Relation between Microstructure and Charge Transport in Polymers of

ARTICLE pubs.acs.org/JPCC

Relation between Microstructure and Charge Transport in Polymers of Different Regioregularity David P. McMahon,† David L. Cheung,† Ludwig Goris,‡ Javier Dacu~na,§ Alberto Salleo,*,‡ and Alessandro Troisi*,† † ‡

Department of Chemistry and Centre of Scientific Computing, University of Warwick, CV4 7AL Coventry, United Kingdom Materials Science and Engineering Department and §Electrical Engineering Department, Stanford University, Stanford California 94305, United States ABSTRACT: A methodology to link an atomistic description of a polymeric semiconductor with the experimental electrical characteristics of real devices is proposed. Microscopic models of poly(3-hexylthiophene) (P3HT) of different regioregularity are generated using molecular dynamics and their electronic structure determined via an approximate quantum chemistry scheme. The resulting density of trap states and distribution of localized and delocalized states is then compared with that obtained from thin film transistor measurements of P3HT at different regioregularities. The two complementary methodologies provide a converging description of the electron transport in semicrystalline P3HT and the role of regioregularity. States at the valence band edge are localized, but delocalized “band-like” states are thermally accessible and quantitatively characterized. Both theory and experiment agree that contrary to a commonly held belief the trap density and the DOS shape are little affected by the presence of regioregularity defects.

’ INTRODUCTION The charge transport characteristics of semicrystalline polymeric semiconductors depend on the electronic density of states (DOS) and the nature of these electronic states, for example, whether they are localized or delocalized. We normally infer this information from device measurements on the basis of simplified transport models, but it is difficult to validate these models in the absence of an independent evaluation of the DOS.1,2 In principle, the simplest systematic way to modify the DOS while leaving the remaining material parameters as constant as possible is by changing the polymer regioregularity. Small amounts of headto-head defects, introduced in a controllable way by the synthesis, do not dramatically modify the morphology of the crystalline portion of the polymer and are expected to change the shape of the DOS in a way that is reflected in the electrical properties. Electronic structure calculations of polymers have accompanied the development of organic electronics since its early days.3 Band structure calculations of increasing quality have been performed and used to rationalize the optical properties and some of the transport properties.4 However, charge transport in polymers unlike that in crystalline inorganic semiconductors cannot be described as band transport because the charge is localized by the intrinsic disorder of the polymer.5 The first attempts to study the deviation from an idealized band structure due to the presence of controllable disorder focused on the electronic structure of copolymers6,7 and homopolymers with regioregularity defects (including P3HT).8 Specialized numerical methods9 were introduced to study 1D disordered structures, r 2011 American Chemical Society

and it was found that the DOS and charge localization is influenced by the concentration and distribution of the regioregularity defects or the different monomers in copolymers.7,8 Whereas these studies provide a correct qualitative picture of the DOS tail, in agreement with localization theory,5 they fail to describe the actual shape of the DOS and the correct localization length, which is also affected by the subtle geometric irregularities of the polymer. For example, trap states also exist in crystalline regioregular P3HT, whereas the classical theories predict it would have only delocalized states. Being able to describe accurately the DOS shape and the localization length allows the determination of the correct charge transport mechanism. If all relevant states are localized, then one should assume that transport takes place through a sequence of charge hopping events,10 whereas if delocalized states are thermally accessible near the DOS tail, then the charge carrier may hop into these delocalized states and propagate until it is trapped again.11 Only recently has it become possible to compute both the morphology and electronic structure of realistic polymers to predict accurately the shape of the DOS.12,13 These studies finally allow one to test hypotheses on the relation between microscopic and electronic structures, which have been so far largely based on “chemical intuition”. Like all solution-processable semiconducting polymers, P3HT is composed of a chain of conjugated Received: July 22, 2011 Revised: August 23, 2011 Published: August 24, 2011 19386

dx.doi.org/10.1021/jp207026s | J. Phys. Chem. C 2011, 115, 19386–19393

The Journal of Physical Chemistry C

Figure 1. (a) P3HT structure and dihedral angles used in the discussion and (b) head-to-head regioregularity defect.

