a small variation in VOC was observed when varying the cathode metals, which confirms our experiment results that the electrode has a weak influence on VOC in layered PV cells. Fig. 2(b) shows the typical J–V characteristics of the bulk HJ PV cells based on P3HT:PCBM (1 : 0.8), with different metal cathodes using the structure of ITO/PEDOT: PSS/P3HT:PCBM/cathode. It is observed that the dark current of the devices with Au, Ag, and Mg electrodes shows an obvious rectifying behavior, and under illumination, VOC shows the values of 141, 592, and 696 mV. Here, VOC showed a strong dependence on the metal electrodes, and a total of 555-mV variation of VOC was observed, which is contrary to that observed in organic PV cells using the layered structure. In fact, Mihailtechi et al. [23] have reported similar results and explained the obvious dependence of VOC on different cathodes in bulk HJ PV cells by modifying the classical MIM model. However, since the layered and bulk HJ PV cells are both based on organic materials and the mechanisms of light absorption, exciton production, exciton dissociation, and charge
In principle, the VOC of a PV cell is a function of both electric and chemical potential energy gradients [8]. In the conventional inorganic PV cells, electron–hole pairs are photogenerated in the same semiconducting phase, there are no photoinduced chemical potential gradients established, and only a classical built-in potential Vbi is required to separate the carriers. However, the situation is different for organic-based PV cells. Because of the low dielectric constant and weak noncovalent electric interactions in organic materials, the excitons, rather than free carriers, are always produced. It is well recognized that the most efficient exciton dissociation occurs at the D/A interface in organic materials. For simplification, we assume that all the excitons are dissociated at the D/A interfaces in organic PV cells and neglect the dissociation at the M/O interfaces, as has been done by Cheyns et al. [26]. After exciton dissociation, the dissociated electrons and holes are separated into different phases of A and D. This photoinduced charge injection at the D/A interface will establish chemical potential gradients in the organic materials and then affect VOC . At the M/O interfaces, the electrodes can also inject carriers into the organic materials, which can also influence VOC . Knowing the D/A and M/O interface conditions, all the electric variables in organic PV cells can be obtained under open-circuit condition by using the “shooting algorithm,” as described in the Appendix. To determine boundary conditions at the D/A and M/O interfaces, we first consider one material phase (here, phase A) in the simple layered HJ PV cell, which has geometrically “flat” D/A and M/O interfaces, as shown in Fig. 3. D/A Interface: Under illumination, the created excitons diffuse to the D/A interface and are dissociated into electron–hole pairs (polarons). These polarons can be dissociated into free carriers, and the free carriers can also return to polarons. Under steady condition, the number of polarons X is determined by dX = GX − kX X − kD X + γnp dt
(1)
where n and p are the electron and hole densities, respectively; GX is the amount of dissociated excitons into polarons; kX is the decay rate to the ground state; kD is the dissociation rate of a bound pair; and γnp is the excitons created due to the bimolecular capture of free charges at the interface.
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The last term describes the Shockley–Read–Hall (SRH) recombination [26]. Assuming that n in phase A and p in phase D are the same at the interface, then n in phase A can be derived by combining (1)–(3). If the bimolecular recombination dominates at the D/A interface kD αpin (4) n= γkX and if the SRH recombination dominates at the D/A interface n=
2kD αpin . kSRH (kD + kX )
(5)
M/O Interface: The carrier density at the M/O interface usually depends on the potential barrier between the metal and organic materials. When the electric field is relatively low, n can be described by the Richardson–Shockley theory [30] for thermionic emission, i.e., q3 F q(φA − Δφ) . n = NA exp − , with Δφ = kB T 4πε0 εr (6) Here, NA is the LUMO density of states (DOS) of A, φA is the barrier height between A and cathode, Δφ accounts for the barrier lowering effect, ε0 is the vacuum permittivity, εr is the relative dielectric constant of the bulk organic material, and F is the electric field. If the barrier is very thin and the electric field is very large, the carrier tunneling effect becomes important, and the carrier density at the M/O interface will depend on the tunneling probability. According to the Wentzel– Kramers–Brillouin theory 2m V (x) − Edx (7) n ∝ exp −2
Fig. 3. (a) Bilayer HJ PV cell, which has a geometrically “flat” D/A and M/O interface. At the D/A interface, the dissociated hole and electron are still bounded by the Coulombic attractive force. At the M/O interface, thermionic emission and tunneling effect may exist. (b) Calculated LUMO profile for different barriers under light saturation condition. Barrier step: 0.2 eV. The positions of x = 0 and 40 nm refer to the D/A and M/O interfaces, respectively. The LUMO potential at the D/A interface is set as the ground potential. (c) Band diagram of a bilayer HJ PV cell under light nonsaturation condition. ΔV indicates the decrease in VOC under nonsaturation condition. All these do not consider the barrier lowering effect.
