Isotropic charge transport in highly ordered regioregular poly(3-hexylthiophene) monolayer

Charge transport anisotropy in π-stacked poly(3-hexylthiophene-2,5-diyl) (P3HT) monolayers was investigated. The monolayers were prepared using a Langmuir–Blodgett technique and were uniaxial but homogeneous two-dimensional sheets. Nanoscale electrical measurements were carried out using metal electrodes with a submicrometre gap between them in order to exclude breaches that occasionally occur along the chains. A remarkable degree of isotropy in both the conductivity and mobility was found. The conductivity isotropy implies that charge transport is dominated by fatal defects in polymers arising at structural and electrical discontinuities, even in the absence of large morphological defects. It was found that the mobility along the π-stacking direction can exceed that along the polymer chain in monolayers with good crystallinity. This high mobility along the π-stacking direction is thought to be an inherent charge transport characteristic that has so far been obscured in solid state conjugated polymers with complex microstructures.


Introduction
Semiconducting polymers are important materials for upcoming new electronic products, such as electronic paper equipped with photovoltaic cells, which capitalize on the unique features of such polymers, including the fact that they are printable, flexible and offer large-area coverage [1]. Although understanding the mechanism of charge transport in conjugated polymers is an important issue, the Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. complex microstructure and polymer chain conformation present in the solid state prevent the emergence of inherent properties. The study of anisotropy between the electrical conductivity along the polymer chains and in other directions is an attractive approach for clarifying the charge transport mechanism, and has been carried out for films based on conjugated semiconducting polymers with various controlled chain alignments [2][3][4][5][6][7][8].
The regioregular P3HT has been one of the most common organic polymer materials used in organic field-effect transistors (OFETs) [9][10][11][12][13][14] because of its solutionprocessability and relatively high field-effect mobility. The regioregularity-induced lamella-like P3HT chains have a strong tendency to stack together (π − π * stacking) and eventually form a two-dimensional (2D) sheet on an appropriately prepared surface, so that the P3HT crystal structure basically consists of a π-stacked sheet. During the early stages of research in this field, Sirringhaus et al reported that 2D charge transport occurs in P3HT sheets, which they interpreted in terms of extension of polaronic charged states over neighbouring π-stacked polymers [9]. There is a tendency for semiconducting polymers with planar π -electron systems and short intermolecular π -π distances to exhibit high carrier mobility; for example, the newly developed polythiophene, pBTTT, has a short π -π distance of 0.371 nm and a high mobility of 0.2-0.6 cm 2 V −1 s −1 [15]. Nevertheless, no detailed investigations of the effects of increased mobility along the π-stacking direction have yet been carried out.
Attempts have been made to measure the charge transport anisotropy of P3HT using a single-crystal nanosheet [16] and homogeneous monolayer films with a uniaxial chain alignment [17]. However, the reported results contradicted each other. For the uniaxial films, the conductivity along the polymer chain direction was about two times higher than that along the π -stacking direction, whereas for the single crystals, the opposite was the case. If it is assumed that the P3HT has the same crystal structure, it must be concluded that these conflicting results are due to the effect of unrecognized morphological anisotropy in either or both cases. Even in the absence of morphological defects, polymers do not form perfect crystals, because the individual chains are finite and their lengths are variable. Band-based calculations of the electronic properties of perfect P3HT crystals [18] predict a significant amount of anisotropy, with higher conductivity along the polymer chain direction than along the π-stacking direction; however, such anisotropy is unlikely to emerge unless band conduction actually occurs. Therefore, a question arises concerning the underlying mechanism leading to the anisotropy that emerges in imperfect but almost ideal π-stacked polymer crystals.
In the present study, the charge transport properties of highly ordered π-stacked P3HT 2D monolayers were investigated in order to clarify the inherent anisotropy. The monolayers were widely spread and consisted of uniaxially aligned P3HT lamellae, which were artificially compressed using the Langmuir-Blodgett (LB) method. In a previous study on conductivity anisotropy in such monolayers [17], it was found that boundaries or cleavages were rarely observed. Nevertheless, to prevent any possible influence of such defects, the charge transport properties were investigated in very small areas by the use of metal electrodes with a submicrometre gap between them. It was expected that using such an approach to measure the anisotropy would lead to a new understanding of the charge transport mechanism in conjugated polymer materials.