fragments with alkyl side chains added for solubilization (Figure 1). The material forms crystalline domains even in the presence of regioregularity defects (at least for regioregularity 81% and beyond14), and the main characteristics of the crystalline phase of P3HT (e.g., interchain separation and orientation) are experimentally known. It has been part of the conventional wisdom that regioregularity defects cause a major distortion of the polymer chain and a consequent break of the electronic conjugation along the chain.14 Here we test this hypothesis performing classical MD simulations of the crystalline phase of P3HT with different regioregularities and computing its electronic structure. In considering only the crystalline portion of P3HT, we are implicitly making the assumption that the crystalline domains of P3HT, and not the amorphous regions, dominate charge transport in FET devices. This assumption could be preliminarily justified considering that the amorphous regions of P3HT are known to have a much larger band gap,15 essentially because the larger disorder reduces the localization length. For this reason, in the presence of a percolating network or crystalline domains, the hole density will populate only the highest energy edge of the valence DOS, which is provided by the crystalline portion of the material.24 Furthermore, polymer chains ensure the existence of an efficient transport mechanism between crystallites.16 In the rest of the Article, after describing the computational detail used to compute the polymer structure and the DOS, it will be shown that states in the DOS tail are mostly localized but are also energetically close to more delocalized “quasi-band” states that are thermally accessible under device operation. We will then consider the experimental device characteristics of thin film transistors (TFTs) of P3HT with different regioregularities and model this data with the transport model physically closest to the description depicted by the computational study. Both experimental and theoretical data indicate that polymer regioregularity has little or no effect on the shape of the DOS tail and the total density of trap states, and they both agree on the absolute trap state density being in the region of (2 5)  1013 cm 2.

’ COMPUTATIONAL DETAILS The simulated system contained 24 chains of type-I P3HT, each consisting of 40 thiophene rings, arranged into four layers of six chains (schematic in Figure 2) with side chains fully extended and noninterdigitated (as in the most stable polymorph of the polyalkylthiophenes).17 The starting crystal structure was

ARTICLE

Figure 2. 6  4 arrangement of the polymer chains in the simulation box.

Figure 3. Side and top views of three simulation snapshots for different regioregularities. (Only one layer is shown in each case.) Head-to-head defects are highlighted in red.

adapted from the experimental crystal structure of poly(3butylthiophene).18 The separation between chains in the same layer was initially taken to be 3.82 Å (π π stacking distance, taken to be in the x direction), whereas the interlayer spacing (in the z direction) was taken to be 16.2 Å. (This is longer than the interlayer spacing for P3BT to accommodate the longer alkyl chains.) The area of each layer of the simulation box was ∼4  10 13cm2. The intra- and intermolecular interactions were described using the recently published force field of Moreno et al.19 Head-to-head regioregularity defects have been introduced randomly during the setup of the simulation. The systems were studied using constant NPT-MD simulations at 300 K and a pressure of 1 atm. (Temperature and pressure were controlled using a Nose Hoover thermostat and (anisotropic) barostat, with relaxation times of 0.2 and 1.0 ps, respectively.) The periodic boundary conditions force the system in a crystalline phase. It is computationally too demanding and so far never achieved to study with this level of accuracy both the crystalline and amorphous phase of P3HT in the same simulation box, and tests made with open boundaries are unable to reproduce the crystalline structure of regioregular P3HT. The possible tendency of lower regioregularity samples to form larger amorphous regions is neglected so that the simulation is not representative of the whole sample but only of the portions of the sample that dominate the transport characteristics. The equations of motion were integrated using a velocity Verlet algorithm with a time step of 1 fs. Simulations consisted of 5 10 ns of equilibration and 6.5 ns of data gathering. Illustrative snapshots of the equilibrated structure are given in Figure 3. Nonbonded interactions were truncated with a cutoff of 12 Å; following 19387