where m is the electron effective mass, V (x) is the potential of the barrier, and E is the energy of the electron. When the tunneling happens, the carrier density at the M/O interface will rapidly increase. In real devices, the thermionic emission and tunneling injection exist together. In the low electric field, the thermionic emission will dominate, and at high electric field, the tunneling will play a major role. At the medium electric field, there is a transition region where both mechanisms need to be accounted to determine the boundary condition. B. Layered HJ PV Cells
Usually, GX will have a linear dependence on the incident light intensity, i.e., GX = αPin
(2)
where α is a constant. Considering the photoinduced carriers and the carrier generation/recombination process, the free carrier continuity equation at the open circuit condition is ∂n np = kD X − γnp − kSRH . ∂t n+p
(3)
We first consider the light saturation condition in the layered HJ PV cells. Under this condition, there are enough carriers generated at the D/A interface under very intense light, so that almost all the LUMO states of A at the D/A interface are filled. On the other hand, the boundary condition at the M/O interface is set by the injected carriers from the metal, which depends on the M/O barrier height (6). An example for the LUMO potential energy distribution in phase A is calculated and shown in Fig. 3(b) for the M/O barrier height varying from 0.0 to 1.0 eV. It can be seen that, when the M/O interface is with a
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large barrier, the LUMO profile is almost a straight line, and there is no band bending because of the relatively low carrier injection. When the M/O interface is an ohmic contact or very small barrier, an obvious band bending at the M/O interface is observed due to the large amounts of electrons injected from the cathode, causing the electron accumulation that occurred at phase A near the M/O interface. Mihailtechi et al. [23] have noted this band bending and claimed that it could decrease VOC . However, according to our results, regardless if it is an ohmic contact or a nonohmic contact, VOC should be the same. This is because the Fermi level of the metal electrode is apt to be “pinned” to the LUMO level of A (quasi-Fermi level) at the D/A interface, irrespective of the barrier height, as shown in Fig. 3(b). Under nonsaturation condition, the quasi-Fermi level of phase A at the D/A interface is lower than its LUMO level because of the decrease in the injected carrier density at the D/A interface. Because the metal Fermi level has to be aligned to the quasi-Fermi level of phase A at the D/A interface, this will lower VOC , as shown in Fig. 3(c). Here, ΔV indicates the decreased value of VOC in phase A due to the nonsaturation condition. The same situation will also happen in phase D. This explains why VOC decreases with the dropping of the light intensity, as observed in [9] and [13]. As previously discussed, regardless if under light saturation or nonsaturation conditions, the VOC in the layered HJ PV cells seems to mainly depend on the D/A interface condition because of the Fermi-level alignment. This explains why VOC only shows a very weak dependence on the electrodes. However, although the variation of VOC with different electrodes is very small, the trend is clear that the VOC slightly decreases with the increasing metal cathode work function, as shown in the inset of Fig. 2(a). The barrier lowering effect at the M/O interface may account for this phenomenon. The lowered barrier will increase the carrier density at the M/O interface, so that the metal electrode Fermi level is shifted to be lower than the quasi-Fermi level at the D/A interface, as indicated by VLow in Fig. 4(a). The higher the metal work function, the larger the electric field at the cathode interface. Thus, for a high metal work function, a low VOC will be obtained. Now, considering the influence of light injection at the D/A interface and electrode injection at the M/O interface, the VOC expression can be derived by combining (3)–(6). If the bimolecular recombination dominates at the D/A interface qVOC = (HOMOD − ΔD ) − (LUMOA − ΔA ) − UB γkX NA ND kB T kB T ln ln Pin − VLow . (8) − + q αkD q If the SRH recombination dominates at the D/A interface qVOC = (HOMOD −ΔD )−(LUMOA −ΔA )−UB √ 2kB T kSRH (kD +kX ) NA ND 2kB T ln ln P−Vlow . − + q 2αkD q (9) In the preceding expressions, Δ accounts for the Gaussian DOS distribution in organic materials, as shown in Fig. 1(b).
