Density Functional Theory Studies of Hole Mobility in Picene and

Article pubs.acs.org/JPCC

Density Functional Theory Studies of Hole Mobility in Picene and Pentacene Crystals Thao P. Nguyen,† Ji Hoon Shim,*,†,‡ and Jin Yong Lee*,§ †

Department of Chemistry, Pohang University of Science and Technology, Pohang 790-784, Korea Division of Advanced Nuclear Engineering, Pohang University of Science and Technology, Pohang 790-784, Korea § Department of Chemistry, Sungkyunkwan University, Suwon 440-746, Korea ‡

ABSTRACT: We have investigated the electronic properties and hole mobilities of picene and its isomer pentacene using the density functional theory and classical Marcus charge transfer theory. In pristine crystal with herringbone structure, pentacene and picene have drift hole mobilities of 2.147 and 0.644 cm2 V−1 s−1, respectively, which are consistent with recent experimental results. We also show that picene crystal can exhibit maximum mobility up to 2.629 cm2 V−1 s−1 along the π−π stacking direction, while the highest mobility of pentacene crystal exhibits along the herringbone stacking direction. Also the anisotropy of the mobility in the ab plane is 2.4 and 5.6 for picene and pentacene crystals, respectively. Since the air stability of picene is better than pentacene due to lower HOMO levels in picene, we suggest that picene and its homologous phenacenes series are promising candidates toward high mobility organic semiconductor devices with good air stability. This work also sheds light on the favorable or undesirable properties for efficient charge transport in oligoacene and phenacenes series.

I. INTRODUCTION

organic PAH molecules have been studied to search for materials with higher carrier mobility. Among the most popular PAHs, pentacene belonging to the oligoacene homologous series was reported to be a good candidate for a p-type semiconductor that attracted great attention due to its high hole mobility.5 The carbon skeleton of pentacene can be observed in small pieces of graphene with a linear backbone framework as shown in Figure 1. The main

Organic semiconductors (OSCs) have been suggested as promising materials for semiconductor devices. Since the ability to form semiconductivity of polycyclic aromatic hydrocarbons (PAHs) was first explored in 1950 and the first discovery of metallic conductivity in the charge transfer complex TTF−TCNQ was reported, the application of OSCs become an important target because of their distinct advantages.1 For instance, they are lighter, more flexible, lower cost, and more easily shaped compared to copper, silicon, or other inorganic materials. Furthermore, PAHs are made entirely of carbon and hydrogen which can be biodegradable in the environment. Extraordinary features of PAHs include strong electron−electron and electron−phonon interaction and the π electrons which are delocalized throughout the crystal giving the dramatic increase in metallic conductivity. One of the goals in the field of OSCs is to seek materials that can replace amorphous silicon which is used in most thin-film devices nowadays. Amorphous silicon has a mobility of around 0.5−1.0 cm2 V−1 s−1 and requires a very complicated process at very high temperature (360 °C) under plasma influence.2 OSCs can be a potential material to replace amorphous silicon because of their simple process. The problem with OSCs is that they have poorer electronic transport behavior and therefore lower carrier mobility than inorganic semiconductors. Most carrier mobilities of OSCs are in the range of 10−6∼10−4 cm2 V−1 s−1.3 OSCs are considered to have high carrier mobility when their values reach above 0.1 cm2 V−1 s−1.4 Thus, various © 2015 American Chemical Society

Figure 1. Molecular structures of pentacene (A) and picene (B).

building blocks of pentacene are five benzene rings connected to each other in a planar structure. The pentacene single crystal was proved to be the most successful material, exhibiting a hole mobility up to 35 cm2 V−1 s−1 at room temperature.6 The highest hole mobility was observed in thin-film organic field effect transistors (OFETs) reaching up to 3.0 cm2 V−1 s−1.4 However, pentacene is very unstable in air atmosphere and can be oxidized easily. Unfortunately, its degradation in oxygen can Received: November 17, 2014 Revised: April 29, 2015 Published: April 30, 2015 11301

DOI: 10.1021/jp511484d J. Phys. Chem. C 2015, 119, 11301−11310

The Journal of Physical Chemistry C

Article

According to Marcus theory, the reorganization energy is the energy cost by charging a single molecule within the molecular crystals.13−15 In other words, it describes the change of geometry when a neutral molecule undergoes a structural relaxation by addition and removal of a charge carrier. The reorganization energy consists of λi and λo which are the inner and outer sphere reorganization energy, respectively. λo is usually difficult to calculate and needs large computational cost as it requires both electronic polarization and electron−phonon coupling of the surrounding molecules. Because of its small value compared to λi, λo is usually neglected.16 The inner reorganization energy consists of two terms related to geometry relaxation energies λ1 from the neutral state to charged state and λ2 from the charged state to neutral state.

influence the charge transport process to reduce the hole mobility and conductivity.7 It is also the main reason why the results of hole mobility in pentacene are very different in various experimental reports. Hence, other alternative OSCs must be found to show high hole mobility and air stability. Recently, its isomer picene belonging to the phenacene homologous series attracted a lot of interest due to not only its high mobility but a better environmental stability than pentacene. Picene consists of five benzenes rings arranged in an armchair fashion and also can be seen in a small fragment of graphene as shown in Figure 1. In a solid-state system, picene molecules have a herringbone arrangement which is typical for many PAH-based crystals. Okamoto et al. reported an unusual increase in the hole mobility of picene from 1.1 cm2 V−1 s−1 to above 1.75 cm2 V−1 s−1 in OFETs after exposure to O2 atmosphere for 70 h.8 Besides, picene exhibited high temperature of superconductivity, having TC = 18 K when being doped with alkaline metals such as potassium and rubidium.9 Despite these benefits, the electronic properties and hole mobility in the picene single crystal have not been investigated theoretically. In this paper, we performed the ab initio calculations to understand the electronic properties of picene and pentacene and the relationship between charge transport and molecular orientations on these single crystals. This work gives a detailed view inside the properties of picene, making it a promising candidate to replace its isomer pentacene for industrial use.