dx.doi.org/10.1021/jp207026s |J. Phys. Chem. C 2011, 115, 19386–19393

The Journal of Physical Chemistry C Moreno et al., 19 it was unnecessary to use an Ewald summation for systems with small atomic charges. All MD simulations were performed using the LAMMPS simulations package.20 The DOS was computed as an average over 53 MD snapshots taken every 125 ps for each regioregularity to better approximate the DOS in a macroscopic sample and reduce the statistical error (there are no major differences between snapshots). It is assumed that the bulk crystalline DOS is representative of the DOS at the interface between the semiconductor and the dielectric because it is well-known that P3HT displays a similar packing when in contact with SiO2.14 Furthermore, it has been shown that when trichlorosilane-passivated gate dielectrics are used the transportlimiting traps are located in the semiconducting polythiophene film and not at the dielectric surface.21 The electronic structure calculation of such a large system requires an approximate method, and we used the localized molecular orbital method (LMOM), specifically designed to deal with large simulation boxes of semiconducting polymers.22 To reduce the computational cost, we substitute in the calculation the alkyl side chains with methyl groups because these do not significantly contribute to the highest occupied and lowest unoccupied orbitals of the system, that is, those orbitals responsible for the optical and electronic properties. Furthermore, we use only a few frontier orbitals of the monomer units (from HOMO-1 to LUMO) as a basis set to represent the orbitals relevant to the system. In using the LMOM, the polymer is divided into fragments, and the polymer orbitals and orbital energies are obtained by diagonalization of an approximate Fock matrix built from computations, at the DFT//B3LYP/6-31G* level of theory, containing only pairs of spatially close fragments. The detail of the methods is the same as that given in ref 22, where a thorough validation is also presented. In this work, we ignore the possible effect of the dielectric gate in further stabilizing the charge carrier because it was shown experimentally and theoretically in ref 23 that the SiO2 dielectric (used in the experimental section) can stabilize a charge localized on a medium-sized molecule at the gate semiconductor interface by only a few tens of millielectronvolts, and the effect is expected to be much smaller for the more delocalized charges we have here. The electronic structure calculation was performed in the absence of excess charge with the valence and conduction bands completely filled and empty, respectively.

’ RESULTS Energy Distribution of Localized and Delocalized States. Before considering the electronic DOS emerging from these simulations, it is convenient to analyze the dihedral angle distribution between thiophene rings for different regioregularities. (See Figure 4.) In fact, larger distortions from planarity are indicative of conjugation breaking, and broader distributions of dihedral angles are associated with larger disorder in the electronic structure and greater localization. The polymer backbone lies approximately on a plane for all regioregularities. However the inter-ring dihedral angle ϕ1 tends to deviate from planarity by ∼10
in the regioregular case and by ∼20
in the least regioregular case, with dihedral angle distributions broadening as the regioregularity decreases. (For a study of the torsional potential in isolated oligomers, see ref 27.) As a measure of the disorder in the side chains, which can also affect the packing and the electron transport,12 we analyzed the side chain (ϕ2) dihedral angle distribution, which shows an asymmetric distribution with

ARTICLE

Figure 4. Dihedral angle distribution of the angles ϕ1 and ϕ2 (defined in Figure 1) for rr = 56% (magenta), rr = 77% (blue), rr = 92% (green), and rr =1 00% (red). ϕ2 = 90
corresponds to the alkyl chain pointing toward the reader in the 2D representation of Figure 1.

Figure 5. Density of states in the region of the valence band edge for P3HT with different regioregularity. The plots are offset for clarity. The topmost curve was computed considering an ideal crystalline single chain of P3HT of the same size as that considered in the simulation box.

a preference for angles of 270 as opposed to 90
. Also, in this case, a broadening of the distribution is observed as the regioregularity decreases with an additional new peak observed at 180
for the least regioregular models. The presence of side chains with an angle of 180
contributes to the decrease in the packing efficiency and leads to a more disordered structure. The computed valence band DOS is given in Figure 5 for different regioregularities. The most obvious feature of the LMOM computed DOS is the shift of the valence band edge toward lower energies with decreasing regioregularity due to a decrease in conjugation length (reduced average coupling between monomers). The latter is caused by a decrease in the planarity of the polymer backbone and the broadening of the side-chain dihedral angle distribution, which both contribute to a decreased crystallinity of the polymer structure. The reduction in the band gap with increasing regioregularity has been experimentally observed by UPS and IPES experiments.24 There are, however, two more unexpected features that can help in understanding the transport mechanism in these materials. First of all, there is no evident broadening of the DOS in the region between the highest DOS maximum and the high-energy DOS edge with the increase in regioregularity defects, suggesting that the energy distribution and the type of states in the DOS tails are similar for 19388

dx.doi.org/10.1021/jp207026s |J. Phys. Chem. C 2011, 115, 19386–19393

The Journal of Physical Chemistry C

ARTICLE

Table 1. Variation in the Average Dihedral Angle and Local Regioregularity (in degrees, Defined in Text) in the Vicinity of a Hole Trap State (trap) Compared with That of the Whole System (all)a regioregularity

