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J. Phys. Chem. C 2010, 114, 3248–3255
Semiconductor Performance of Phthalocyaninato Lead Complex and Its Nonperipheral Substituted Derivatives for Organic Field Effect Transistors: Density Functional Theory Calculations Aimin Zhong,‡ Yongzhong Bian,† and Yuexing Zhang*,† Department of Chemistry, UniVersity of Science and Technology Beijing, Beijing 100083, China, and College of Chemistry and Molecular Engineering, Peking UniVersity, Beijing 100871, China ReceiVed: NoVember 29, 2009; ReVised Manuscript ReceiVed: January 14, 2010
Density functional theory (DFT) calculations were carried out to investigate the semiconductor performance for the organic field effect transistor (OFET) of PbPc, PbPc(R-OC2H5)4, and PbPc(R-OC5H11)4 {Pc2- ) dianion of phthalocyanine; [Pc(R-OC2H5)4]2- ) dianion of 1,8,15,22-tetraethoxyphthalocyanine; [Pc(R-OC5H11)4]2) dianion of 1,8,15,22-tetrakis(3-pentyloxy)phthalocyanine} in terms of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy, ionization energy (IE), electron affinity (EA), and their reorganization energy (λ) during the charge-transport process. On the basis of Marcus electron transfer theory, transfer integral (t) and field effect transistor (FET) properties for the three compounds with known crystal structure have been calculated. In line with the experimental result that PbPc can also work as an n-type semiconductor in addition to a p-type one, theoretical calculations reveal that PbPc has relatively large electron affinity to ensure effective electron injection from Au electrode. Introducing four ethoxy groups on the nonperipheral positions of PbPc decreases both the hole and electron injection barrier relative to Au electrode, and the hole and electron reorganization energy becomes very balanced, making PbPc(R-OC2H5)4 a better ambipolar semiconductor material than PbPc. However, nonperipheral pentyloxy substitution lifts the energy level of both HOMO and LUMO and thus decreases both the IP and EA value of PbPc, resulting in improved hole injection ability but worsened electron injection process. The transfer mobility for electron is revealed to be as large as 0.39 cm2 V-1 s-1 for PbPc and 0.16 cm2 V-1 s-1 for PbPc(R-OC5H11)4. The present work will be helpful to understand the electronic nature for PbPc to work as ambipolar semiconductor and to rationally design novel semiconductor materials for OFET usage. Introduction Since the first report in 1986, organic field-effect transistors (OFETs) have attracted increasing research interest because of their potential applications in the field of integrated circuits, flexible displays, gas sensor, and low-cost electronic devices.1–3 Great progress has been made on developing new molecular semiconductors for p-type, n-type, and ambipolar OFETs in recent years.4–6 However, despite the intrinsic ambipolar nature for both hole and electron transfer of the organic materials in terms of theory,7–9 most of the reported semiconductors have only p-type property, with very few n-type semiconductors and ever fewer single-component organic semiconductors exhibiting ambipolar charge transfer property in practical OFET devices.10,11 Phthalocyanines have received extensive attention in the past century because of their peculiar and unconventional chemical and physical properties.12–15 In particular, phthalocyanines have been intensively studied as an active semiconductor layer of OFET due to their excellent semiconductivity.16 In addition, H2Pc (Pc2- ) dianion of phthalocyanine), NiPc, and sodium salts of sulfonated phthalocyaninato nickel NiPc(SO3Na)x as semiconductor material for p-type OFET have been studied theoretically and experimentally by the group of Kratochvı´lova´ in recent years.17,18 Similar to the case for π conjugated organic oligomers and polymers, n-type and ambipolar OFETs based * To whom correspondence should be addressed. E-mail: yxzhang@ ustb.edu.cn. † University of Science and Technology Beijing. ‡ Peking University.