λ i = λ1 − λ 2

(1)

When only the total reorganization energies are interested, λ1 and λ2 are calculated directly from adiabatic potential energy surfaces as follows λ1 = E2 − E3

(2)

λ 2 = E4 − E1

(3)

As shown in Figure 2, E1 is the energy of the neutral state in the optimized geometry of neutral molecules. E2 is the energy

II. THEORETICAL AND COMPUTATIONAL METHODS The crystal structures of picene and pentacene were taken from Cambridge crystallographic database sample 50785 (a = 8.480 Å, b = 6.154 Å, c = 13.515 Å, Z = 2 and α = 90°, β = 90.46°, γ = 90°) and sample 50783 (a = 6.239 Å, b = 7.636 Å, c = 14.330 Å, Z = 2 and α = 76.98°, β = 88.14°, γ = 84.42°), respectively.10,11 The molecular geometries of neutral and ionized states were obtained by using density functional theory (DFT) calculations with the hybrid B3LYP functional using the Gaussian 09W program.12 The 6-31G++(d,p) basis set was used for monomers and 6-31G(d,p) basis set for dimers. In OFETs, the charge was injected into the system from metal or conducting oxide electrodes and migrates across the organic layer. Charge carrier transport describes the hopping process from one molecule to another molecule. The electron and hole mobilities describe how quickly an electron and hole can move from a molecule to another molecule, respectively. Higher hole mobility is desired for utilization as a p-type semiconductor. The hole/electron transfer process between identical molecules is expressed as M±···M → M···M±. Because of the electron−phonon coupling and intermolecular electronic coupling, the charged molecule will undergo a structural relaxation to reach the optimum geometry in the charged state. The geometry distortion of a molecule is referred to as a polaron. The injected charge will leave the molecule very quickly and transfer to the neighboring molecule, so the charged molecule goes back to its neutral form (M) with geometry relaxation. In order to calculate the hole/electron mobility, there are two important parameters, namely, the reorganization energy between M and M+/M− and the charge transfer integral within the molecular dimer. The reorganization energy can be obtained for monomer molecules; however, the reorganization energy for multiple molecules gives a more realistic description considering the intermolecular interactions in the crystal structure.

Figure 2. Reorganization energies for neutral and cationic molecules.

of the charged state with the optimized geometry of the neutral molecule. E3 is the energy of the charged state with the optimized geometry in charged molecules. E4 is the energy of the neutral state with the optimized geometry in charged molecules. An alternative way to calculate the reorganization energy is based on the normal-mode analysis by obtaining the sum of the relaxation energies contributing to each vibrational mode 1 λ1(2) = ∑ λ i = ∑ kiΔQ i2 = ∑ Siℏωi 2 (4) i where ΔQ is the displacement along the normal modes shown in Figure 2 between charged and neutral geometries; ki is the force constant with respect to each normal mode; ωi is the frequency; and Si is the Huang−Rhys factor measuring the electron phonon strength for the ith normal mode. The evaluation of the reorganization energies represented by this method can be calculated by the DUSHIN program by Reimers.17 11302



Article

Now we assume that the motion of charge is a homogeneous random walk in crystal and does not depend on any directions. In this case, the diffusion coefficient can be evaluated from

Another important quantity is the transfer integral which reflects the strength of the interaction in the dimer configuration. When two isolated molecules create a dimer, two HOMO (LUMO) levels from each molecule combine to make HOMO and HOMO−1 (LUMO and LUMO+1) in a dimer. In a simplified energy splitting in dimer (ESD) method, the charge transfer integral (t12) is approximated as half of the energy difference between HOMO and HOMO−1 for hole transfer, whereas LUMO and LUMO+1 is for electron transfer.13−15 The value of t12 is only accurate when the two localized valence monomer structures M1*−M2 and M1−M2* can be obtained from one another by a symmetric transformation. In this case, the site energies between two monomers are equal to each other (ε1 = ε2) 1 t12 = (E HOMO − E HOMO − 1)2 − (ϵ2 − ϵ1)2 2 1 ΔE = (E HOMO − E HOMO − 1) = 2 2

D=

Pi =

(6)

1 2 t12 = ⟨ϕHOMO |Ĥ |ϕHOMO ⟩

1 2 S12 = ⟨ϕHOMO |ϕHOMO ⟩ 1 1 ϵ1 = ⟨ϕHOMO |Ĥ |ϕHOMO ⟩

2 2 ϵ2 = ⟨ϕHOMO |Ĥ |ϕHOMO ⟩

where t12 is the transfer integral considering no electrostatic polarization effects; ϵ 1 and ϵ 2 are the site energies corresponding to monomer 1 and monomer 2; and S12 is the spatial overlap integral between the HOMOs (LUMOs) of two monomers. Finally, the effective transfer integral teff is obtained by considering the electrostatic polarization effect. The Marcus theory describes the charge transfer rate k as below ⎛ λ ⎞ 1 t 2 exp⎜ − ⎟ ⎝ 4kBT ⎠ 4πλkBT

ed 2k 2kBT

(10)

III. RESULTS AND DISCUSSION 3.1. Air Stability of Picene and Pentacene Molecules. For organic semiconductors, the air stability in the environment is one of the most important features as well as the charge transport characteristic.26 The ionization energy describes the energy necessary to remove electrons from the neutral molecule A0 to create a cation A+. The higher IP values indicate that the molecule is difficult to become a cation in an environment to react with OH− (H2O) or O2− (O2) existing in the atmosphere. As shown in Table 1, the IP value of pentacene is smaller than that of picene. Hence, it is indicated that pentacene is more sensitive to the reaction with ion OH− or O2−. With the reaction with oxygen, the carbon atoms at 6 and 13 positions of pentacene (middle ring, the most reactive position) will be substituted by oxygen to form hydroquinone (6,13-pentacene-

