Theoretical Study of Charge Carrier Transport in Organic

Article pubs.acs.org/JPCC

Theoretical Study of Charge Carrier Transport in Organic Semiconductors of Tetrathiafulvalene Derivatives Huixue Li,*,†,‡ Renhui Zheng,‡ and Qiang Shi*,‡ †

College of Life Science and Chemistry, Tianshui Normal University, Tianshui, Gansu 741001, China State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China

‡

ABSTRACT: The density functional theory and hopping model were employed to calculate the charge carrier mobility of four planar polycyclic aromatic hydrocarbon fused tetrathiafulvalene derivatives. The effect of halogen substitution and nitrogen substitution were also investigated. Dinaphtho-tetrathiafulvalene (DN-TTF) and diquinoxalinotetrathiafulvalene (DQ-TTF) were revealed to be primarily hole transport materials due to their high electron injection barrier relative to the work function of the Au electrode. Halogen substituted TFDQ-TTF and TClDQ-TTF were found to have lower HOMO and LUMO energy levels, such that the electron injection barriers are lowered and the hole injection barriers are elevated. The large transfer integral and small reorganization energy for electron transport also suggest that they have relatively large electron mobilities. The calculated results were in good agreement with the experiment ones. Our result shows that withdraw-electron groups introduced in aromatic fused tetrathiafulvalene derivatives is a rational way to obtain good n-type organic semiconductors.

1. INTRODUCTION Over the last several decades, the field of organic optoelectronic devices (e.g., organic light-emitting diodes, field effect transistors (OFETs), and solar cells) has attracted much research effort.1−9 Organic electronic devices have many desirable properties, such as lightweight, low cost, flexibility, low-temperature device fabrication, versatility of chemical synthesis, and ease of processing. However, in many of the devices mentioned above, their performance depends critically on how efficiently charge carriers can move between the πconjugated units; that is, the charge carrier mobility of the organic materials is the key to many important applications.10−12 Organic semiconductor materials can be classified as p-type or n-type according to which type of charge carrier is more efficiently transported through the material. In fact, all organic semiconductors allow hole and electron transport.13 In molecular electronic devices, another important issue is whether charge carriers can be injected efficiently into the organic semiconductors. For example, the HOMO level of many organic semiconductors is in the range of −4.8 to −5.3 eV, which aligns well with the work function of gold (4.8−5.1 eV), thus the injection of holes into the HOMO level is easily achieved using gold electrodes. On the other hand, the LUMO level often lies much higher at around −3 to −4 eV. When gold electrodes are used, n-type transport is much harder to achieve due to the extremely high injection barrier of 2−3 eV.14 However, to construct OFET devices for applications, it is very important to search for new types of materials, especially n-type or ambipolar organic semiconductors. © 2012 American Chemical Society

In the literature, acene (e.g., oligoacenes, triphenylene, and rubrene),15−20 oligothiophene (pentathienoacene and linearly thiophene), and their derivatives21−23 are the most studied low weight organic semiconductors, whereas polythiophene, polyparaphenylenevinylene, polyfluorene derivatives, and oligothiophene-functionalized truzene are the most studied polymer semiconductors.14,21,24 Pentacene is well-known as an excellent hole transferring material. Currently, its hole mobility >5.0 cm2/V s has been obtained.25 When all hydrogen atoms of pentacene are substituted by fluorine atoms, the compound is turned into perfluoropentacene, and the fabricated OFET transports electrons more efficiently than holes, with a high electron mobility of 0.11−0.22 cm2/V s.26−28 In this paper, we will present theoretical investigations of the charge carrier mobility of four planar polycyclic aromatic hydrocarbon fused tetrathiafulvalene (TTF) derivatives. Tetrathiafulvalene-7,7′,8,8′-tetracyanoquino-dimethane (TTF-TCNQ) was discovered by Ferraris in 1973 as a chargetransfer salt.29 From then on, TTF and its derivatives have been intensively studied.30−34 TTF derivatives are generally soluble in various solvents, which permits the processing using inexpensive deposition techniques, such as spin-coating and inkjet printing. With the introduction of different substituents in the 2, 3, 6, and 7 positions of the TTF core,30 the electronic and the structural characteristics of the TTF derivative can also been modified.31−33 The aromatic fused TTF derivatives are highly planar structures, which favors intermolecular π−π Received: February 15, 2012 Revised: May 7, 2012 Published: May 14, 2012 11886