on phthalocyanine semiconductor are relatively scarce, especially for an OFET device with only one kind of phthalocyanine material as active layer.16 As a consequence, designing phthalocyanine molecules suitable for an n-type or ambipolar semiconductor will be very helpful for both phthalocyanine and OFET fields. Among all the phthalocyanine semiconductors, PbPc is one of the few molecules showing the ambipolar property with a single semiconductor material as active layer.16 In 2006, Yasuda et al fabricated high-performance ambipolar OFETs with PbPc as active layer and Parylene-C as insulator layer.19 The devices with a Au source-drain electrode showed hole mobility on the order of magnitude of 10-3 cm2 V-1 s-1 for both hole and electron. However, the electronic structure and intrinsic semiconductor properties of this kind of novel ambipolar semiconductor materials is still unclear. Despite the facts that peripheral substitution can alter the molecular orbital energy level of phthalocyaninato metal complexes and that series of nonperipheral substituted phthalocyaninato lead complexes have been synthesized,20,21 the semiconductor properties of these complexes have not been studied so far. Besides the experimental studies over the preparation and fabrication techniques of organic OFETs, great efforts have been paid to the theoretical aspect, including understanding the nature of organic semiconductors, the relationship between OFET performance and molecular structures, and designing novel molecular materials with high OFET performance, in the past two decades.7,17,18,22–28 Theoretically, the intrinsic semiconducting
10.1021/jp9113305 2010 American Chemical Society Published on Web 02/02/2010
DFT Calculations of PbPc and Its Derivatives property of OFET material is influenced not only by the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) energy, ionization energy (IE) and electron affinity (EA), reorganization energy for hole and electron of single molecule, but also by the transfer integral for hole and election and corresponding charge transfer distance in the solid state. The semiconductor nature (p-type, n-type, or ambipolar) of material is mainly determined by the HOMO/ LUMO and IE/EA of a molecule, which ensures the effective charge injection from the source electrode. Once charge is injected to the semiconductor, the charge transfer mobility of the organic seminconductor can be calculated by reorganization energy, transfer integral, and corresponded transfer distance using theoretical modes treating carrier motion in the solid state. In general, the p- and n-type semiconductors should possess high HOMO and low LUMO energy, respectively, which in turn results in small ionization energy and large electron affinity (at least 3.0 eV), both of which should actually be close to the work function potential of the source-drain electrodes (5.1 eV for Au electrode), yielding smaller charge injection barrier for hole and electron, respectively, to ensure the effective charge injection from the source electrode. As expected, the ambipolar semiconductors are those materials simultaneously with high HOMO and low LUMO energy as well as small ionization potential and large electron affinity. As a result, in terms of both injection barrier and charge transfer mobility, molecular design toward ambipolar organic semiconductors should aim for compounds with both low LUMO and high HOMO, large electron affinity and small ionization potential, and small intrinsic electron and hole reorganization energy in nature. Following this finding, the charge transfer mobility for organic molecules such as pentacene, perfluoropentacene, sexithiophene, oligothienoacenes, and bis(phthalocyaninato) rare earth doubledecker complexes M(Pc)2 (M ) Y, La) have been investigated on the basis of theoretical calculations using Marcus theory.22–28 In particular, the recent progresses in developing computational tools to assess the carrier mobility in organic molecular semiconductors at the first-principles level and some rational molecular design strategies for high mobility organic materials were outlined by Shuai’s group,29 making theoretical aspects very successful in helping experimental studies on the OFET property. In this paper, on the basis of our research interests in OFETs7,26–28,30–33 and accumulation in the theoretical studies,34–39 we describe the HOMO and LUMO energy, ionization energy (IE), electron affinity (EA), and the reorganization energy of the series of phthalocyaninato lead complexes PbPc, PbPc(ROC2H5)4, and PbPc(R-OC5H11)4. On the basis of a hopping mechanism, the transfer integral and charge mobility values for this series of compounds with known crystal structure are also calculated using density function theory (DFT) method. The present theoretical effort toward understanding the OFET properties of phthalocyaninato lead complexes will be useful in designing superior ambipolar functional organic semiconducting materials with good OFET performance. Methodology and Computational Details There are generally two typical modes in treating carrier motion in the solid state: the coherent band model and the incoherent hopping model. As the hopping mechanism has been proved to be the dominant mechanism in organic semiconductors at high temperature and is advocated by Bre´das and other scientists,25,40–45 we adopted a hopping model in this work. Charge transfer can be described as a self-exchange electrontransfer reaction between a neutral molecule and a neighboring
