Substrate-Dependent Morphology and its Effect on Electrical Mobility

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Substrate-Dependent Morphology and its Effect on Electrical Mobility of Doped PEDOT Thin Films Juan Felipe Franco-Gonzalez, Nicolas Rolland, and Igor V. Zozoulenko ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b08774 • Publication Date (Web): 02 Aug 2018 Downloaded from http://pubs.acs.org on August 5, 2018

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ACS Applied Materials & Interfaces

Substrate-Dependent Morphology and its Effect on Electrical Mobility of Doped PEDOT Thin Films. Juan Felipe Franco-Gonzalez†, Nicolas Rolland and Igor V. Zozoulenko*. Laboratory of Organic Electronics, Department of Science and Technology, Linköping University, SE-601 74 Norrköping, Sweden. KEYWORDS: PEDOT, Computational Microscopy, Molecular Dynamics Simulations, Thin Films, Electrical Mobility, Silicon, Substrate, Graphite ABSTRACT: Deposition dynamics, crystallization, molecular packing, and electronic mobility of poly(3,4ethylenedioxythiophene) (PEDOT) thin films are affected by the nature of the substrate. Computational microscopy has been carried out to reveal the morphology-substrate dependence for PEDOT thin films doped with molecular tosylate deposited on different substrates including graphite, Si3N4, silicon and amorphous SiO2. It is shown that the substrate is instrumental in formation of the lamellar structure. PEDOT films on the ordered substrates (graphite, Si3N4, silicon) exhibit preferential face-on orientation, with graphite showing the most ordered and pronounced face-on packing. In contrast, PEDOT on amorphous SiO2 exhibits the dominant edge-on orientation, except in the dry state where both packings are equally presented. The role of water and the porosity of the substrate in formation of the edge-on structure on SiO2 is outlined. Based on the calculated morphology, the multi-scale calculations of the electronic transport and percolative analysis are performed outlining how the character of substrate affects the electron mobility. It is demonstrated that good crystallinity (PEDOT on graphite substrate) and high content of edge-on (PEDOT on SiO2 substrate) are not enough to achieve the highest electrical in-plane mobility. Instead, the least ordered material with lower degree of the edge-on content (PEDOT on silicon substrate) provides the highest mobility because it exhibits an efficient network of π-π stacked chain extending throughout the entire sample.

1. Introduction Morphology of semiconducting polymers is considered to be a decisive factor determining the performance of thin film devices. 1 Morphology is given by the molecular orientation within the thin films, crystalline order and crystal sizes of the semiconducting material. These morphology aspects influence the energetics and physical properties of the system. For example, optoelectronic properties are very sensitive to the solidstate arrangement;2-3 charge generation, exciton diffusion and local charge transport are affected by the crystalline lattice organization;4 and, formation of amorphous regions can act as barrier or traps in charge transport.5 These features can be controlled by the manufacture protocol where the postprocessing of thin films is mostly dominated by the choice of a washing solvent, polymer additives, deposition method, (e.g. spin-coating, spry-coating, drop-casting) and substrate treatment. 1, 6 The substrate, for instance, can be functionalized, solvent/doping treated or temperature treated.7 In addition, the substrate leads to the formation of a specific motif of molecular packing of the polymer on the interface with the substrate (i.e. edge-on or face-on orientations). This molecular packing might be different to the one in the bulk of the film.8-9 It has been proven that the dielectric chemistry of the surface of the substrate strongly affects the alignment of n-type organic semiconductor polymers.10 The authors showed that the orientation of the polymer changes with a variation of the dielectric

surface on the substrate, where, in most of the cases a mixture of unit cell orientations in the polymer are obtained. However, very little is known about the influence of the solid lattice ordering and molecular characteristics of the substrate on the polymer orientation. With this respect, the role of the substrate is instrumental to achieve the features of the morphology of the thin film leading to the high values of conductivity which is important for the device applications. It is recognized that different synthesis procedures lead to different morphologies on the thin films. For example, crystalline polymers can be obtained by vapor phase polymerization whereas more amorphous polymers are obtained by both the traditional chemical oxidative synthesis and by electropolymerization.11-12 However, the post-treatment methodology used after the synthesis significantly affects the morphology.13 One of the most known and studied organic semiconducting polymers is poly(3,4-ethylenedioxythiophene) (PEDOT). 14-15 Some of the reasons for that are that thin films of doped PEDOT can be used in a various applications such as biosensors,16 implantable drug delivery devices, 17energy storage,18 thermoelectronic devices19-20 and supercapacitors.21-22 Regarding the morphology of PEDOT thin films, Aasmundtveit and et. al wrote in 1999 “The actual mechanism behind the preferred orientation is not yet known”.23 Nevertheless, even

