Evolution of the pentacene exciton band width in pentacene–tetracene blends Open Access

The electronic and optical properties of molecular solids are governed by inter-molecular coupling mechanisms,^1–6 which significantly depend on the molecular arrangement in these materials. This is true for charge carriers, i.e., electrons and holes, in organic semiconductors but also for the lowest electronic excitations, which in the vast majority of organic semiconductors form strongly bound excitons. The nature and dynamics of these excitons determine the entire photophysical behavior of the corresponding material. Substantial progress in the microscopic understanding of such excitons has been achieved in previous years, and often the inter-molecular exciton coupling is determined by a superposition of two coupling mechanisms: Coulomb (dipole–dipole) coupling and charge transfer coupling.⁷ 

In real applications, organic semiconductors are used in the form of thin films or even blends, which can be far from a long-range crystalline order. Thus, it is important to rationalize the consequences of such disorder on exciton behavior in relevant materials. Furthermore, blends of organic semiconductors can be a powerful tool to tune physical properties or to determine the role of aggregation (solid-state) effects, as they allow for a variation in the strength of the inter-molecular interactions.^8–13 The latter can, for instance, be realized by mixing weakly interacting molecules, with the effect that inter-molecular interactions between molecules of one material are continuously reduced by the incorporation of the second material as a spacer. Investigations of the electronic excitations of a material in this manner require the admixture of spacers, which have a larger optical gap, to keep the excitation spectrum undisturbed.

In this study, we report on the variations of the inter-molecular exciton coupling in pentacene as a function of the increasing admixture of tetracene as a spacer. Pentacene is one of the most widely studied model organic semiconductors, and the inter-molecular exciton coupling and the resulting anisotropic photophysical properties in pentacene crystals are quantitatively well understood.^1–3,7,14 We control the inter-molecular coupling via the introduction of tetracene, which has a larger band gap and interrupts the pentacene–pentacene interaction. Using optical absorption spectroscopy and electron energy-loss spectroscopy of the mixed films, we demonstrate how the pentacene Davydov splitting and the exciton band width evolve upon increasing tetracene admixture.

Thin mixed films with the molar ratios pentacene:tetracene of 4:1, 3:1, 2:1, 1.5:1, 1:1, 1:1.5, 1:2, and 1:3 were prepared via physical vapor deposition (PVD) in a high vacuum chamber. In the following, we denote the films with p_xt_1−x (pentacene_x:tetracene_1−x). For PVD, the substances are placed in a crucible, which is positioned over a thermal heater. The crucibles are slowly heated up to evaporate any remaining impurities in the source material, which can be pumped out by the vacuum pump. The molecules slowly begin to evaporate with increasing temperature and distribute in a cone above the furnace. The thin film is deposited onto a cleaved potassium bromide (KBr) single crystal substrate (purchased from Korth Kristalle GmBH), placed exactly in the middle above both furnaces.

To obtain high-quality polycrystalline films with reproducible composition, the evaporation rate as measured using a quartz microbalance was adjusted, e.g., 2 nm/min for pentacene and 0.5 nm/min for tetracene in the case of a p_0.8t_0.2 film. The sublimation temperature depends on the materials: pentacene started at 145 °C and tetracene at 75 °C. These temperatures only serve as a guideline and should be readjusted during every growth. The pressure during deposition was 2 × 10⁻⁸ mbar.

In all cases, the film thickness was about 100 nm. This thickness allows for the best results in optical absorption and EELS measurements. A representative example is shown in Fig. 1, where a p_0.8t_0.2 film was grown on top of a KBr substrate. As can be seen, the film is homogeneous.

Each film was characterized using a Bruker Vertex 80 V spectrometer in the VIS and IR ranges at 77 K and room temperature, respectively. This spectrometer is additionally equipped with a microscope that allows measurements of the films with a lateral resolution of about 50 μm × 50 μm. This provides us with information on the lateral homogeneity of the corresponding films.