J. Phys. Chem. C, Vol. 114, No. 7, 2010 3249 radical cation (p-type) or radical anion (n-type) in the hopping model. The rate constant for charge transfer (W) of weak coupling system with t , λ( can be modeled by classical Marcus theory43,44
W ) (t2 /p)(π/λ(kBT)1/2exp(-λ( /4kBT) where t is the transfer integral, λ( the reorganization energy, kB the Boltzmann constant, and T the temperature. Neglecting the influence of intermolecular interaction on the molecular deformation, the reorganization energy λ+ or λ- for hole or electron transfer, respectively, is therefore calculated as the sum of (a) the energy required for reorganization of the vertically ionized neutral 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. That is
λ( ) (E*( - E() + (E* - E) In this equation, E is the energy of neutral molecule in neutral geometry, E* is the energy of neutral molecule in cation or anion geometry, E( is the energy of cation or anion in cationic or anionic geometry, and E*( is the energy of cation or anion in neutral geometry. To achieve high charge carrier mobility, the reorganization energy needs to be minimized.2,25,42,45–54 The transfer integral t depends on the relative arrangement of the molecules in the solid state and describes the intermolecular electronic coupling, which needs to be maximized to achieve high charge carrier mobility. Only the nearest neighbor molecules in the crystals were taken to evaluate the transfer integrals, and the direct dimer Hamiltonian evaluation method9,55 was used. The electronic coupling for hole/electron transfer in the direct scheme can be written as 0,site1 0,site2 t ) 〈ΦHOMO/LUMO |F0 |ΦHOMO/LUMO 〉 0,site1 0,site2 where ΦHOMO/LUMO and ΦHOMO/LUMO represent the HOMO or LUMO of isolated molecules 1 and 2, respectively, among the neighbor molecules, and F0 is the Fock operator for the dimer for a fixed pathway in which the superscript zero indicates that the molecular orbitals appearing in the operator (the density matrix, for instance) are unperturbed. The Fock matrix is evaluated as
F0 ) SCεC-1 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 direct method in calculating transfer integral has been proved to be simple, efficient, and reliable,9,56,57 in comparison with the site energy andoverlapcorrectedsplittingschemeofValeevandco-workers.58–60 Given the rate constant for charge transfer (W) between two neighboring molecules, the diffusion coefficient can be evaluated as25,56,61,62
D)
1 〈x(t)2〉 1 ≈ 2d t 2d
∑ ri2WiPi i
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J. Phys. Chem. C, Vol. 114, No. 7, 2010
Figure 1. Schematic molecular structure of PbPc (a), PbPc(R-OC2H5)4 (b), and PbPc(R-OC5H11)4 (c). (d) side view of part c.
In the above equation, i represents a specific transfer pathway with ri being the transfer distance (intermolecular center to center distance), 1/Wi the transfer time, and d the spatial dimension, which is equal to 3 for the crystal. Pi is the relative probability for the ith pathway
Pi ) Wi /
∑ Wi i
The basic assumption is that the charge transfer is a slow process in which the solvent and solute molecules have enough time to come to equilibrium. This is pertinent for the soft organic system. The drift charge transfer mobility, µ, is then evaluated from the Einstein relation:62
µ)
e D kBT
The molecular structures of the series of phthalocyaninato lead complexes are shown in Figure 1. The structures and spectroscopic properties of these complexes have been reported in previous work.35,37 The structures of the cation and anion of these complexes were calculated with the density functional theory (DFT) method at the B3LYP level63,64 using LANL2DZ basis sets65,66 and were verified by frequency calculation. The B3LYP functional has been widely employed for calculating reorganization energies of charge transport processes,7,22–28,67,68 and the LANL2DZ basis set has been proved feasible for calculating large molecules with heavy metal such as yttrium, lanthanum, and lead.7,34–37 The calculated spin contamination in the cations and anions is small and negligible. All the calculations were performed using the Gaussian 03 program69 with the IBM P690 system at the Shandong Province High Performance Computing Centre. Results and Discussion Geometric Structure. Like the structure of the neutral molecules reported previously,37 the energy-minimized structures of cations of these phthalocyaninato lead complexes optimized at the B3LYP/LANL2DZ level are of C4V symmetry for PbPc and C4 symmetry for PbPc(R-OC2H5)4 and PbPc(R-OC5H11)4.