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though the enormous amount of data has been published and a big advance has been achieved since then to measure and characterize the morphology and dynamics of semiconducting polymers in thin films, the interactions involved in the deposition of the polymeric material on the substrate and its molecular packing are still unclear. Yet, many studies report conflicting models for the PEDOT morphologies which are not always consistent with each other references.24-25 Nowadays, X-ray-based techniques such as GrazingIncidence Wide-Angle X-ray Scattering (GIWAXS), WideAngle X-ray Scattering (WAXS) and Small-Angle X-Ray Scattering 1, 26-27 as well as X-ray photoelectron spectroscopy (XPS)28-29 have become a popular tool to characterize the interface of the polymeric thin film and the substrate. These techniques are however limited to both nanoscale-size and time-scale of milliseconds. This makes it difficult to provide a detailed structural and dynamics information on these heterogeneous interfaces. Due to this reason, computational techniques are used when experimental techniques cannot reach specific resolution on length- and/or timescale. Therefore, in order to reveal the interactions involved in the molecular packing hidden in the experimental data, Computational Microscopy is currently emerging as the powerful technique to uncover the interactions involved in thin film organization. 30-33 Computational microscopy is considered as in silico microscopy because it is able to describe by classical molecular dynamics (MD) simulations the molecular organization that are not accessible using any experimental microscopy. Due to this it has been widely accepted as a powerful tool that can complement available experimental techniques such as the above mentioned GIWAXS and XPS as well as Atomic Force Microscopy (AFM) and Transmission Electron Microscopy (TEM).31 A computational microscopy of the crystallization of doped PEDOT under water evaporation from the solution to the dry phase has been recently performed by the present authors, where the effect of the intrinsic features of PEDOT (e.g. chain length, oxidation level, solvent content)34 and the type of counter-ion35, and ionic diffusion36 were evaluated. These studies addressed the crystallization in the bulk, and therefore the effect of the substrate on the morphology of the thin film still remains unexplored. In this work, we study the effect of the substrate on the morphology and electrical mobility of PEDOT doped with Tosylate (PEDOT-TOS). We start with the polymeric material dissolved in the solvent (water), then drop-cast the polymer solution onto the substrate and evaporate the solvent until the dry thin film is reached. Based on the simulated morphology, we then perform multi-scale calculations of the electronic transport, outlining how the character of substrate affects the thin film morphology, which, in turn, impacts the electron mobility. We believe that the findings reported in the present work provide the essential atomistic insight (not achievable by conventional experimental means), revealing the effect of the substrate on molecular packing and molecular mobility, which will help to guide the material design for better device performance. 2. Results In this work, we study in situ the structure and dynamics of the crystallization of PEDOT-TOS in the presence of the substrate throughout the water evaporation at 100ºC. This section

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is organized in such a way that all the phenomena that occur simultaneously in the polymeric matrix as water evaporates from the polymeric solution throughout the dry thin film, are revealed and discussed. They are: (1) deposition of PEDOT chains onto the substrate; (2) π-π stacking and formation of nano-crystals of PEDOT; (3) promotion of specific alignment and orientation of PEDOT chains on the surface of the substrate; and (4) coordination of TOS molecules to PEDOT chains as water evaporates and interact with the substrate. Finally, the electrical mobility is calculated and discussed in terms of the final molecular packing of PEDOT on the substrate. 2.1. Deposition of PEDOT The deposition of PEDOT-TOS onto a 10 × 10 nm-size substrate can be followed as water evaporates throughout the snapshots in Figure 1b-e for each type of substrate. We consider four different types of substrates often used in PEDOT manufacturing, including graphite, Si, Si3N4 and SiO2. The first three represent an ordered periodic lattice, whereas the last one is amorphous. The entire simulation time is 120 ns. The buried area of the surface of the substrate (i.e. the area where the polymeric chains are in direct contact with the substrate) increases as water evaporates (See Figure 1a). In the dry film, graphite and Si3N4 are buried around 99% whereas the buried area is lower for Si and SiO2 (91% and 80% correspondingly). Different rates of PEDOT deposition are observed for each type of substrate throughout the water evaporation, and defined in terms of the percentage of the buried area as water evaporates.(See SI for the definition of the buried area). The deposition rate of PEDOT is ranked in decreasing order as follows: graphite, Si3N4, Si and SiO2. A strong interaction of the polymer particles with graphite as compared to silicon-based substrates leads to the highest buried area for the graphite substrate in comparison to Si and SiO2. Graphite, which is composed by four layers of graphene supports the ππ interaction with PEDOT chains, while this is not the case for silicon-based substrates where such the interaction is absent. The differences in the deposition rate between silicon-based substrates, Si3N4, Si and SiO2 is explained as follows: SiO2 is amorphous and porous and therefore, it is capable to adsorb water into the substrate and then it delays the deposition of PEDOT chains (For the illustration see Fig. S2 in SI showing the formation of the water layer on SiO2 interface; see also Sec. 2.4 for further discussion of the role of water). Si promotes a slower deposition rate than Si3N4 because the columbic interactions are higher for the latter. (Note that in contrast to Si3N4, point charges at each atom in Silicon are equal to zero). For various material and device applications, these aspects of the PEDOT deposition shed a light on the manufacturing process of the thin film when both rate and efficiency of the PEDOT deposition need to be controlled. 2.2. Crystallization and crystal sizes of PEDOT Crystallization of PEDOT chains into π-π stacked crystallites takes place already at early stages of water evaporation, see Figure 1. The π-π crystallites are formed in the polymeric solution and remain stable all along the evaporation process until the film reaches the dry phase. Figures 2 a-d show the X-ray diffraction patterns (XRD) calculated for the simulated