Dtrap

Dall

R trap

Rall

0.50

21.6 (2.9)

31.4 (1.2)

0.31 (0.17)

0.44

0.75

16.5 (2.5)

24.3 (1.5)

0.12 (0.09)

0.23

0.90

13.5 (1.7)

17.8 (0.6)

0.07 (0.07)

0.08

1.00

10.5 (1.2)

14.0 (0.8)

0.00 (0.00)

0.00

a

Data in parentheses are the standard deviations (null for the last column).

Figure 6. (Top) Average localization length of P3HT with regioregularities of rr = 56% (magenta), rr = 77% (blue), rr = 92% (green), and rr = 100% (red). The error bars included for a few selected points are larger in the tail region, indicating the coexistence of localized and delocalized states in that region. (Bottom) Localization of the orbital density for the state at the band edge (darker blue regions correspond to higher density) on each monomer (represented as spheres) for different regioregularities.

all regioregularities. Moreover, the DOS for the more regioregular systems displays, just outside the band tail region, oscillations that can be clearly ascribed to quasi-band states. To confirm this assignment a calculation of the DOS of an idealized perfectly crystalline structure of the same size is also included in Figure 5, and oscillations with similar spacing (due to the finite size of the simulation box) are clearly evident. Note that the broadening of the idealized crystal structure is arbitrary, whereas the shapes of the other DOSs are not affected by the small broadening of the individual level introduced to compute the DOS. It seems therefore that the electronic structure of the more regioregular polymer can be seen as being composed of a relatively narrow region of tail states and a much broader region of quasi-band states. These states can be described as band states perturbed by a nonperiodic weak potential.25 To characterize more precisely the nature of the states at different energies, we computed the average localization length as a function of the electronic energy. Localization length, Lα, Ærαæ)2, for the eigenstate α was defined as Lα2 = 4∑ipiα(ri where piα is the orbital density on the ith monomer, ri is its center of mass, and Ærαæ is the “center-of-orbital” density, calculated as Ærαæ = ∑ipiαri.26 piα is computed from the coefficients defining the orbital α, cαk, and the overlap matrix Skl between the basis set orbital as piα = ∑k,l on i cαkSklcαl. (The summation is limited to the basis function localized on the ith monomer.) The average localization length as a function of energy is given in Figure 6. Away from the band edge, all states are very delocalized (∼80 90 Å which is approximately half of the box length and so the actual localization length is likely higher than this). In the vicinity of the valence band edge, the localization length becomes significantly shorter. The highest energy occupied state is generally the most localized, usually within 5 7 monomers, and this special state is represented more explicitly also in Figure 6. Whereas upon increasing the regioregularity the average localization length increases, only for very low regioregularity (100 ps. The structural deformations of the polymer, in fact, persist for these long times so that trap states tend to be localized in the same region of space, whereas their energy fluctuates by a few meV because of the polymer thermal motions. Energy fluctuation causes the energy ordering of these trap states to be altered during the dynamics. Figure 7 represents the orbital density of the highest energy occupied orbital for one of the simulations. The density is localized around one of two possible regions, indicating that there are two high-energy occupied orbitals permanently localized in the same region that intermittently become the highest occupied orbital of the system. Comparison with the Experimental Results. The computational results point to the presence of delocalized “bulk” states and a tail of localized “trap” states. It is reasonable to assume that in this system transport takes place by promotion of the localized hole in the delocalized states. Of the proposed transport models for polymeric materials, the mobility edge (ME) model,34 which assumes that charge carriers (holes) occupying states at energies below a predefined ME have mobility μ0 and those in states above ME are essentially trapped, has the closest characteristics to what emerges from the simulation. Hence the effective mobility μ that characterizes the performance of the transistor is the average mobility of all of the carriers, mobile and trapped, and is a function of the band mobility μ0 as well as the trap distribution. This model has been successfully applied to singlecrystalline, polycrystalline, and polymeric organic FETs.35 On the basis of our simulations, we expect that the trap density extracted from modeling the characteristics of P3HT transistors should not depend strongly on the regioregularity of the semiconductor. Hence, measurements of field-effect mobility in TFTs were made to compare charge transport in P3HT of different regioregularities in material having sufficiently high molecular weight (Mw ≈ 130 160 kDa) to ensure high performance 19390