Zhong et al. This result indicates that the molecular symmetry of these complexes remains unchanged upon oxidation, suggesting the high symmetry of the HOMO of these complexes. On the contrary, the symmetry of the anion for these phthalocyaninato lead complexes decreases to C2V for PbPc and to C2 for PbPc(ROC2H5)4 and PbPc(R-OC5H11)4, indicating that introducing one electron to the degenerate LUMO of these phthalocyaninato lead complexes induces different structural variation for the two opposite isoindole rings (say along x axis direction) in comparison with that for the other two opposite isoindole rings (say along y axis direction). Table 1 shows the change in bond lengths for PbPc and PbPc(R-OC5H11)4 upon oxidation and reduction on the basis of calculation results. As can be seen, the lengths for Pb-N1, N1-CR, CR-Cβ, and Cγ-Cδ in PbPc increase by 0.011, 0.002, 0.003, and 0.073 Å, respectively, upon oxidation, while the length for CR-N2, Cβ-Cγ, Cβ-Cβ, and Cδ-Cδ decrease by 0.0002, 0.005, 0.002, and 0.006 Å, respectively. However, upon reduction, the bond length (except for Pb-N1 bond) variation of two opposite isoindole rings in the x axis direction shows the same trend as upon oxidation while that in the other two opposite isoindole rings (in the y axis direction) exhibits the contrary trend. This induces the decrease of molecular symmetry from C4V for the neutral compound to only C2V for the reduced specie. It is worth noting that except for the Pb-N1 bond, the change in bond length upon both oxidation and reduction is not very significant. When the Pb-N1 bond is involved, the average bond length variation upon oxidation is only 0.005 Å, while the variation upon reduction is 0.007 and 0.009 Å for the two opposite isoindoles in two different directions. When excluding the Pb-N1 bond, the bond length variation decreases to 0.003 Å upon oxidation and to 0.005 and 0.009 Å upon reduction, indicating the very slight change in the bond length within phthalocyanine rings for PbPc upon either oxidation or reduction and in turn the very small reorganization energy for both hole and electron transfer (vide infra). Nevertheless, the bond length variation upon reduction is larger than that upon oxidation, suggesting the much larger reorganization energy for an electron of PbPc in comparison with the reorganization energy for a hole. As expected, the introduction of four bulky 3-pentyloxy groups in PbPc(R-OC5H11)4 increases the change value of bond length upon both oxidation and reduction. As can be seen, the average change in bond length for PbPc(R-OC5H11)4 upon oxidation is much larger than that for PbPc, 0.006 vs 0.005 Å. It is also true for the reduction process, with the average bond length change for two opposite isoindole rings in x and y direction of 0.007 and 0.010 Å and the total bond length change of the whole molecule of 0.009 Å. As in PbPc, the bond length change in PbPc(R-OC5H11)4 upon oxidation is smaller than upon reduction, suggesting the much larger reorganization energy for electron of PbPc(R-OC5H11)4 in comparison with the reorganization energy for hole. Due to the smaller steric hindrance of ethoxy group than the 3-pentyloxy group, the bond length changes of PbPc(R-OC2H5)4 for both oxidation and reduction processes are smaller than those of PbPc(R-OC5H11)4 but larger than those of PbPc. Also, the bond length change in PbPc(R-OC2H5)4 upon oxidation is smaller than upon reduction. These results indicate that the reorganization energy for hole in PbPc(R-OC2H5)4 is smaller than the reorganization energy for electron and both the reorganization energy for hole and electron in PbPc(R-OC2H5)4 is smaller than that in PbPc(R-OC5H11)4 but larger than in PbPc.
DFT Calculations of PbPc and Its Derivatives
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TABLE 1: Comparison of the Optimized Structural Parameters between the Neutral Molecule and Its Cation and Anion for PbPc and PbPc(r-OC5H11)4 PbPc parametera Pb-N1 N1-CR N1-CR2 CR-N2 CR2-N2 CR-Cβ CR2-Cβ2 Cβ-Cγ Cβ2-Cγ2 Cγ-Cδ Cγ2-Cδ2 Cβ-Cβ Cδ-Cδ Cγ1-O O-C1
PbPc(R-OC5H11)4
neutralb
cation
anion isoindole x
anion isoindole y
neutralb
cation
anion isoindole x
anion isoindole y
2.334 1.393
2.345 1.395
2.314 1.403
2.333 1.393
1.343
1.343
1.330
1.366
1.468
1.471
1.476
1.451
1.404
1.399
1.403
1.411
1.407
1.415
1.410
1.402
1.421 1.420
1.419 1.413
1.419 1.418
1.433 1.428
2.334 1.398 1.388 1.342 1.342 1.469 1.467 1.416 1.402 1.415 1.405 1.422 1.414 1.383 1.485
2.340 1.405 1.386 1.342 1.343 1.466 1.471 1.416 1.394 1.427 1.414 1.422 1.405 1.367 1.497
2.314 1.407 1.398 1.329 1.329 1.481 1.474 1.413 1.402 1.416 1.406 1.421 1.414 1.395 1.479
2.338 1.396 1.389 1.364 1.366 1.455 1.449 1.420 1.410 1.407 1.399 1.435 1.423 1.400 1.478
a N1, nitrogen atom joined to the central metal; N2, aza nitrogen atom not joined to the central metal; R, β, γ, δ, mean carbon atoms in isoindole units beginning from N1; suffix 1 of C atoms means atoms on the same side of the alkoxy substituents, while suffix 2 means atoms on the other side of the alkoxy substituents; C1, the tertiary carbon atom of 3-pentyloxy. b Data taken from ref 37.