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Fig. 4. (a) Influence of barrier lowering on VOC . Δφ represents the value of barrier lowering, and VLow indicates the decreased VOC due to the barrier lowering. (b) Variation of electric field at the M/O interface with the M/O barrier and the film thickness under light saturation condition (semilogarithm scale). (c) Field-dependent barrier lowering.
UB is the polaron binding energy UB = q 2 /4πε0 εr a, and a is the initial separation distance of the electron–hole pair at the D/A interface. VLow accounts for the lowered voltage due to the barrier lowering. The rest accounts for the influence of light intensity. The value of VLow depends on the M/O interface condition. For the case of the layered HJ PV cells, they have geometrically “flat” D/A and M/O interfaces, and the effective thickness from the D/A interface to the M/O interface is large (usually several tens of nanometers). Thus, the electric field at the M/O interface is relatively small, and then, VLow is very low, as shown in
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Fig. 4(b) and (c). Thus, VOC shows a weak dependence on the electrodes, which is consistent with the reported study [26]. C. Bulk HJ PV Cells Different from the layered HJ PV cells, a strong dependence of VOC on the electrodes in bulk HJ PV cells was observed [Fig. 2(b)]. In theory, the VOC of the bulk HJ PV cells should obey the same mechanism as that of the layered HJ PV cells, because both of them are based on organic materials and obey the same operation principles. Compared with the layered HJ PV cells, the essential difference is the distinct device structure. In the bulk HJ PV cell, the D (polymer) and A (fullerene) materials are mixed together to form the interpenetrating network. This structure makes the D and A domains very small. In addition to the “nonflat” D/A interface, the average distance from the D/A interface to the M/O interface (effective thickness) is significantly decreased, compared to the layered HJ PV cell, which will influence the electric field at the M/O interface. The trend in Fig. 4(b) has shown that the electric field is expected to become very large when the M/O barrier is very high and the effective thickness is very small. Considering the extremely small effective thickness in bulk HJ PV cells, even the carrier tunneling effect may occur when there is a high M/O barrier. This will cause a large barrier lowering and, thus, a large value of VLow . The higher the barrier, the larger the value of VLow . Compared with the Ag and Mg electrodes, the barrier for the Au electrode is the highest, and thus, the VOC is expected to be the smallest. Another point that must be noted is that the interpenetrating network in bulk HJ PV cells enables the electrode to make contact with both the D and A phases. The carrier distribution in the bulk HJ PV cells is then changed from a unipolar distribution to an ambipolar distribution, compared with that in the layered HJ PV cells. Due to the ambipolar carrier distribution, holes also exist near the cathode in the D domains under open-circuit condition. Like applying a positive voltage, these holes will further increase the value of VLow . Thus, VOC will become smaller. Compared with those near the Ag and Mg electrodes, the holes near the Au electrode are the most in number because of its high work function, and then, VOC is expected to be the smallest. Combining the extremely small D/A dimensions and the ambipolar carrier distribution in bulk HJ PV cells, both of them determine why VOC has a strong dependence on the electrodes. The preceding discussions are based on the assumption that the VOC of the bulk HJ PV cells obeys the same mechanism as that of the layered HJ PV cells. To validate the correctness of the assumption, it is needed to investigate if the VOC in the bulk HJ PV cells obeys the same expression as that in the layered HJ PV cells. According to (8) or (9), VOC should have a linear relation with the logarithm of light intensity. As the prediction, VOC indeed linearly depends on the logarithm of light intensity, as shown in Fig. 5(a). In addition, the lines with the slope of about 60 mV/dec means that the bimolecular recombination dominates at the D/A interface, as reported earlier [10]. According to (8) or (9), the temperature can also affect VOC . By lowering the temperature, VOC will increase. This has widely been observed in both layered and bulk HJ PV
Fig. 5. (a) Variation of VOC with the light intensity for devices with different P3HT:PCBM weight ratios. The weight ratios are labeled in the graph after metal names. (b) Variation of VOC with the different ratio of P3HT: PCBM (1 : 0.8, 1 : 2 and 1 : 4). All the devices have the same structure, except the metal cathode.
