Two-Dimensional Di ﬀ usion of Excitons in a Perylene Diimide Monolayer Quenched by a Fullerene Heterojunction

: The structural and functional properties of organic heterojunctions play a vitally important role in the operation of organic devices, but their properties are di ﬃ cult to measure directly due to the buried interfaces that are typically formed. We have grown model heterojunctions consisting of two monolayer-thick organic semiconductors and used these bilayers to explore the two-dimensional dynamics of excitons. The heterostructures are formed by sequential deposition of monolayers of perylene-3,4,9,10-tetracarboxylic-3,4,9,10-diimide (PTCDI) and fullerene (C 60 ) on hexagonal boron nitride (hBN). The morphology of these bilayers was characterized using atomic force microscopy and showed clear di ﬀ erences in the C 60 growth kinetics on hBN and PTCDI. The variation in the ﬂ uorescence of PTCDI-C 60 heterostructures with increasing fullerene coverage showed a reduction in intensity consistent with exciton di ﬀ usion and quenching. We use a simple model for the intensity dependence to determine the two-dimensional exciton di ﬀ usion length in a PTCDI monolayer, ﬁ nding a value of 17 ± 3 nm for this parameter.


■ INTRODUCTION
Heterostructure formation by the sequential deposition of distinct molecular species represents a promising route to engineer the functional properties of organic devices as well as enabling the growth of model heterointerfaces. 1−6 Organic heterostructures are typically characterized at the molecular scale using scanning tunneling microscopy, and although this has been extremely successful, the requirement for conductive surfaces limits compatibility with subsequent optical measurements. 7,8 This motivates the formation of analogue heterostructures on insulating surfaces, on which both the morphology and functional properties of organic films may be measured and compared systematically. 9− 12 We have recently demonstrated that atomic force microscopy (AFM) can be used under ambient conditions to acquire images of molecules on an insulating surface with submolecular resolution, allowing the correlation of supramolecular order and optical properties. Specifically, we have shown that the fluorescence of monolayer (ML)-thick supramolecular assemblies formed on the hexagonal boron nitride (hBN) surface may be measured 13−15 and, in a separate study, that epitaxial supramolecular heterostructures may also be formed on hBN. 2 In this paper, we explore the fluorescence of model heterostructures formed by the sequential growth of monolayers of two organic semiconductors through the deposition of C 60 on preformed supramolecular arrays of perylene-3,4,9,10-tetracarboxylic-diimide (PTCDI), thus forming a bilayer heterojunction. The fullerene islands quench fluorescence, and we show that the dependence of emission intensity on coverage provides an insight into the transport of excitons within the PTCDI monolayer. This represents a lowdimensional analogue of experiments in which bulk heterostructures composed of a fluorophore and an exciton quenching layer, typically fullerene, are used to determine exciton diffusion lengths. 16−19 In our case, the geometry of the heterostructures allows the decoupling of exciton diffusion in different directions and we are able to measure the twodimensional diffusion length of excitons in PTCDI parallel to the molecular plane.

■ METHODS
Substrates were prepared using the scotch tape method to mechanically exfoliate hBN crystals onto a Si wafer on which a SiO 2 layer had been grown thermally, as described in our earlier work. 13−15 To deposit molecular films, clean substrates were loaded into a vacuum chamber (base pressure 10 −8 mbar) and annealed at approximately 450°C prior to the deposition of PTCDI and C 60 from two Knudsen cells, which were heated to 442 and 374°C, respectively. The deposition rate of each species was determined using a quartz crystal microbalance and calibrated from AFM measurements of thick films of each molecular species. The temperature of the hBN on SiO 2 substrates during growth was controlled using a type C thermocouple and a tantalum heating element. After deposition, the chamber was vented to nitrogen and samples were removed for characterization under ambient conditions using AFM and fluorescence spectroscopy.
To characterize the sample morphology, AFM measurements were carried out using the Asylum Research Cypher S atomic force microscope with Multi75AL-G silicon cantilevers from Budges Sensors. Fluorescence measurements were acquired using the HORIBA MicOS fluorescence spectrometer with a 405 nm delta diode excitation source. The pulse rate of the delta diode excitation source was 100 MHz, with a typical pulse width of 45 ps. The excitation source was used in combination with a clean-up (405 nm longpass) filter, which reduced the average power from its maximum (1.4 mW) to less than 100 μW. To eliminate the effect of optical interference in the photoluminescence intensity, with a more detailed description given in the Supporting Information (SI), all fluorescence measurements were acquired from few-layer hBN flakes, identified through their optical contrast on 90 nm SiO 2 substrates.

