Excitonic coupling dominates the homogeneous photoluminescence excitation linewidth in semicrystalline polymeric semiconductors

TL;DR

This study measures the homogeneous excitation linewidth in a semicrystalline polymer semiconductor, revealing excitonic coupling as a dominant factor influencing linewidth broadening at low temperatures.

Contribution

It introduces a two-dimensional coherent photoluminescence excitation spectroscopy method to quantify linewidths in polymer semiconductors, highlighting the role of excitonic interactions.

Findings

Linewidth always exceeds 110 meV at 8 K

Linewidth shows spectral dependence, minimal near the 0-0 peak

Excitonic coupling significantly influences linewidth broadening

Abstract

We measure the homogeneous excitation linewidth of regioregular poly(3-hexylthiophene), a model semicrystalline polymeric semiconductor, by means of two-dimensional coherent photoluminescence excitation spectroscopy. At a temperature of 8\,K, we find a linewidth that is always $\gtrsim 110$\,meV full-width-at-half-maximum, which is a significant fraction of the total linewidth. It displays a spectral dependence and is minimum near the 0--0 origin peak. We interpret this spectral dependence of the homogeneous excitation linewidth within the context of a weakly coupled aggregate model.

Equations

$${\gamma }_{iso}\propto \frac{t}{L_x^2}.$$

$${\gamma }_{agg}\propto \frac{J}{L_y^2}.$$

$$r=\frac{{\gamma }_{iso}}{{\gamma }_{agg}}=\frac{t}{J}{\left(\frac{L_y}{L_x}\right)}^2\sim \mathrm{0.09.}$$

$$\frac{L_y}{L_x}\propto \sqrt{r\frac{J}{t}}\sim \mathrm{0.09.}$$

Full text

Unravelling optical and electronic properties from disordered energy landscapes, and correlating these to complex solid-state microstructures, are fundamental issues in the materials science of disordered semiconductors. For example, in polymeric semiconductors Treat et al. (2015); Ostroverkhova (2016), the structure-property interdependence is such that the excitation spectral lineshapes are governed fundamentally by the interplay of electronic interactions occurring within a given polymer chain and between adjacent chain segments, which is a strong function of microstructure Spano and Silva (2014). Regioregular poly(3-hexylthiophene) (P3HT) is amongst several materials that have provided a platform to develop understanding of such interplay, since its absorption and photoluminescence (PL) spectral lineshape can be analyzed using well-established concepts pertaining to molecular aggregates. This allows to extract intricate information on the magnitude of excitonic coupling, the extent of energetic disorder and the amount of correlation in the disordered energy landscape Yamagata and Spano (2012); Paquin et al. (2013). However, extensive PL measurements on isolated P3HT chains at low temperature reveal that the energy of the PL spectrum can vary over a large spectral range throughout the visible Thiessen et al. (2013). This suggests instead that bulk lineshapes are predominantly the product of a large inhomogeneously broadened distribution of chromophore energies, which is conformational in origin at the single-molecule level, and which add up to produce the bulk spectrum. Indeed, mixed quantum-classical atomistic simulations demonstrate that energetic disorder of single P3HT chains arises through the interplay of excited-state delocalization and electron-hole polarization, governed by intrachain torsional disorder, and giving rise to a heterogeneous distribution of chromophore energies Simine and Rossky (2017). Intriguingly, while the PL origin emission spanned a broad spectral range at 4 K, its linewidth only varied from $\sim 10$–30 meV and the spectral lineshape was essentially invariant Thiessen et al. (2013), in contrast to the broad lineshapes with very strong microstructure dependence in bulk films Paquin et al. (2013). The single-chain PL data at low temperature reported in ref. 6 thus pose the following fundamental materials physics question: are excitonic models based on photophysical aggregates sufficient to describe quantitatively spectral lineshapes in semicrystalline polymeric semiconductors, or is the governing factor the conformation-induced disorder of individual chains? The answer to this question necessitates knowledge of the homogeneous spectral linewidth of P3HT in the solid state, with polymer molecular weight and dispersity characteristics comparable to the material reported in ref. 6. A rigorous measurement of the homogeneous lineshape of bulk P3HT films has not been reported to the best of our knowledge.