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morphologies at each evaporation step for every type of the substrate. The XRD patterns exhibit a sharp peak in the range of q = 1.75-1.80 Å-1 at all evaporation stages, which signifies the presence of π-π stacking between PEDOT chains. The value of the vector qπ-π decreases as the water evaporates, which is consistent with the GIWAXS measurements of Palumbiny and et al. for PEDOT-PSS for the case of pure water. 37 By using the relation = 2/, the π-π distance dπ-π is calculated from the XRD patterns and reported in Figure 2e. For all the substrates, dπ-π increases as water is evaporated, which we attribute to the decrease of the electrostatic screening due to water molecules, which apparently affects the vander-Waals interaction between PEDOT chains. It is interesting to note that dπ-π is practically the same (within the standard deviation) for graphite, Si3N4, and SiO2, and the decrease of dπ-π is rather small (1-2% difference between the dry samples and samples with 59% w.t.). The size of the π-π stacked crystallites, L, at each evaporation step can be calculated using the Scherrer’s equation38 = 2/∆ , (1) where K ≈ 0.93 is the shape factor and ∆q is the full width at the half maximum of the π-π peak. To extract ∆q a Lorentz fitting was applied at each evaporation step. Figure 2f shows that the π-π crystals size decreases from the polymeric solution to the dry thin film, where a value of L/dπ-π ≈ 3 in the dry face is observed for all the substrates, which corresponds to 3 π-π stacking distances (i.e. 4 stacked chains in a crystallite, and about of 1.1 nm-size). Interestingly, the crystallite size L exhibits different behavior as a function of water content for different substrates. For Si3N4, the L remains constant all along the water evaporation, and for SiO2 it monotonically decreases. For the hydrophobic substrates (graphite and Si) the crystals size L first increases as water evaporates to 26 %w/w and then starts to monotonically decrease until a dry phase is reached. It can be also noted that for the case of Si3N4 the π-π stacking peak intensity decreases as the water is evaporated, which represents an opposite trend as compared to other substrates. It is difficult to pinpoint the exact reason for the abovementioned features including the dependence of dπ-π and L on water content and the substrate type (especially taking into account that the effects at hand are rather weak). Indeed, these features can be a result of a subtle interplay of a number of factors including the difference in the crystallinity/hydrophobicity of the substrates, the difference in water and counterion distribution, the difference in lamellar structure, just to mention a few. The formation of the nano-structure, namely, lamellar structure of PEDOT,1 is evidenced by the formation of the corresponding peak of the 100 reflection (from the h00 family). According to Aasmundtveit et. al.23 100 reflection corresponds to the perpendicular direction of PEDOT backbone (c-axis) (q100=0.45 A-1) (i.e. the direction perpendicular to a plane of PEDOT crystallites). For all the substrates, the corresponding q100 peaks increase as water evaporates (corresponding to the decrease of the real space distance between crystallites). This is expected since PEDOT chains get close to each other as water is removed. The size of the nano-crystals in the lamellar direction, L100, is evaluated by the Scherrer’s equation in the same way as it was done above with the Lorentz fitting and showed in Figure 2g. L100, is increased as the film reaches its

dry phase and it is different for different type of substrates. Graphite and Si3N4 promote the largest structures while silicon promotes the smallest ones. The dynamics of the formation of the nano-structure shows fluctuations in the lamellar size (larger standard deviations) at higher values of solvent content until the solvent content of 4 %w/w is reached and the lamella size L100 is stabilized. However, in all the substrates, during the thin film formation there is an increase of the L100 value until some particular solvent content is reached and after then, it reaches saturation. The lamellas can grow while the polymer material is embedded into the solvent. Once the solvent starts to be at lower proportion than the polymer, a structural rearraignment occurs leading to the decrease of the lamella size. It is remarkable that the formation of the lamella structure is strongly enhanced in the presence on the substrate, while the lamella structure is very weak when the substrate is absent as shown in the previous studies on the bulk of the thin film.34-35, 39 Hence, one of the important conclusion of the present study is that the presence of the substrate is instrumental in formation of the lamellar structure. Last but not least, a broad shoulder around q*=1.25 Å-1 is exhibited at all the XRD patterns in each substrate (marked as * in Figures 2a-d). This shoulder is also observed in the experiments and is attributed to the amorphous halo40 in PEDOT due to the local structural disorder which is an indication that the samples are amorphous. This is the reason why only the 100 reflection is seen in the XRD and not any other k’s of the family h00. 2.3. Molecular Orientation: face-on vs edge-on In this section we discuss the molecular orientation of PEDOT crystallites on the substrate, i.e. face-on vs edge-on. In order to measure and quantify the orientation of PEDOT chains, the angle between the normal of the plane of thiophene ring with the z-axis, φ, was calculated together with the distance of the geometric center of the thiophene ring to the surface of substrate, Z (see Figure 3a). Figures 3b-e show the evolution of the probability distribution function P(φ) along the evaporation process for graphite, Si3N4, Si and SiO2 respectively. The peaks in the distribution of P(φ) close to 0 o correspond to the face-on orientation, whereas those at higher φ closer to 90o corresponds to the edge-on one. For the case of graphite an unimodal distribution P(φ) is centered at φ=10º along the evaporation process until the dry phase is reached. For the dry phase the peak in the P(φ) is the most narrow and most pronounced in comparison to all other substrates. This is an indication that graphite promotes the most ordered and crystalline PEDOT with most chains in the face-on orientation (See Figure 3b). For the case of Si3N4 the distribution P(φ) in a dry phase shows a broad peak 10 ≤ φ ≤ 30º which corresponds to the face-on orientation, which is apparently not that pronounced as in the case of graphite. For silicon PEDOT does not seem to have a preferential orientation as water evaporates where several orientations are exhibited. In the dry phase the broad distribution of angles 0 ≤ φ ≤ 50º reveals that PEDOT on silicon does not exhibit welldefined preferential orientation. There are however some crystallites in the well-defined face-on orientation which is revealed by a peak around φ=10º. And finally, amorphous SiO2 in a dry phase shows a bimodal P(φ) distribution around angles φ=20º and φ=80º, which means that SiO2 promotes both



