Anisotropic Charge Transport in Bisindenoanthrazoline-Based n-Type

Article pubs.acs.org/JPCC

Anisotropic Charge Transport in Bisindenoanthrazoline-Based n-Type Organic Semiconductors Xiao-Yu Zhang and Guang-Jiu Zhao* State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, 457 Zhongshan Road, Dalian 116023, China S Supporting Information *

ABSTRACT: In this work, we theoretically investigated the charge-transport properties in bisindenoanthrazoline-based n-type organic semiconductors at the first-principle DFT level based on the Marcus−Hush theory. The relationship between molecular packing and charge transport for DADF and DADK, which are of different geometries as a novel n-type bisindenoanthrazilines (BIDAs) organic semiconductor, was presented. We theoretically demonstrated that DADK single crystal possesses considerable electron-transfer mobility, which is about three times larger than that of DADF. The predicted maximum electron mobility value of DADK is 0.373 cm2 V−1 s−1, which appears at the orientation angle near 72°/252° of conducting channel on the reference planes a−c. In addition, the angle dependence of mobility in all two crystals shows remarkable anisotropic behavior. The calculated results indicate that DADK may be an ideal candidate as a high-performance n-type organic semiconductor material. We also demonstrated that the molecular geometry of organic semiconductor plays an important role in determining the molecular stacking, electronic properties, and charge-transport behaviors. Theoretical investigation of organic semiconductors is helpful for evaluating the charge-transport behaviors to realize better charge-transfer efficiency and design higher performance electronic materials.

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INTRODUCTION With the remarkable advantages of organic materials in lowcost, chemical synthesis, and processability during the past decades,1−3 it is therefore no surprise that organic semiconductors have been of broad current interest to many scientists, not only for the intrinsic scientific challenges but also for an enormous potential applications in electronic and optoelectronic devices,4−20 such as organic light-emitting diodes (OLEDs),4−9 organic photovoltaic cells (OPVCs), 1 0 − 1 3 and organic field-effect transistors (OFETs).14−20 So topics of current research are essential to understanding and improving these devices. The most critical parameter in the performance of electronic devices is the hole (for p-type semiconductors) or electron (for n-type semiconductors) transport.21−23 To our knowledge, the mobility of hole or electron is increased in solid-state organic semiconductor when the intermolecular π orbital overlap is maximized.24 From both a fundamental and practical point of view, it is essential to understand the relationship between the © 2012 American Chemical Society

hole or electron transport and molecular packing in the crystal structure. Polycyclic heteroaromatics, as one type of the most popular organic semiconductors, have attracted enormous interest due to the extended planar backbone framework, which can improve intermolecular interactions because of π-conjugation.25−30 In the past decades, the extensive investigations focused on p-type (hole-transport) organic semiconductors have been performed.31−44 Pentancene and rubrene, which are the famous representatives of p-type organic semiconductors, have superior charge-transport properties compared with amorphous silicon.45,46 It has been reported that pentancene has the highest field-effect hole mobility for thin film transistors.47,48 However, the development of n-type organic semiconductor materials has still largely lagged behind p-type Received: April 4, 2012 Revised: June 4, 2012 Published: June 6, 2012 13858