To address this question, here we evaluate the homogeneous excitation linewidth in a P3HT bulk film in order to compare with the linewidths measured using single-molecule spectroscopic techniques. We do so by means of two-dimensional coherent PL excitation (2D-PLE) spectroscopy Tekavec et al. (2007). This ultrafast probe belongs to the family of 2D optical spectroscopies Fuller and Ogilvie (2015) that measure a nonlinear optical response via the time-integrated and spectrally-integrated PL intensity. We choose to implement 2D coherent spectroscopy because these techniques can distinguish between homogeneous and inhomogeneous linewidths Tokmakoff (2000). We find that, at 8 K, the solid-state homogeneous linewidth is up to an order of magnitude broader than in isolated chains. We interpret these observations as excitonic coupling effects in photophysical aggregates Spano and Silva (2014).

P3HT with weight-average molecular weight ($M_{\textrm{w}}$) of 113 kg/mol, dispersity (D) of 1.5, and 99% regioregularity was cast from a chloroform solution as described in detail in Supplemental Material 111See Supplemental Material at [URL will be inserted by publisher] for details of the experimental measurements and analysis.. In this high $M_{\textrm{w}}$ regime, the microstructure of P3HT films solution-cast from good solvents consists of crystalline domains embedded in chain-entangled phases Reid et al. (2012), with exciton coherence length of $\sim 5$ thiophene monomer units along chains, and extending over $\sim 2$ chain segments in the interchain direction under the processing conditions employed here Paquin et al. (2013).

Fig. 1(a) shows the absorption spectrum of a film produced by this procedure. Within the weakly-coupled H-aggregate model developed by Spano Spano (2005); *Spano2007, we extract a free-exciton bandwidth of $W=63\pm 5$ meV from the ratio of the 0–0 and 0–1 absorbance peaks Clark et al. (2007, 2009). This is consistent with $W$ reported by Paquin et al. Paquin et al. (2013) for films of P3HT with similar $M_{\textrm{w}}$ and processed under similar conditions as the sample studied here.

We examine the excitation lineshape by means of 2D-PLE spectroscopy. The collinear pulse sequence used to acquire a 2D spectrum is shown in Fig. 1(b) Note (1). We collect the time-integrated PL intensity as a function of inter-pulse delays $t_{21}$ and $t_{43}$ (coherence times) at a fixed population time delay $t_{32}$. Acousto-optic modulators modulate the phase difference of the first pulse pair $\phi_{21}$ (pulses 1 and 2, which we denote as the ‘pump’ pulses) and the second pulse pair $\phi_{43}$ (pulses 3 and 4, ‘probe’ pulses) at distinct frequencies in the kHz range. This allows demodulation of the measured PL intensity using phase-sensitive detection with reference waveforms built from a mix of these two phase modulation waveforms. We thus extract simultaneously the so-called rephasing and nonrephasing signals at each delay point $t_{21}$ and $t_{43}$, producing 2D coherence decay maps, which are Fourier-transformed on both time axes to obtain the 2D coherent excitation spectrum. A detailed description of the experimental technique and analysis is provided in Supplemental Material Note (1). All measurements reported here were taken using a pulse fluence of $4.2$ $\mu$J cm*-2* and at a temperature of 8 K.

A typical set of early-time 2D-PLE spectra is depicted in Fig. 2. The purely absorptive (real-part) spectrum (Fig. 2(c)) is the sum of the rephasing (Fig. 2(a)) and the nonrephasing (Fig. 2(b)) spectral components. The complete response, including the imaginary spectra, is presented in Supplemental Material Note (1). We observe in all these a diagonal peak at 2.05 eV, corresponding to the 0–0 absorption feature in Fig. 1(a). To higher energies along the diagonal, we observe the low-energy tail of the 0–1 replica. We also observe weak 0–0/0–1 cross peaks, most prominent at $(E_{21},E_{43})=(2.05,2.19)$ eV in the nonrephasing spectrum. These data are consistent with previous measurements in P3HT films De Sio et al. (2016); Song et al. (2015) and in P3HT aggregates suspended in solution Song et al. (2014). Slight differences in lineshape can be ascribed to differences in microstructure and in our distinct experimental implementation of the 2D coherent probe Perdomo-Ortiz et al. (2012).