Experimental
The molecular layers in the present study were prepared by a liquid-crystal hybridized LB method [19][20][21], and were ideally spread monolayers consisting of uniaxially aligned P3HT lamellae. The P3HT, which was purchased from Aldrich, had >98.5% head-to-tail couplings (Mw = 87 000 with Mw/Mn = 1.6). It was attached to the water surface via co-spreading with 4 -pentyl-4-cyanobiphenyl (5CB) liquid-crystal molecules, and compressed by a barrier in order to prepare a P3HT monolayer containing 5CB. Brewster angle microscope (BAM) observation declared that the monolayer consists of very wide single-crystal monodomains [20], which were wider than a few hundred µm squares, on the water. The monolayer was then transferred onto a solid substrate (figure 1(a)), and the 5CB was evaporated by gentle heating at about 40 • C. Grazing-incidence x-ray diffraction (GI-XRD) measurements indicated that the spacing of the π -π stacking was 0.38 nm [19]. The polarized absorption spectra shown in figure 1(b) exhibit optical anisotropy indicating unique molecular alignments over a wide area, with polymer lamellae aligned parallel to the compressive barrier wall, although the residual absorption peak in the direction perpendicular to the polymer chain indicates that the structural anisotropy is not perfect. An electron spin resonance (ESR) study of such monolayers indicated that, within each single-crystal monodomain, the polymer chain directions had a spread of ±30 • [17]. Although multilayer construction while maintaining the rigid 2D sheet structure has been previously demonstrated by repeated transfer of monolayers [19], in the present study only single monolayers were transferred onto the electrodes to maintain the two-dimensionality of the system. Figure 1(c) shows a typical atomic force microscopy (AFM) image of a P3HT monolayer. The surface was very smooth, where a root mean square (RMS) of a number of AFM images was 0.416±0.08 nm. It can be seen that very few distinct grain boundaries are present over a wide area, although some linear structures can be identified. It is known that P3HT forms a variety of fibril structures via a self-assembly process, and the morphology of these structures has been clearly confirmed from AFM images [12][13][14]. However, as seen in figure 1(c), in typical AFM images of LB-processed P3HT monolayers, little structure was found because of the homogeneity of the monolayers. It is thought that artificial compression on a water surface and suitable choice of a constituent polymer with a high molecular weight are effective in preventing fibril structure formation.
For the electrical measurements, metal electrodes embedded in a SiO 2 layer were used. The electrodes were fabricated by standard electron-beam lithography, evaporation and lift-off, combined with reactive-ion etching. 50 nm thick titanium-gold electrodes were embedded in a SiO 2 film with a thickness of 100 nm that was thermally grown on a highly doped n-type Si substrate. The electrode surface was flattened by mechanical polishing procedures [22] until the height difference between the SiO 2 and the metal was reduced to less than a few nanometres ( figure 1(d)). This was done to minimize any deformation of the P3HT monolayer. Mechanical polishing was used to remove surplus deposited metal. Prior to monolayer deposition, substrates with electrodes were washed in acetone and hydrophobized by dipping in a 96% HMDS (hexamethyldisilazane) solution for 10 min. In this study, more than 40 two-terminal devices with a gap length (L) and width (W ) varying in the range 100-600 nm and 250-2000 nm, respectively, and 15 four-terminal cross-type devices with L and W varying in the range 300-650 nm, were used. The molecular orientation of the transferred monolayer was controlled to align it with the designated direction.