TABLE 2: Energies of Molecular Frontier Orbitals and HOMO-LUMO Gap (in eV) for PbPc, PbPc(r-OC2H5)4, and PbPc(r-OC5H11)4a EHOMO ELUMO gap a
PbPc
PbPc(R-OC2H5)4
PbPc(R-OC5H11)4
-5.31 -3.16 2.15
-5.20 -3.21 1.99
-4.76 -2.75 2.01
Data taken from ref 37.
Energy Level of HOMO and LUMO. The calculated HOMO and LUMO energy together with the HOMO-LUMO gap for PbPc, PbPc(R-OC2H5)4, and PbPc(R-OC5H11)4 are tabulated in Table 2. The energy level of HOMO and LUMO of PbPc, -5.31 and -3.16 eV, is much lower than those of CuPc, the most common phthalocyanine semiconductor, -4.93 and -2.75 eV, indicating that electron injection to the LUMO is easier for PbPc while electron loss from the HOMO is harder in comparison with CuPc. The introduction of four ethoxy groups onto the nonperipheral positions of the phthalocyanine ring of PbPc leads to an increase in the HOMO energy to -5.20 eV and the somewhat decrease in the LUMO energy to -3.21 eV for PbPc(R-OC2H5)4. These results indicate a smaller injection barrier for both hole and electron from the work potential of gold electrode for PbPc(R-OC2H5)4 in comparison with PbPc, rendering PbPc(R-OC2H5)4 a more effective semiconductor materials for ambipolar OFET than PbPc in term of charge injection. Changing the four ethoxy groups of PbPc(ROC2H5)4 to 3-pentyloxy groups further increases the energy level of HOMO and LUMO to -4.76 and -2.75 eV, respectively, revealing the improved hole injection but worsened electron injection of PbPc(R-OC5H11)4 in comparison to PbPc(R-OC2H5)4. As a result, PbPc(R-OC5H11)4 can work as a better p-type semiconductor but worse n-type one than PbPc and PbPc(ROC2H5)4. Ionization Energies (IE) and Electron Affinities (EA). To give more information about the ease of injection of hole or electron from the Au source electrode into semiconductor layer in the OFET devices, the adiabatic and vertical ionization energies (IEa and IEv) and the adiabatic and vertical electron affinities (EAa and EAv) for the series of compounds PbPc, PbPc(R-OC2H5)4, and PbPc(R-OC5H11)4 were calculated, and the results are organized in Table 3. The vertical ionization
TABLE 3: Vertical and Adiabatic Ionization Energies and Electron Affinities (in eV) of PbPc, PbPc(r-OC2H5)4, and PbPc(r-OC5H11)4 IEvert IEadia EAvert EAadia
PbPc
PbPc(R-OC2H5)4
PbPc(R-OC5H11)4
6.35 6.32 2.04 2.15
6.20 6.11 2.17 2.28
5.71 5.63 1.72 1.89
energy or electron affinity, IEv or EAv, reflects the difference in energy between the optimized neutral molecule and the corresponding cation or anion in the geometry of neutral molecule. As expected from the orbital energy, both the IEv and EAv of PbPc, 6.35 and 2.04 eV, are larger than those of CuPc, 6.03 and 1.58 eV. It is well-known that the barrier for hole or electron injection is the energy difference between the ionization potential or electron affinity of the material and the work function of the electrode (Au electrode in the present case), respectively. Tuning the electron affinity and ionization potential is an important strategy to change the carrier polarity of material. In general, materials with large IEv and EAv will show an advantage as n-type organic semiconductor in terms of charge injection. The increased IEv and EAv for PbPc in comparison with CuPc indicate that the injection barrier for hole is increased while the injection barrier for electron is decreased relative to Au electrode, suggesting PbPc showing an advantage vs CuPc as an n-type organic semiconductor in term of charge injection. According to previous research,45 materials with an electronic affinity locating in the range of 3.00-4.00 eV can ensure efficient electron injection from common gold electrode and show advantage as a good n-type semiconductor for OFETs. The EAv of PbPc, 2.04 eV, approaches the suggested electronic affinity for an n-type semiconductor, therefore suggesting PbPc can work as an n-type semiconductor. In addition, the very small hole injection barrier for PbPc relative to Au electrode, 1.25 eV, also shows it retains a good p-type semiconductor property. In fact, the improving extent for electron injection in PbPc is larger than the worsening extent for hole injection due to the decreased HOMO-LUMO energy gap in PbPc in comparison with CuPc. As a consequence, PbPc can work as semiconductor materials for both hole and electron transfer and thus show an ambipolar OFET property, which corresponds well with the
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Zhong et al.