dx.doi.org/10.1021/jp207026s |J. Phys. Chem. C 2011, 115, 19386–19393

The Journal of Physical Chemistry C (μ > 10 2 cm2 V 1 s 1). P3HT has been shown to crystallize forming 2D lamella planes parallel to the semiconductor dielectric interface, and hence we use 2D electronic structures to model the devices. As a result, a constant DOS Dband equal to 2  1014 cm 2 eV 1 has been assumed in the band below ME,31 whereas the density of traps is defined as Dtrap = min(DBand, (Ntail/Eb)e E/Eb). The ME is defined, without loss of generality, as E = 0 eV. Hence the trap distribution is made of two distinct functions. Away from the ME, the traps are found in an exponential tail characterized by Ntail and Eb. Eb describes how fast the trap density decays as a function of energy, and its precise physical origin is still debated. For instance it has recently been shown that Eb is related to the statistical fluctuations of the individual lattice spacings, or paracrystalline disorder, along the π π stacking direction. When the tail density reaches Dband, the trap distribution becomes constant (and equal to Dband). Hence the total density of trap states is given by Nt = Dband  Eb  [1 + ln(Ntail/(Dband  Eb))]. Because Dband is fixed, the trap distribution is completely determined by two parameters, that is, Eb and either Nt or Ntail. This composite trap distribution was chosen to mimic the result that states in the band near the bandedge may be localized. Whereas the mobility in the band μ0 obtained from the model is inversely proportional to the value of the band DOS (within reasonable estimates), the trap distribution (Ntail and Eb) depends on it only weakly. To model the TFT characteristics using the ME model, we discretized the charge distribution in the transistor channel into 2D planes parallel to the semiconductor dielectric interface in agreement with the lamellar morphology and orientation of P3HT. Invoking the gradual channel approximation36 allows us to neglect dEx/dx in solving for the electrostatic variables in the channel, where x is the direction along the channel. Hence the charge distribution in the different planes is determined iteratively by applying Gauss’s law at each layer, similarly to the procedure followed by Horowitz for charges uniformly distributed on a series of molecular monolayers.37 The carrier density is divided into mobile and trapped carriers assuming quasi-thermal equilibrium in the previously defined DOS. The drift current in the different lamella planes is given by Ii = qμ0Wnm i (x)Ex(x), where q is the electron charge, nm i is the mobile carrier density (in cm 2) in the ith layer, W is the channel width, Ex is the x component of the electric field, and x is the direction along the channel. Integrating alongR the channel allows us to express the current as Ii = qμ0(W/L) 0VD nm i (V) dV, where L is the channel length, VD is the drain-to-source voltage, and the V dependence of the mobile carrier density represents the dependence of the carrier distribution on the potential drop across the channel (VG V, where VG is the gate voltage). Therefore, for N layers, the total current (I = ∑N i = 1 Ii) is calculated as a function of geometry (W,L), applied voltages (VD, VG), band mobility (μ0), and parameters of the DOS (Dband, Nt, and Eb). Highly doped Si coated with a 200 nm layer of thermal SiO2 was used as a substrate. P3HT was spin-coated from dichlorobenzene on octadecyltrichlorosilane-treated substrates, and top contacts were evaporated. The contact configuration and the relatively long channels (200 μm) ensured that the devices were limited by the channel resistance. The mobility in the band μ0, Nt, and Eb were obtained by least-squares fitting to the ME model a set of temperature-dependent transfer curves (Table 2). The agreement between measured and modeled transfer curves is remarkable for the measured voltage and temperature range (Figure 8). The trap distribution is the same for the low and high

ARTICLE

Table 2. Mobility Edge Model Parameters Obtained from the Measurements of P3HT Thin Film Transistors with Different Regioregularities μ (cm2 V