dx.doi.org/10.1021/jp301536z | J. Phys. Chem. C 2012, 116, 11886−11894

The Journal of Physical Chemistry C

Article

zero in the Marcus equation in eq 1 because only self-exchange reactions were involved. As the organic crystals are usually weak polar materials, the environmental contribution to the relaxation energy is on the order of a few tenths of an electronvolt.47 We thus neglect the influence of intermolecular interaction on the molecular deformation and their contributions to the reorganization energy. The reorganization energy is calculated as the sum of (a) the energy required for reorganization of the vertically ionized neutral structure to the cation or anion geometry and (b) the energy required to reorganize the cation or anion geometry back to the neutral equilibrium structure on the ground-state potential energy surface.48,49 Alternatively, the potential energy surfaces of the neutral and charged molecules can be modeled as a set of displaced harmonic oscillators.40,50,51 Assuming that one knows the vibrational frequencies and displacements of each mode of the donor and acceptor states, the normal-mode analysis partitions the total reorganization energy into the contributions from each vibrational mode

stacking interactions. In addition, intermolecular S···S interaction, as well as possible weak hydrogen bonding31 can lead to relatively tight packing that favors charge carrier transport.32,33 Rovira et al. have studied charge mobility of TTF derivatives contained thiophene, benzene, tetrahydrothiophene and 1,4dithiane rings, and found that the crystal stacking and S···S interactions affect the charge mobilities crucially.32 The herringbone crystal structure of dithiophene-tetrathiafulvalene (DT-TTF) have shown good performance for OFETs with mobility 1.4 cm2/V s.32 Biphenyl fused TTF (DBP-TTF) have been used to fabricate OFET on a SiO2 substrate by vacuum deposition, and a high hole mobility of 0.11 cm2/V s was observed.35 OFET device fabricated using phenyl fused TTF (DB-TTF) from solution also shows a better hole mobility of 1.0 cm2/V s.36 Due to the strong electron-donating property of TTF derivatives, their thin films are easily damaged by oxygen and moisture, in other words, the films are not stable in air. Fused aromatic rings and another heterocycles with electron-deficient nitrogen are introduced to the TTF skeleton. The formed TTF derivatives can reduce the π electrons delocalization, accordingly the ability to donate electron is weakened, thus the airstability could be improved.37 TTF derivatives with aromatic fused naphthane, quinoxaline, and quinoxaline attached halogen atoms rings, such as dinaphtho-tetrathiafulvalene (DN-TTF), and diquinoxalino-tetrathiafulvalene (DQ-TTF) have been synthesized. The OFET devices fabricated with these compounds were shown to have good charge mobilities.37,38 Naraso et al. have reported the main properties of these devices. DN-TTF and DQ-TTF both show p-type property, while fluorine and chlorine substituted DQ-TTF exhibited properties of n-type material.38 In order to investigate the effect of fused aromatic rings and electron-withdrawing substituentshalogen groups to TTF skeleton, we calculated the transfer integrals and charge mobilities, and the values agree with the experiments. Our calculations could be helpful in further developments of semiconducting materials based on TTF derivatives.