In general, the diagonal width of the zero-time 2D coherent rephasing spectrum represents the inhomogeneous linewidth, here limited by the excitation laser bandwidth, and the antidiagonal spectrum displays the homogeneous dephasing Tokmakoff (2000). However, as pointed out by Siemens et al. Siemens et al. (2010), inhomogeneous and homogeneous broadening mechanisms need to be evaluated simultaneously to extract reliable quantitative values from 2D coherent excitation spectra, which is challenging to do analytically for systems with cross peaks. We have carried out numerical simulations of 2D coherent spectra using a three-state model, consisting of the ground state and 0–0 and 0–1 vibronic replica, as described in Supplemental Material Note (1). We have taken into account the 0–0 and 0–1 relative spectral weight and the excitation laser spectrum explicitly. We also include a phenomenological Gaussian inhomogeneous broadening with spectral width $\sigma$ for the 0–0 and 0–1 peaks, and a common dephasing rate $\gamma$. In the simulations displayed in Fig. 3, we have used $\sigma=130$ meV full-width-at-half-maximum, which is consistent with the disorder widths used in to model absorption and PL lineshapes in P3HT Paquin et al. (2013). Fig. 3(a) and (b) show the real part of the rephasing and nonrephasing spectrum, respectively, for $2\gamma=30$ meV, which corresponds to the upper end of the spectral linewidth distribution measured in the single-chain experiments of Thiessen et al. Thiessen et al. (2013) In Fig. 3(c) and (d), we show the simulated spectra with $2\gamma=90$ meV. In both cases, 0–0/0–1 cross peaks can be identified in the simulated spectra, as observed experimentally in Fig. 2. However, in the situation of narrow homogeneous broadening (top row), these peaks are more readily identified compared to when the homogeneous linewidth is a more significant fraction of the inhomogeneous linewidth (bottom row). We find that we can best represent our measured 2D-PLE spectra using $2\gamma=90$ meV, indicating that the homogeneous linewidth in the solid state is substantially broader than the spectral linewidths measured for isolated polymer chains.

Returning to the experimental measurement, Fig. 4(a) displays the modulus of the 2D-PLE rephasing spectrum, i.e. the photon-echo spectrum, in this neat P3HT film at 8 K. We have chosen to analyze this spectrum measured at a population time $t_{32}=50$ fs to avoid artefacts due to time-overlap of the $\sim 13$-fs pulse pairs. We demonstrate in Supplemental Material that the spectral linewidth does not evolve over this initial population waiting period Note (1), thus this measurement is equivalent to the usual zero-time photon-echo spectrum. We display the antidiagonal slice, centered at $E_{21}=E_{43}=2.10$ eV, over the blue dashed line in Fig. 4(a), as open circles in Fig. 4(b). The corresponding slice for our simulation with $2\gamma=90$ meV is represented by the black continuous curve, which reproduces the width of the diagonal peak on top of the 0–0/0–1 cross peaks. From this comparison, we estimate that the homogeneous linewidth in our P3HT films is $90\pm 10$ meV. The spectral resolution of this time-domain measurement is, in principle, limited by the measurement range in $t_{21}$ and $t_{43}$, the coherence time variables depicted in Fig. 1(b). For the spectrum reported in Fig. 4(a), we have measured 2D coherence decay functions over 100-fs time windows Note (1), which implies a resolution of $\sim 20$ meV. The homogeneous linewidth extracted in Fig. 4(b) is therefore well within our experimental resolution.

This PL excitation linewidth is roughly an order of magnitude broader than the lower limit in the single-chain PL spectra reported by Thiessen et al. Thiessen et al. (2013), who investigated P3HT with $M_{\textrm{w}}$ that is near the transition in polymer microstructure from a nonentangled, paraffinic to an entangled, semicrystalline, two-phase morphology in bulk films Paquin et al. (2013); Reid et al. (2012). In that work, while the emission energy of individual P3HT chains varied substantially over much of the visible range, the PL spectral lineshape was found to be nearly invariant over measurement of hundreds of different chains. The lineshape was found to be strongly dominated by the 0–0 emission peak, with a narrow width spanning from $\sim 10$ to $25$ meV in the spectral range accessible by our 2D-PLE measurements. While PL excitation (PLE) spectral measurements on single molecules are significantly more challenging than PL experiments, we expect PLE spectra of comparable width. We must therefore invoke a homogeneous broadening mechanism that accounts for the large difference in linewidth in going from isolated P3HT chains to that in the bulk.

The homogeneous excitation linewidth $2\gamma$ is related to the optical dephasing time $T_{2}$ via the time-energy uncertainty principle, $T_{2}=\hbar/\gamma$. From the bulk spectrum of Fig. 4(b), we extract $T_{2}=15\pm 2$ fs. In an isolated chain, we infer from the measurements of Thiessen et al. Thiessen et al. (2013) a value of $T_{2}\sim 50$–130 fs. Employing two-color, three-pulse photon echo peak shift measurements in dilute chloroform solution, Wells and Blank concluded that intrachain excitons in P3HT reflect dynamic broadening due to strong, selective exciton-vibrational coupling that is dominated by only two motions — one high-frequency bond stretch and a low-frequency torsional motion Wells and Blank (2008). Although at the low concentrations at which those measurements were carried out chain aggregation was considered to be suppressed, Raithenel et al. point out that even in solution at such low concentrations, ‘loose’ aggregates are formed, and in fact can dominate the optical response Raithel et al. (2016). Therefore, given that the rephasing measurements reported by Wells and Blank were carried out in solution and at room temperature, we might expect that the dephasing dynamics are intermediate between those measured here and those inferred from measurements reported by Thiessen et al. We thus consider that the $T_{2}$ derived from the low-temperature single-chain measurements reflect a limiting case of that intrachain dephasing mechanism given the low temperature of the measurement and that the polymer chains were on a silica substrate under vacuum. Qualitatively, we suggest that the additional broadening seen in our bulk measurements results from interchain photophysical aggregate effects.