1

μ0 (cm2 V

1

Eb

Nt

(%)

(kDa)

s )

s )

(meV)

(cm 2)

97

158

0.03

0.5

22

1.8  1013

84

130

0.012

0.3

26

2  1013

RR

MW

1

1

Figure 8. Transfer curves (points) and ME model fit (lines) of P3HT thin film transistors spun from DCB with molecular weights of 158 (97% RR, top panel) and 130 KDa (84% RR, bottom panel).

regioregularity material; therefore, the higher mobility in the more regioregular material is entirely attributable to the band mobility μ0 rather than to traps, suggesting that it is limited by scattering at defects. There are many points of agreement between the results of the atomistic modeling and that of the fitting. First of all, both theory and experiments agree that the shape of the DOS tail is not affected by regioregularity and neither is the total trap concentration. Even more importantly, both methods agree on the absolute density of traps. There is not a rigid cutoff energy in the calculated DOS where one can separate localized and delocalized states, but if one takes the computed DOS maximum as a 19391

dx.doi.org/10.1021/jp207026s |J. Phys. Chem. C 2011, 115, 19386–19393

The Journal of Physical Chemistry C reasonable mobility-edge energy, then the computed 2D trap density is 4.7  1013 cm 2, in striking agreement with the experiment. This level of similarity between completely independent evaluations of the P3HT electronic structure strongly suggests that the atomistic model and the associated electronic structure calculation are representative of the realistic situation and that the simplifications introduced by the ME model capture the correct physics of transport in semicrystalline polymers. The modeling results further suggest that a more physical fit to transport data should include a mobility μ0 that gradually decreases as a function of energy in the vicinity of the ME. The cross validation between the two methods also serves to support the assumption, discussed in the introduction, that the semicrystalline domains of P3HT and not the amorphous regions dominate charge transport in FET devices. Whereas this assumption is reasonable for films made with polymers having moderate-to-high regioregularities and a high-enough molecular weight to ensure intercrystallite connectivity, such as those analyzed here, it is likely to break down for materials having low regioregularity, depending on their degree of crystallinity, and low molecular weight. The similarity of the DOS deriving from the computation and the experiment can be considered to be a validation of this hypothesis and can serve as an a posteriori indication that there are probably no additional trap states (e.g., at the interface between the semiconductor and the dielectric) not considered by the proposed model.

’ CONCLUSIONS The study of the band structure of polymers has always been considered to be relevant for charge transport but alone insufficient to make a direct connection with the experimental charge mobility. We illustrated the role and significance of band states in polymers by showing how these states coexist with trap states in the DOS tail. Both modeling and experiment quantitatively agree on the density of trap in the crystalline regions of P3HT (a trap state every 13 32 thiophene units). The excellent agreement allows one to use the results of the modeling to provide a microscopic interpretation of the results. For example, not only do we find that a small decrease in regioregularity has little effect on the number of traps but we also can explain the chemical origin of this fact. We find that traps are found in correspondence with more planar regions of P3HT, which are normally found away from head-to-head defects. Consequently, increasing the number of head-to-head defects does not significantly alter the occurrence of these trap states. From the modeling point of view, we achieved a truly consistent and multiscale description from the trap states described with atomistic chemical detail to the electric characteristics of the full device. This approach, which was used here to reveal the effect of regioregularity on P3HT devices, can be applied to all semicrystalline polymers and can be extended for the study of other properties such as optical properties. Hopefully, the application of this type of study to other polymers can contribute to the development of a structure/property relation for this complicated class of materials. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]; [email protected].