dx.doi.org/10.1021/jp303235x | J. Phys. Chem. C 2012, 116, 13858−13864

The Journal of Physical Chemistry C

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ones.49−52 Therefore, it is desirable to search for the practical ntype organic semiconductor materials with high mobility and air stability.53,54 Recently, ladder polycyclic aromatic molecules, which contain imine nitrogens, have attracted considerable interest in the development of n-type semiconductors due to increased electron affinity and enhanced propensity of πstacking.55−57 Furthermore, Ahmed et al. have reported the synthesis, crystal structures, and properties of novel n-type bisindenoanthrazolines (BIDAs).58 Because the experimental results demonstrate that the BIDA is a promising new class of n-type semiconductors for organic electronics and optoelectronics,58 we theoretically study the charge mobilities of BIDAs and simulate the angular-resolution mobilities. The electrical anisotropy as an intrinsic property of organic semiconductors has attracted much attention.59−64 Sundar et al. observed a strong anisotropy of the field-effect mobility with the a−b plane of single crystals of rubrene for the first time in 2004.62 Kahn and coworkers used direct and inverse photoemission spectroscopy and some other experimental methods to study the ntype doping of a variety of electron transport materials.34−37,42−44 Although there are several computational studies for the electrical anisotropy,65−68 a systemic investigation of anisotropic mobilites is still lacking. According to Marcus− Hush theory,69,70 Han and coworkers developed a method to simulate the angular resolution anisotropic mobility that correlates with the underlying electronic properties and the molecular packing.71−75 Interested in designing high-performances n-type semiconductors materials, we have been motivated to make a full and accurate theoretical investigation about the relationship between the charge-transport properties and the molecular packing. Here we only considered two molecular models of BIDAs with the little difference of structures: one is ether in DADF; the other is carbonyl in DADK. The molecular structures are shown in Figure 1. The crystal structures can be found in ref 58; the crystal structures of DADF and DADK demonstrated distinct stacking modes.

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THEORETICAL AND COMPUTATIONAL METHODOLOGY The DFT with Becke’s three-parameter hybrid exchange function with Lee−Yang−Parr gradient-corrected correlation functional (B3LYP functional) was employed to optimize the geometric structures both in the neutral and charged states and to calculate the reorganization energies, while the absorption spectra were simulated using the TDDFT method with B3LYP functional. The 6-31 g+(d,p) was chosen as basis sets throughout the whole process.76 All calculations were carried out by the quantum chemical Gaussian09 program package.77 In addition, all of the electronic coupling calculations in different molecular dimers are implemented in the Amsterdam density functional (ADF) program with the local density functional VWN in the conjunction with the PW91 gradient corrections.78 The TZ2P basis set was chosen as basis sets throughout the whole process. The systematic error will be eliminated by comparing due to the same method chosen during the whole calculation process. Reorganization Energy. The reorganization energy usually consists of the internal and external contributions. The internal reorganization energy is caused by the molecular geometric relaxation, and the external reorganization energy is induced by polarization of the surrounding molecules. When charge transfer occurs, no outer solvent reorganization exists in condensed-state systems, so we only consider the internal reorganization energy.79,80 The reorganization energy λ can be evaluated directly using the adiabatic potential energy surface method,81−83 which can be shown as follows λ = λi(1) + λi(2) = (E*0 − E0) + (E*+ / − − E+ / −)

(1)

Here E0 and E± are the energies of the neutral and cation/anion molecules in their lowest energy geometries, respectively; E*0 and E*± represent the energies of the neutral and cation/anion monomers with the geometries of the cation/anion and neutral species, respectively, where λ1 corresponds to the geometry relaxation energy of one neutral molecule from the most stable geometry of the ionic state to the lowest energy geometry of the neutral state, and λ2 corresponds to the geometry relaxation energy of one cation/anion molecule from the most stable geometry of the neutral state to the lowest energy geometry of the ionic state.34,81,84 This description holds that the λi(1) and λi(2) terms are close in energy as long as the potential energy surfaces are harmonic.81 Then, we can calculate the adiabatic ionization potential (IP) and electron affinities (EAs) by the following equation

Figure 1. Molecular structures of DADF (a) and DADK (b).

In the present work, density functional theory (DFT) has been employed to investigate the geometric structures, molecular orbitals, and reorganization energies of DADF and DADK monomers. The absorption spectra have been simulated using time-dependent density functional theory (TDDFT) method. In addition, the effective electronic couplings and charge-transport mobilities have been deduced based on firstprinciples quantum mechanics (QM) calculations combined with Marcus−Hush theory,69,70 which is similar to that of Han et al.71,72 The anisotropic electron-transfer mobilities of these two materials DADF and DADK are also simulated by angularresolution expression. Through theoretical study, we will show that even if the structures of molecules are quite similar, they will exhibit very different intrinsic properties.