(7)

For the efficient charge transfer process, the materials should have a small reorganization energy and large transfer integral. Finally, the charge mobility can be calculated from the Einstein relation μ=

ki Σiki

where di is the ith hopping distance, and γi is the angle of the ith hopping jumps between adjacent molecules to the plane of interest. In herringbone structures on the same ab plane, the γi = 0. θi − ϕ is the angle between the hopping paths and the conducting channel. In this study, temperature was set up at 300 K. Note that there are several restrictions of Marcus theory in calculating the charge transport. The requirement is that the electronic coupling has to be small as compared to λ/4 which corresponds to the activation energy in a charge transfer process; the thermal relaxation (geometric relaxation) has to be fast compared to the transfer so that the system can be in thermal equilibrium during transfer. Also the theory has been restricted in the high-temperature case.20,21 Nevertheless, the Marcus theory is widely used and gives very good agreement to the experimental results.22 We believe that the theory is still suitable to give prediction on the charge transfer of organic semiconductors and is widely used in many applications. Also, this theory has been proven to be useful for getting insight into the relation between the electronic structures and the charge transport properties23−25

We assume that H is the Kohn−Sham Hamiltonian of a dimer that includes two monomers. Their frontier highest occupied molecular orbitals (HOMO) are denoted as ϕ1HOMO and ϕ2HOMO. Then t12, S12, ϵ1, and ϵ2 were calculated as

4π 2 h

(9)

The magnitude of hole mobility on a single crystal also depends on the conducting channel and the specific surface of the organic crystal. The angular resolution anisotropic mobility can be given by19 e μϕ = ∑ kidi2Pi cos2 γi cos2(θi − ϕ) 2kBT i (12)

(5)

1

k=

i

Summing over all possible hops leads to the drift mobility as e μdrift = D kBT (11)

t12 − 2 (ϵ1 + ϵ2)S12 2 1 − S12

∑ di2kiPi

where n is the spatial dimension and n = 3 in this system; ki is the charge transfer rate along each direction; i is the specific hopping pathway with hopping distance d; and Pi is the relative probability

The problem arises when the two monomers are not equivalent and placed in different positions in crystal space. To avoid the errors induced by the different site energy, the direct method is used to calculate the transfer integral directly through orthogonalized monomer orbitals.18 teff =

1 2n

(8)

where e is the electronic charge; d is the transport distance from the molecular center to center in a dimer; and kB is the Boltzmann constant. 11303



Article

Table 1. Calculated HOMO−LUMO Gaps, Reorganization Energies, Ionization Potentials, and Electron Affinities for Pentacene and Picene Single Molecules p-type basis sets H−L gap (eV) λh (meV) λe (meV) IPtheo (eV) IPexp (EV)32 EAtheo (eV) EAexp (eV)32 a

pentacene a

picene b

2.186 2.236 91 92 130 124 6.130 5.92 6.63 ± 0.05 1.492 1.115 1.392 ± 0.043

a

b

4.187 4.250 180 180 266 258 7.050 6.84 7.51 ± 0.02 0.419 0.013 0.5420 ± 0.0080

Basis sets 6-31G**(d,p). bBasis sets 6-31G.

quinone) that is the dominant impurity found in pentacene (Figure 3), and the π conjugation of the system is destroyed. Pentacenequinone is expected to induce trap states in the band gap of pentacene.27,28 It is also reported that the hole mobility is dramatically reduced with this oxygen substitution in pentacene.7 The air stability of molecules can be understood by examining their HOMO−LUMO energy levels. It is believed that there is a close relationship between the HOMO energy level and IP and the connection between LUMO energy level and EA values.29,30 In Figure 4, the destabilization of the HOMO level in oligoacenes leads to an extreme sensitivity to the oxidation, and so the application in real devices should be limited. In contrast, phenacenes have better air stability as they do not suffer from the HOMO level destabilization and the LUMO stabilization effect. Experiments for p-type materials have shown that the HOMO level needs to be more than 5.2 eV below the vacuum level to have air stability.31 Hence, the application of phenacenes under environment can be more promising than oligoacenes. 3.2. Reorganization Energies of Picene and Pentacene Single Molecules. We investigated the charge transfer and electronic characteristic of picene and pentacene single molecules in terms of its hole and electron reorganization energies, energy gap, ionization potential (IP), and electron affinity (EA) as shown in Table 1. Reorganization energies for hole transfer calculated from adiabatic potentials are 91 and 180 meV for pentacene and picene, respectively. Because of lower hole reorganization energy, it is suggested that pentacene shows the higher intrinsic hole transfer rate and, hence, higher mobility than picene. On the contrary, both pentacene and picene are expected to exhibit poor ability in the electron transport because the reorganization energies for the electron are much larger than those for the hole. This is obvious because pentacene and picene are p-type semiconductors, and thus the majority carrier should be hole. The total reorganization energies using normal mode analysis of eq 4 have similar results indicating the accuracy of our

Figure 4. Calculated frontier orbitals of phenacenes (A) and oligoacenes (B) (basis set 6-31G++(d,p)).

calculation. Figure 5 describes the dominated modes that contribute to the reorganization energies. In the reorganization energy of electron and hole in both picene and pentacene, the main contribution is shown in the frequency range of 1300− 1700 cm−1. Picene belongs to the C2v symmetry point group where the reorganization energies are dominated by A1 modes. In neutral picene, the most contributed modes locate at 1412 and 1676 cm−1. In cation picene, the most contributed modes are at 1410, 1634, and 1656 cm−1. Pentacene has higher symmetry than picene, belonging to the D2h point group where most of the reorganization energies come from Ag modes. The most contributed modes are located at 1434 and 1575 cm−1 for the neutral pentacene structure and shift to 1450 and 1568 cm−1 for the cation pentacene. As shown in Figure 5, the number of modes and their contribution to the internal reorganization energy are larger in picene than pentacene. As a result, picene has higher reorganization energy than pentacene. We calculated the reorganization energies for picene and pentacene’s homologous series as shown in Figure 6. The reorganization energies of pentacene reduce with the number of

Figure 3. Molecular structures of pentacene before and after contacting to oxygen. The substituted oxygen atom is indicated with red spheres. 11304



Article

Figure 5. Comparison of hole hopping reorganization energy at vibrational frequencies for neutral λ1 and cationic λ2 molecules of (A) neutral picene; (B) neutral pentacene; (C) cationic picene; and (D) cationic pentacene (basis set 6-31G).