1/2 ⎛ λ ⎞ V 2⎛ π ⎞ ⎜ ⎟ exp⎜ − ± ⎟ ℏ ⎝ λ±kBT ⎠ ⎝ 4kBT ⎠

(2)

i

λi =

ki ΔQ i 2 2

(3)

Here, the summations run over all the vibrational normal modes. ΔQi represents the displacement along normal mode (NM) i between the equilibrium geometries of the neutral and charged molecules, ki and ωi are the corresponding force constants and vibrational frequencies, and Si denotes the Huang−Rhys factor measuring charge-phonon coupling strength. We calculated the reorganization energies using the density functional theory (DFT) level with the B3LYP functional and the 6-31G* basis set, the NM analysis and the Huang−Rhys factors are obtained through the DUSHIN program.52,53 The transfer integral V depends on the relative arrangement of the molecules in the solid state. Here, we took the crystal structures of each TTF derivatives to generate possible intermolecular hopping pathways. The electronic coupling can be obtained by direct dimer Hamiltonian evaluation method39,54 using the PW91PW91/6-31G* basis set, which was found to be simple and reliable.43,55 In this method, the electronic coupling for hole or electron transfer in the direct scheme can be written as

2. COMPUTATIONAL APPROACHES In this section, we briefly review the methods employed in this study to calculate the charge carrier mobility. In the incoherent hopping model,39−43 the charge carrier transport is described as a series of self-exchange electron transfer reactions between a neutral molecule and a neighboring anion (n-type materials) or cation (p-type materials). The basic assumption is that at sufficiently high temperature, the dynamical disorder of the site energies strongly localizes the charge, and the thermal assisted hopping becomes the dominant mechanism in charge carrier transport.44 Classical Marcus theory was employed to calculate charge transfer rates for organic materials45,46 ket =

∑ λi= ∑ Siℏωi

λ=

0,site1 0,site2 V = ⟨ϕHOMO/LUMO |F0|ϕHOMO/LUMO ⟩

ϕ0,site1 HOMO/LUMO

(4)

ϕ0,site2 HOMO/LUMO

where and represent the highest occupied molecular orbital (HOMO) or lowest unoccupied molecular orbital (LUMO) of isolated molecules 1 and 2, respectively; F0 is the Fock operator for the dimer, and the subscript zero indicates that the molecular orbitals appearing in the operator are unperturbed by the neighbor molecules. The Fock matrix is evaluated as

(1)

F0 = SCεC −1

where V is the transfer integral, λ± is the reorganization energy (λ+ or λ− is used for hole or electron transfer, respectively), kB is the Boltzmann constant, and T is the temperature. To achieve high charge carrier mobility in organic semiconductors, the reorganization energy needs to be minimized, and the intermolecular charge transfer integral needs to be maximized. The free energy difference for electron transfer ΔG was set to

(5)

where S is the overlap matrix for the dimer taken from the crystal structure, and the Kohn−Sham orbital C and eigenvalue ε are obtained by diagonalizing the zeroth-order Fock matrix without any self-consistent field iteration. The charge transfer mobility, μ, is then evaluated from the Einstein relation56 11887



μ = eD/kBT

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(6)

where D is the isotropic charge diffusion coefficient, which can be simulated by the random walk technique.43 The charge is only allowed to hop between nearest neighbor molecules, and the dimers are taken from crystal structures as a reference structure and any given molecule as the initial charge center. The hopping rate ket for a specific pathway is computed by eq 1, the intermolecular center distance is employed as the hopping distance. The hopping probability was evaluated as Pi = (ket)i/ ∑i(ket)i. The denominator is a sum over all the possible hopping pathways. The hopping time along the specified direction is 1/ket. At each step in the simulation, a random number r is generated that uniformly distributed between 0 and 1. If ∑i =j−11 pi < r ≤ ∑i =j 1pi (accumulated probability), then the charge is allowed to go along the jth direction. Each simulation lasts from a few tens to a few hundreds of a microsecond. Then, the diffusion coefficient is obtained as D = limt→∞⟨l(t)2⟩/6t, where l(t)2 is the mean squared displacement. A converged diffusion coefficient, which shows a linear relationship between the square of the diffusion distance and the diffusion time, was obtained by two thousand trajectories simulating.