cells [13], [32], [33]. Then, it can be concluded that the VOC of the bulk HJ PV cells obeys the same mechanism as that of the layered HJ PV cells and the different dependences of VOC on the electrode origin from their distinct structure. According to our explanation, the VOC of the bulk HJ PV cells can be changed by modulating the effective thickness of phases D and A. To verify, the different D and A ratios are used in the blend layer. For a high PCBM ratio, the PCBM domain is expected to be enlarged. This means that the effective thickness of phase A will become large. For a high M/O barrier, the increased thickness of phase A will effectively decrease the electric field. As a result, the value of VLow will become small, and VOC is expected to become large. However, for a low M/O barrier, the change in the electric field is relatively small, and then, the increase in VOC is expected to be small. Fig. 5(b) shows the variation of VOC for the devices with different P3HT:PCBM ratios. As expected, for the Au electrode, VOC is increased from 141 mV (P3HT:PCBM 1 : 0.8 weight ratio) to 381 mV (P3HT:PCBM 1 : 2 weight ratio) and further increased to be 463 mV (P3HT:PCBM 1 : 4 weight ratio). For
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the Ag electrode, VOC is increased from 592 mV (P3HT:PCBM 1 : 0.8 weight ratio) to 716 mV and then almost kept constant. In addition, the variation of VOC for the Mg electrode is the smallest. These results are in accordance with the expectation and thus confirm the validity of the proposed explanation. As previously stated, the VOC of the bulk HJ PV cell strongly depends on its interpenetrating structure, which is to say that their VOC can be influenced by the morphology of the blend layer. After thermal annealing, the D and A domains increase due to the phase separation. Correspondingly, the D and A effective thicknesses are increased, which explains why VOC is usually enhanced after the thermal annealing for bulk HJ PV cells [14], [20]. VOC of bulk HJ PV cells also strongly depends on the electrodes. This gives us a way to increase the VOC of the bulk HJ PV cells by using interface engineering. In fact, many works have been done to increase VOC of bulk HJ PV cells by modifying the interface between the blend layer and the electrode [34]–[37]. However, because the VOC of the layered HJ PV cells only slightly depends on the electrodes, there are few papers that focus on interface engineering to increase VOC of this structure. V. C ONCLUSION The VOC of layered and bulk HJ PV cells has shown different dependences on the electrodes. When the electrode is changed, the VOC of the layered HJ PV cells almost remains constant, whereas the VOC of the bulk HJ PV cells shows an obvious variation. The experimental results and analysis have shown that the VOC ’s of the two types of PV cells follow the same mechanism and are mainly determined by the light-injected carriers at the D/A interface and the electrodes. However, their distinct structures lead to the different dependences of VOC on the electrodes. The layered HJ PV cells have geometrically “flat” D/A and M/O interfaces, which make the effective thickness from the D/A interface to the M/O interface very large. The large effective thickness leads to a thick barrier and a low electric field at the M/O interface. Thus, the barrier lowering is low. Under this condition, the light-injected carriers at the D/A interface tend to “pin” the Fermi level of the electrodes. As a result, VOC shows only a very weak dependence on the work function of the electrodes. On the other hand, the formation of the interpenetrating network in bulk HJ PV cells greatly decreases the D and A domain dimensions, which make the effective thickness of the D and A domains very small. When there is a very high potential barrier at the M/O interface, the electric field will be very high at the M/O interface, and even the carrier tunneling effect may occur. Thus, barrier lowering becomes large. At the same time, the ambipolar carrier distribution will further increase the barrier lowering effect. Under this condition, the light-injected carriers at the D/A interface can no longer “pin” the metal Fermi level. Thus, a strong dependence of VOC on the metal electrodes for bulk HJ PV cells is observed. A PPENDIX Let consider one dimension case, as shown in Fig. 3(a). Considering phase A where electrons are transported and holes can be neglected, the transport equation and Poisson equation