The thin films on the KBr substrate can be directly mounted into the chamber of the spectrometer without further processing. KBr allows easy measurements of the optical absorption data as it is transparent in the entire relevant measurement range. The VIS data provide insight into the disorder induced spectral changes in the energy range of the lowest excitons. The obtained IR data were analyzed to double-check the composition of the mixed layers (for further analysis, see the supplementary material).

Further electronic excitation data have been obtained by carrying out electron energy-loss spectroscopy (EELS) in transmission. For EELS measurements, the thin films were transferred onto an electron microscopy grid. The KBr substrate was dissolved in distilled water, and the floating thin film was then caught with the electron microscopy grid and, subsequently, transferred into the spectrometer.

EELS was performed with a custom-made electron energy-loss spectrometer, which is able to detect electronic excitations as a function of momentum transfer.^15,16 The kinetic energy of the incoming electrons is 172 keV. We note that at such high primary beam energy, only singlet excitations are possible. The sample temperature can be chosen in the range of 20–380 K.¹⁶ To keep organic single crystals undamaged for as long as possible, the sample temperature was always kept at 20 K, which also minimized thermal broadening in the spectra. The energy and momentum resolutions have been set to 85 meV and 0.04 Å⁻¹, respectively. The measured signal in EELS is proportional to the loss function Im[−1/ϵ(q, ω)] and can be determined for different momentum transfers q. The pressure in the spectrometer was about 2 × 10⁻¹⁰ mbar.

Since organic materials are often damaged by fast electrons, we repeatedly checked our samples for any sign of degradation. It turned out that under our measurement conditions, the spectra remained unchanged for about 10 h. Samples that showed any signature of degradation were not considered further but replaced by freshly prepared thin films. Data from different films were reproducible. Numerous investigations of organic semiconductors using EELS in the past have revealed detailed insight into the exciton properties of the respective materials; see, e.g., Refs. 17–21.

We start the presentation of our results with the optical absorption spectra of the p_xt_1−x films measured in the visible range at 77 K, as shown in Fig. 2.

The pentacene spectrum (black curve) consists of (at least) four components, visible as maxima or shoulders, respectively. These absorption data are in very good agreement with previously published data from pentacene single crystals and thin films.^22–25 We observe a pronounced first peak whose energy position of 1.83 eV indicates the optical bandgap. The spectral feature at 1.97 eV has been assigned to the upper Davydov component, which results from the intermolecular exciton interaction between the two symmetrically inequivalent molecules in the pentacene unit cell.^7,26,27 Two additional features at about 2.14 and 2.26 eV can be observed, which demonstrates that exciton coupling in the solid state has a substantial impact on the spectral weight distribution in the excitation spectra of pentacene. Recent theoretical studies of the solid-state exciton coupling in pentacene have demonstrated that the complete spectral shape can only be rationalized taking into account a strong coupling of molecular Frenkel and charge-transfer (CT) excitons within a multiparticle basis set in addition to the vibronic coupling.^7,14 Furthermore, it was shown that the observed Davydov splitting in the polarization-dependent optical absorption data of single crystals can only be quantitatively described based on this complex mixture of Frenkel, CT excitons, and vibrational states.^7,14 In more detail, it has been shown that the quite high intensity of the first peak is a result of electron–vibron coupling and that the third visible peak predominantly arises from charge transfer excitons mixed with Frenkel excitons. Every change in coupling will change the spectral shape, and in our blends, the coupling is significantly reduced, as can be seen, e.g., by the reduction of the Davydov splitting discussed below.

The admixture of tetracene, which can be regarded as increasing the introduction of static disorder, induces quite large changes in the absorption signals shown in Fig. 2. The lowest energy excitation (lower Davydov component) shows a substantial shift to higher energies, while the second feature (upper Davydov component) is characterized by much smaller energy variations. Recently, equivalent data for tetracene–pentacene thin-film blends at room temperature have been reported by Zeiser et al.⁸ 

We have analyzed the respective peak positions by fitting the corresponding absorption profile using Gaussian functions (see in the supplementary material), and we show the results of this fit in Fig. 3.