Figure 2. Molecular electrostatic potential map (MEP) of the TTFs. In blue are the positive and in red the negative potential areas.

structure commonly found in planar molecule crystal. We take out the neighboring two molecules from the crystal structure and work out the S···H−C and S···S interaction energies by nature bond orbital analysis (NBO); the S···H and S···S bond lengths are 0.299 and 0.374 nm respectively, and the secondorder stabilization energies E(2) ij are 0.58 and 0.37 kcal/mol, which match the reported values.57,58 However, the herringbone structure is not always the most favorable packing, as the remaining TTF derivatives are all parallel packing, with displacements along the long and short molecular axes between adjacent molecules. MEPs in Figure 2 show that the charge distributions of DQ-TTF, TFDQ-TTF, and TClDQ-TTF are alternatively positive and negative on the benzene rings, whereas the N, F, and Cl atoms are negatively charged and the pyrazine rings are positively charged. In order to exhibit most favorable electrostatic interaction, the two nearest parallel molecules of DQ-TTF shift 0.390 nm along the direction of the long molecular axis and form a face-to-face πstacking. The interplanar distance is about 0.34 nm and the shortest intermolecular S···S distance is 0.361 nm. The 1,3dithiole rings are also overlapped with the pyrazine rings, giving rise to columns of molecules (Figure 3). Thus, the crystal packing of DQ-TTF can be described as being built up from a series of columns of DQ-TTF along the a direction. On the other hand, the neighboring columns form a herringbone arrangement other than parallel packing,37 both the molecules (along a + b) are in almost a plane and are reinforced by C− H···N (the distance of hydrogen bond is 0.25 nm) and S···S contacts. The crystal structure of TFDQ-TTF is different from DQTTF,38 the two nearest parallel molecules shift 0.190 nm along the direction of the long molecular axis where the interplanar distance is about 0.339 nm and an intermolecular short S···S contact is 0.361 nm. Both the neighboring molecules (along b) are in almost a plane and are reinforced by C−H···N (0.27 nm) and S···S contacts. In addition, due to greater electronegativity and smaller atomic radius of fluorine, the F···H distance between both the nearest molecules in a plane (along b) is 0.262 nm, which indicates there is strong F···H hydrogen bond. These factors above-mentioned keep the parallel packing of molecules in the unit cell in order to be at a minimum of the total interaction energy. Consequently, all the molecules in TFDQ-TTF crystal are parallel instead of the herringbone arrangement of neighboring columns. In the crystal structure of TClDQ-TTF,38 the molecules are parallel packing, but the shift long molecular axis is 0.981 nm, which is the longest among these compounds. The electron-withdrawing chlorine atoms are sandwiched by the electron-donating TTF parts, and the

3. RESULTS AND DISCUSSION All of the molecular structures of the compounds studied in this paper are shown in Figure 1.

Figure 1. Molecular structures of TTF derivatives (H atoms are omitted).

3.1. Intermolecular Interactions. Crystal structure is one of the most important properties that determine the charge carrier transport pathways and mobility in organic molecular crystals. Generally speaking, the short ranged van der Waals interaction is the main factor determining the crystal structure of organic molecules. However, other intermolecular interactions such as electrostatic and hydrogen bond may also are the main driving forces. As the van der Waals interaction is the most difficult to model using the DFT theory (although we note that there are significant advances in this area), we concentrate on the electrostatic and draw the molecular electrostatic potential (MEP) map of the TTF derivatives, which are shown in Figure 2. For the MEP map of DN-TTF, the positive charges locate at the hydrogen atoms and the negative ones at the sulfur atoms, and the naphthyl rings are also slightly negatively charged. The MEP map implies that the DN-TTF molecules are not likely to pack face-to-face since this will lead to strong electrostatic repulsion, while it is possible to form a face-to-edge configuration where the side H atoms with positive charge lies close to the molecular plane of another molecule with partial negative charges. This is in accordance with the actual crystal structure of DN-TTF,37 which is the herringbone 11888



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Figure 3. Charge hopping pathways schemes for TTF derivatives, which were reported in refs 37 and 38.