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for electron under the open-circuit condition (current J = 0) can be expressed as Jn (x) = −qμn n(x)
∂n(x) ∂U (x) + qDn =0 ∂x ∂x
∂2 q U (x) = n(x). ∂x2 ε
(A1) (A2)
The electric potential U (x) and the electric field F (x) have the relation ∂U (x) = F (x). ∂x
(A3)
If the boundary conditions (carrier concentrations) are known, the electric parameters in phase A can numerically be achieved by using the preceding equations based on the so-called “shooting algorithm”: At the first grid point D/A interface, the potential of LUMO is set to zero; then, the Fermi-level EF can be obtained by EF = −(kT /q) ln(NA /n), where NA is the LUMO density of states in phase A, which is assumed to be 2.8 × 1025 m−3 in this work. All the parameters at the D/A interface are known, except the electric field F (0). Guess a value for F (0). Then, the electron concentration in the next grid point i is calculated by discretization of (A1). Once the electron concentration in point i is known, one can calculate the electrostatic potential and the electric field in point i by (A2) and (A3). This is repeated until one arrives at the M/O interface, and the second boundary condition (electron concentration) at the M/O interface is checked. This is repeated with improved guesses of F (0) until the second boundary condition is fulfilled. The same method can be used in phase D. R EFERENCES [1] N. S. Sariciftci, L. Smilowitz, A. J. Heeger, and F. Wudl, “Photoinduced electron transfer from a conducting polymer to buckminsterfullerene,” Science, vol. 258, no. 5087, pp. 1474–1476, Nov. 1992. [2] G. Yu, J. Gao, J. C. Hummelen, F. Wudl, and A. J. Heeger, “Polymer photovoltaic cells: Enhanced efficiencies via a network of internal donoracceptor heterojunctions,” Science, vol. 270, no. 5234, pp. 1789–1791, Dec. 1995. [3] Z. Tan, C. Yang, E. Zhou, X. Wang, and Y. Li, “Performance improvement of polymer solar cells by using a solution processible titanium chelate as cathode buffer layer,” Appl. Phys. Lett., vol. 91, no. 2, pp. 023 509-1– 023 509-3, Jul. 2007. [4] M. Y. Chan, S. L. Lai, M. K. Fung, C. S. Lee, and S. T. Lee, “Dopinginduced efficiency enhancement in organic photovoltaic devices,” Appl. Phys. Lett., vol. 90, no. 2, pp. 023 504-1–023 504-3, Jan. 2007. [5] W. J. Potscavage, Jr., S. Yoo, and B. Kippelen, “Origin of the open-circuit voltage in multilayer heterojunction organic solar cells,” Appl. Phys. Lett., vol. 93, no. 19, pp. 193 308-1–193 308-3, Nov. 2008. [6] J. Y. Kim, K. Lee, N. E. Coates, D. Moses, T. Q. Nguyen, M. Dante, and A. J. Heeger, “Efficient tandem polymer solar cells fabricated by allsolution processing,” Science, vol. 317, no. 5835, pp. 222–225, Jul. 2007. [7] C. F. Zhang, S. W. Tong, C. Y. Jiang, E. T. Kang, D. S. H. Chan, and C. X. Zhu, “Simple tandem organic photovoltaic cells for improved energy conversion efficiency,” Appl. Phys. Lett., vol. 92, no. 8, pp. 083 310-1– 083 310-3, Feb. 2008. [8] B. A. Gregg and M. C. Hanna, “Comparing organic to inorganic photovoltaic cells: Theory, experiment, and simulation,” J. Appl. Phys., vol. 93, no. 6, pp. 3605–3614, Mar. 2003. [9] J. A. Barker, C. M. Ramsdale, and N. C. Greenham, “Modeling the current-voltage characteristics of bilayer polymer photovoltaic devices,” Phys. Rev. B, Condens. Matter, vol. 67, no. 7, pp. 075 205-1–075 205-9, Feb. 2003. [10] L. J. A. Koster, E. C. P. Smits, V. D. Mihailetchi, and P. W. M. Blom, “Device model for the operation of polymer/fullerene bulk heterojunction
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Chunfu Zhang received the B.Eng. degree in optoelectronic technology and the M.Eng. degree in microelectronics from Xidian University, Xi’an, China, in 2002 and 2005, respectively. From August 2005 to July 2009, he was working toward the Ph.D. degree with the Silicon Nano Device Laboratory (SNDL), Department of Electrical and Computer Engineering, National University of Singapore (NUS), Singapore. He is currently a Research Staff with SNDL. He is also with the Institute of Microelectronics, A∗STAR, Singapore. His current research interests are solar cells based on organic materials.
