Investigation of non-linear dependence of exciton recombination efficiency on PCBM concentration in P3HT:PCBM blends

Enhancement of charge separation is one of the key issues being explored to improve the efficiency of polymer solar cells. Of the various methods experimented, bulk heterojunction structures with acceptor-donor interfaces have been found to give high quantum efficiencies (QE) [1, 2]. In bulk heterojunctions, the parent organic compound is blended with another compound, having suitable band alignment, to act as an acceptor or a donor. This enables the efficient dissociation of the excitons to generate free carriers that contribute to the photo-induced current. One of the commonly explored blends for photovoltaic applications consists of a polymer donor and a fullerene-based acceptor, like poly (3-hexylthiophene) (P3HT) and a fullerene derivative [6, 6] phenyl-C61-butyric acid methyl ester (PCBM). Power conversion efficiencies higher than 6% have been demonstrated in a recent report for polymer-fullerene blends [3, 4]. To increase the QE further, research is being done on ternary blends [5] and with incorporated nanoparticles [6].

However, with new organic semiconductor material systems being synthesized, an understanding of the fundamental electronic interactions and the influence of morphology, composition and properties of the blends, is essential. Various studies on the optical and electrical properties of P3HT PCBM blends have been done [7, 8] where the majority of these works focus on photocurrent studies involving the mechanisms and efficiencies of free carrier generation and transfer. For P3HT PCBM thin films, one possible mechanism leading to enhanced free carrier generation is the dissociation of excitons at the donor and acceptor interfaces for which the excitons need to diffuse to an interface before it is lost by radiative recombination or trapping. When the electron gets transferred into the PCBM, leaving the hole in the P3HT molecule, forms a charge transfer state, which dissociates under the influence of external electric field giving photocurrent. Thus the free carrier concentration, which plays a crucial role in the photocurrent generation in devices, depends strongly on the blend composition. Mechanisms of exciton transfer towards the interface are still unclear [9, 10]. Reports have shown charge transfer radius to be much larger than the exciton diffusion length, indicating exciton delocalization in the P3HT domain to be responsible for carrier generation [10, 11]. However, independent of the mechanisms involved, experiments have shown P3HT: PCBM solar cell devices with a blend ratio of 1:1 to have the highest power conversion efficiencies [12].

While the photocurrent is influenced by various factors like free carrier generation, carrier mobilities and carrier collection efficiencies and has been studied collectively, the influence of the individual factors require more understanding. In this work, we have performed photoluminescence (PL) quenching measurements to separately investigate only the exciton dissociation efficiencies, which is the first important step towards the generation of photocurrent. P3HT PCBM blend films are known to form phase separated domains [13]. On absorption of a photon, the photo-generated exciton can either dissociate under the influence of PCBM and contribute to the photocurrent or can recombine radiatively to give luminescence. Thus, the extent of PL quenching due to the presence of the acceptor molecule/domain can be directly associated with the exciton dissociation efficiency. In this work, we performed a systematic study on the efficiency of PL quenching in P3HT: PCBM blends as a function of PCBM concentration and the excitation intensity. We have proposed a mean field model to understand the role of PCBM concentration on the exciton recombination which provides further insight on the charge carrier dynamics and dependence of exciton dissociation efficiencies on other parameters.

Thin films of P3HT: PCBM blended samples were deposited on ITO coated glass substrate by spin coating. The PCBM concentration in the films was varied in the range of 0 to 60 percentage. The thicknesses of the samples were typically 150 nm as measured using a surface profilometer. All the samples were post-growth annealed at 110 °C for 30 min for which the device performance and phase separation are reported to be optimized [14]. Absorption spectra were measured with a broadband source. PL spectra were recorded with excitation of 488 nm from an Argon laser in the backscattered geometry.

The absorption spectrum of pure P3HT has two peaks at 521 nm and 547 nm with one shoulder at 594 nm (figure 1(a)). These three bands can be attributed to the 0–2, 0–1 and 0–0 transitions [8, 15]. The absorption of the films reduced significantly in the visible range with an increasing amount of PCBM due to the decrease in the number of P3HT molecules and negligible absorption of PCBM in this energy range. The changes in absorption spectra with PCBM concentration for an excitation wavelength of 488 nm is shown in figure 1(b).

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Room temperature PL spectrum of pure P3HT (figure 2(a)) has two peaks around 655 nm and 715 nm attributed to the exciton recombination from 0–0 and 0–1 transition respectively [16]. Both the PL peaks decrease monotonically with increasing PCBM concentration as shown in figure 2(a). The PL peak intensities were determined by fitting each spectrum with two Gaussians (figure 2(b)). The PL emission efficiencies were estimated by normalizing the PL intensities using the absorption of the films at the excitation wavelength of 488 nm. Thus all samples have equal absorbance, and the difference in PL emission comes primarily from the change in the rate of exciton dissociation mediated by the PCBM molecules. The decrease in the PL intensities of the P3HT: PCBM films with increasing PCBM concentration was measured for different excitation intensities (figure 3(a)).