ARTICLE

’ ACKNOWLEDGMENT A.T., D.C., and D.M. are grateful to ERC, EPSRC and Leverhulme Trust for supporting their research. D.C. is grateful to Prof. Guido Raos for helpful suggestions. A.S. and J.D. gratefully acknowledge support from the National Science Foundation in the form of a Career Award and the Center for Advanced Molecular Photovoltaics (award no. KUS-C1-015-21), made by King Abdullah University of Science and Technology (KAUST). ’ REFERENCES (1) Zaumseil, J.; Sirringhaus, H. Chem. Rev. 2007, 107, 1296–1323. (2) Kaake, L. G.; Barbara, P. F.; Zhu, X. Y. J. Phys. Chem. Lett. 2010, 1, 628–635. (3) Grant, P. M.; Batra, I. P. Solid State Commun. 1979, 29, 225–229. (4) (a) Suhai, S. Phys. Rev. B 1983, 27, 3506–3518. (b) Bredas, J. L. J. Chem. Phys. 1985, 82, 3808–3811. (c) Ambroschdraxl, C.; Majewski, J. A.; Vogl, P.; Leising, G. Phys. Rev. B 1995, 51, 9668–9676. (d) Salzner, U.; Lagowski, J. B.; Pickup, P. G.; Poirier, R. A. Synth. Met. 1998, 96, 177–189. (5) Mott, N. F.; Davis, E. A. Electronic Processes in Non-Crystalline Materials; Clarendon: Oxford, U.K., 1979. (6) Galvao, D. S.; Dossantos, D. A.; Laks, B.; Demelo, C. P.; Caldas, M. J. Phys. Rev. Lett. 1989, 63, 786–789. (7) Dossantos, D. A.; Quattrocchi, C.; Friend, R. H.; Bredas, J. L. J. Chem. Phys. 1994, 100, 3301–3306. (8) Dossantos, D. A.; Bredas, J. L. J. Chem. Phys. 1991, 95, 6567– 6575. (9) Dean, P. Rev. Mod. Phys. 1972, 44, 127-&. (10) (a) B€assler, H. Phys. Status Solidi B 1993, 175, 15–56. (b) Baranovski, S. E. Charge Transport in Disordered Solids with Applications in Electronics; Wiley: West Sussex, U.K., 2006. (11) Street, R. A.; Northrup, J. E.; Salleo, A. Phys. Rev. B 2005, 71, 165202–165213. (12) Cheung, D. L.; McMahon, D. P.; Troisi, A. J. Am. Chem. Soc. 2009, 131, 11179–11186. (13) Vukmirovic, N.; Wang, L. W. J. Phys. Chem. B 2009, 113, 409–415. (14) Sirringhaus, H.; Brown, P. J.; Friend, R. H.; Nielsen, M. M.; Bechgaard, K.; Langeveld-Voss, B. M. W.; Spiering, A. J. H.; Janssen, R. A. J.; Meijer, E. W.; Herwig, P.; de Leeuw, D. M. Nature 1999, 401, 685–688. (15) (a) Chen, T. A.; Wu, X. M.; Rieke, R. D. J. Am. Chem. Soc. 1995, 117, 233–244. (b) Korovyanko, O. J.; Osterbacka, R.; Jiang, X. M.; Vardeny, Z. V.; Janssen, R. A. J. Phys. Rev. B 2001, 64. (c) Brown, P. J.; Thomas, D. S.; Kohler, A.; Wilson, J. S.; Kim, J. S.; Ramsdale, C. M.; Sirringhaus, H.; Friend, R. H. Phys. Rev. B 2003, 67. (16) (a) Kline, R. J.; McGehee, M. D.; Kadnikova, E. N.; Liu, J.; Frechet, J. M. J. Adv. Mater. 2003, 15, 1519–1522. (b) Jimison, L. H.; Toney, M. F.; McCulloch, I.; Heeney, M.; Salleo, A. Adv. Mater. 2009, 21, 1568-+. (17) (a) Prosa, T. J.; Winokur, M. J.; Moulton, J.; Smith, P.; Heeger, A. J. Macromolecules 1992, 25, 4364–4372. (b) Kline, R. J.; DeLongchamp, D. M.; Fischer, D. A.; Lin, E. K.; Richter, L. J.; Chabinyc, M. L.; Toney, M. F.; Heeney, M.; McCulloch, I. Macromolecules 2007, 40, 7960–7965. (18) Arosio, P.; Moreno, M.; Famulari, A.; Raos, G.; Catellani, M.; Meille, S. V. Chem. Mater. 2008, 21, 78–87. (19) Moreno, M.; Casalegno, M.; Raos, G.; Meille, S. V.; Po, R. J. Phys. Chem. B 2010, 114, 1591–1602. (20) Plimpton, S. J. Comput. Phys. 1995, 117, 1–19. (21) Chabinyc, M. L.; Salleo, A.; Wu, Y. L.; Liu, P.; Ong, B. S.; Heeney, M.; McCulloch, I. J. Am. Chem. Soc. 2004, 126, 13928–13929. (22) McMahon, D. P.; Troisi, A. Chem. Phys. Lett. 2009, 480, 210–214. (23) Hulea, I. N.; Fratini, S.; Xie, H.; Mulder, C. L.; Iossad, N. N.; Rastelli, G.; Ciuchi, S.; Morpurgo, A. F. Nat. Mater. 2006, 5, 982–986. 19392