TABLE 4: Reorganization Energies (in eV) of Hole- And Electron-Transport Processes for PbPc, PbPc(r-OC2H5)4, and PbPc(r-OC5H11)4 λ+ λ_
PbPc
PbPc(R-OC2H5)4
PbPc(R-OC5H11)4
0.06 0.22
0.17 0.25
0.17 0.32
previous experimental findings that PbPc displays an ambipolar semiconductor property when being fabricated into OFETs.19 In line with the change in the energy of their HOMO and LUMO, the introduction of four ethoxy and 3-pentyloxy groups onto the nonperipheral positions of phthalocyaninato lead complex induces the decrease in IEv, from 6.35 eV for PbPc to 6.20 eV for PbPc(R-OC2H5)4 and 5.71 eV for PbPc(R-OC5H11)4, the increase in EAv from 2.04 eV for PbPc to 2.17 eV for PbPc(R-OC2H5)4, but the decrease in EAv to 1.72 eV for PbPc(ROC5H11)4. The calculated results indicate that introduction of alkoxy groups on the nonperipheral position of phthalocyaninato lead significantly decreases the hole injection barrier relative to Au electrode but increases the electron barrier for PbPc(ROC5H11)4. Interestingly, the electron injection barrier in PbPc(ROC2H5)4 also decreases, rendering PbPc(R-OC2H5)4 a more appreciate ambipolar semiconductor materials in term of charge injection than PbPc. Reorganization Energy (λ(). Intrinsic reorganization energy is calculated from adiabatic potential energy surfaces, that is, the sum of the relaxation energies when molecular geometry changes from the neutral to the ionized state and the opposite process. The calculated reorganization energy (λ() for holetransport and electron-transport process of the three compounds is listed in Table 4. The calculated λ+ of PbPc, 0.06 eV, is much smaller than λ_, 0.22 eV, suggesting the higher transfer mobility for hole than for electron. It is also true for PbPc(R-OC2H5)4 and PbPc(R-OC5H11)4, which show reorganization energy for hole (λ+) of 0.17 and 0.17 eV and reorganization energy for electron (λ-) of 0.25 and 0.32 eV, respectively. In addition, the reorganization energy for both hole-transport and electrontransport exhibits some increase from PbPc to PbPc(R-OC2H5)4 and PbPc(R-OC5H11)4. As can be seen from Table 4, the reorganization energy for hole and electron in PbPc(R-OC2H5)4 is 0.17 and 0.25 eV, respectively. Though the increase of reorganization energy will decrease the transfer mobility, the greater balance reorganization energy for hole and electron in PbPc(R-OC2H5)4 than in PbPc will induce the balance transfer mobility for hole and electron, which is very important for constructing ambipolar OFET in integrated circuits. These results together with the appropriate charge injection barrier for both hole and electron in PbPc(R-OC2H5)4 make it an ideal ambipolar semiconductor material. On the contrary, the reorganization energy for hole and electron in PbPc(R-OC5H11)4, 0.17 and 0.32 eV, shows a very large difference. It is worth noting that the reorganization energy for hole in PbPc(R-OC5H11)4 is comparable to that in PbPc(R-OC2H5)4, indicating that PbPc(ROC5H11)4 is a very good p-type semiconductor in term of both charge injection and reorganization energy. It is well-known that there is a strong coupling between the geometric and electronic structures in the π-conjugated systems.7,67 As a consequence, when removing an electron from the HOMO or adding an electron into the LUMO, some bond lengths should change due to the change of electronic structures. The smaller the geometric deformation is, the smaller the internal reorganization energy is. The change in the internal reorganization energy of these compounds thus can be well rationalized by their geometry deformation during oxidation and reduction. As
Figure 2. The molecular orbital map for the HOMO (top) and LUMO (buttom) of PbPc (left) and PbPc(R-OC5H11)4 (right).