■ RESULTS AND DISCUSSION
The growth of both PTCDI and C 60 is carried out by sublimation in vacuum and studied using AFM under ambient conditions, as described above. Figure 1 shows the morphology of sub-monolayer coverages of each component molecule PTCDI (Figure 1a−c) and C 60 (Figure 1d,e). Figure 1c shows needlelike islands with monolayer height formed following the deposition of 0.3 monolayers (ML) of PTCDI on a hBN substrate held at 135°C. The average length and areal density of PTCDI islands were 6.4 ± 1.5 μm and 0.027 ± 0.008 μm −2 , respectively. High-resolution images show that PTCDI forms a canted packing structure with inter-(a 1 ) and intra-(a 2 ) row lattice vectors a 1 = 1.74 ± 0.10 nm and a 2 = 1.48 ± 0.10 nm subtended by an angle γ = 87 ± 2°(see Figure 1a,b), in agreement with the previous work. 14 In contrast to PTCDI monolayers grown on alkali-halide substrates, where molecular dewetting leads to a reorganization of the film structure, 20−22 PTCDI monolayers were found to be stable on hBN. The lateral dimensions of the islands show a strong dependence on substrate temperature; results for a range of substrate temperatures are shown in the SI.
At sub-monolayer (0.3 ML) coverage, when grown at room temperature, C 60 was found to form monolayer islands of irregular shape with second layers also observed (see Figure  1d). The presence of monolayers was confirmed by an island step height measurement of 0.8 ± 0.1 nm, corresponding to one monolayer. From high-resolution AFM images, C 60 was found to arrange in a hexagonal packing structure, with a lattice constant of 1.0 ± 0.1 nm, in good agreement with C 60 thin films deposited on both conductive and insulating substrates 23−26 (see Figure 1d inset). From large area AFM images, the average size and areal density of C 60 islands grown at room temperature were found to be 0.46 ± 0.07 μm and 2.9 ± 0.2 μm −2 , respectively. As the growth temperature of C 60 was increased, the size of monolayer islands increased while the island density decreased and at a growth temperature of 216°C only faceted bilayer islands were observed; see Figure  1e. Further results showing the dependence of the morphology of C 60 islands on coverage and substrate temperature are included in SI.
The transition from monolayer to bilayer C 60 islands has been reported previously in studies of growth on other insulating substrates. 21−24,27−31 However, the transition to bilayer growth occurs at a higher growth temperature (178°C) on hBN than on the alkali-halide substrates explored in the literature. The observed transition to bilayers at higher temperatures as well as the Arrhenius-type behavior of the island density discussed in the SI suggests that the growth of C 60 on hBN is kinetically limited. 22, 32,33 Having established the morphology of both PTCDI and C 60 on hBN, molecular heterostructures were formed by the sequential deposition of the two species. A 0.3 ML coverage of PTCDI was first deposited onto hBN substrates held at The Journal of Physical Chemistry C Article elevated temperatures (135°C) to form monolayer islands much larger than the typical interisland separation of C 60 on hBN; note also that these samples have exposed hBN between the PTCDI islands, allowing a direct comparison of the growth of C 60 on PTCDI and hBN. The substrate was then cooled to room temperature prior to the deposition of 0.3 ML of C 60 from a second Knudsen cell. The growth of C 60 on hBN and PTCDI is strikingly different (Figure 2a,b); the islands grown on PTCDI (marked by a blue arrow in Figure 2b) are of monolayer height but are much smaller and have higher areal density than those growing on the exposed hBN (marked by a green arrow). Specifically, the island density on PTCDI (45 ± 8 μm −2 ) was an order of magnitude higher than on hBN (4.7 ± 0.3 μm −2 ). Nevertheless, the overall coverage of C 60 was the same on the PTCDI monolayer and the surrounding hBN layer implying that the diffusion length of C 60 is small compared with the dimensions of the PTCDI islands.