Figure 6. Reorganization energy for hole transport of picene homologous series (phenacenes) and pentacene homologous series (oligoacenes).

Figure 7. Ionization potential energies (y-axis) of phenacenes and oligoacenes with 2−7 phenyl rings. Phenacene regression: y = −0.175x + 7.97. Oligoacenes regression: y = −0.505x + 8.703.

phenyl rings. However, it also leads to worse instability with more phenyl rings as the IP values also decrease dramatically (Figure 7). Therefore, hexacene (6 rings) and heptacene (7 rings) are usually ignored in experiment. The reorganization energies of phenacenes are higher than oligoacenes and also decrease as the number of the phenyl rings increases. The trend is not in a linear fashion, so we predicted a better hole mobility in chrysene (4 rings) as well as fluminene (6 rings) and [7]phenacene (7 rings). The IP values also decrease but very slightly as the number of phenyl rings increases (Figure 7). It indicates a good air stability of phenacene molecules and their potential for better p-type semiconductors in the environment. In fact, the mobility of fluminene was observed in FET that reached as high as 3.7 cm2 V−1 s−1, while picene has μ = 1.4− 3.2 cm2 V−1 s−1 under an O2 atmosphere.33,34

3.3. Charge Transport Properties of Picene and the Pentacene Single Crystal. Here we describe the charge transport properties in the picene and pentacene crystals. The reported crystalline structures of picene and pentacene based on the X-ray diffraction analysis show the packing of molecules with the typical herringbone structure within the ab plane. In Figure 8, we combined multiple unit cells to show the interaction of one picene molecule with neighboring molecules. Considering the orientation of the central molecule to the neighboring molecule in the ab basal plane, channels 1 and 3 represent the herringbone arrangement in the crystal for both picene and pentacene crystals, while channel 2 corresponds to the π−π stacking arrangement along the b* axis for picene crystal and the a* axis for pentacene. For both picene and 11305



Article

Figure 9. Energy level diagram of the frontier orbitals for picene dimers along channel 1.

of two monomers were combined and created LUMO+1, LUMO, HOMO, and HOMO−1 in the dimer configuration. Along channel 1, the energy level splitting between HOMO and HOMO−1 is about 0.336 eV. In contrast, the energy splitting between LUMO and LUMO+1 is 0.133 eV, which is twice as small, indicating a poor electron transport in this material. The hole transfer integral t shows different values for different channels as seen in Table 2. Although the ESD method gives the same trend as the direct method for the transfer integral of picene and pentacene, it overestimated the results by a factor of 2 or 3. In the results of the direct method for picene crystal, channel 2 has the highest effective charge transfer integral and is predicted to be the best pathway of charge transport. For channel 2, the dimers are symmetric, and two monomers are equivalent under the symmetric transformation. Consequently, the electrostatic polarization effect becomes negligible with approximately equivalent site energies ϵ1 ∼ ϵ2. So, the effective charge transfer integral would be similar to the value obtained from the ESD method (teff ≅ t12 ≅ (ΔE/2)). This tendency was also observed in channels 4 and 5 in picene and channels 2, 4, and 5 in pentacene crystal where all of them adopt a π−π stacking arrangement. Along the herringbone arrangement, however, two monomers are not equivalent in symmetry, and hence two monomers polarized each other causing different site energy values (ϵ1 ≠ ϵ2) and (teff ≠ (ΔE/2)). So, the direct method produced a much reduced charge transfer integral along the herringbone arrangement than the ESD method. Note that the highest charge transfer integral in the pentacene crystal is along the herringbone arrangement because the π−π overlap is not so big as compared with picene crystal. Thus, it would be a good strategy for better charge transport in picene crystal to produce the crystals that

Figure 8. Hopping pathways within picene (A) and pentacene crystals (B).

pentacene, channel 4 is the hopping between the central molecule to the next nearest neighbor molecules, and channel 5 is the hopping along the c* axis. Using the indicated hopping pathways, we consider the molecular dimers for the calculation of charge transport properties. Charge transfer integrals obtained by the ESD and direct methods were compared in Table 2. In the ESD method, the geometries of the dimers were optimized (B3LYP/6-31G(d,p)) where the center of mass distance and the angle between molecular planes were fixed by freezing the coordinate of the central rings. In the direct method, we performed single-point calculations on the given dimer structures using the GGA/PW91 functional and a basis set of TZP (triple-ζ with polarization). Figure 9 describes the energy level diagram of a picene dimer along channel 1 shown in Figure 8. LUMO and HOMO levels

Table 2. Calculated Hole Transfer Integrals for Picene and Pentacene Dimers Using Both Direct and ESD Methods direct method channel picene

pentance

t1 t2 t3 t4 t5 t1 t2 t3 t4 t5

ESD method

t (eV)

ε1 (eV)

ε2 (eV)

S

teff (eV)

HOMO (eV)

HOMO−1 (eV)

ΔE/2 (eV)