IP = E+ − E0

(2)

EA = E− − E0

(3)

Intermolecular Electronic Coupling. The evolution of electronic coupling V is based on the molecular orbitals of the conjugated molecules. The method we choose to calculate the intermolecular electronic coupling V of each dimer in organic semiconductors can be found in refs 78, 85, 86. The geometries for dimer calculations are selected from the observed X-ray crystal structure. The intermolecular electronic coupling V can be calculated directly by the spatial overlap (Sij), charge-transfer integral (Jij), and site energies (ei, ej),85 which can be written as Vij = 13859

Jij Sij(ei + ej)/2 1 − Sij2

(4)



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projecting the different hopping pathways.71,73 The equation of angular resolution anisotropic mobility can be given by e μϕ = ∑ Wri i2Pi cos2 γi cos2(θi − ϕ) 2kBT i (12)

For calculating the intermolecular electronic coupling V, we need to calculate the spatial overlap (Sij), charge-transfer integral (Jij), and site energies (ei, ej) ei(j) = ⟨ψi(j)|H |ψi(j)⟩

(5)

Sij = ⟨ψi|H |ψj⟩

(6)

Jij = ⟨ψi|H |ψj⟩

(7)

where ri, γi, and θi reflect the intermolecular packing parameters in the organic single crystals. ri is the ith hopping distance, γi is the angle of the ith hopping pathway relative to the transport plane of the organic crystal molecular stacking layer, and θi and ϕ are defined as the orientation angle of the projected electronic coupling pathways of different dimer types and the conducting channel relative to the same reference axis (generally using the crystallographic axis), respectively. So, the angle between the different pathways and the conducting channel is θi − ϕ. Pi and Wi can be calculated by eqs 10 and 8, respectively. For the hopping pathways on the basal transport stacking layer in the organic crystal, the values of ri are 0°. Equation 12 provides an analytic function to determine the angular resolution anisotropic mobilities for any type of organic semiconductors by relating the crystal packing and electron coupling V to the outer measuring channel angle ϕ.

where H is the dimer system Kohn−Sham Hamiltonian, and Ψi(j) represents the monomer HOMOs (for hole transport) or LUMOs (for electron transport) with Löwdin’s symmetric transformation, which can be used as the orthogonal basis set for calculation.86 Hopping Rate and Angular Resolution Anisotropic Mobility. It is generally accepted that the transport of hole/ electron in organic semiconductors takes place via charge carrier hopping between neighboring molecules at room temperature. On the basis of Marcus−Hush theory,69,70,87,88 the hole/electron transport for an organic semiconductors can be described by a hopping mechanism.89−91 The hopping rate (W) can be expressed as V2 ⎛ π ⎞ W= ⎜ ⎟ ℏ ⎝ λkBT ⎠

1/2

⎛ λ ⎞ exp⎜ − ⎟ ⎝ 4kBT ⎠

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RESULTS AND DISCUSSION The molecular geometries of DADF and DADK are fulloptimized at DFT with B3LYP/6-31+g(d,p) level to calculate the reorganization energies based on the adiabatic potential energy surface. From the Figure 1, we can find that DADF and DADK molecules have a common heptacyclic framework with a highly planar ring that includes a core of anthrazoline ring with two imine nitrogens in the backbone. The calculated results of relaxation energies λi(1) and λi(2) as well as reorganization energies λ for DADF and DADK are also listed in Table 1. We compared the reorganization energies of these

(8)

where V is the effective electronic coupling between neighboring molecules, λ is the reorganization energy, kB is the Boltzmann constant, and T is the temperature, which is 298 K in our calculation. If we assume that there is no correlation between chargehopping motions and the hopping motion is a homogeneous random walk,71,73,90 then the diffusion coefficient (D) caused by the hopping rate is deduced by eq 9 1 1 D = lim ≈ t →∞ 2n t 2n

