Pentacene Crystal Growth on Silica and Layer-Dependent Step-Edge

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

Pentacene Crystal Growth on Silica and LayerDependent Step-Edge Barrier From Atomistic Simulations Otello Maria Roscioni, Gabriele D'Avino, Luca Muccioli, and Claudio Zannoni J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b03063 • Publication Date (Web): 19 Nov 2018 Downloaded from http://pubs.acs.org on November 22, 2018

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The Journal of Physical Chemistry Letters

Pentacene Crystal Growth on Silica and LayerDependent Step-Edge Barrier From Atomistic Simulations Otello Maria Roscioni,† Gabriele D’Avino,‡ Luca Muccioli,∗,† and Claudio Zannoni† Dipartimento di Chimica Industriale “Toso Montanari”, University of Bologna, Viale Risorgimento 4, I-40136 Bologna, Italy, and Institut Néel, CNRS and Grenoble Alpes University, 25 Rue des Martyrs, F-38042 Grenoble, France E-mail: [email protected]

∗

To whom correspondence should be addressed Dipartimento di Chimica Industriale “Toso Montanari”, University of Bologna, Viale Risorgimento 4, I-40136 Bologna, Italy ‡ Institut Néel, CNRS and Grenoble Alpes University, 25 Rue des Martyrs, F-38042 Grenoble, France †

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ACS Paragon Plus Environment


Abstract Understanding and controlling the growth of organic crystals deposited from the vapor phase is important for fundamental materials science and necessary for its application in pharmaceutical and organic electronics industries. Here this process is studied for the paradigmatic case of pentacene on silica by means of a specifically tailored computational approach inspired by the experimental vapor deposition process. This scheme is able to reproduce the early stages of the thin film formation, characterized by a quasi layer-by-layer growth, thus showcasing its potential as a tool complementary to experimental techniques for investigating organic crystals. Crystalline islands of standing molecules are formed at a critical coverage, as a result of a collective reorientation of disordered aggregates of flat-lying molecules. The growth then proceeds by sequential attachment of molecules at the cluster and then terrace edges. Free energy calculations allowed us to characterize the step edge barrier for descending the terraces, a fundamental parameter for growth models for which only indirect experimental measurements are available. The barrier is found to be layer dependent (approximately 1 kcal/mol for the first monolayer on silica, 2 kcal/mol for the second monolayer) and to extend over a distance comparable with the molecular length.

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The fabrication of efficient organic electronics devices often relies on the growth of nearly defect-free physisorbed thin films and epitaxial nanostructures of organic semiconductors by depositing molecules from a vapor phase on an inert inorganic or organic substrate. 1,2 Despite the important technological advances in the manufacturing of organic thin films, several open physical problems still stand out, namely the understanding of the initial steps of nucleation and growth, 3,4 the influence of substrate on the occurrence of crystalline polymorphs and on different forms of epitaxy, 5–7 the mechanism and magnitude of the diffusion of molecules on a crystalline surface, 8 the range of validity of kinetic growth theories originally developed for inorganic atom-by-atom growth, 9–11 and also the determination of the microscopic parameters appearing in those theories. 12 Among others, a very important concept is the Ehrlich-Schwoebel barrier (ESB), 13,14 the extra energy required for the deposited unit (atom or molecule) to overtake a terrace step. A low downward barrier favors a layer-bylayer growth, while a high one results in the growth of mounds with a progressive increase of surface roughness. 15 Unfortunately, the internal degrees of freedom and anisotropy of organic molecules make the picture more complicated with respect to inorganic systems, and recent studies hinted to a layer-dependent ESB, 16 and to the essential role of molecular conformation and orientation in decreasing the barrier. 12,17 In this letter, we investigate these issues by simulating the growth of pentacene on amorphous SiO2 , 1 by atomistic Molecular Dynamics (MD) simulations. With respect to most experimental techniques, MD provides the required sub-nanometric resolution, together with the possibility of evaluating related thermodynamic observables. Still, the computational approach is technically challenging, since nucleation and growth processes are often controlled kinetically, rather than thermodynamically, with the final outcome depending for instance on the deposition speed and temperature. 18,19 Moreover, the real timescales for nucleation and growth stand as major challenges to atomistic simulations. In the present work, we take advantage of our previous deposition studies 20,21 and robust force field parametrizations, 22,23 to address the growth of pentacene crystalline films on amorphous SiO2 with a