0.130 −0.142 −0.114 0.000 0.000 −0.173 0.059 0.100 −0.001 0.000

−5.318 −5.100 −4.675 −5.008 −5.136 −4.525 −4.371 −3.923 −4.294 −4.423

−4.590 −5.124 −5.315 −5.007 −5.112 −3.904 −4.197 −4.532 −4.285 −4.424

−0.013 0.014 0.012 0.000 0.000 0.020 −0.006 −0.011 0.000 0.000

0.066 −0.070 −0.054 0.000 0.000 −0.089 0.033 0.054 −0.001 0.000

−5.219 −5.438 −5.264 −5.468 −5.534 −4.345 −4.584 −4.371 −4.554 −4.627

−5.555 −5.589 −5.619 −5.468 −5.537 −4.758 −4.667 −4.741 −4.563 −4.628

0.168 0.075 0.178 0.000 0.002 0.206 0.041 0.185 0.004 0.001

11306



Article

promote the π−π stacking structure where the overlap between two monomers would be enhanced. The calculated transfer integral of the selected molecular dimers in the ab plane can also be observed in the band structure of picene crystal. Here, we performed the band structure calculation for picene crystal and computed the density of states (DOS) using WIEN2k codes with GGA-PBE functional.35 Figure 10 shows the Brillouin zone of solid picene

structures of picene are clearly shown. The bandwidth of HOMO in picene is estimated from the overall contribution of each electron coupling in every hopping direction of picene crystal. Since there are mostly no charge transports in channels 4 and 5, the sum of total electron coupling in channels 1, 2, and 3 is 0.19 eV. This is very consistent with half of the bandwidth of HOMO indicating the accuracy of our calculation. In addition, the largest valence band dispersions in the ab plane occur from point (0,1,0) to (0,0,0), from (0,0,0) to (−1,1,0), and from (0,0,0) to (1,1,0) directions. The (0,1,0) → (0,0,0) direction corresponds to the b* direction including channel 2. The (0,0,0) → (−1,1,0) and (0,0,0) → (1,1,0) directions correspond to the a* + b* direction which includes channels 1 and 3. We also observe a quasidegeneracy in the conduction band which includes four bands from LUMO and LUMO+1 of the isolated picene molecule. The quasidegeneracy is believed to be favorable for a high transition temperature in the superconductivity because it has the role of increasing the DOS near the Fermi level.36 Using the transport distances from center-to-center of monomers in various channels, the hole mobilities of four channels are obtained (Table 3). The highest hole mobility is observed along π−π stacking of channel 2 with the value of 2.629 cm2 V−1 s−1. The herringbone configurations have the hole mobilities of 1.661 and 1.165 cm2 V−1 s−1 along channels 1 and 3, respectively. The calculated drift mobility of picene is 0.644 cm2 V−1 s−1. The reported hole mobility of picene is 1.3 cm2 V−1 s−1 measured in air, and its mobility in vacuum is 30% lower (∼0.9 cm2 V−1 s−1).43 Hence, our theoretical results are very consistent with the observed mobility in experiments. The hole mobilities are calculated to be highest in the ab plane. Therefore, Figure 12 describes the anisotropic hole mobility of picene crystal. On the basis of the anisotropic mobility, we can predict the angle of conducting transistor relative to the reference axis to obtain the highest and lowest hole mobility in molecular crystal. The angle-dependent mobility of picene crystal in the ab plane is calculated as described in eq 12

Figure 10. Brillouin zone of picene crystal. The path for the calculation of the band structure is indicated by a green line.

describing the orientation relative to the crystal lattice and the path used in the band structure. In Figure 11, the band

μϕ = 0.594 cos2(32.18° − ϕ) + 1.058 cos2(90° − ϕ) + 0.279 cos2(140.38° − ϕ)

For channel 4, the calculated value is too small, so we ignore this channel. Our result indicates that ϕ = 80° or 260° directions will lead to maximum mobility of 1.363 cm2 V−1 s−1. The minimum mobility reaches to 0.57 cm2 V−1 s−1 along ϕ = 170° or 350°, and the anisotropy is estimated by 2.4. Note that

Figure 11. Band structure and density of states (DOS) of picene crystal.

Table 3. Calculated Frontier Orbital Energies, HOMO−LUMO Gaps, Hole Transfer Integral, and Hole Reorganization Energy for Picene and Pentacene Dimers

picene

pentacene

channel

HOMO (eV)

LUMO (eV)

H−L gap (eV)

t (eV)

t1 t2 t3 t4 t5 t1 t2 t3 t4 t5

−5.219 −5.438 −5.264 −5.468 −5.545 −4.345 −4.584 −4.371 −4.554 −4.627

−1.407 −1.332 −1.390 −1.213 −1.299 −2.537 −2.452 −2.535 −2.340 −2.388

3.812 4.106 3.874 4.255 4.246 1.808 2.132 1.836 2.214 2.239

0.066 0.070 0.054 0.000 0.000 0.089 0.033 0.054 0.001 0.000 11307

ki (s‑1) 3.194 3.593 2.138 0.000 0.000 1.901 2.614 7.000 2.400 0.000

× 1013 × 1013 × 1013

× × × ×

1014 1013 1013 1010

d (Å)

μi(cm2 V−1 s−1)

D (cm2/s)

μdrift(cm2 V−1 s−1)

5.187 6.153 5.310 8.479 14.49 4.696 6.254 5.161 7.680 16.005

1.661 2.629 1.165 0.000 0.000 8.102 1.976 3.603 0.003 0.000

0.017

0.644

0.056

2.147



Article

Figure 12. (A) Illustration of projected different hopping paths to a transistor channel in the ab plane of a picene crystal; θ1, θ2, θ3, and θ4 are the angles along channels 1, 2, 3, and 4 relative to the reference crystallographic a axis; φ is the angle of a transistor channel relative to the reference crystallographic a axis. (B) The predicted anisotropic mobility in the ab plane.

