Analytical model for the photocurrent-voltage characteristics of bilayer MEH-PPV/TiO2 photovoltaic devices
© Chen et al; licensee Springer. 2011
Received: 28 January 2011
Accepted: 19 April 2011
Published: 19 April 2011
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© Chen et al; licensee Springer. 2011
Received: 28 January 2011
Accepted: 19 April 2011
Published: 19 April 2011
The photocurrent in bilayer polymer photovoltaic cells is dominated by the exciton dissociation efficiency at donor/acceptor interface. An analytical model is developed for the photocurrent-voltage characteristics of the bilayer polymer/TiO2 photovoltaic cells. The model gives an analytical expression for the exciton dissociation efficiency at the interface, and explains the dependence of the photocurrent of the devices on the internal electric field, the polymer and TiO2 layer thicknesses. Bilayer polymer/TiO2 cells consisting of poly[2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene] (MEH-PPV) and TiO2, with different thicknesses of the polymer and TiO2 films, were prepared for experimental purposes. The experimental results for the prepared bilayer MEH-PPV/TiO2 cells under different conditions are satisfactorily fitted to the model. Results show that increasing TiO2 or the polymer layer in thickness will reduce the exciton dissociation efficiency in the device and further the photocurrent. It is found that the photocurrent is determined by the competition between the exciton dissociation and charge recombination at the donor/acceptor interface, and the increase in photocurrent under a higher incident light intensity is due to the increased exciton density rather than the increase in the exciton dissociation efficiency.
The polymer-based photovoltaic (PV) cells consisting of conjugated polymer as electron donor (D) and nanocrystals as electron acceptor (A) are of great interest due to their advantages over conventional Si-based cells, such as low cost, easy-processability, and capability to make flexible devices [1–3]. Generally, the p-type conducting polymer acts as both electron donor and hole conductor in the photovoltaic process of the device, while the n-type semiconductor serves as both electron acceptor and electron conductor. The electron donor and acceptor can be intermixed into bulk architecture or cast into a bilayer structure in the PV devices [4–13]. The latter architecture is attractive for efficient devices, because the photogenerated electrons and holes are, to a great extent, confined to acceptor and donor sides of the D/A interface, respectively, where the spatial separation of electrons and holes will minimize the interfacial charge recombination and facilitate the transport of charge carriers toward correct electrodes with greatly reduced energy loss at wrong electrodes [1–3].
The primary processes involved in the photocurrent generation in a polymer-based PV cells include the exciton generation in the polymer after absorption of light, exciton diffusion toward the D/A interface, exciton dissociation at the D/A interface via an ultrafast electron transfer. The kinetics of the charge-carrier separation and recombination at the D/A interface imposes a great effect on the cell efficiency, and modeling the kinetics of the interfacial charge separation and recombination will offer a good way to understand the efficiency-limiting factors in the devices and to inform experimental activities. For this purpose, several theoretical models dealing with the interfacial charge separation and recombination have been developed in the past years. However, most of them are based on either Monte Carlo (MC) simulation [14–21] or numerical calculations [22, 23], and only a few models offer analytical expressions [5, 24–26]. Furthermore, the previous studies mainly focused on understanding the influences of interfacial dipoles [14, 20], energetic disorder [15, 20], light intensity , interface morphologies [18–22], and electrostatic interactions , on the interfacial charge separation and recombination at the organic/organic interfaces. The quantitative analysis of the charge transfer mechanism at the organic/inorganic interfaces in the polymer-based PV cells has been scarcely explored so far. Commonly, the photoinduced interfacial charge transfer from the polymers to inorganic semiconductors is explained by the exciton dissociation at the D/A interface due to the favorable energy match between the D and A components, without considering the role of the interfacial electric field [16, 27–31]. Breeze et al  proposed an analytical expression including the interfacial electric field for the exciton dissociation efficiency in bilayer MEH-PPV/TiO2 photovoltaic device, which only expresses the dependence of exciton dissociation efficiency on the polymer layer thickness, not on the TiO2 layer thickness. To understand the influence of TiO2 layer thickness on the exciton dissociation efficiency, one needs to consider the electrical properties of the system. In other words, more factors, such as voltage drop across the TiO2 layer, field-dependent mobility, field-dependent exciton dissociation, and charge recombination at the D/A interface, are necessarily to be incorporated into the model.