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non-equilibrium simulation scheme based on atomistic molecular dynamics. We simulated the growth of two complete monolayers of pentacene, monitored with the help of standard observables accessible from in-situ measurements, 24 such as coverage as a function of time, surface roughness and height, but also by visual inspection of the sample and by following the average tilt angle (see supporting information). The evolution of the layer coverage (Figure 1a) shows profiles which are characteristic of a quasi layer-by-layer growth, consistent with experimental measurements. 1,25 This scenario is confirmed by the very similar position of the steps in the plot of the maximum and minimum film height, and by the low value and typical undulations of the roughness 15 (Figure 1a,b). Roughening is not observed, in accord with experiments indicating it to occur at coverages exceeding four molecular layers (monolayers, ML). 25 Also, the coverage at which the growing island of the first ML (ML1) becomes an infinite 2D surface (in our case 0.85 and 0.75 for ML1 and ML2, respectively) is in accord with the percolation threshold of drain-source current measured in organic thinfilm transistors in real time during deposition (0.67-0.80 ML). 24,26 The overall agreement of the macroscopic growth parameters with literature results, on the one hand validates the simulation model, and on the other hand somehow conceals peculiar features of the growth that cannot be easily detected directly by standard characterization techniques. A first detail appearing upon observing the snapshots in Figure 1 is the presence of horizontal pentacene molecules between the silica surface and ML1. Following Werzer et al., 27 which found that the existence of such a layer was necessary for interpreting x-ray reflectivity measurements for the same system, we label the collection of these molecules “interface layer” (IL), although the thickness of the IL here is lower than the one reported in reference 27 (7–9 ˚ A). The existence of one or several wetting layers of flat molecules was reported in several studies, also for pentacene 28–30 and the insertion of organic ILs has been utilized as a technique to passivate or attenuate the interaction with metallic surfaces. 31 In our case molecules belonging to the IL cover only partially the silica surface, and we cannot exclude that the actual fraction of flat-lying molecules could be overestimated because of our unrealistically high deposition

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Figure 1: (a) Evolution of layer coverage of individual MLs. The interface layer (IL) consists of flat-lying molecules on the SiO2 surface. Molecules were assigned to the different layers on the basis of the off-plane position of their center of mass. (b) Maximum, minimum, average height and root mean square roughness of the pentacene film. Simulation snapshots after the deposition of (c) 750, (d) 1125, and (e) 1750 molecules. rate. Some molecules belonging to the IL are in fact able to diffuse on the bare surface, but become kinetically trapped below the growing ML1 terrace, while some others are immobile on specific positions on the silica surface. We suggest that these immobile IL molecules could play a role in the nucleation of ML1 on silica. Sadowski and coworkers ascribed the higher nucleation density for the first ML with respect to higher ones to a pentacene-layer interaction possibly stronger than the one with silica. 32 Our evaluation of such interactions is coherent with this picture, and gives an adsorption free energy of about 1±1 kcal/mol for a pentacene molecule on bare silica, and 9±1 kcal/mol on top of ML1. However, the silica surface has in our case a RMS roughness of about 2. ˚ A, higher than one of ML1 (0.7 ˚ A). The estimation of the nucleation density is currently out of the reach of atomistic simulations, but it is very interesting to determine the actual dimension of the critical nucleus, which

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conventionally is defined as the minimum size of a cluster that will become stable by adding one more particle, where the cluster is assumed to possess a structure similar to the one of the crystal. 15 Fitting the experimental distributions of island size with growth models typically yields to critical nuclei size of a few units for elongated rigid molecules like pentacene, sexiphenyl, sexithiophene. 11,25,33 Simulations reveal a more complex picture, which is exemplified by the snapshots in Figure 2. In fact, two types of nuclei can be identified: amorphous and partially diffusing aggregates, formed by flat-lying molecules with parallel orientation (Figure 2 a-c), with a critical size of 3-5 units, and a much larger crystalline one of standing molecules (Figure 2 d-e), actually constituting the initial seed of a growing island. The critical dimension of this second type of nucleus is monolayer-dependent (about 130 and 30 molecules for ML1 and ML2, see Figure 2 f and g), while the size of the first type is probably controlled by the energy barrier for surface diffusion (a video showing the formation of the first type of nucleus on ML2 is available as web-enhanced object), and by the deposition flux, as indicated by growth theories. 11 The transition from one type of nucleus to the other can be followed by monitoring the average tilt angle (Figure S1). In our simulation conditions ML1 forms upon the coalescence of a few close amorphous nuclei. After the formation of the ML1 island, a quick depletion of mobile flat-lying molecules in the neighborhood occurs (cf Figure 2 c vs d), while for ML2 the density of ”free” pentacene molecules outside the island is negligible. It is likely that with a more realistic (lower) deposition flux, the growth of both types of nuclei would be diffusion limited, and hence that each amorphous nucleus would generate an island, thus reconciling the experimental finding of very low critical sizes with the two-step growth process illustrated here. The two-step nucleation of crystalline islands appears to be a quite general mechanism for elongated π-conjugated molecules, as it was already observed in MD simulations of pentacene and sexithiophene on C60 , 20,21 and of small pentacene clusters on SiO2 . 34,35 A reorientation process, following the initial formation of a small nucleus of lying molecules, was also suggested for the vapor growth of para-sexiphenyl on the basis of simulated annealing force-field simulations, 36 and also by Monte Carlo simu-