Figure 13. (A) Illustration of projected different hopping paths to a transistor channel in the ab plane of a pentacene crystal; θ1, θ2, θ3, and θ4 are the angles along channels 1, 2, 3, and 4 relative to the reference crystallographic b axis; ϕ is the angle of a transistor channel relative to the reference crystallographic b axis. (B) The predicted anisotropic mobility in the ab plane.

the mobility of picene can reach 1.1 cm2 V−1 s−1 only when the device was exposed to O2 for around 4 h.8,37 Here, we suggest that the highest mobility up to 1.363 cm2 V−1 s−1 can be obtained in vacuum by choosing the correct direction of a conducting channel within the ab plane of a picene single crystal. This result on the angle-dependent anisotropic mobility can help us to get a high performance of organic semiconductor materials. The mobility of picene can clearly surpass the amorphous silicon level. In pentacene crystal, we used a similar approach to obtain the transport properties (Figure 13). The transfer integral is higher than picene with 0.089 and 0.054 eV along channels 1 and 3, respectively. Pentacene has two times lower reorganization energy than picene; therefore, the hole mobility will be larger than that of picene. The drift mobility calculated for pentacene is approximately 2.147 cm2 V−1 s−1 which is close to the experimental result of μ ≈ 3−7 cm2 V−1 s−1.4,38,39 However, our results are smaller than the recent report of hole mobility of 11.2 cm2 V−1 s−1 in ultrapure pentacene single crystal where a homogeneous current flows through the sample and the impurity 6,13-pentacenequinone was removed.6 This difference might be understood by the anisotropic mobility of pentacene crystal as follows. The angular anisotropic mobility function in the ab plane of pentacene is

in the ab plane reaches a maximum of 5.470 cm2 V−1 s−1 along the angles of ϕ = 40°and 220°. The minimum value reaches 0.976 cm2 V−1 s−1 along the angles of ϕ = 40° and 220°. Note that the anisotropy of mobility in pentacene is 5.6, which is much larger than that of picene. This indicates that the observed mobility should be sensitively affected by the arrangement of crystal or preparation of the materials. The illustration shown in Figure 13 is similar in shape and direction with the experimental anisotropic mobilities by Lee et al.40 Although the calculated results are larger than the experimental results, it can be understood by the air sensitivity of pentacene in the hole mobility. So, we suggest that our results can be reproduced in the measurement of pure pentacene crystal. We also investigated the dramatic decrease of hole mobility when pentacene was exposed to oxygen. We assumed that pentacene was oxidized into 6,13-pentacenequinone, which was proposed by Diels−Alder reactions.41 Using 6,13-pentacenequinone dimers, we performed the same process to calculate the charge transport properties. The reorganization energy of 6,13-pentacenequinone had not changed much compared to pentacene, with λ = 98.22 meV. However, the charge transfer integral was reduced significantly in 6,13-pentacenequinone crystal. Assuming the same herringbone configuration of pentacene dimers, the charge transfer integrals along channels 1 and 3 were −0.007 and −0.001 eV, respectively, which were an order of magnitude smaller than those of pentacene. As a result, the carrier mobility decreased significantly, and it was expected that the quinone molecules did not participate in the

μϕ = 5.381 cos2(41.45 − ϕ) + 0.180 cos2(88.76 − ϕ) + 0.881 cos2(136.4 − ϕ)

We also ignored channel 4 due to its low effect on the total mobility of pentacene. The calculated anisotropic hole mobility 11308



Article

Notes

transport of charge carriers. Indeed, the calculated mobility of pentacenequinone is 0.05 cm2 V−1 s−1 which is much lower than that of pentacene crystal.4 Because the conjugated π system of pentacene molecules was destroyed with the substituted oxygen atoms, the overlap of HOMO in quinone is reduced significantly. We also checked the charge transfer integral in pentacenequinone−pentacenequinone and pentacene−pentacenequinone dimers in various angles and confirmed that it is reduced significantly in all cases of oxidized pentacene. In addition, the HOMO level of pentacene reduces from −4.88 eV to approximately −6.52 eV in pentacenequinone (calculated from B3LYP/6-31G++(d,p)). If we consider the hole transfer between the pentacene and pentacenequinone molecules, the difference in HOMO levels induces the energy barrier of 1.64 eV for hole to jump from pentacene to pentacenequinone. Thus, it is obvious that the pentacenequinone molecules do not participate in the transport of hole carrier but act as trapping sites in the pentacene crystal. Moreover, the pentacenequinone molecule has a different shape from the pentacene molecule, thus distortion in the pentacene crystal also induces the scattering sites.42 Hence, we expected the mobility would be reduced when pentacene dimers are fully or partially oxidized into pentacenequinone. This requires a vacuum condition for the materials to operate, which is not reliable and convenient in real application. In contrast to pentacene, picene was observed to have an increase in hole mobility of 30% in air, compared to the case of vacuum.43 It is suggested that picene and the oxygen molecule create an electron donor−acceptor pair and undergo a completely different charge transfer mechanism.6 Electrons are expected to transport from the picene molecule to the oxygen molecule, leading to a higher concentration of holes available for conduction in picene. However, the explanation for this behavior is still not clear, and more details are required in future research.

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This research was supported by Global Frontier Program through the Global Frontier Hybrid Interface Materials (GFHIM) of the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2013M3A6B1078870).