The heterostructure islands in Figure 1b differ from the morphology previously observed for PTCDI and C 60 codeposited on calcium fluoride (CaF 2 ), where dewetting from the substrate leads to smaller multilayered PTCDI islands with more complicated island morphologies. 34 A significant difference in our work is the much larger, flat monolayer PTCDI islands that can be formed on hBN; these allow the kinetically limited growth of C 60 islands without a dominant contribution to nucleation from sites such as PTCDI step edges.
AFM images of PTCDI/C 60 heterostructures in regions close to PTCDI island edges (see Figure 2c) reveal a similar morphology to that in Figure 1, as indicated by the height profiles in Figure 2d,e, which confirms the monolayer height of C 60 on PTCDI (in Figure 2c,f,g, the upper left shows regions of C 60 growth on hBN whereas the lower right shows the PTCDI/C 60 heterostructure). Interestingly, the C 60 islands are present on both sides of the step edges of the PTCDI monolayer, with second layers of C 60 that appear to grow across the edge of the PTCDI island. In addition, as the C 60 thickness is increased, we observe many areas of the second layer C 60 . For a given coverage (e.g., Figure 2f), the second layers were more prevalent on islands growing on the hBN (Figure 2f upper left) than on PTCDI (lower right). This suggests that on the smaller fullerene islands formed on PTCDI, incident C 60 molecules may diffuse to the island edge and undergo thermally activated downward hopping; however, on the larger islands formed on hBN, nucleation of a second C 60 layer occurs. This implies that the diffusion length of C 60 on C 60 lies in the range of the typical island dimensions on hBN (460 ± 70 nm) and PTCDI (180 ± 20 nm).
To investigate the fluorescence of heterostructures, a set of samples were prepared with progressively thicker films (0− 0.92 ML) of C 60 overgrown on PTCDI (0.93 ML). The fluorescence of sublimed PTCDI monolayers was measured using a 405 nm pulsed excitation source (photon energy E ex = 3.06 eV, spot size ∼ 2 μm; see the SI). The spectra (Figure 3a) show a strong 0−0 peak at 2.208 ± 0.002 eV and a 0−1 satellite peak at 2.045 ± 0.002 eV, in good agreement with PTCDI films deposited on hBN from solution. 14 These peaks were clearly resolved in the spectra of C 60 -PTCDI heterostructures but with an intensity that progressively decreased with increasing coverage of C 60 . To eliminate errors due to optical interference, all fluorescence measurements were taken from few-layer optically thin hBN flakes, which were easily identifiable by the optical contrast of both the hBN flake on 90 nm SiO 2 and the adsorbed PTCDI monolayers (the dependence of the spectra on hBN flake thickness is discussed in the SI). Figure 3a shows spectra averaged over several thin hBN flakes. Errors due to misalignment of the PTCDI islands with the laser spot were avoided since the PTCDI islands could be resolved using optical microscopy (see the SI).
The peak intensity for varying C 60 coverage is shown in Figure 3b and does not follow a linear dependence, as might be expected were the PTCDI fluorescence simply quenched by the overlying C 60 islands. Instead, our data is consistent with an effective quenching area that exceeds the physical island size due to the capture of excitons that are excited remotely and then diffuse laterally to the boundary of the C 60 island. We approximate C 60 islands as nonoverlapping regular circles of The Journal of Physical Chemistry C Article radius, R = (C/πn) 1/2 , for a given surface coverage, C, and island density, n. The effective capture radius is therefore given by R + δ, where δ is the diffusion length. The fluorescence intensity, S, is therefore given by, S = S 0 (1 − πn(R + δ) 2 ). Figure 3b inset shows the expected linear dependence ((S 0 − S)/S 0 πn) 1/2 = R + δ, obtained by rearranging the intensity dependence above. The intercept of the linear fit corresponds to a diffusion length δ = 17 ± 3 nm (we have excluded the 0.93 ML coverage of C 60 when extracting our estimate for the exciton diffusion length since the model is not valid for coverages approaching 1 ML due to island merger).