face-on and edge-on orientations. Additionally, it exhibits a face-on orientation which is less parallel to the surface in comparison to other substrates. This can be attributed to the porosity of the substrates and non-ordered character of the surface of the SiO2 substrate. Figures 3f-i show the probability distribution, P(φ, Z) for the Z-dependent orientation of PEDOT chains at two different solvent contents. The value of the P(φ, Z) increases as PEDOT gets closer to the substrate and P(φ, Z) shows pronounced peaks in the vicinity of the substrate (Z ≈1-2 nm). This means that a high population of PEDOT chains are well ordered when they are close to the substrate. Our findings therefore indicate that the preferential orientation in the PEDOT thin film introduced by the substrate is maintained over a rather short distance close to the surface. Farther away of this distance this preferential orientation is lost. Note that the thickness of the PEDOT film deposited on the substrate is 3-4 nm as can be easily seen in Figure 4a-d that shows the electron density in polymeric chains. Note also, Z-dependent orientation of PEDOT chains can be different at different solvent contents. For example, for silicon the thin film is more amorphous in the dry phase than e.g. at 15% w.t, see Figure 3h. For the case of SiO2, the edge-on orientation is completely dominant for a hydrated thin film, while for the dry face both phases are equally present, see Figure 3i. 2.4. Role of water and TOS molecules In this section, we focus on the role of water in the mechanism behind the molecular packing of PEDOT onto the substrates during the deposition process. Figure 4a-d shows the partial electron density profile along the z-direction for PEDOT at each evaporation step. Most of the substrates exhibit pronounced peaks at multiple integer values of π-π stacking distance, dπ-π, from the surface of the substrate (indicated by dashed lines), which is attributed to the presence of the faceon motif. This is not the case on SiO2, where a mixture of both edge-on and face-on orientations is obtained and therefore, the π-π multiple peaks for the PEDOT density are much less pronounced. In addition, the density of PEDOT decreases along z direction as indication of an inhomogeneous distribution of PEDOT in the thin film. The distribution of the TOS molecules as a function of the distance from the substrate is showed in Figures 4e-h. As expected, the density distribution of TOS follows the one of PEDOT, c.f. Figure 4e-h and Figure 4a-d. For the substrates that support preferential face-on arrangement (graphite, Si3N4 and silicon), for each π-π staking on PEDOT in the vicinity of substrate there is a corresponding peak in the TOS distribution. It is interesting to note that TOS molecules coordinate with PEDOT chains by one TOS molecule for one monomer unit of PEDOT (see Figure S1). SiO2 shows three main peaks at the distances corresponding to the lamella spacing, de,T. This is due to the edge-on packing supported by SiO2 as discussed in the previous section (see the schematic illustration in Figure 4). The distribution of water molecules as a function of the distance to the substrate during evaporation steps is shown in Figures 4i-l. It exhibits a different behavior for different substrates. Graphite exhibits the lowest water densities close to the substrate. This is expected due to its hydrophobic nature. The distance between the surface of the substrate and the first