We also measured the absorption spectra of the p_xt_1−x films in the visible range at room temperature. The full data sets are shown in the supplementary material.

For increasing tetracene fractions, a considerable decrease in the Davydov splitting (see Fig. 4) and changes in the relative intensities of the two Davydov components are observed. Results obtained at room temperature show the same trend as the results obtained at 77 K. This indicates that the addition of tetracene molecules to the pentacene lattice leads to significant changes in the intermolecular exciton coupling. This is in very good agreement with recently published results on the Davydov splitting in mixed films of pentacene and picene, or diindenoperylene, respectively²⁸ (see also the discussion below). We note that the Davydov splitting in pure pentacene is visibly temperature dependent, in agreement with data in the literature.^24,29,30

Knowledge of the exciton dispersion is important for a full understanding of the photophysical behavior of a material. For pentacene, the exciton dispersion has been investigated experimentally and theoretically,^14,17 and a very good understanding has been achieved. The exciton band structure is predominantly determined by charge-transfer exciton coupling between nearest-neighbor pentacene molecules, giving rise to exciton bands with a band width of about 100 meV.^14,17,31 The existence of exciton bands requires exciton delocalization over several unit cells, and it is intriguing to see how the disorder impacts this delocalization.

We have determined the momentum dependence of the lowest exciton feature in the mixed films as a function of tetracene admixture using EELS. Recently, we have shown that such data from polycrystalline pentacene films give a good measure of the exciton dispersion comparable to that observed for single crystals.¹⁸ EELS data have been taken for mixed films with compositions p_0.8t_0.2, p_0.67t_0.33, p_0.5t_0.5, and p_0.33t_0.67. The data for the p_0.8t_0.2 thin film are shown in Fig. 5, and EELS measurements of the p_0.33t_0.67, p_0.5t_0.5, and p_0.67t_0.33 thin films can be found in the supplementary material.

The data in Fig. 5 cover a momentum range up to 0.4 Å⁻¹. We have not determined data for larger momentum because then the exciton branch resulting from the upper Davydov component is the energetically lowest band,^14,17 and this makes an unambiguous assignment of the excitation features impossible. Note that previous calculations demonstrate that the band structure for the thin-film phase and the single-crystal phase of pentacene is very similar.³² 

In the p_0.8t_0.2 thin film spectra, a well-defined first peak at about 1.86 eV is present, which is followed by a satellite structure with peaks at 2.12 and 2.32 eV. The spectral shape and the energy of this peak and the satellite features are in good agreement with the results of optical measurements, taking into account the lower energy resolution of the EELS data. We observe an upshift of the spectra as compared to pure pentacene, which is in good agreement with our optical absorption data presented above.

The energy positions of the lowest excitation feature have again been analyzed by fitting a Gaussian profile to the respective peak for all momentum values. In Fig. 6, we show a summary of all the exciton dispersions measured in p_xt_1−x thin films. In addition, the corresponding data for pure pentacene films are included.¹⁸ 

In Table I, we show the parameters for the dispersion curves according to the equation above for all measured mixed films and for pure pentacene.

These data can now be used to determine the exciton band width W = 8J_eff for the different films, which is a measure for the coherent exciton delocalization in a crystal. In Fig. 7, we show a comparison of the exciton band width obtained in this way and the Davydov splitting read of the optical data. For pure, crystalline pentacene, these two quantities are expected to be identical: W = DS = 8J_eff.⁷ 

Figure 7 clearly reveals that the reduction of the exciton band width W occurs much faster with increasing tetracene admixture than that of the Davydov splitting. We note that the evolution of the exciton band width also shows a plateau-like behavior after the initial decrease. The difference between the Davydov splitting and the exciton band width represents the different physical origins of these two quantities. The formation of an exciton band structure requires the presence of sizable, undisturbed pentacene regions with a length comparable to the spatial exciton coherence length.³³ On the other hand, in order to obtain Davydov split states, it is only necessary that smaller (e.g., nearest-neighbor-like) pentacene clusters exist.