In this article, we propose a simple analytical model to describe the exciton dissociation and charge recombination rates at the D/A interface for the bilayer MEH-PPV/TiO2 cells by modeling the photocurrent-voltage characteristics of the devices. Not only this model is successful in describing the effect of the internal electric field at the D/A interface on exciton dissociation efficiency, but also describes the dependence of the exciton dissociation efficiency on the polymer and TiO2 layer thicknesses. We verify our model by fitting the measured experimental data on bilayer MEH-PPV/TiO2 devices under different conditions. The results obtained from the model show that the photocurrent of the devices is determined by the competition between the exciton dissociation and the charge recombination at the D/A interface; the exciton dissociation efficiency increases with either the increase in the forward electric field or the decrease in the thicknesses of polymer and/or TiO2 layers. In addition, it is found that a higher incident light intensity leads to a higher photocurrent density, but a lower exciton dissociation efficiency.
where E p (E n) is the electric field in the polymer (TiO2 ) layer, ε p (ε n) is the polymer (TiO2) dielectric constant, l (d) is the polymer (TiO2) layer thickness, and Q is accumulated charge density at the polymer/TiO2 interface.
where α is the polymer absorption coefficient, and L p the exciton diffusion length.
where l 0 is the nearest neighbor hopping distance, k B the Boltzmann constant, T the absolute temperature, q the elementary charge, and E a the thermal activation energy at zero field per molecule. In our calculations, we take E a = 0.18 eV for MEH-PPV, which is comparable to the value of thermal activation energy 0.2 eV , and take l 0 = 0.3 nm in the MEH-PPV molecules by referring to the typical distance of 0.6-1 nm between hopping sites in organic materials .
Figure 5a shows that, for the devices with different TiO2 thicknesses (d), when V - V 0 > 0, i.e., E p(E n) > 0, η CT increases with the increasing forward applied voltage, indicating that the forward electric field is beneficial to the exciton dissociation efficiency as indicated in Figure 3a. When the forward electric field is large enough (V > -0.4 V here), η CT for the device with d = 65 nm is larger than the calculated one for the device with d = 120 nm, which is in agreement with the result that a thicker TiO2 film leads to a higher series resistance and a lower photocurrent .
As for the devices with different polymer thicknesses (l) (Figure 5b), the similar dependence of the dissociation efficiency η CT on the applied voltage is obtained, i.e., a higher the forward electric field results in a larger exciton dissociation efficiency η CT. However, the thicker polymer film leads to a much smaller exciton dissociation efficiency in the whole applied voltage region. It is very likely due to the slower hole transfer rate in the polymer film as a result of the weakened internal electric field by the increased polymer film thickness, which leads to the smaller exciton dissociation rate at the D/A interface and further the lower exciton dissociation efficiency [5, 51].
Figure 5c shows the influences of various incident intensities on the exciton dissociation efficiency η CT. It is found that η CT decreases with increasing the incident intensity at same applied voltage. The similar phenomenon that the efficiency of charge separation per incident photon decreases with increasing the incident light intensity has also been observed in bilayer TiO2/PdTPPC  and TiO2/P3HT  cells in the absence of internal electric field, and was attributed to the occurrence of exciton-exciton annihilation within the polymer layer. In our case, this phenomenon can be understood as follows. Although a higher incident intensity creates more excitons in the polymer layer and generates higher free electron and hole densities at the D/A interface, the higher densities of the charge carriers at the interface increases the charge recombination probability at the same time; moreover, as discussed above, the increasing forward applied voltage will enhance the exciton dissociation efficiency at the D/A interface. In other words, there is a competition between exciton dissociation and charge recombination at the D/A interface and the last result is that the exciton dissociation efficiency η CT decreases as shown in Figure 5. This important result indicates that the increase in the photocurrent density under a higher incident light intensity is due to the increase in exciton density rather than the increase in the exciton dissociation efficiency, which is useful to optimize device performance.
An analytical model for the photocurrent-voltage (J ph-V) characteristics of the bilayer polymer/TiO2 photovoltaic cells is developed, where the generation of free charges takes place via dissociation of photogenerated excitons. The model describes the dependence of photocurrent generation on the device geometry and gives an analytical expression for the exciton dissociation efficiency. The experimental J ph-V data of the MEH-PPV/TiO2 devices are satisfactorily fitted to the model. Results show that increasing TiO2 or the polymer layer in thickness will reduce the exciton dissociation efficiency η CT in the device and further the photocurrent. It is found that the photocurrent is determined by the competition between the exciton dissociation and charge recombination at the D/A interface, and the increase in photocurrent under a higher incident light intensity is due to the increased exciton density rather than the increase in the efficiency η CT. Our results indicate that a thinner polymer layer combined with a thinner TiO2 layer favors the higher exciton dissociation efficiency in the bilayer devices. The model will provide information on optimization of device performance by investigating the effects of material parameters on device characteristics.
controlled intensity modulated photo spectroscopy
highest-occupied molecular orbital
indium tin oxide
This work was supported by the "100-talent Program" of Chinese Academy of Sciences, the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, and the President Foundation of Hefei Institute of Physical Sciences.
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