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layer of water is smaller on the hydrophilic substrates, Si3N4, and especially SiO2. The latter exhibits the peak closest to the substrate with the greatest intensity as compared to other substrates. It is attributed to the capability of this substrate to adsorb water due to its high porosity. (The porosity of substrates is presented in Table S1 in SI). An evolution of the water distribution in polymeric films during evaporation in shown in Figure 4 i-l. For the case of SiO2, the water is accumulated close to the surface, whereas for other substrates water is largely distributed in the bulk of the polymeric film (especially for hydrophobic surfaces of graphite and Si). A snapshot showing water accumulated on the SiO2 surface is presented in Figure S2 in SI. The distance between the first water density peak and the second one on SiO2 corresponds to the lamella periodicity distance, de,W, associated to the edge-on orientation of PEDOT on this substrate. It can be noted that the first water peak is located at shorter distance to the substrate than the first layers of PEDOT. The second peak is located at Z=1.2 nm which means that it is located between two 100 edge-on planes of PEDOT as schematically shown in the inset to Figure 4. It also coincides with the second maximum of the TOS-peaks and the deepest valley in PEDOT density profile. Based on these insights, we attribute the formation of the edge-on configuration on SiO2 substrate (as opposed to face-on formation on other substrates) to the effect of water and the high porosity of SiO2. Indeed, the face-on configuration arises due to interaction between the p-orbitals in the polymeric chains and the atoms of the substrate. For a highly porous SiO2, water penetrates between the PEDOT and the substrate, thus screening the interaction. Taking into account a highly hydrophobic nature of PEDOT chains, this apparently prevents a formation of the face-on configuration and hence promotes the edge-on arrangement. To our knowledge, there are no any systematic experimental studies of the effect of the substrate on the molecular packing of PEDOT thin films (i.e. edge on vs face on). Most available experimental studies of PEDOT-TOS reporting the GIWAXS measurements (where the character of the molecular packing can be extracted from) have been done for glass substrates; 19 and silicon substrates35, 41 (note that glass mostly consists of SiO2, and a surface of silicon wafer is covered by amorphous SiO2 layers). This is consistent with our simulations which predict a preferential edge-on orientation for the SiO2 substrate for a not completely dry state. (Note that it is expected that even nominally dry PEDOT films would contain some amount of water). We hope that our calculations will motivate systematic experimental studies addressing the effect of different substrates on character of molecular packing. 2.5. Electrical Mobility on dry Thin Film Figure 5a shows the distributions of the in-plane electrical mobility P(µ) calculated for each substrate (these distributions accumulate results from the different MD frames, disorder realizations and field orientations). According to this plot, mobilities follow a log-normal distribution (i.e. the distributions appear as Gaussian distributions in the µ log-scale plot). Interestingly, Strelniker et. al. 42 have shown that in a simple hopping percolation model the distribution of resistivity P(ρ) evaluated on systems of a given size L can be approximated by a log-normal form where the mean resistivity is independent of the size and where the variance is inversely proportional to


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L.42 Although the hopping model used in the present work is more complex than in their study, one can nevertheless expect that the mean values of the mobility distributions is representative of an infinite system. It is thus relevant to discuss the mobility differences between substrates in term of the mean values (dashed lines), even if the standard deviation of the distributions is significant due to the small system sizes studied herein. The results showed that the highest electrical mobility is obtained for silicon substrate, followed by in decreasing order by SiO2, Si3N4 and graphite substrates. In order to understand the obtained results let us first correlate the relative mobility and the relative crystallinity (see Figure 5b). The relative crystallinity for each substrate was calculated from the XRD patterns as the maximum intensity at the 100 reflection peak (i.e. at the lamella peak) with respect to the one for graphite (I100(substrate)/I100(graphite)). Graphite was chosen as the reference substrate because (a) it shows the highest 100 reflection peak in the XRD patterns (see Figure 2) and (b) it promotes the most ordered and homogenous molecular packing as discussed in the previous sections. Figure 5b shows that the mobility is increased linearly as the relative crystallinity is reduced. In previous experimental works, 19, 43 it was reported that the mobility increases with the crystallinity. However, in these works, the crystallinity was related to the content of the edge-on configuration. Based on that, we calculate in this work the proportion of thiophene rings in edge-on configuration, f(ϕ> 45°) by integrating the range of P(φ > 45°),

> 45° = ∑ ∑ . The dependence of the mean mobility on f(ϕ> 45°) is shown in Figure 5b. Graphite is the most crystalline but the one with the lowest content of edge-on and therefore with the lowest mobility. Indeed, it is the edge-on configuration that promotes the in-plane mobility because of the possibility of the effective π-π coupling, see the percolation analysis below for more details. SiO2 corresponds to the highest content of edge-on which results in the high inplane electrical mobility as expected. The highest in-plane mobility is however for silicon. Even though it does not have the highest content of the edge-on configuration (see Figure 3d,h), it promotes the apparition of a rather disordered polymer phase (lowest crystallinity) with more uniform distribution of orientations of the chains (homogeneous color map in Figure 3h, 0% w.t.), which supports the effective coupling between the chains. Thus, it is the interplay between the amorphicity and the content of the edge-on orientation that produces the highest in-plane electrical mobility value. Further insight into mobility-morphology dependence for different substrates can be obtained from the percolation- and transfer integral analysis introduced in our previous study of the mobility in bulk PEDOT.44 Figure 5c shows the percolations curves and the transfer integral distributions, P(|H|), in the dry phase for different surfaces, giving the probability of finding the transfer integral with a given value |H|. From right to left, the distributions exhibit one well-defined peak at high transfer integral values (denoted as “A”), corresponding to two chains in π-π stacking. Obviously, these two chains can be part of the same very well defined crystallite, as depicted in the inset to Figure 5c, but they can also be part of a rather amorphous phase provided that a few of their monomers are well aligned. Then a broad distribution of intermediate transfer integral values (denoted as “B”) corresponding to misaligned chains, that can be associated with amorphous part of the thin film as well, or grain boundary between two crystallites (see