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While the non-linear decrease in PL emission was observed for all cases, the PL quenching was found to be more efficient for higher excitation intensities, i.e. for higher exciton densities. To understand our observations, we propose a phenomenological model based on mean field theory which, in its simplified form, is adequate to explain the experimental results.

The carrier generation in P3HT and PCBM, and the decay channels, considered in the simulation, are schematically shown in figure 3(b). The total P3HT molecule concentration is given by A₀, of which à and A are the concentrations of photo-excited molecules having holes either as an exciton or as a free carrier and un-excited molecules, respectively. Details of the model are given in the supplementary document. In this model we assign two decay channels of the exciton population, (i) the excitons can recombine at a rate K_R giving PL and (ii) the excitons can dissociate, forming charge transfer state, by transfer of electrons to PCBM (having concentration S) at a rate β which includes collectively all mechanisms of exciton dissociation. The concentration of electrons present in P3HT is given by e. In the absence of any external bias in our optical measurements, the charge transfer exciton eventually recombines non-radiatively with a rate given by K_NR. Let L be the incident photon flux and α denote the absorption coefficient of P3HT at the excitation wavelength. The emitted photon flux due to radiative recombination of the electrons and holes is given by γ which can be measured as the PL signal.

The rate equations governing the processes are given by,

$$\begin{eqnarray}&&\dot{e}=\alpha LA-(\beta S+{K}_{R}\tilde{A})e\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&\dot{\tilde{A}}=\alpha LA-\left({K}_{R}e+{K}_{NR}\right)\tilde{A}\end{eqnarray} \tag{ 2 }$$

In a stationary state, $\tilde{A}\to {\tilde{A}}_{s},\,e\to {e}_{s},A\to {A}_{s},$ and equations (1) and (2) gives,

$$\begin{eqnarray}&&{e}_{s}=\displaystyle \frac{{K}_{NR}}{\beta S}{\tilde{A}}_{s}\end{eqnarray} \tag{ 3 }$$

We define I(S) as the ratio of the PL emission efficiency in the presence of S fraction of PCBM to that of pristine P3HT. Thus,

$$\begin{eqnarray}&&I\left(S\right)=\displaystyle \frac{\dot{\gamma }(s)}{\dot{\gamma }\left(0\right)}\end{eqnarray} \tag{ 4 }$$

where the emitted photon flux for S amount of PCBM is given by $\dot{\gamma }(S)={K}_{R}{e}_{s}{\tilde{A}}_{s}$

On substitution, we eventually get,

$$\begin{eqnarray}&&I(S)=1-\displaystyle \frac{S}{2S* }\left(\sqrt{1+\displaystyle \frac{4S* }{S}}-1\right)\end{eqnarray} \tag{ 5 }$$

where,

$$\begin{eqnarray}&&S* =\displaystyle \frac{\,{K}_{NR}\,{K}_{R}\alpha L{A}_{0}}{\beta \,{({K}_{NR}+\alpha L)}^{2}}\end{eqnarray} \tag{ 6 }$$

Figure 3(a) shows the fit of the measured PL emission efficiency data (normalized for the emission of pristine P3HT), i.e. I(S), using the model described above (equation (5)). We find good agreement of the theoretical fit to the experimental data, where the only free parameter is S* which depends on the exciton population and material properties like recombination rates and carrier trapping rates. An increase in the PL quenching efficiency implies a decrease in I(S), which requires a decrease in S* (for a given S). The model predicts a non-monotonous dependence of S* on L as shown by the solid line in figure 3(c). Experimentally obtained values of S* are in congruence with theoretical fit using equation (5) (figure 3(c)). For higher excitation intensities, with increasing exciton population, S* is found to decrease, indicating better PL quenching. Our measurements on the same set of samples for different excitation intensities concur with this theoretical prediction (figure 3(a)). For a 1:1 P3HT/PCBM blend, we found an increase in the PL quenching efficiency from 70% to 91% when the excitation influx was increased six-fold.

We observed saturation of PL quenching efficiency in P3HT PCBM blend thin films with increasing PCBM concentration. The saturation happens around 1:1 blend ratio for which the highest QE in solar cells have been reported. Thus, we find that the exciton dissociation efficiency plays a vital role in determining the quantum efficiency of P3HT: PCBM based photovoltaic devices. For higher PCBM concentrations, the decrease in QE may result from decreased carrier mobilities. Our excitation intensity dependent measurements show that PL quenching efficiencies similar to 1:1 blend ratio can be obtained for a much lower PCBM content if we go to higher excitation intensities. We have proposed a mean field phenomenological model which tallies well with our experimental observation. Though the mechanisms involved in the dissociation/dislocation of excitons in these systems are controversial, our mean field approach can explain the experimental observations satisfactorily. Thus PL quenching measurements along with the model proposed can be applied to other organic semiconductor blend systems to identify compositions that could give optimum performances as solar cells.

The authors would like to thank the Centre for NEMS and Nanophotonics (CNNP) at IIT Madras for facilitating the sample fabrication and Department of Science and Technology (Project No. ECR/2015/000147), India, for funding the project.