shown in Table 1 and described in the Geometric Structure section, the average bond length variation upon oxidation in all these three phthalocyaninato lead complexes is smaller than upon reduction, and the average bond length variation upon both oxidation and reduction increases from PbPc to PbPc(R-OC2H5)4 and PbPc(R-OC5H11)4 with the introduction of alkoxy groups, corresponding well with the trend for reorganization energy. It is worth pointing out that the degree of geometry change upon oxidation or reduction correlates to the orbital composition of HOMO and LUMO. That is, the bonds including atoms with large contribution to the HOMO or LUMO would have larger geometry deformation upon oxidation or reduction. As can be seen from Figure 2, the HOMO of PbPc and PbPc(R-OC5H11)4 mainly distributes over all the carbon atoms of the four isoindole rings. In contrast, the LUMO of these complexes concentrates on only two opposite isoindole rings and the orbital distribution on the other two isoindole rings significantly decreases, corresponding well with the different structural variation for isoindole rings along the x axis direction in comparison with that along the y axis direction. The different orbital distribution for HOMO and LUMO also well rationalizes the much larger reorganization energy for electron than for hole in these complexes. Intermolecular Electronic Coupling (V) and Charge Transfer Mobility (µ). With the help of single crystal X-ray diffraction analysis results for PbPc and PbPc(R-OC5H11)4, charge transfer integrals between one randomly selected molecule and all its possible neighbors are calculated in Table 5. The hopping routes for PbPc and PbPc(R-OC5H11)4 are displayed in Figures 3 and 4, respectively. Charge transfer integrals between one randomly selected molecule (m0) (middle molecule in blue) and all its possible neighbors (m1-m10) are calculated on the basis of the experimental crystal structures in the direct scheme. As can be seen in Figure 3 and Table 5, among the 10 dimers between m0 and m1-m10 in the crystal of PbPc, the largest transfer integrals for hole and electron are obtained for route 3 with the value of 258.99 and 60.11 meV, respectively, indicating the most favorable hole and electron transfer in this transfer route. Routes 4 and 2 display the smallest transfer integral of only 0.80 and 0.39 meV for hole and electron, respectively, indicating the most unfavorable route for hole and
DFT Calculations of PbPc and Its Derivatives
J. Phys. Chem. C, Vol. 114, No. 7, 2010 3253
TABLE 5: Hopping Pathways, Center Mass Distance, Electronic Coupling, and Mobility of PbPc (space group P1j) and PbPc(r-OC5H11)4 (space group P21/c) pathway 1 2 3a 4a 5a 6 7 8 9 10
PbPc (P1j) from m0 distance (Å) V+ (meV) V- (meV) 12.889 12.889 6.518 13.003 8.260 11.015 16.000 8.800 7.558 5.308
mobility µ- (cm2 V-1 s-1)
a
2.28 2.28 258.99 0.80 67.81 12.99 4.76 11.01 33.04 1.46
0.40 0.39 60.11 4.63 19.54 1.63 3.25 11.37 19.57 18.40
PbPc (P1j) from m0′ distance (Å) V+ (meV) V- (meV) 12.889 12.889 6.311 12.734 8.405 11.015 16.001 8.799 7.559 5.307
1.21 1.21 270.41 13.86 42.66 13.01 4.74 11.06 32.99 1.42
1.18 1.18 55.84 9.58 57.55 1.61 3.24 11.40 19.48 18.43
PbPc(R-OC5H11)4 (P21/c) distance (Å) V+ (meV) V- (meV) 17.07 17.16 14.02 14.44 5.99 17.16 17.07 14.44 10.52 10.52
0.39 (merging all paths as total20 transfer routes) 0.30 (with average transfer distanceand integral) 0.32 (with paths from m0) 0.43 (with paths from m0′)
0.76 0.50 11.91 2.49 145.73 0.50 0.78 2.49 0.68 0.65
0.23 0.27 0.13 0.76 73.93 0.27 0.23 0.76 4.25 4.26 0.16
Data in boldface show the much significant differences between pathways from m0 and m0′ in the crystal of PbPc.
Figure 3. The hopping routes in the crystal of PbPc with space group P1j starting from two different molecular centers. Blue: randomly selected molecule center m0. Red: the other molecule center near m0 (named as m0′). Brown: molecules in the same layer as m0 and m0′.