The resulting samples have the structure of a bottomcontact FET device, since the underlying highly doped silicon substrate acts as a gate (G), and the metal electrodes act as the drain (D) and source (S) terminals, as shown in figure 1(e). Measurements were carried out using a variable temperature prober (TPP-4 Lakeshore Co., Ltd) and a Keithley 4200 semiconducting parameter analyser in vacuum at about 1 × 10 −5 Pa under dark conditions at room temperature. The devices exhibited p-channel FET characteristics, although clear current saturation was hardly observed in contrast to the case for spin-coated P3HT thin-film FETs. Figure 2(b) shows typical I D -V G characteristics measured by successive back and forth sweeping. The lack of hysteresis in these curves suggests that little or no carrier trapping sites exist. The effective field-effect mobility was estimated using the standard formula in the linear

Results and discussion
where C is the capacitance of the 100 nm thick SiO 2 dielectric. The mobility determined for the monolayer FET was 0.002-0.2 cm 2 V −1 s −1 , which represents a wide spread of two orders of magnitude. The highest mobility value is large, and is comparable to the reported values for P3HT thinfilm FETs with both long (several tens of micrometres) [10] and short (less than 1 µm) [14] channel lengths, even though in the present study the channel layer consists of only a single monolayer. It is thought that the wide variation in the mobility values is caused by variations in the surface conditions of the metal electrodes following mechanical grinding, which lead to large differences in the contact resistance of each device. To overcome this, the carrier transport anisotropy was measured using the cross-type electrodes shown in the inset of figure 3(a). Using this setup, measurements can be carried out simultaneously in the two orthogonal directions. Because of the proximity of the electrodes to each other during the polishing process, it is expected that they have similar contact resistances. Figure 3(a) shows the I -V characteristics of four randomly selected cross-type devices. It is clear that the current flowing parallel ( ) and perpendicular (⊥) to the polymer chains is very similar. Moreover, the relative magnitudes of the parallel and perpendicular currents did not show the same trend. In two of the devices, the parallel current was larger, but in other devices, the opposite was the case or no difference was observed. Fifteen such devices with different channel lengths and widths were investigated, and the conductance (G) and conductivity (σ ) were estimated using dI /dV at V D = 0 V. The results are listed in detail in table S-1 in the online supplementary data (stacks.iop.org/JPhysD/46/425303/mmedia). The channel length and width were evaluated from AFM images, because they were slightly different from the initial design values. The anisotropic ratios, G /G ⊥ and σ /σ ⊥ , were distributed around a value of 1.0, and their average was 1.056 and 1.096, respectively, indicating that the P3HT monolayer is practically electrically isotropic. Using the same cross-type electrodes, the conductivity anisotropy of other organic materials was also measured. Figure 3(b) compares the conductivity ratio obtained in this work for P3HT monolayers to that for single-crystal rubrene [23] and a single polydiacetylene bi-layer, the data for which is shown in figure S-1 in the online supplementary data (stacks.iop.org/JPhysD/46/425303/mmedia). For singlecrystal rubrene, the conductivity was found to be higher along the b-axis than along the a-axis, which is consistent with a previous report [24]. Polydiacetylene exhibited very large anisotropy, which is also in agreement with previously obtained results indicating 14 times higher mobility [25] and eight times higher conductivity [26] along the polymer chain direction than along the transverse direction. It can thus be concluded that the use of cross-type electrodes is an effective means of measuring the conductivity anisotropy of organic materials. The isotropy of the P3HT monolayers in the present work is noteworthy. Figure 3(c) shows the conductivity σ and carrier mobility µ for twelve devices, with three devices being excluded because of their abnormal I D -V G curves due to large leakage current. The average mobility ratio (µ /µ ⊥ ) for the twelve devices was 1.076. The magnitude of σ and µ for each device is seen to be correlated, although not perfectly. Figure 3(d) shows the ratios σ /σ ⊥ and µ /µ ⊥ for each device. It can be seen that the range of variation for µ /µ ⊥ is smaller than that for σ /σ ⊥ . Since the twelve devices shown in figures 3(c) and (d) are arranged in order of increasing channel length, it is fairly certain that there is no dependence on channel length. It is likely that the lack of perfect correlation between σ and µ is due to unintentional variations in channel length, contact resistance and degree of misalignment between the channel direction and molecular axis in the monolayer. Nevertheless, the similarity in the average values of G /G ⊥ , σ /σ ⊥ and µ /µ ⊥ , 1.056, 1.096 and 1.076, respectively, suggests that these variations are random and small.