This very rough consideration is, of course, not able to describe the observed band width and Davydov splitting (Fig. 7) quantitatively. Recently, detailed calculations of the Davydov splitting in pentacene films mixed with picene or diindenoperylene using a mixed Frenkel-charge-transfer Hamiltonian that incorporates vibronic coupling have demonstrated that a quantitative understanding of the pentacene Davydov splitting in such mixed films can be achieved taking into account changes in the lattice constants upon admixture of the second molecular species and the effect of occupational disorder as induced by this admixture.²⁸ We emphasize that these calculations could even capture the non-linear, plateau-like behavior of the DS evolution around x = 0.7 (p_xt_1−x). The evolution of the DS has been ascribed to be predominantly due to changes in the electron and hole charge-transfer integrals between neighboring pentacene molecules, which are reduced with increasing static disorder (increasing tetracene admixture).

Following these instructive results, we attributed the changes in the exciton band width to a reduction in the exciton coherence length caused by the interruption of the pentacene inter-molecular charge transfer exciton coupling upon tetracene introduction plus related disorder contributions in the pentacene distances and relative orientations. The band width reduction is much larger than that of the Davydov splitting since larger, undisturbed pentacene regions are required for the formation of a delocalized, dispersive exciton.⁷ Optical studies of tetracene–pentacene blends have shown that at very low pentacene concentrations, the average number of pentacene–pentacene neighbors is too small to observe pentacene-based homofission; instead, heterofision has been observed.⁸ This is in good agreement with the substantial exciton band width reduction discussed here. We note that the observed exciton band width reduction is not due to a reduction of the crystallite size in our blends, as shown in the supplementary material.

In contrast to the quite strong temperature dependence of the Davydov splitting and the exciton band width in pure pentacene, we do not see a temperature dependence of the Davydov splitting for the mixed films studied here (see our results above and the supplementary material). For pure pentacene, recent work on exciton–phonon coupling has concluded that anharmonic effects result in temperature-dependent exciton localization,³⁴ which provides an explanation of the recently observed substantial exciton band width reduction upon increasing temperature.¹⁸ Our results for the mixed films indicate that such anharmonic contributions (dynamic disorder) become suppressed or at least of minor importance compared to the static disorder caused by tetracene admixture.

We have prepared thin films of the organic semiconductor pentacene with the addition of tetracene as a spacer via physical vapor deposition. The films were characterized by optical absorption spectroscopy and electron energy-loss spectroscopy. The optical absorption showed that the admixture of tetracene, which represents the increasing introduction of static disorder, induces quite large changes in the absorption signals—a considerable decrease in the Davydov splitting and changes in the relative intensities of the two Davydov components are observed. We have determined the momentum dependence of the lowest exciton feature in the mixed films as a function of tetracene admixture using electron energy-loss spectroscopy. We demonstrate that the exciton band width in pentacene strongly decreases with increasing tetracene concentration. We ascribe the changes in the exciton band width to a reduction in the exciton coherence length caused by the interruption of the pentacene intermolecular charge transfer exciton coupling upon tetracene introduction.

See the supplementary material for the crystallite size analysis in films of pentacene–tetracene, infrared and VIS spectroscopy data of mixed films taken at room temperature, and electron energy loss spectroscopy data of mixed films taken at 20 K.

The authors are grateful to Roland Hübel and Frauke Thunig for technical assistance and to Lukas Graf and Louis Philip Doctor for their assistance in the EELS experiments. The financial support by the Volkswagen Foundation for refugee Ukrainian scientists (No. 9C001) is acknowledged.

The authors have no conflicts to disclose.

Kateryna Hubenko: Data curation (equal); Formal analysis (equal); Investigation (equal); Writing – original draft (lead); Writing – review & editing (equal). Anncharlott Kusber: Formal analysis (supporting); Methodology (supporting); Writing – review & editing (supporting). Marco Naumann: Formal analysis (supporting); Methodology (equal). Bernd Büchner: Project administration (equal); Supervision (lead). Martin Knupfer: Conceptualization (lead); Data curation (equal); Formal analysis (equal); Project administration (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.