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lations of model rod-like particles. 37 Moreover, an increasing number of experimental reports is appearing concerning two-step nucleations process for organic crystals in solution. 3,38,39 Our findings suggest that the two step model could possibly be extended to crystallization on surfaces by vapor deposition and adopted in the corresponding theories. (a)

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0 −20 −40 −60 −80 −80 −60 −40 −20 0 20 40 60 −80 −60 −40 −20 0 20 40 60 −80 −60 −40 −20 0 20 40 60 −80 −60 −40 −20 0 20 40 60 80 x (Å) x (Å) x (Å) x (Å)

Figure 2: Simulation snapshots highlighting the nucleation and growth of ML1 on the SiO2 surface (not shown), taken after deposition of (a) 250, (b) 300, (c) 350, (d) 400, (e) 450 molecules. In-plane positions of the centers of mass of pentacene molecules during the formation of a crystalline nucleus for ML1 (f) and ML2 (g). The color code indicates the number of neighbours (“bonds” in the crystallographic literature 15 ). The title annotation of each panel indicates the total number of deposition attempts and the number of molecules in the growing monolayer, classified according to the off-plane position of their center of mass. A snapshot of the crystalline aggregate formed on top of ML1 is given as an inset in the rightmost panel of (g).

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Table 1: In-plane experimental (room temperature) and simulated (MD, 300 K) crystal cell parameters for pentacene HT, 40 LT, 41 and TF 42 polymorphs; corresponding parameters from separate simulations of ML1, and ML2 on top of ML1, at 300 K. d is the interlayer spacing, calculated as the off-plane distance between the centroids of two subsequent monolayers. polymorph HT HT MD LT LT MD TF TF MD ML1 ML2

a (˚ A) b (˚ A) 6.27 7.79 6.14 7.79 6.06 7.90 6.00 7.90 5.96 7.60 5.91 7.61 5.97 8.07 6.14 8.17

d (˚ A) γ (deg) tilt (deg) 14.11 84.6 24.8 13.95 84.7 24.0 14.50 85.8 21.2 14.78 85.8 21.4 15.40 89.8 5.9 15.43 89.8 7.6 86.7 20.7 14.47 87.3 24.6

After the completion of the deposition, the sample was equilibrated at room temperature in order to characterize the structure of the two complete monolayers. The analysis of the intra-layer intermolecular distance distribution, N (x, y) (see Figure S6) reveals the presence of long-range order in both MLs, and allows the calculation of the two-dimensional lattice parameters. 21 Table 1 compares such lattice parameters with those of the most common crystalline polymorphs of pentacene, namely the two high temperature (HT) 40 and low-temperature (LT) 41 bulk forms, and the thin film (TF) phase. 42,43 The agreement between MD simulations and experiments for known polymorphs, within 2% for the lattice vectors, a and b, and the interlayer spacing d, quantifies the accuracy of the force field. The cell parameters obtained for the two MLs deposited on SiO2 are slightly different one from each other, and broadly consistent with those of the two bulk phases. The polymorphism of pentacene, especially when crystals are grown from vapor on amorphous SiO2 , is a longlasting issue that triggered much experimental 44–48 and theoretical work. 34,49–51 Most recent experiments showed that both TF and HT polymorphs can grow on SiO2 , with a layer-bylayer growth of the (metastable) TF phase at high rates, and a three-dimensional growth mechanism leading to the formation of the HT structure above a critical thickness of 30 ML. 48 Notwithstanding such a complex scenario, governed by phenomena characterized by

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length and timescales largely exceeding those attainable in our simulations, we emphasize that our high-temperature, high-rate of deposition simulations are able to correctly describe the layer-by-layer growth of the first MLs yielding a realistic molecular packing.

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Figure 3: Spacefill representation of the terrace edges (a, b), topographic maps (c, d), and free energy maps (e, f) for the displacement of a pentacene molecule across preformed step edges of ML1 (left panels) and ML2 (right panels).