To examine this idea more formally, let us consider a simple two-dimensional free-exciton model of an aggregate composed of polymer chains of length $L_{x}$ that are assembled to form a lamellar stack of length $L_{y}$. Excitonic coupling effects, both along and between chains, are incorporated by an intrachain hopping integral $t$, and an interchain hopping integral $J$. Typically, one finds that $J/t\sim 0.1$ within a hybrid HJ aggregate model Yamagata and Spano (2012); Paquin et al. (2013). For an isolated chain, the homogeneous linewidth scales as Note (1)

[TABLE]

This is consistent with the results presented by Arias et al. on J aggregates Arias et al. (2013). Including the interchain term and assuming $L_{x}\gg L_{y}$, one obtains a similar expression along the interchain stacking direction Note (1),

[TABLE]

The ratio of our measured homogeneous linewidth to the most narrow linewidths measured by Thiessen et al. Thiessen et al. (2013) allows us to relate $J/t$ to the aspect ratio of the aggregate domain:

[TABLE]

Rearranging this, and assuming $J/t\sim 0.1$, we find that

[TABLE]

This aspect ratio is consistent with two-dimensional exciton coherence functions in P3HT films, modeled by Paquin et al. using a disordered Holstein lattice Hamiltonian representing hybrid HJ aggregates Paquin et al. (2013). This is particularly so considering that our picture here does not include electron-vibration coupling effects accounted for in the Holstein lattice, which would localize the exciton further within the polymer backbone. Furthermore, the coherence function modeled by Paquin et al. was based on the steady-state PL spectral lineshape, which reflects an equilibrium distribution of more highly localized excitons. Therefore, our simple model rationalizes the nearly order-of-magnitude difference in dephasing times in the bulk compared to isolated chains. Physically, additional fluctuations in the exciton energy due to fluctuations in excitonic coupling between $\pi$ electrons across chains gives rise to more rapid dephasing than in isolated chains, even in the weak coupling aggregate regime. Indeed, Yamagata et al. highlight the role of short-range charge-transfer-mediated coupling in small-molecule aggregates Yamagata et al. (2014), and we suggest that these types of intermolecular interactions are responsible for the additional optical dephasing pathways observed in our measurements reported here. These arguments support our proposal that large homogeneous broadening in the bulk, in contrast to isolated chain, is due to interchain photophysical aggregate effects.

These solid-state contributions on the homogeneous linewidth are consistent with other photophysical consequences of even weak aggregate formation, revealed by means of single-aggregate spectroscopy measurements. For example, Raithenel et al. show that subtle aggregation of P3HT chains produces strong red shifts and broadening in comparison to spectra from isolated-chain Raithel et al. (2016). Hu et al. observed that long-range exciton transport depends strongly on aggregate order Hu et al. (2014), further highlighting the importance of interchain interactions on exciton dynamics. In a further study, Hu et al. demonstrated that dielectric-induced stabilization of nonradiative charge-transfer states very sensitively controls PL quantum efficiencies in suspended P3HT aggregates Hu et al. (2015), consistent with the role proposed by Yamagata et al. of charge-transfer components of excitonic coupling Yamagata et al. (2014), indicating once again the key role the environment play in dictating photophysics in aggregates.

The clear excitonic signatures on the homogeneous PL excitation linewidth, derived from our 2D-PLE measurements, reveal the importance of employing photophysical aggregate models to describe the bulk optical properties of polymeric semiconductors. This conclusion is in contrast to that reached by Thiessen et al. Thiessen et al. (2013), where the bulk spectral lineshapes were assumed dominated by the chain-conformation-dependent combination of single chromophores within a broad inhomogeneous distribution. We put forth here that excitonic effects are not minor contributions to the optical properties of this class of semiconductor materials, and we highlight the richness of information on exciton-environment coupling dynamics reported by the nonlinear spectroscopic techniques employed in this work.