∑ i

ri2WP i i

Table 1. The calculated relaxation energies λi(1) and λi(2) as well as reorganization energies λ in DADF and DADK (in electronvolts)

(9)

where n is the spatial dimensionality, i means the ith pathway, ri is the intermolecular center-of-mass distance between two neighboring molecules, W is the intermolecular hopping rate, and P is the hopping probability, which can be calculated by eq 10 Pi =

Wi ∑i Wi

hole transfer

electron transfer

molecule

λi(1)

λi(2)

λ

λi(1)

λi(2)

λ

DADF DADK

0.0873 0.1485

0.0851 0.1463

0.1724 0.2948

0.0906 0.1295

0.0919 0.1259

0.1825 0.2554

two molecules. One can clearly find that the relaxation energies λi(1) and λi(2) are nearly identical whether in DADF or DADK. The reorganization energies λ for hole transfer and electron transfer of DADF are almost equal, which are both obviously smaller than those of DADK. High reorganization energy is not helpful for higher carriers transport,94−96 so we suggest that DADK is proposed to function as a more high efficiency n-type semiconductor than the p-type one based on our calculated results. To our knowledge, the ionization potential and electron affinity are relevant to the ability of coming across the energy barrier and injecting the metal electrodes or empty orbitals for the holes and electrons. In addition, the frontier orbital characteristics are significant to understand the charge-transfer efficiency, so we compare the IPs, EAs, and the molecular frontier orbital energies (HOMO and LUMO) as well as the energy gaps of DADF and DADK monomers. The energy gaps are the energy difference between highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital

(10)

On the basis of the Einstein relation, the drift mobility for charge carrier (hole/electron) transport can be evaluated in organic semiconductors e μ= D kBT (11) In these parameters, it indicates that the rate of charge hopping depends on two microscopic parameters: the effective electronic coupling V and the reorganization energy λ. So, some efforts have been made to improve the charge mobility of organic semiconductor materials by optimizing these two parameters.92−94 The magnitude of the field-effect mobility in a particular transistor channel depends on the specific surface of organic crystal. Therefore, the anisotropic mobility of charge transport in organic semiconductors is an intrinsic property.62 Han et al. presented a model to simulate the anisotropic mobility (μϕ) by 13860



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band in DADF is due to π−π* transition, whereas the absorption band of DADK assigns to n-π* transition.58 It is confirmed that even if the molecular structures have a little difference, significant changes will occur in the intrinsic properties. The intermolecular electronic coupling V is another important parameter of charge-transfer capability of materials. The molecular packings of crystal DADF and DADK are presented in Figure 3. The angles between the hopping pathways of P, T, T1, and T2 dimer types and the reference axis are given in Figure 3, which are labeled as θP, θT, θT1, and θT2, respectively. The orientation angle of the conducting channel relative to the reference axis is Φ. From Figure 3, it can be noted that DADF and DADK have parallel and antiparallel geometries, respectively. The molecular packing diagram in Figure 3a shows that DADF exhibits a slipped face-to-face πstacking along the b axis. Similar to the π-stacking motif in DADF, DADK forms face-to-face slipped packing structure along the a axis, which is shown in the Figure 3b. We arbitrarily chose one molecule M as the initial position for the charge transport. The intermolecular electronic couplings with all neighboring molecules in a dimer model are theoretically calculated. In organic crystals, neighboring molecules can be characterized as transverse dimer T, parallel dimer P, and longitudinal dimer L. The most important four dimers are shown in Figure 3. The dimers of molecule D with neighboring molecules are defined as P, T1, T2, and T3, respectively. These four dimers are in the same molecular stacking layer. The electronic coupling between the molecules in the same organic packing layer for the most organic single crystals is much stronger than that between the molecules in two adjacent molecular stacking layers. We did not discuss the L dimer (out of transport layer plane) because the charge transport in crystals is 2D transport,81 whereas the electronic coupling of the L dimer calculated is very small, which means that the charge transport between layers (L dimer) is less efficient and negligible. We introduce the nearest-neighbor approximation based on Han et al. work,71−75 which means we only consider the interaction between the adjacent molecules. The effective intermolecular electronic couplings V for electron (LUMO) transport in these four cases are calculated with PW91 functional and TZ2P basis set using the DFT method. The effective intermolecular electronic couplings V for electron transport of each packing mode in DADF and DADK crystal are listed in Table 3. Moreover, intermolecular center-of-mass distances of various packing modes are also shown. Because the face-to-face stacking with larger orbital overlap and shorter