the inset to Figure 5c for illustration). Finally, there is a third peak (denoted as “C”) corresponding to a double π-π stacking distance, that is actually not contributing to the transport (because short-circuited by the direct π-π stacking). These distributions provide a global, averaged information over the material and its crystallinity, rather similar to the structural information provided by XRD patterns. Graphite for instance, which is the most ordered thin film, shows a π-π stacking peak A centered around slightly higher values of the transfer integral than other substrates (because mainly due to very welldefined crystallites with perfect π-π stacking), and a low “amorphous” contribution (peak B, mainly due to grain boundaries between crystallites). As such, one would be tempted to predict a high mobility for this material since the hopping rate between the chains is proportional to the transfer integral. However, as we have demonstrated in our previous work, it is the effective π-π stacking supporting percolative paths throughout the entire sample, not the long-range order, that is essential to enhance the electrical performances.44 To outline this aspect, let us consider percolation curves shown in Figure 5c. The percolation curve shows the proportion of chains in the biggest cluster in the material when all the connections between chains with a transfer integral below a threshold (the abscissa of the plot) are removed.45 All the curves show a sharp increase from 0 to 1, i.e. from a system where all chains are disconnected to a system where all chains are connected. The transfer integral threshold corresponding to this transition indicates an onset for the conduction in the system, because it indicates what transfer integral value the charge carriers need to face to travel in the whole system. Clearly, it is a position of the percolation threshold relatively to the peaks in the transfer integral distributions, P(|H|), that determines the mobility of the system. Indeed, for Silicon, SiO2 and Si3N4, the threshold is located at the π-π stacking peak (peak “A”) of the transfer integral distribution, see Figure 5c. This means that the connectivity in the system is good and it is the efficient transfer via π-π stacked chains that represents the factor limiting the charge transport. On the other hand, in graphite the threshold is located in the region “B” and therefore the charge transport is limited by the inefficient connection through misaligned chains. Apparently, in this material, the connectivity is rather poor because there are no conduction paths involving only π-π stacking throughout the entire sample. This is an interesting paradox that makes the connection between morphology and mobility so subtle: if the material is very well-ordered, the volume fraction of perfect π-π stacking is huge because almost all material is crystalline. However, to move on a large distance a charge carrier has to jump over grain boundaries, that represent a negligible volume fraction but that will limit the transport anyway because these jumps are so inefficient. The above analysis outlines the fact that good crystallinity (graphite substrate) and high content of edge-on (SiO2 substrate) are not enough to achieve high electrical mobility. Instead, a less ordered material with lower degree of the edge-on content (Silicon substrate) promotes the emergence of an efficient network of π-π stacking extending throughout the material, via rather disordered chains connected by a few stacked monomers: eventually, this morphology provides the highest mobility. This is consistent with recent experimental studies that showed that it is the presence of the efficient network due to the π-π linked chains, rather than good crystallinity of the material that ensure the high electronic mobility in the device.46-49



3. Conclusions Computational microscopy has been performed in order to investigate the structure and crystallization dynamics of PEDOT thin films grown on different substrates with different crystallic lattices and water affinities including graphite, silicon, as Si3N4, and SiO2. The first three substrates have a periodic ordered lattice, whereas SiO2 is an amorphous one. Deposition, crystallization and molecular packing of PEDOT as well as the role of water and TOS in the formation of the final motif of the thin films were studied in situ as water were evaporated. We demonstrate that the substrate is instrumental in formation of the lamellar structure in the polymeric thin film. Ordered substrates, (graphite, Si3N4, silicon) exhibits preferential face-on orientation, with graphite showing the most ordered and pronounced face-on packing. In contrast, amorphous SiO2 exhibits the dominant edge-on orientation, except in the dry state where both packings are equally presented. We outline the important role of water molecules and the high porosity of SiO2 in the formation of edge-on structure. Indeed, in the highly porous SiO2, water penetrates between the PEDOT and the substrate, thus screening the interaction between the p-orbitals in the polymeric chains and the atoms of the substrate, which eventually leads to the edge-on arrangement. Our predictions concerning substrate-dependent face-on vs edge-on orientation are consistent with available experimental results. In order to understand the impact of the substrate on the electron mobility, we perform the multi-scale transport calculations. Based on the calculated morphology we compute the transfer integrals between electronic states in polymer chains and calculate corresponding hopping rates using the MillerAbrahams formalism. We then construct a transport resistive network, and calculate the mobility using master equations technique. The calculated mobility is analyzed using the percolative network approach. We find that substrate strongly affects the mobility of the thin film. We demonstrate that good crystallinity (PEDOT on graphite substrate) and high content of edge-on (PEDOT on SiO2 substrate) are not enough to achieve the highest electrical in-plane mobility. Instead, the least ordered material with the lower degree of the edge-on content (PEDOT on silicon substrate) provides the highest mobility because it exhibits an efficient network of π-π stacked chain extending throughout the entire sample. To the best of our knowledge, we are not aware of any systematic studies of the effect of the substrate on the material morphology and electrical performance of PEDOT-based devices. We therefore hope that our results and predictions would motivate further experimental and theoretical studies addressing substrate-dependent morphology and its effect on electrical mobility in PEDOT thin films. 4. Methods Computational Simulation: The computational methodology used in this work has been described in detail and extensively validated in previous reports by the authors on similar systems.34-35, 39 The Molecular Dynamics (MD) Simulations described in this work were performed using the LAMMPS software package.50 The parameters for PEDOT and TOS were taken from the General AMBER Force Field (GAFF)51 as