The intermediate steps of the deposition protocol provide realistic morphologies of growing crystalline islands, which are employed in the following for the calculation of the step edge or Ehrlich-Schwoebel barrier. ESB has been rarely calculated so far for organic molecules, and most often through energy minimization techniques, whose results are limited by the arbitrariness of the molecular path chosen 12,17,52 and do not include entropic effects, 37 and therefore are sometimes contradictory or at variance with experiments. A paradigmatic case is that of sexiphenyl, for which the barrier is extremely sensitive to the tilt angle of the monolayer, going from 6 to 15 kcal/mol 12 for tilts of 43 and 17 degrees, respectively, 12 and for

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which a wide range of values is obtained by varying the calculation method. 12,17 The drawbacks of energy minimization schemes is overcome here by performing free energy driven MD simulations 53 at room temperature, in which a pentacene probe molecule is pushed by a biasing force to move across the steps without any further restriction on its pathway. The calculations were performed at terrace edges of ML1 and ML2, corresponding to the growth of pentacene on SiO2 (submonolayer coverage, Figure 3a) and of pentacene on ML1 (coverage between 1 and 2 MLs, Figure 3b). The results of this procedure are the maps shown in the panels e and f of Figure 3, representing the free energy landscape experienced by the pentacene probe molecule across the step edge. The vertical positions at which the free energy is minimized at a given x, y coordinate give instead rise to the topography maps (panels c,d). The free energy maps are clearly correlated with the topography, with two distinct regions above and below the step (left and right side of the maps, respectively). The minimum of the free energy is found near the boundary between the two regions and, as expected, corresponds to the lattice site at the step where the probe molecule would like to insert, contributing to the island growth. For ML1, we observe that the probe molecule gains 5-6 kcal/mol when reaching this favorable site from the top of the ML1 terrace (points at the very left of Figure 3c), while the stabilization is larger for molecules diffusing on SiO2 (points on the very right side of Figure 3c), confirming that the adsorption energy of pentacene is larger on ML1 than on silica. We note that, contrary to what discussed in reference 32, there not seem to be a (reorientation) barrier for approaching the step edge from the bottom layer: in other words, it is always possible to follow a path downward in energy towards the minimum moving from the right to the center of the maps. We conjecture that the slower growth of ML1 and the higher nucleation density reported for pentacene on silica with respect to higher monolayers 32 could be instead attributed to the larger roughness of the SiO2 potential energy surface with respect to the ones of the monolayers, which would hamper the diffusion of organic molecules, forced to undergo multiple trapping/detrapping steps.

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Figure 4: Plot of the average free energy versus the distance from the edge step for the center of mass of pentacene molecule moving either on top of ML1 (blue) or ML2 (red), highlighting the existence of a step-dependent energy barrier. Line widths correspond to standard deviations calculated along all different possible paths.

Displacing the probe molecule from the top monolayer towards its edge, an energy barrier is instead evident in both MLs. This is indeed the step edge ESB barrier, which determines the downward rate of pentacene molecules and the growth mechanism itself, and it is represented in a more concise way in Figure 3b, where all possible different pathways in Figure 3a and Figure S7, corresponding to additional sampling regions, have been averaged and plotted versus the distance of the molecular centroid from the step edge. Two main fundamental pieces of information arise from this analysis: the first is that the barrier is not sharp but it extends inside the terrace, over a distance comparable with the molecular length; conversely, the energy drops very quickly after reaching the maximum value. The second insight concerns the magnitude of the barrier, which is clearly layer-dependent and amounts to approximately 1.3 kcal/mol for ML1 and 2.2 kcal/mol for ML2. We attribute this increase, observed also experimentally for di-indenoperylene, 16 to the rougher topography of the silica surface with respect to ML1, which translates also into a higher positional disorder at the terrace edge, and finally to a less sharp and well defined barrier. Concerning the ESB for pentacene on pentacene, the value here predicted for ML2, ∆G =2.2 kcal/mol for ML2, is as expected lower than what obtained by Clancy and coworkers with more constrained computational