■

(1) Ferraris, J.; Walatka, V.; Perlstei, J. H.; Cowan, D. O. Electron Transfer in a New Highly Conducting Donor-Acceptor Complex. J. Am. Chem. Soc. 1973, 95, 948−949. (2) Ashton, Q. A. Aromatic Polycyclic Hydrocarbons − Advances in Research and Applications; ScholarlyEditions: Atlanta, USA, 2013. (3) Xiaodi, Y.; Qikai, L.; Zhigang, S. Theoretical Modelling of Carrier Transports in Molecular Semiconductors: Molecular Design of Triphenylamine Dimer Systems. Nanotechnology 2007, 18, 424029− 424035. (4) Yamashita, Y. Organic Semiconductors for Organic-field Transistors. Sci. Technol. Adv. Mater. 2009, 10, 024313−024322. (5) Hu, W.; Bai, F.; Gong, X.; Zhan, X.; Fu, H.; Bjorn-holm, T. Organic Optoelectronics; Wiley-VCH: Germany, 2013. (6) Jurchescu, O. D.; Baas, J.; Palstra, T. T. M. Effect of Impurities on the Mobility of Single Crystal Pentacene. Appl. Phys. Lett. 2004, 84, 3061−3063. (7) Kalb, W. L.; Mattenberger, K.; Batlogg, B. Oxygen-related Traps in Pentacene Thin Films. Phys. Rev. B 2008, 78, 035334−035344. (8) Okamoto, H.; Kawasaki, N.; Kaji, Y.; Kubozono, Y.; Fujiwara, A.; Yamaji, M. Air-assisted High-performance Filed-effect Transistor with Thin Films of Picene. J. Am. Chem. Soc. 2008, 130, 10470−10471. (9) Mitsuhashi, R.; Suzuki, Y.; Yamanari, Y.; Mitamura, H.; Kambe, T.; Ikeda, N.; Okamoto, H.; Fujiwara, A.; Yamaji, M.; Kawasaki, N.; Maniwa, Y.; Kubozono, Y. Superconductivity in Alkali-metal-doped Picene. Nature 2010, 464, 76−79. (10) De, A.; Ghosh, R.; Roychowdhury, S.; Roychowdhury, P. Acta Crystallogr., Sect. C 1985, 41, 907−909. (11) Mattheus, C. C.; Dros, A. B.; Baas, J.; Meetsma, A.; de Boer, J. L.; Palstra, T. T. M. Acta. Crystallogr., Sect. C 2001, 57, 939−941. (12) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. Gaussian 09, revision A.02; Gaussian Inc.: Wallingford Ct, 2009. (13) Marcus, R. A. Electron Transfer Reaction in Chemistry: Theory and Experiment. Rev. Mod. Phys. 1993, 65, 599−610. (14) Barbara, P. F.; Meyer, T. J.; Ratner, M. A. Contemporary Issues in Electron Transfer Research. J. Phys. Chem. 1996, 100, 13148− 13168. (15) Cornil, J.; Bredas, J. L.; Zaumseil, J.; Sirringhaus, H. Ambipolar Transport in Organic Conjugated Materials. Adv. Mater. 2007, 19, 1791−1799. (16) Mohakud, S.; Ayan, D.; Pati, S. K. Concepts and Methods in Modern Theoretical Chemistry: Statistical Mechanics; CRC Press: Boca Raton, FL, 2013. (17) Reimers, J. R. A Practical Method for The Use of Curvilinear Coordinates in Calculations of Normal-mode-projected Displacements and Duschinsky Rotation Matrices for Large Molecules. J. Chem. Phys. 2001, 115, 9103−9109. (18) Valeev, E. F.; Coropceanu, V.; Filho, D. A. S.; Salman, S.; Bredas, J.-L. Effect of Electronic Polarization on Charge-Transport Parameters in Molecular Organic Semiconductors. J. Am. Chem. Soc. 2006, 128, 9882−9886. (19) Wen, S. H.; Li, A.; Song, J.; Deng, W.; Han, K.; Goddard, W. A., III First-Principles Investigation of Anistropic Hole Mobilities in Organic Semiconductors. J. Phys. Chem. B 2009, 113, 8813−8819.

IV. CONCLUSION We have performed the calculation of the hole mobility in molecular crystals of picene and pentacene, and our calculation agrees well with the existing experimental results. In the electronic properties of oligoacenes and phenacenes, phenacenes have better air stability compared to oligoacenes. If the phenyl rings are added to the structure of picene, the hole mobility becomes larger, and the air stability is preserved. In the case of oligoacenes, however, their HOMO levels become very unstable indicating an extreme sensitivity to ambient environment. In fact, the existence of heptacene is still questionable until now, and the research for oligoacenes stops at pentacene.44 From the calculation of the angle-dependent hole mobility, we reveal that the highest value of the hole mobility is observed along the π−π stacking arrangement in picene crystal and the herringbone arrangement in pentacene crystal. The highest hole mobility of 1.363 cm2 V−1 s−1 can be observed in picene, and it can be enhanced further by increasing the π−π stacking overlap. With the distinct advantage of picene and its air stability, we suggest that picene and its homologous series are promising organic semiconductors with high hole mobility.

■

REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (J.H.S.). Tel.: +82-54-279-2344 *E-mail: [email protected] (J.Y.L.). Tel.: +82-031-299-4560. 11309