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implemented in moltemplate code.52 Water molecules were represented by the SPC/E model.53 Substrates were built using the VMD software with the inorganic builder plugin. 54 The Lennard-Jones (LJ) and Coulombic interactions were cutoff at 1.2 nm with a k-space scheme of particle-particle particlemesh (pppm) for the Coulombic case as implemented in LAMMPS. A neighbor list updated every step and cutoff at 1.4 nm. We considered the chain length of PEDOT as 12 repeated monomer units. These setups include 80 PEDOT chains with an oxidation level of 33.3% each (charge of a PEDOT chain equals to +4). Partial charges on each atom of PEDOT and TOS molecules were calculated using firstprinciples density-functional theory (DFT) functional WB97XD55 with the 6-31+g(d)56 basis set as implemented in Gaussian 09, revision E.01 2009.57 The partial charge per atom were taken from the fitting to electrostatic potential (ESP) population analysis58 as implemented in Gaussian suite. The corresponding number of TOS to balance the charges of the system were considered in a proper proportion. In our simulations, we start from a diluted polymeric solution where PEDOT and TOS molecules were randomly placed in the simulation box. Then, solvent was removed from the surface of the solution in 9 steps until reach a dry thin film. Therefore, the box is initially solvated with 30000 water molecules. A typical size of the computational box is 10 × 10 × 22 nm3. The system was then minimized and water equilibrated with PEDOT-TOS restraint 2 ns run of a canonical nVT ensemble using Nose-Hoover thermostat.59-61 Then, a production run of 50 ns without any restraint is performed with a Nose-Hoover thermostat. The time integration method of Verlet62 is applied. Then, solvent was consecutively removed in 9 steps, such as the solvent concentration was reduced, approximately, from 70 %w/w (initial solution) to 59 %w/w, 42 %w/w, 26 %w/w, 15 %w/w, 8 %w/w, 4 % w/w, 2 %w/w, 1 %w/w and finally 0 % w/w (i.e. a dry phase). The system was equilibrated in each step by a nVT ensemble for 10 ns run. At each step, solvent was removed at the top of the interface of the polymeric solution and vacuum. In all simulations, the temperature was kept close to the boiling point of the solvent, 100 °C for water. At the final state of the dry thin film a short equilibration run for 5 ns were performed at 300 K. Solvent accessible surface area, SASA, was calculated as implemented in GROMACS, with the probe radius being 0.14 nm, which corresponds to the size of the water molecule, see ref.34for details. MD Analysis: All the snapshots were prepared using Tachyon as implemented in VMD software.54 X-ray diffraction (XRD) patterns were calculated on the simulated system as described by Coleman et. al.63 and implemented in LAMMPS. Partial densities were calculated using GROMACS 2016.64 Mobility Calculations: The electrical mobility of the dry thin films has been evaluated following the method developed in our previous work.44 While the details of the method can be found in the above paper, here for the sake of completeness we present a brief description of the calculations. PEDOT doped with Tosylate negative counterions is a ptype material where the electrical transport is due to the thermally-assisted hopping of polarons/bipolarons via the states in the valence band. This physical picture can be modeled by a resistive network built based on the thin films morphology. A


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resistive network is a graph that mathematically describes the conduction paths in the physical system. It comprises a set of transport units, referred to as the nodes, that can accommodate a charge carrier; these nodes correspond to the states in the valence band and are depicted by points located in space. It also comprises a set of weighted links between some pairs of nodes, referred to as the edges of the graph. The weight of the edges is the charge carrier hopping rate between the connected nodes. It is supposed that a PEDOT chain can accommodate one charge carrier per three monomer units, and therefore four nodes are associated to each PEDOT in the system at hand. (We consider a chain length N=12 monomer units). These four nodes are localized in the geometrical center of the corresponding chain, which is a reasonable simplification since it has been shown that the charge carriers can be delocalized over one entire single chain in such heavily doped system.65 In addition, energies Ei are associated to every single node i in the system. These energies correspond to the energies of the states in the valence band, which tail of the density of states (DOS) is well described by a Gaussian with typical broadening σ ~ 0.1 eV. 65-67 Thus, these energies are drawn from a random truncated gaussian distribution with a standard deviation of 0.1 eV (truncated means only energies above 0.1 eV from the Gaussian mean value are taken into account). Two nodes (i, j) in the network are linked by an edge if their separation is less than 12Å (note that nodes belonging to the same PEDOT chain are automatically linked since the distance is null); above this value any hopping rate is negligible. Hopping rates ωij for the charge carriers are then associated to each edge within a modified Miller-Abrahams formalism:68 =

!

exp &

'∆()* +, -

.,

(2)

where ω0 is a prefactor, Hij is the so-called transfer integral between states corresponding to the nodes i and j, ∆Eij is the energy difference between states i and j, ∆/ = / – / – 123 ∙ 53 , with F being the electric field and 53 = r3 − 53 , 53 referring to the position of the node i. The dimer projection method at the ZINDO level69 was used to calculate the transfer integral Hij between nodes belonging to different chains (note that all corresponding MOs are calculated using GAUSSIAN0957 package for PEDOT chains as obtained from the MD simulations; the transfer integrals are evaluated for the neutral chains for the four highest MOs in the valence band). For the case where sites i and j belong to the same chain, the transfer integral is arbitrarily set to |Hij|=1eV, which greatly exceeds typical values of the inter-chain transfer integrals. As a result, the intra-molecular transfer rate is much higher than the inter-molecular one, and the limiting step for charge transport through the volume is linked to the efficiency of the inter-molecular transport. With these well-defined resistive networks, relative mobilities for the different substrates are finally calculated. Let P be the number of charge carriers in the system and pi the carrier occupation probability at node i, such that = ∑ 8 . The Master Equation describing the stationary state is: ∑,>− 8 91 − 8 ; + 8 1 − 8 = 0, ∀