dx.doi.org/10.1021/jp207026s |J. Phys. Chem. C 2011, 115, 19386–19393

The Journal of Physical Chemistry C

ARTICLE

(24) Kanai, K.; Miyazaki, T.; Suzuki, H.; Inaba, M.; Ouchi, Y.; Seki, K. Phys. Chem. Chem. Phys. 2010, 12, 273–273. (25) The coexistence of localized and delocalized states suggests that a Gaussian disordered model (assuming all states localized) is unsuitable in this case. For comparison with other works, we have fitted the DOS edge with a Gaussian function finding, for example, a width of 0.165 eV for both regioregularities 77 and 100%. (26) Cheung, D. L.; Troisi, A. J. Phys. Chem. C 2010, 114, 20479– 20488. (27) Fratini, S.; Ciuchi, S. Phys. Rev. Lett. 2009, 103, 266601. (28) Kilina, S.; Enrique R. Batista, E. R.; Yang, P.; Tretiak, S.; Saxena, A.; Martin, R. L.; Smith, D. L. ACS Nano 2008, 2, 1381–1388. (29) Barford, W.; Lidzey, D. G.; Makhov, D. V.; Meijer, A. J. H. J. Chem. Phys. 2010, 133, 044504. (30) Rivnay, J.; Noriega, R.; Northrup, J. E.; Kline, R. J.; Toney, M. F.; Salleo, A. Phys. Rev. B 2011, 83. (31) (a) Northrup, J. E. Phys. Rev. B 2007, 76, 245202–245206. (b) Street, R. A.; Northrup, J. E.; Salleo, A. Phys. Rev. B 2005, 71, 165202–165202. (32) McMahon, D. P.; Troisi, A. Phys. Chem. Chem. Phys. 2011, 13, 10241–10248. (33) McMahon, D. P.; Troisi, A. ChemPhysChem 2010, 11, 2067– 2074. (34) Salleo, A.; Chen, T.; V€olkel, A.; Wu, Y.; Liu, P.; Ong, B.; Street, R. Phys. Rev. B 2004, 70, 115311–115311. (35) (a) Chang, J. F.; Sirringhaus, H.; Giles, M.; Heeney, M.; McCulloch, I. Phys. Rev. B 2007, 76, 205204. (b) Kalb, W. L.; Batlogg, B. Phys. Rev. B 2010, 81, 035327. (c) Kalb, W. L.; Haas, S.; Krellner, C.; Mathis, T.; Batlogg, B. Phys. Rev. B 2010, 81, 155315. (d) Oberhoff, D.; Pernstich, K. P.; Gundlach, D. J.; Batlogg, B. IEEE Trans. Electron Devices 2007, 54, 17–25. (e) Pernstich, K. P.; Rossner, B.; Batlogg, B. Nat. Mater. 2008, 7, 321. (f) Sirringhaus, H. Adv. Mater. 2005, 17, 2411–2425. (g) Xie, H.; Alves, H.; Morpurgo, A. F. Phys. Rev. B 2009, 80, 245305. (h) Zhao, N.; Noh, Y.-Y.; Chang, J.-F.; Heeney, M.; McCulloch, I.; Sirringhaus, H. Adv. Mater. 2009, 21, 1. (36) Pierret, R. Semiconductor Device Fundamentals; Addison-Wesley: Reading, MA, 1996. (37) Horwitz, G. In Organic Electronics: Materials Manufacturing and Applications; Klauk, H., Ed.; Wiley-VCH: Weinheim, Germany, 2006.

19393

dx.doi.org/10.1021/jp207026s |J. Phys. Chem. C 2011, 115, 19386–19393