Shi-Wun Tong received the B.S. and Ph.D. degrees in materials engineering from the City University of Hong Kong, Kowloon, Hong Kong, in 2001 and 2005. After graduation, she joined the Hong Kong Applied Science and Technology Research Institute Company Ltd., Hong Kong, as an Engineer. In 2006, she joined the Silicon Nano Device Laboratory, Department of Electrical and Computer Engineering, National University of Singapore, Singapore, as a Research Fellow. She is the author or a coauthor of more than 30 publications. Her research interests include organic-based solar cells and light-emitting devices.
Chang-Yun Jiang received the B.S. degree from Guangxi Normal University, Guilin, China, in 1990, the M.S. degree from Sichuan Normal university, Chengdu, China, in 1993, and the Ph.D. degree in material science and device physics from South China University of Technology, GuangZhou, China, in 2005. From 1993 to 2001, he was with the Physics Department, Guangxi Normal University, as a Lecturer and then an Associate Professor. In 2005, he joined the Institute of Microelectronics, A∗Star, Singapore, where he was engaged in research on organic/polymer solar cells. Since February 2009, he has been with the Institute of Materials Research and Engineering, A∗Star. He is the author or a coauthor of more than 40 journal and conference proceeding papers. His current research interests include organic/polymer optoelectronics, dye-sensitized solar cells, and nanocrystal/organic hybrid solar cells.
ZHANG et al.: ORIGIN OF DIFFERENT DEPENDENCES OF OPEN CIRCUIT VOLTAGE ON ELECTRODES
En-Tang Kang received the B.S. degree in chemical engineering from the University of Wisconsin, Madison, in 1978 and the Ph.D. degree in chemical engineering from the State University of New York at Buffalo, Buffalo, in 1983. In 1984, he joined the Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore, where he is currently a Professor. He is on the Editorial Advisory Board of Polymers, Plasma Processes and Polymers, J. Adhesion Science &. Technology, and Recent Patents on Engineering. His research interests include exploring new roles of polymers in nanoscience, molecular electronics, and biomolecular engineering.
Daniel S. H. Chan (M’79–SM’96) received the B.Sc., M.Sc., and Ph.D. degrees in electrical engineering from University of Manchester Institute of Science and Technology, Manchester, U.K., and Salford University, Salford, U.K., respectively. He joined the Hong Kong Polytechnic, Kowloon, Hong Kong, as a Lecturer in 1977, and in 1980, he joined National University of Singapore, Singapore, where he is now a Professor with the Department of Electrical and Computer Engineering. His main research interests are in characterization techniques, photovoltaics, silicon device physics and reliability.
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Chunxiang Zhu (S’97–M’02) received the B.Eng. and M.Eng. degrees from Xidian University, Xi’an, China, in 1992 and 1995, respectively, and the Ph.D. degree from The Hong Kong University of Science and Technology, Kowloon, Hong Kong, in 2001, all in electrical engineering. He then joined the Department of Electrical and Computer Engineering, National University of Singapore, Singapore, where he is currently an Associate Professor and with the Silicon Nano Device Laboratory. He has authored or coauthored more than 100 publications in refereed journals and conference proceedings. His research interests include high-k gate-stack technology on Si, Ge, and SiGe substrates for CMOS applications; high-k dielectrics for metal–insulator–metal capacitors in radio-frequency and mixed-signal integrated-circuit applications, polysilicon thin-film transistors, and organic/polymeric electronics.