(LUMO). All data are calculated with DFT method at the level of B3LYP/6-31+g(d,p) and presented in Table 2. Table 2 Table 2. Calculated Ionization Potentials (IPs), Electron Affinities (EAs), and Molecular Frontier Orbital Energies (HOMO and LUMO) As Well As Energy Gaps (H−L gap) with the Method B3LYP/6-31+g(d,p) molecule

IP (ev)

EA (ev)

HOMO (eV)

LUMO (eV)

H−L gap (eV)

DADF DADK

6.708 7.345

−1.522 −1.996

−5.580 −6.225

−2.612 −3.074

2.968 3.151

shows that DADK has the lower molecular frontier orbital energies (both HOMO and LUMO) compared with DADF. It can also be found that the IP value increases when the HOMO energy level decreases, whereas the absolute value of EA increases when the LUMO energy level decreases. Because LUMO energy level decreases can make the charge carrier more stable and electron affinity increases can reduce the sensitivity of mobile electrons,97,98 it is indicated that DADK should be more favor to function as n-type organic semiconductor than DADF. Figure 2 shows the simulated absorption spectra of DADF and DADK in tetrahydrofuran (THF) solution with PCM

Figure 2. UV−visible absorption spectra of DADF and DADK in tetrahydrofuran (THF) solution with PCM model.

model. The theoretical simulations of absorption spectra are performed by TDDFT method with B3LYP/6-31+g(d,p). One can note that the absorption spectrum of DADF shows three main bands: the maximum absorption peaks are 300, 384, and 478 nm, respectively. However, it is distinctly seen that DADK has only one broad and strong absorption band, especially in the range of 300−400 nm. The simulated results are wellconsistent with the corresponding experimental ones by Ahmed and his colleagues.58 It has been reported that the absorption

Figure 3. Comparison of molecular packings and charge hopping pathways in DADF (a) and DADK (b) with the center-of-mass distance and the angle of the projected electronic coupling pathways relative to the reference axis. 13861



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Table 3. Calculated Electronic Couplings V for Electron Transport (meV) and Corresponding Intermolecular Center-of-Mass Distances r (Å) for Different Hopping Pathwaysa DADF pathway P T T1 T2 maximum mobility a

V

For these four frontier molecular orbitals, most of the electrons were localized over the planar heptacyclic framework, whereas some electrons were distributed over the terminal atoms out of the planar framework. Compared with the HOMOs, the LUMOs have a broader conjugated system; that is to say, the delocalization of the LUMOs suppressed the charge recombination and facilitated electron movement.99 Above all, the extended π-conjugated system in LUMOs suggested that DADF and DADK might be better candidates as n-type organic electronic materials than p-type ones. Because understanding the anisotropic mobility can help control the orientation of transistor channel relative to the reference axis of molecular crystal,61,62,74 the angular resolution anisotropic electron-transfer mobilities in DADF and DADK single crystals are given in Figure 5. The angular-resolution

DADK r

0.020 14.382 22.063 4.738 0.732 17.224 0.059 15.143 0.142 cm2 V−1 s−1

V

r

0.173 13.700 72.633 3.595 0.004 15.224 1.376 13.018 0.373 cm2 V−1 s−1

Simulated maximum mobilities are given in the last line (T = 300 K).