Table 1. HOMO and LUMO Energies (eV), HOMO-LUMO Gaps (Egap/eV), Vertical Ionization Potentials and Electron Affinities (IPvert, EAvert/eV), and Reorganization Energy (meV) by Both the AP and NM Methodsa reorganization energy molecule

HOMO

LUMO

Egap

IPvert

EAvert

λ+/AP (B3LYP)

λ+/AP (B3P86)

DN-TTF DQ-TTF TFDQ-TTF TClDQ-TTF

−4.829 −5.351 −5.576 −5.734

−1.321 −2.223 −2.515 −2.723

3.508 3.128 3.061 3.011

6.137 6.654 6.867 6.955

−0.163 −1.015 −1.304 −1.584

227.5 230.5 258.5 239.8

224.4 228.0 250.0 230.0

a

λ+/ NM

λ−/AP (B3LYP)

λ−/AP (B3P86)

λ−/ NM

233 233 230 237

132.6 190.9 237.3 211.9

133.0 189.2 224.5 197.8

137 197 230 186

AP: adiabatic potential, NM: normal mode.

interplanar distance of 0.331 nm is the shortest among all the TTF derivatives. An intermolecular short S···S contact is 0.489 nm. In contrast, the shortest contact between chlorine atom and sulfur atom of neighboring molecules is 0.390 nm, which indicates the Cl···S interaction is more remarkable.59 The neighboring columns both molecules (along b) are reinforced by C−H···N (the distance of hydrogen bond is 0.310 nm), Cl···S and S···S contacts. The sandwiched arrangement of molecules in the TClDQ-TTF cell can keep at a minimum of the total interaction energy. All of the crystal structures and charge hopping pathways are showed in Figure 3. 3.2. Frontier Orbitals. Before current can flow through the transistor channel in OFETs, charges have to be injected from the source-drain electrodes into the semiconductor. On a direct metal-semiconductor junction without any doping, the barrier height at the metal-semiconductor interface is given by the difference between the metal work function and the semiconductor HOMO or LUMO. The smaller the barrier height, the more easily charges are injected. For OFETs with Au

source-drain electrodes, to ensure effective charge injection from the source electrode, the p-type semiconductors should possess high HOMO energies. On the contrary, n-type materials should possess low LUMO energies, such that they lie close to the work function potential of the Au electrodes. Once electron-withdrawing groups such as nitrogen, fluorine, and chlorine were incorporated into the p-type semiconductors, the HOMO and LUMO energy levels of the compounds become lower, such that the injection of electron becomes easier, and they may become ambipolar or n-type semiconducing materials.21,24,60−63 The HOMO and LUMO energy levels, vertical ionization potentials, vertical electronic affinities, and internal reorganization energies for the series of TTF derivatives were calculated, the data are summarized in Table 1. When heteroatomic nitrogen, fluorine, and chlorine atom substitute for carbon and hydrogen atoms of DN-TTF to become DQ-TTF, TFDQ-TTF, and TClDQ-TTF, both the HOMO and LUMO energies decrease, as well as the energy 11889



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Table 2. Components of Substituting Atoms at the Frontier Molecular Orbital for the Title Compounds Computed at the B3LYP/6-31G* DN-TTF

DQ-TTF

TFDQ-TTF

TClDQ-TTF

HOMO

LUMO

HOMO

LUMO

HOMO

LUMO

HOMO

LUMO

0.0(H) 0.9(C)

0.0(H) 28.4(C)

0.0(H) 6.31(N)

0.0(H) 45.95(N)

1.62(F) 5.75(N)

2.13(F) 44.14(N)

2.46(Cl) 6.47(N)

2.02(Cl) 42.46(N)