It is interesting to compare the diffusion length determined from our analysis to the published value, 9.9 nm for PTCDI-C8, 17 an alkylated derivative of PTCDI. In this previous study, a PTCDI-C8 thin film was overgrown on quaterterrylene and excitons were quenched at the interface. This lower value may reflect the fact that excitons need to diffuse across a barrier formed by solubilizing alkyl chains to access the quaterterrylene interface. The three-dimensional structure adopted by molecules in this previous experiment results in a more complex coupling of electronic and vibrational modes and the associated π-stacked structures can lead to other possible excitations, such as charge-transfer excitons and excimers. These processes can influence both diffusion of excitons and the photoluminescence of organic crystals and thick films 35 compared with both isolated molecules and monolayers at interfaces. 10, 36 Interestingly, the structural organization inherent in the monolayers formed in our model heterostructures provides a route to decouple different modes of exciton diffusion; in the present case, the diffusion is parallel to the planes of the adsorbed molecules. Similar measurements for thin films of the closely related molecule perylene-3,4,9,10-tetracarboxylic dianhydride (PTCDA) 18,19 yield values of the diffusion length in the range 10−15 nm.
Our experiments do not provide direct information about the mechanism for exciton/charge transfer between PTCDI and fullerene, which results in quenching. However, in our experiments, we are able to confirm using AFM that PTCDI and fullerene molecules are nearest neighbors and so it is conceivable that ultrafast charge transfer between the highest occupied molecular orbital (HOMO) of the two molecules could be responsible for exciton quenching, 37 in addition to the Forster mechanism, which occurs due to exciton transfer. Such effects would require a favorable alignment of the molecular orbitals of both species, which is suggested by values available in the literature, 17,38−41 although it is important to note that these values serve only as a guide, since structural differences between isolated molecules, bulk crystals, and heterojunctions and molecules adsorbed on surfaces would be expected to lead to modest shifts in the energies of HOMO and lowest unoccupied molecular orbital levels (LUMO).

■ CONCLUSIONS
The formation of controlled heterostructures formed by the sequential deposition of monolayers of different molecular species opens up new directions in the research of the growth mechanisms of organic heterojunctions and their fundamental properties. The use of high-resolution AFM provides direct information about the molecular scale structure and growth of organic thin films of relevance to heterojunctions in organic devices and in this work has been used to determine the growth morphology of model interfaces that we show can be used to explore exciton diffusion in two dimensions. For the monolayer considered here, diffusion is parallel to the interface and the plane of the molecular π system; however, it is possible to envisage the formation of monolayers of molecules with an upright geometry, thus allowing a systematic study of the relationship of geometry and structural organization to exciton diffusion. We extract an effective length of 17 ± 3 nm, over which excitons within the PTCDI monolayer can migrate to the perimeter of C 60 islands. Although this extracted value is similar to those of other organic systems, it is noteworthy that the value we obtain is still relatively large given the lack of πstacking within the PTCDI monolayer. This work highlights the possibility of exploring exciton diffusion and quenching in a much wider variety of heterojunctions, including those based on semiconducting polymers of relevance to photovoltaic and light-emitting devices, and plan to explore these materials in our future work.

* S Supporting Information
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.9b01413.
Temperature-and coverage-dependent growth of neat films of PTCDI and C 60 on hBN, in addition to Arrhenius plots of the island area densities; data showing the effect of optical interference, arising from the thickness of the underlying hBN flake, on the fluorescence of PTCDI on hBN; AFM images of the morphology of C 60 /PTCDI heterostructures, from which island statistics were extracted and used in the interpretation of optical data (PDF) Figure 3. (a) Fluorescence spectra of PTCDI and PTCDI-C 60 heterostructures, (the coverage of PTCDI was maintained at 0.93 ± 0.05 ML) acquired from thin hBN flakes (<2 nm) were averaged over multiple flakes and are shown for a series of C 60 coverages up to 0.92 ML. (b) The total integrated count of the 0−0 peak of PTCDI (2.208 eV) was extracted from the Lorentzian fitting and is plotted against the absolute C 60 coverage measured using AFM. Taking island densities and coverages extracted from AFM images, the average island radius (C/nπ) 0.5 is shown plotted against the effective radius over which PTCDI is quenched (S 0 − S/S 0 nπ) 0.5 , from which an exciton diffusion length of 17 ± 3 nm was extracted under the assumptions stated in the main text ((b) inset).