distance can contribute to the higher electronic coupling, it can be noted that T dimer is the most important electron-transport pathways. The electronic coupling V of T dimer in both DADF and DADK is much larger than those in others dimers, which indicates that the T direction is the dominant conducting channel. The largest transfer integrals for DADF and DADK are 22.063 and 72.633 meV at pathway T. It indicates that the parallel packing mode usually yields larger coupling term than other packings because the cofacial stacking structure is excepted to offer more efficient orbital overlap. Another important reason is that the T dimers for DADF and DADK have shorter intermolecular distance compared with other dimers, which are 4.738 and 3.595 Å, respectively. One can find that the T packing mode of DADK crystal produces the largest electronic coupling (V = 72.633 meV), which is ∼3.3 times larger than the counterpart of crystal DADF. Moreover, the calculated maximum electronic mobilities are presented in Table 3. The DADK has the preferred transport property for electron, with the electron mobility as large as 0.373 cm2 V−1 s−1, which is 2.6 times larger than that of DADF. The close packing of the molecules in crystal has the strong electronic couplings of the π-conjugated orbitals, which determines the high mobility. The small change in the molecular structures is responsible of this significant change in electronic property. This result confirms that DADK crystal is more favor to function as n-type organic semiconductor, which is in good agreement with the result discussed above for the reorganization energy. Our theoretical study on the charge transport is under the ideal conditions at room temperature, which can assist to understand the charge transport property in detail. To better understand the difference of electronic couplings in these two crystals, we compare the frontier molecular orbital shapes of DADF and DADK. Figure 4 illustrates the HOMOs and the LUMOs of optimized DADF and DADK monomers.

Figure 5. Angular-resolution anisotropic mobility curves of DADF (a) and DADK (b) crystals (cm2 V−1 s−1).

anisotropic electron-transfer mobility measurements for novel n-type BIDAs are not yet reported. It can be seen from Figure 5 that the angle dependence of electron-transfer mobility in all of these two single crystals shows remarkable anisotropic behavior. Interestingly, the maximum electron mobilities both appear in T dimer direction for DADF and DADK crystals because the T dimer has the strongest electronic coupling of LUMOs and the shortest center-of-mass distance. Therefore, the maximum electronic mobilities for DADF and DADK are near 90°/270° and 72°/252° in the angle-resolution figure, which are 0.142 and 0.373 cm2 V−1 s−1, respectively. The difference can be derived from the relative magnitude of electron-transfer integrals. It is indicated that electrons in DADK crystal are intrinsically much more mobile than electrons in DADK crystal. The distribution of angularresolution anisotropic mobility can help us to understand the charge-transport property and get high-performance organic semiconductor materials.

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CONCLUSIONS In our study, we theoretically investigated the DADF and DADK as novel n-type BIDAs semiconductors to understand the relationship between molecular packing and charge transport based on Marcus−Hush theory. Through theoretically computation, these two singlet crystals both show the promising performance in terms of charge transport properties. In addition, the curves of electron-transfer mobility also demonstrate that DADF and DADK have remarkable anisotropic behaviors. DADK has the favorable electrontransport ability with the mobility as high as 0.373 cm2 V−1 s−1, which is nearly three times larger than that of DADF. So, DADK should be more favor to function as n-type organic semiconductor than DADF. It is indicated that DADK may be an ideal candidate as a high-performance n-type organic

Figure 4. Highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of optimized DADF (a) and DADK (b) monomers. 13862



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semiconductor material. One significant finding is that the molecular geometry of the organic semiconductor plays an important role in determining the molecular stacking, electronic properties, and charge-transport behaviors. The theoretical investigation of organic semiconductors is helpful for evaluating the charge transport behaviors to realize better charge transfer efficiency and design higher performance electronic materials.

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ASSOCIATED CONTENT

S Supporting Information *

The complete author list of references with more than 10 authors is presented. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +86-411-84379692. Fax: +86-411-84675584. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by NSFC (nos. 20903094 and 20833008) and NKBRSF (nos. 2007CB815202 and 2009CB220010). G.J.Z. also acknowledges the financial support from DICP and CAS.

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