gaps of them. In order to explore the effect of these heteroatoms, we made a systematic analysis on the molecular orbital population of these compounds. It was based on the planar geometrical structure optimized at the B3LYP/6-31G* levels. The square sum of all atoms in the compound indicates the contribution of each atom to one molecular orbital, and the calculated data are shown in Table 2. With regard to HOMO and LUMO orbitals, the substituted C atom ingredients in DNTTF are 0.9% and 28.4%, simultaneously, the N atom in DQTTF are 6.31% and 45.95%, respectively. As we know, nitrogen atom has lower energy, which makes the HOMO and LUMO of DQ-TTF lower than DN-TTF. The substituted atom ingredients of the LUMO orbitals change more obviously. The difference between the LUMO of DN-TTF and the LUMO of DQ-TTF is the largest (0.9 eV), the difference between one of DQ-TTF and TFDQ-TTF is only 0.29 eV, the difference between DQ-TTF and TClDQ-TTF is 0.5 eV, and the two latter differences are smaller relatively. The differences between the HOMOs of title compounds do not have the above trend, because there are small changes between the substituted atom ingredients. When fluorine and chlorine atoms substitute for the hydrogen atoms, heavy atom ingredients increase in the frontier molecular orbitals of TFDQ-TTF and TClDQ-TTF, and thus the HOMOs and LUMOs of TFDQ-TTF and TClDQ-TTF are lower than those of DQ-TTF. Furthermore, chlorine atom has empty 3d orbitals to accommodate any delocalization of the π-electrons, but the 3s and 3p being the next unoccupied atomic orbitals on fluorine atom are prohibitively high in energy.64 This makes the electronically delocalized extension of TClDQ-TTF be larger than that of TFDQ-TTF, so the HOMO and LUMO of TClDQ-TTF are lower. As expected, when halogen substitution of fluorine or chlorine is introduced to the TTF derivatives, the HOMO and LUMO energy levels decrease which leads to increase in the injection barrier for holes but a decrease in the injection barrier for electrons (assuming Au source-drain electrodes). The vertical ionization potential of DN-TTF (6.137 eV) is closer to the work function potential of common gold electrode (ca. 5.1 eV),33 and a larger difference between the vertical electronic affinity and gold electrode (−0.163 eV). This implies that the compound is p-type rather than n-type. On the contrary, TClDQ-TTF is n-type rather than p-type. The frontier molecular orbitals of the title compounds are shown in Figure 4. 3.3. Charge Carrier Mobility. Room temperature mobility is obtained through a random walk simulation based on the Marcus rates. We have used 2000 trajectories for the statistics average, which was found to be reliable as previously reported.43 The simulated mobilities are gathered in Table 3 and compared with the available experimental results. We find that the calculated values are reasonably close to all the measured values. The relationship of squared displacement l(t)2 and time t about the hole hopping of DN-TTF is depicted in

Figure 4. Frontier molecular orbitals of the title compounds.

Figure 5, where results for 10 simulations and the average over 2000 simulations are shown. The linear relation for l(t)2/t shows that the simulated trajectory is long enough. The configurations of TTF derivatives were calculated using B3LYP/6-31G* level in vacuum using Gaussian 03,65 and no symmetry restriction is added during the structure optimization. As reported before for similar TTF derivatives, the DNTTF molecule adopts a distorted boat conformation in the neutral ground state66 but a planar conformation for the +1 and −1 charged states. However, experimental crystal structures have shown that neutral DN-TTF molecules also adopt a planar conformation,37 so the planar geometry is used to calculate the reorganization energy. For the other compounds, i.e., DQ-TTF, TFDQ-TTF, and TClDQ-TTF, the stable configurations of their molecules including charged and neutral states are planar obtained by both theoretical computation and experiment. Table 1 lists the reorganization energies calculated by two different methods, which were obtained by adiabatic potentials and normal-mode analysis (NM). Their values are very close to each other except for the λ+ of TFDQ-TTF and λ of TClDQTTF. The NM method used here is based on a displaced harmonic oscillator mode. However, possible anharmonic effects and mode mixing effects67 may cause differences between results from NM method deviate from those from AP method, especially the relatively larger differences between the λ+ of TFDQ-TTF and λ of TClDQ-TTF from both the methods. For the adiabatic potential energy surface method, although it is one of the most widely used methods to assess molecular reorganization energy, the calculated accuracy still depends on the selection of DFT and basis set. In addition, the method excludes the molecular interaction between adjacent molecules in the crystal, which may cause additional errors.68,69 In addition, some references have pointed out that the B3P86 functional could be better than the B3LYP one to 11890



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Table 3. DFT/PW91PW91-Calculated Transfer Integrals in TTF Derivatives (in meV) with Different Hopping Pathway and Carried Out Hole and Electron Mobilities (in cm2/V s) DN-TTF pathway 1 2 3 4 5 6 μ+ μ− μ(exp.)