(3)

This equation is solved for the pi via the iterative approach described by Yu et. al.70, and the mobility is calculated according to: A=

∑),*,)G* B) C) 9D'C* ;E3 ∙F)* HE I

(4)

Thin films mobilities were calculated at 300K with an electric field intensity23 = 10 JKL'D and P = 96. For each substrate, calculations were repeated for 17 MD frames and 50 gaussian disorder realizations (i.e. random energies of the nodes). In order to ensure that different MD frames correspond to structurally uncorrelated samples, we compute the autocorrelation functions (ACF) for the Root-Mean-Square-Deviation and for the total energy, see Sec. S6 in the Supplementary Information. Furthermore, 20 different field orientations were investigated, corresponding to 23 = 23 M3 cos Q + R3 sin Q where θ is the field orientation, ranging from 0º to 360º with step 20º, and M3, R3 is the system of axis parallel to the substrate surface; clearly, the orientation of the PEDOT chains relative to the substrate surface will strongly impact the resulting in-plane mobility.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Additional sections: Radial Distribution Functions (RDF), Partial Densities and water as a mediator of edge-on structure.

AUTHOR INFORMATION Corresponding Author * e-mail: [email protected]

Present Addresses †Present Address: Autonomous University of Madrid, Medicine Campus, c/Arzobispo Morcillo, 4, Lab-3, 28049, Madrid, Spain.

Funding Sources This work was supported by the Swedish Energy Agency (383321), Swedish Research Council (2017-04474 and 2016-05990), and the Knut and Alice Wallenberg Foundation through the project The Tail of the Sun. IVZ thanks the Advanced Functional Material center at Linköping University.

ACKNOWLEDGMENT Ioannis Petsagkourakis, Drew Evans, Robert Brook, and Simone Fabiano are acknowledged for numerous stimulating discussions. The computations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at NSC and HPC2N.

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Figure 1. a, Percentage of the buried area of the polymeric material on each substrate at different evaporation stages. b-e, Deposition of



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PEDOT-TOS as water is evaporated (for selected evaporation steps) onto graphite, silicon, Si3N4 and amorphous SiO2 substrates, respectively. H atoms are not shown, substrates are in gray, PEDOT chains are blue, TOS are red, O from water are cyan.

Figure 2. a-d, XRD patterns calculated for the simulated thin films at each evaporation step for graphite, Si3N4, silicon and amorphous SiO2 substrates, respectively. The colour bar at the left shows a water content. e, π-π stacking distance, dπ-π, extracted from a Lorenz fitting on the calculated XRD patterns at different solvent content for every substrate. f-g, Size of the π-π crystals, L/dπ-π and size of nano-crystals in the lamella periodicity, L100, respectively. L/dπ-π and L100 are calculated using the Scherrer’s equation and at different solvent contents.


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Figure 3. a, Definition φ and Z: φ is defined as the angle between the normal of the plane of thiophene ring with the axe z. Z is the distance of the geometric center of the thiophene ring and the surface of substrate. b-e, Angle φ and probability distribution function P(φ) as a function of solvent content for graphite, Si3N4, silicon and amorphous SiO2, respectively. f-i, Probability distribution, P(φ,Z) for graphite, Si3N4, silicon and amorphous SiO2 substrates, respectively. Upper maps correspond to a solvent content of 15 % w.t and bottom maps correspond to the dry films. Color box denotes the population of thiophene rings.



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Figure 4. a-d, Electron density profile along Z-direction of PEDOT chains at different solvent content. e-h, Electron density profile along Z-direction of TOS molecules as solvent evaporates. i-l, Electron density profile along Z-direction of water as solvent evaporates. Columns from left to rights correspond to graphite, Si3N4, silicon and amorphous SiO2 substrates. The inset schematically shows both face-on and edge-on orientations of PEDOT (blue), the coordination of TOS (green points) in presence of water (cyan background) and substrate (gray).


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Figure 5. a, Mobility distribution for each substrate in the dry thin film. b, The mean mobility vs relative crystallinity and the content of the edge-on configurations, f(ϕ> 45°); the mean mobility for different surfaces are normalized to the one of Si. c, Percolative analysis of the mobility calculations. Filled areas correspond to the transfer integrals distributions normalized to the maximum value. Solid lines are the corresponding percolation curves. The inset illustrates the peaks in the transfer integral distribution: π-π stacking connection (peak “A”), misaligned chain connection (region “B”), a double π-π stacking distance (peak “C”). (Each curve in (a) corresponds to 17 MD frames, 50 gaussian disorder realizations and 20 different field orientations).

Table of Contents (TOC)


Substrate-Dependent Morphology and its Effect on Electrical Mobility

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