The question then arises as to what the underlying mechanism is for the isotropic conductivity observed in the P3HT monolayer used in the present study. It is thought that the principal factor involved is carrier hopping due to the presence of fatal defects in the polymer crystal. The average length of the P3HT molecules used in the present study was estimated to be approximately 110 nm. Because of their finite length, polymers can never form perfect 2D crystals. Furthermore, in a polymer crystal, electrical defects exist not only at the ends of each polymer chain but also at the ends of π-conjugated regions, where a structurally discontinuous node exists. The high regioregularity of the molecules and the high degree of crystallinity lead to extensive charge delocalization along the conjugated polymer backbone, which is the effective πconjugation length. As seen in figure 1(b), the main peak in the optical adsorption spectra for the P3HT monolayer is at approximately 555 nm. Recently, a revaluation of the effective π -conjugation length by Takimiya and co-workers [27] indicated that increasing the π-conjugation length leads to a red shift in the adsorption around 500 nm. For example, for 48 T and 96 T oligothiophenes, the adsorption peaks were found at longer wavelengths of 551.4 nm and 556.5 nm, respectively. For 48 T-96 T oligothiophenes, the molecular length, i.e., the π -conjugation length, is 18.6-37.2 nm.
Here, it was assumed that the π-conjugation length in the P3HT monolayer is approximately 25 nm and that the location of nodes with neighbouring polymers is irrelevant. Figure 4(a) shows the simulated defect distribution in an area of 100 × 100 nm 2 . The defects, which correspond to the ends of polymer chains or to π -conjugation nodes, are indicated by black dots. It can be seen that the defect distribution appears isotropic. Figure 4(b) shows a relative neighbourhood graph [28] for the defect distribution shown in figure 4(a), obtained by dividing the 2D molecular sheet into small segmented areas. This is achieved by connecting two points by an edge whenever there is no third point that is closer to them than they are to each other. An additional rule is also applied, by which no two points are connected if the distance between them is more than 5 nm. The resulting segments correspond to structurally and electrically continuous regions of the sheet that are bounded by defects.
In regioregular poly(3-octylthiophene), the spatial extent of polaronic charged states has been determined based on the full-width at half-maximum of the spin distribution to be approximately 10 thiophene rings, which corresponds to a length of 4 nm, by ESR [29] and light-induced electronnuclear double-resonance measurements [30].
Charge delocalization makes polaronic states energetically stable, although it is possible that such states cannot exist in segments that are too small. In figure 4(c), segments that are wider than a circle with a radius of 5 nm are coloured. Assuming that charge transport occurs by hopping of polaronic charges from coloured segments to neighbouring coloured segments, this figure indicates that this will occur equally well in the directions parallel or perpendicular to the polymer chain. It is therefore considered that a uniform defect distribution is the origin of the isotropic conductivity in the P3HT monolayer.
However, the spatial extent of polaronic charges may not be well represented by a simple shape like a circle. Longitudinal or transverse extension of polaronic states should closely correlate with the transport mobility in the corresponding direction, because the charges will not only hop but also undergo transport in wider segments. Although the spatial shape of polaronic states cannot be directly determined, it can be assumed to have an effect on charge transport. Figure 3(e) shows a plot of the mobility ratio µ /µ ⊥ against either µ || or µ ⊥ . It can be seen that the ratio tends to decrease with increasing mobility, which implies that improving the crystal quality would cause a larger increase in µ ⊥ than in µ || . Good ordering in the crystal can cause the effective πconjugation length to increase, leading to a decrease in the defect density and an increase in the size of the segmented areas. This could lead to the emergence of true intrinsic charge transport characteristics, which are associated only with the interior of segments. Therefore, one possible explanation for the preferential increase in µ ⊥ as the overall mobility increases is that the mobility along the π-stacking direction is inherently higher than that along the chain. There are several single molecule measurements of highly effective charge transport through π-stacking molecular backbone [31] and two molecules bridged by π -stacking interactions [32]. The degree of charge delocalization along the π -stacking direction is expected to be comparable to that along the polymer chain, and is thus larger than has been supposed.

Conclusions
The remarkable degree of isotropy observed in this study is thought to be an inherent characteristic of charge mobility in P3HT π-stacked layers. It is suggested that the conductivity isotropy is due to the presence of an isotropic distribution of defects in the monolayers. It is likely that the larger anisotropic ratios previously measured for P3HT films included the effects of morphological defects, i.e., linear boundaries and/or cleavages along the polymer chains. Such defects can significantly decrease the conductivity in the transverse direction. The results of the present study indicated that the mobility in the π -π stacking direction can exceed that along the polymer chains in monolayers with good crystallinity. The present results and discussion lead to the conclusion that there is no reason why the mobility along the π -stacking direction cannot be larger than that along the polymer chain. It should also be pointed out that this may have already been achieved for nanostructures in various polymer materials with close π -π distances.