r/Å

Vh

4.74 46.1 5.93 139.0 5.14 −23.48 18.16 0.029 19.63 0.0084 19.25 0.0010 1.788 ± 0.112 0.224 ± 0.010 0.38−0.42 (p-type)37

DQ-TTF

TFDQ-TTF

TClDQ-TTF

Ve

r/Å

Vh

Ve

r/Å

Vh

Ve

−17.4 11.90 −40.0 0.67 0.135 0.0066

4.88 14.71 14.77 5.75 6.51

81.13 −1.19 −1.31 96.10 −29.5

49.1 3.11 4.20 1.33 1.96

3.86 6.64 7.04 8.27 19.38 17.83 0.294 ± 0.016 1.124 ± 0.062 0.1 (n-type)38

38.81 −12.7 33.81 2.06 −0.60 0.25

−68.2 −0.73 1.51 0.08 0.94 −1.35

1.592 ± 0.097 0.978 ± 0.044 0.2 (p-type)38

r/Å

Vh

10.25 −18.2 6.10 51.60 12.79 −3.63 12.89 −1.98 13.03 37.85 22.17 −1.39 0.234 ± 0.015 1.255 ± 0.063 0.11 (n-type)38

Ve −36.6 63.37 −1.94 −1.66 −37.58 1.12

calculate the structural parameters for sulfur-containing molecules,70−72 and we have also performed calculations of the hole and electron reorganization energies of all the TTF derivatives at B3P86/6-31G* level. In comparison with the previous results obtained at B3LYP/6-31G* level, the calculated reorganization energies differs slightly, with the largest derivation for hole/electron reorganization energy of 9.8/14 meV (both for TClDQ-TTF), so the reorganization energies calculated using these two functionals are rather similar. The results of NM analysis at the B3LYP/6-31G* level are displayed in Figures 6 and 7. The contributions of each normal mode is charted out, one can see that high frequency parts (1200−1620 cm−1), which are the C−C single and CC, C N double bonds from aromatic rings and tetrathiafulvalene stretching modes, contribute mainly to reorganization energy. Lower frequency parts (100−700 cm−1), which include the S− C single bonds stretching modes, also act on reorganization energy. For TFDQ-TTF and TClDQ-TTF, Cl has empty 3d

Figure 5. Squared displacement vs simulation time for the hole transport of DN-TTF.

Figure 6. Contribution of the vibrational modes to the cationic relaxation energy for TTF derivatives. 11891



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Figure 7. Contribution of the vibrational modes to the anionic relaxation energy for TTF derivatives.

orbitals to accommodate delocalization of the π-electrons, but the next unoccupied atomic orbitals on F is the 3s, which are high in energy that π-electrons cannot be well accommodated. The larger delocalization of π-electrons for TClDQ-TTF could be the reason that the reorganization energies of TClDQ-TTF are slightly smaller than those of TFDQ-TTF. The reorganization energy of TFDQ-TTF for both the electron and hole transfer are the largest in all the compounds, and the hole reorganization energy (258.5 meV) from adiabatic potential is slightly larger than the electron one (237.3 meV). Also the largest electronic coupling term (−68.2 meV) is almost twice that of the hole transfer integral (38.8 meV). The calculated electron mobility (1.124 cm2/V s) of TFDQ-TTF is larger than the hole mobility (0.294 cm2/V s). Our computed results are in agreement with experimental data (0.1 cm2/V s),38 which suggests that TFDQ-TTF is n-type material. The reorganization energy and charge transfer integral of TClDQTTF are similar to those of TFDQ-TTF, the hole reorganization energy (239.8 meV) is also larger than the electron one (211.9 meV). In all possible pathways of charge transport, the largest value of electron transfer integral (63.4 meV) is greater than that of hole transfer (51.6 meV). The calculated electron mobility is 1.255 cm2/V s and the hole mobility 0.234 cm2/V s. This also indicated that TClDQ-TTF prefers n-type to p-type material, which is consistent with the experimental performance (the observed electron mobility was 0.11 cm2/V s38). The electron mobilities of TClDQ-TTF are slightly larger than one of TFDQ-TTF, apart from small reorganization energy of TClDQ-TTF, for chlorine atom, the large radii would result in mild electrostatic repulsion when the π-electron delocalize in its vicinity, which indicates in their crystal structures, the interplanar distance of TClDQ-TTF is 3.33 Å and that of TFDQ-TTF is 3.39 Å. For DN-TTF and DQ-TTF, their hole reorganization energies are larger than the electron ones too, nevertheless,