Article

(20) Picon, J. D.; Bussac, M. N.; Zuppiroli, L. Quantum Coherence and Carriers Mobility in Organic Semiconductors. Phys. Rev. B 2007, 75, 235106−235115. (21) Cheung, D. L.; Troisi, A. Modelling Charge Transport in Organic Semiconductors: From Quantum Dynamics to Soft Matter. Phys. Chem. Chem. Phys. 2008, 10, 5941−5952. (22) Stehr, V.; Pfister, J.; Fink, R. F.; Engels, B.; Deibel, C. First Principles Calculations of Anisotropic Charge-Carrier Mobilities in Organic Semiconductor Crystals. Phys. Rev. B 2011, 83, 155208− 155221. (23) Deng, W.-Q.; Goddard, W. A., III Predictions of Hole Mobilities in Oligoacene Organic Semiconductors from Quantum Mechanical Calculations. J. Phys. Chem. B 2004, 108, 8614−8621. (24) Coropceanu, V.; Cornil, J.; Filho, D. A. S.; Olivier, Y.; Silbey, R.; Bredas, J- L. Charge Transport in Organic Semiconductors. Chem. Rev. 2007, 107, 926−952. (25) Winkler, M.; Houk, K. N. Nitrogen-Rich Oligoacenes: Candidates for n-Channel Organic Semiconductors. J. Am. Chem. Soc. 2007, 129, 1805−1815. (26) Liu, H.; Mu, J.; Lee, J. Y. Charge Transport Properties of Stacking Bisindenoanthrazolines: DFT Studies. J. Phys. Chem. B 2011, 115, 8409−8416. (27) Wang, L.; Duan, G.; Ji, Y.; Zhang, H. J. Electronic and Charge Transport Properties of peri-Xanthenoxanthene: The Effects of Heteroatoms and Phenyl Substitutions. J. Phys. Chem. C 2012, 116, 22679−22686. (28) Jurchescu, O. D.; Baas, J.; Palstra, T. T. M. Electronic Transport Properties of Pentacene Single Crystals upon Exposure to Air. Appl. Phys. Lett. 2005, 87, 052102−052104. (29) Guo, X. G.; Ortiz, R. P.; Zheng, Y.; Hu, Y.; Noh, Y. Y.; Baeg, K. J.; Facchetti, A.; Marks, T. J. Bithiophene-Imide-Based Polymeric Semiconductors for Field-Effect Transistors: Synthesis, StructureProperty Correlations, Charge Carrier Polarity, and Device Stability. J. Am. Chem. Soc. 2011, 133, 1405−1418. (30) Ahmed, E.; Earmme, T.; Ren, G. Q.; Jenekhe, S. A. Novel n-type Conjugated Ladder Heteroarenes: Synthesis, Self-Assembly of Nanowires, Electron Transport, and Electroluminescence of Bisindenoanthrazolines. Chem. Mater. 2010, 22, 5786−5796. (31) Ioannis Kymissis. Organic Field Effect Transistors: Theory, Fabrication and Characterization; Springer Science: NY, USA, 2009. (32) All thermodynamics data cited herein come from the following source unless otherwise noted: Lias, S. G. “Ionization Energy Evaluation” in NIST Chemistry WebBook, NIST Standard Reference Database Number 69; Linstrom, P. J., Mallard, W. G., Eds.; June 2005; National Institute of Standards and Technology: Gaithersburg, MD, 20899 (http://webbook.nist.gov). (33) Kawasaki, N.; Kubozono, Y.; Okamoto, H.; Fujiwara, A.; Yamaji, M. Trap States and Transport Characteristics in Picene Thin-film Filed-effect Transistor. Appl. Phys. Lett. 2009, 94, 043310−043312. (34) Komura, N.; Goto, H.; He, X.; Mitamura, H.; Eguchi, R.; Kaji, Y.; Okamato, H.; Sugawara, Y.; Gohda, S.; Sato, K.; Kubozono, Y. Characteristics of [6]phenacene Thin Film Filed-effect Transistor. Appl. Phys. Lett. 2012, 101, 083301−083304. (35) Blaha, P.; Schwarz, K.; Madsen, G. K. H.; Kvasnicka, D.; Luitz, J. Wien2k: an Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties; Karlheinz Schwarz, Techn. Universität Wien, Austria, 2001. (36) Roth, F.; Gatti, M.; Cudazzo, P.; Grobosh, M.; Mahns, B. .; Buchner, B.; Rubio, A.; Knupfer, M. Electronic Properties of Molecular Solids: The Peculiar Case of Solid Picene. New J. Phys. 2010, 12, 103036−103043. (37) Kubozono, Y.; He, X.; Hamao, S.; Teranishi, K.; Goto, H.; Eguchi, R.; Kambe, T.; Gohda, S.; Nishihara, T. Transistor Application of Phenacene Molecules and Their Characteristics. Eur. J. Inorg. Chem. 2014, 24, 3806−3819. (38) Klauk, H.; Halik, M.; Zschieschang, U.; Schmid, G.; Radlik, W. High-mobility Polymer Gate Dielectric Pentacene Thin Film Transistors. J. Appl. Phys. 2002, 92, 5259−5263.

(39) Kelly, W.; Muyres, D. V.; Baude, P. F.; Smith, T. P.; Jones, T. D. High Performance Organic Thin Film Transistors. Mater. Res. Soc. Symp. Proc. 2003, 771, L6.5.1−L6.5.10. (40) Lee, J. Y.; Roth, S.; Park, Y. W. Anisotropic Field Effect Mobility in Single Crystal Pentacene. Appl. Phys. Lett. 2006, 88, 252106− 252108. (41) Reddy, A. R.; Bendikov, M. Diels-Alder Reaction of Acenes with Singlet and Triplet Oxygen- Theoretical Study of Two State Reactivity. Chem. Commun. 2006, 1179−1181. (42) Zschieschang, U.; Ante, F.; Yamamoto, T.; Takimiya, K.; Kuwabara, H.; Ikeda, M.; Sekitani, T.; Someya, T.; Kern, K.; Klauk, H. Flexible Low-Voltage Organic Transistors and Circuits Based on a High Mobility Organic Semiconductor with Good Air Stability. Adv. Mater. 2010, 22, 982−985. (43) Voz, C.; Marsal, A.; Moreno, C.; Puigdollers, J.; Alcu-billa, R. Comparison Between the Density-of-states of Picene Transistors Measured in Air and Under Vacuum. Synth. Met. 2012, 161, 2554− 2557. (44) Mondal, R.; Tonshoff, C.; Khon, D.; Neckers, D. C.; Bettinger, H. F. Synthesis, Stability, and Photochemistry of Pentacene, Hexacene, and Heptacene: A Matrix Isolation Study. J. Am. Chem. Soc. 2009, 131, 14281−14289.

11310


Density Functional Theory Studies of Hole Mobility in Picene and

Recommend Documents