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schemes (6-7 kcal/mol 17 ), and in good agreement with the value of 1.6 kcal/mol obtained by Malliaras and coworkers by fitting real-time X-ray scattering spectra with a distributed growth model. 54 Actually in reference 54, the above-mentioned barrier was obtained for the third monolayer and upwards, with undetermined values for ML1 and ML2; similar outcomes were reported for indenoperylene. 16 These findings suggest that for the first few monolayers, notwistanding the abundant evidences of a quasi Stranski–Krastanov type of growth for pentacene, 55–58 and then of the existence of a non-zero ESB, the experimental determination of the barrier is particularly challenging. Our unbiased free-energy simulations offer then a valuable and independent estimation of this important growth parameter, with magnitudes consistent with the observed layer-by-layer growth. Summarizing, the molecular resolution provided by MD simulations allowed the observation of specific features of the growth of pentacene on amorphous silica. A first one is the presence of an interface layer of molecules lying flat below the first crystalline monolayer. This layer does not cover uniformly the substrate and is composed of immobilized molecules that are positioned on surface sites with high interaction energy. Indeed the SiO2 potential energy surface, albeit less attractive for pentacene molecules with respect to the one of the first monolayer, is rougher and favors molecular trapping. Another important observation is that the formation of crystalline islands develops in two separate nucleation and growth steps: in the first, long-living, partially diffusing aggregates of a few flat-lying parallel molecules form and grow. In the second step, occurring at a critical size which is layer and substrate dependent (about 100 and 30 molecules for ML1 on SiO2 and ML2 on ML1, respectively), a lying-to-standing transition occurs, accompanied by the onset of crystalline order; after that, the growth proceeds via attachment of incoming molecules at terrace edges as in standard nucleation and growth models. These observations then call for a refinement of such models which were originally derived for simpler atomic systems, in which shape anisotropy and flexibility are irrelevant factors. Free-energy calculations were employed to measure the kinetic barrier for the descent of realistic step edge morphologies obtained from MD

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deposition simulations. We found that, much as for the critical nucleus size, the step edge barrier is remarkably layer-dependent and connected to the positional order at the terrace step, with higher order giving rise to a larger barrier. The overall agreement obtained with available experimental data for pentacene suggests that the proposed methodology could be successfully applied to other organic materials, also in a predictive perspective. Molecular dynamics simulations of crystal growth can indeed provide microscopic information that is hardly accessible experimentally and contribute to the design of improved growth models faithfully describing the fascinating process of organic crystal growth.

Computational Methods All Molecular Dynamics simulations were run with the open source program NAMD 2.11, 59 at constant volume and temperature, and adopting 3D periodic boundary conditions both for slab and actual 3D geometries. Pentacene was deposited on a 15 × 15 nm2 silica surface, at the rate of one molecule every 250 ps, closely following the non equilibrium scheme described in reference 21. The deposition simulation was performed at a temperature of 500 K, a value that is considerably higher than those normally employed in deposition experiments, but well within the range of thermodynamic stability of solid pentacene. The high temperature was purposefully adopted as a mean to speed up molecular motion, in order to compensate for the unrealistically high deposition flux and to allow the observation of nucleation and growth in a time scale accessible to atomistic simulations. SiO2 was modeled with the CLAY force field, 60 while pentacene with the generalized AMBER force field 61 and ab initio atomic charges; 22 standard Lorentz-Berthelot mixing rules were used for Lennard-Jones interactions. The free energy landscape experienced by a pentacene molecule in the proximity of step edges was calculated at 300 K with the adaptive biasing force (ABF) algorithm. 53 Adsorption free energies were calculated with a very similar scheme, on portions of the silica and ML1 surfaces with dimensions of 2 × 2 nm2 . Detailed computational procedures are provided in

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the Supporting Information.

Acknowledgments We are indebted to Aldo Brillante, Raffaele Della Valle, Elisabetta Venuti, Cristiano Albonetti, Tobias Cramer, Adolf Winkler, Frank Schreiber and Yoann Olivier for stimulating discussions and suggestions. We acknowledge CINECA Supercomputing Center for granting resources through the ISCRA project “GrowPTF” (HP10BIO07Y). The research leading to these results has initially received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement n. 212311 of the ONE-P project and n.228424 of the project MINOTOR. We also thank MIUR-PRIN 2015XJA9NT (Molecular Organization in Organic Thin Films via Computer Simulation of their Fabrication Processes) for further financial support.

Supporting Information Extended computational details; evolution of the tilt angle during the deposition; IL, ML1 and ML2 center of mass positions as a function of the number of deposited molecules; comparison of the positional order in ML1 and ML2 with simulated pentacene polymorphs; in-plane radial distribution of molecular centers of mass for ML1 and ML2; free energy and topography maps for two additional step edges of ML1 and ML2; example of NAMD collective variable input file for the free energy scan; movie of the formation of a crystalline nucleus on the ML1 surface at 400 K via diffusion of pre-deposited molecules.

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Pentacene Crystal Growth on Silica and Layer-Dependent Step-Edge

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