the hole transfer integrals are larger than the electron ones. For DN-TTF, the most largest hole transfer integral is 139 meV as charges hop along pathway 2. Correspondingly, the largest electron transfer integral is −40.0 meV along pathway 3. As to DQ-TTF, its largest hole transfer integral is 96.1 meV along pathway 4, and the largest electron transfer integral is 49.1 meV along pathway 1. The results show that the hole transport ability of DN-TTF (the computed hole mobility is 1.788 cm2/V s) are better than that of electron transport (the computed electron mobility is 0.224 cm2/V s), which also agrees with the experiment (the observed hole mobility is 0.38−0.42 cm2/V s37). DQ-TTF is similar to DN-TTF, and it is also a p-type material where the computed hole mobility is 1.592 cm2/V s and the electron one is 0.978 cm2 /V s; the observed hole value is 0.2 cm2/V s.38 In this work we have assumed charges hop in a pure crystal without any defects. In fact, the experimental results were characterized in thin film devices, where a thin film is usually quite ordered up to a few ten nanometers in size.73 So the effects of grain boundaries and charge traps may not be neglected. This is the possible reason that the predicted mobilities were larger than the observed ones by 1 order of magnitude.74

4. CONCLUSIONS The hole and electron mobilities of four planar TTF derivatives were investigated computationally. When nitrogen and halogen atoms are introduced to these semiconducting materials, the HOMO and LUMO energy levels decrease in the order of DNTTF, DQ-TTF, TFDQ-TTF, and TClDQ-TTF, which means that the injection barrier of holes increase and the injection barrier of electrons decrease for OFETs with common gold electrodes. The reorganization energies for both the hole and electron transfer increase in the order of DN-TTF, DQ-TTF, TClDQ-TTF, and TFDQ-TTF. This shows that substitution 11892



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with fluorine has larger effect on TTF compared with substitution with chlorine. Moreover, the injection barriers of electron are lower than the unsubstituted DN-TTF and DQTTF,and these results indicate that both the substituted compounds can act as n-type materials. Unsubstituted DN-TTF and DQ-TTF are revealed to work only as p-type semiconductors due to their high electron injection barrier relative to the work function of Au electrodes and the low electron mobilities. On the contrary, the electron mobilities of substituted TFDQ-TTF and TClDQ-TTF were found to be larger than the hole mobilities. TClDQ-TTF has a lower LUMO than their fluorinated counterparts for delocalization of π-electrons into the unoccupied 3d orbitals that are not available in fluorine atom. This is advantageous for decreasing the barrier of electron injection, and making the compound more stable when oxygen and moisture exist. If other electron-withdrawing groups, for instance cyano-, nitro-, and carboxyl groups, are introduced to DQ-TTF, it is possible to obtain better n-type materials due to larger electronegativity. Furthermore, if the residual hydrogen atoms of TClDQ-TTF or TFDQ-TTF are substituted with Cl or F atoms, which turn into perchlorinated or perfluorinated DQTTF, the LUMO energy levels of these compounds will be expected to be even lower; thus, they may be more excellent ntype materials owing to smaller injection barrier.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (H.-X.L.); [email protected] (Q.S.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (No. 91027015, 20903101, and 21071110), the 973 program (Grant No. 2011CB808502), the Chinese Academy of Science, and the key laboratory for new molecule material design and function of Tianshui Normal University. We thank Prof. Zhigang Shuai for the code to calculate the charge transfer integrals.

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Theoretical Study of Charge Carrier Transport in Organic

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