electron transfer in routes 4 and 2. The second largest transfer integral for hole and electron is found for routes 5 and 9 with the value of 67.81 and 19.57 meV, respectively. These results indicate that π-π stacking mode with very large overlap is the most favorable for both hole and electron transfer, followed by herringbone stacking mode, while the edge-to-edge coplanar stacking mode is very unfavorable for charge transfer. Reexamining the crystal of PbPc (with P1j space group) shows that there are two different types of PbPc molecules having different environment in the crystal (Figure 3, in blue and red). The transfer integrals between molecule m0′ (middle molecule of Figure 3 in red) and all its possible neighbors (m1′-m10′) are also calculated on the basis of the experimental crystal structures in the direct scheme, and the results are organized in Table 5. Comparing all the transfer routes starting from m0 and m0′ indicates that only routes 3-5 show some differences in transfer distance, with the value of 6.518, 13.003, and 8.260 Å for m0 and 6.311, 12.734, 8.405 Å for m0′, respectively, while the other transfer routes almost have the same transfer distance and thus will reflect the same packing mode. The same as the case for m0, the largest transfer integral for hole and electron is found for route 3′ with the value of 270.41 and 55.84 meV, and route 5′ gives the second largest transfer integral for both hole and
electron with the value of 42.66 and 57.55 meV, respectively. Both dimer m0′-m3′ and m0′-m5′ take π-π stacking mode with very large overlap, indicating again that π-π stacking mode with very large overlap is the most favorable route for hole and electron transfer in PbPc crystal. In addition, most of the calculated transfer integrals for both hole and electron from m0 have the same order of magnitude as from m0′. These results indicate that choosing m0 or m0′ as center in fact has no significant difference for hopping pathways and calculated electronic couplings. The derivative of PbPc with four bulky 3-pentoxy groups, PbPc(R-OC5H11)4, has a different crystal space group, different hopping pathways and center mass distance (r), and therefore different transfer integral in comparison with PbPc. According to the calculation result, the largest transfer integral for hole and electron among all the possible routes in the crystal of PbPc(R-OC5H11)4 is 145.73 and 73.93 meV, respectively, for pathway 5 (Figure 4 and Table 5). Though the largest hole transfer integral in the crystal of PbPc(R-OC5H11)4 is more than 100 meV smaller than that of PbPc, the electron transfer integral of the former is larger than that of the latter, indicating the very strong electronic coupling of the LUMO in PbPc(R-OC5H11)4 despite the p-type semiconductor nature. Except for the largest transfer integral for hole and electron in route 5, all the other pathway in the crystal of PbPc(R-OC5H11)4 show a much smaller transfer integral of less than 10 meV. These results indicate that both hole and electron transfer in the crystal of PbPc(R-OC5H11)4 for most routes is less favorable in comparison with that in the crystal of PbPc. This together with the larger reorganization energy for hole of PbPc(R-OC5H11)4 reveals that PbPc(ROC5H11)4 is not a good p-type semiconductor materials in comparison with PbPc, despite the decreased hole injection barrier. The total charge transfer mobility in the crystal of PbPc and PbPc(R-OC5H11)4 is calculated according to the Marcus equation and Einstein relation, and the results are tabulated in Table 5. Due to the larger transfer integral and the much smaller reorganization energy of PbPc than PbPc(R-OC5H11)4, the charge transfer mobility for hole calculated for PbPc will be significantly larger than that for PbPc(R-OC5H11)4. This is also true for the charge transfer mobility for electron. As can be seen from Table 5, the calculated electron transfer mobility of PbPc is 0.32 cm2 V-1 s-1 for the pathway from m0 and 0.43 cm2 V-1 s-1 for the pathway from m0′, about 2 times of that for
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Figure 4. The hopping routes in the crystal of PbPc(R-OC5H11)4 (space group P21/c).
PbPc(R-OC5H11)4, 0.16 cm2 V-1 s-1, indicating that PbPc can also work as a good n-type semiconductor. When merging all paths from m0 and m0′ together and summarizing all the total 20 transfer routes, the calculated electron transfer mobility of PbPc is 0.39 cm2 V-1 s-1. It is noteworthy that the calculated intrinsic electron transfer mobility of PbPc in crystal is much larger than the experimental electron transfer mobility of 10-3 cm2 V-1 s-1,19 indicating that the OFET performance of PbPc could be further improved. It is worth noting that, due to the lack of crystal structure for PbPc(R-OC2H5)4, the charge transfer mobility in this complex cannot be calculated with this method. However, because of the smaller and more balance hole and electron reorganization energy in PbPc(R-OC2H5)4 than in PbPc(R-OC5H11)4, the former would show larger and more balance charge transfer mobility than the latter, supposing the similar molecular packing is adopted. This, together with the fact that both hole and electron injection barriers in PbPc(R-OC2H5)4 are very small, renders it a very good ambipolar semiconductor material for OFET applications. Conclusion The semiconductor properties of a series of phthalocyaninato lead complexes including PbPc, PbPc(R-OC2H5)4, and PbPc(R-
OC5H11)4 have been systematically investigated by DFT calculations. The modest ionization energy and relatively large electron affinity of PbPc ensure the effective hole and electron injection from Au electrode and make PbPc show ambipolar semiconductor property. Introducing four ethoxy groups on the nonperipheral positions of PbPc decreases both the hole and electron injection barrier relative to Au electrode and the hole and electron reorganization energy becomes very balanced, making PbPc(R-OC2H5)4 a better ambipolar semiconductor material than PbPc. However, nonperipheral 3-pentyloxy substitution lifts the energy level of both HOMO and LUMO and thus decreases both the IP and EA value of PbPc, resulting in an improved hole injection ability but worsened electron injection process and the change of semiconductor nature from ambipolar to only p-type. Acknowledgment. Financial support from the Natural Science Foundation of China, Beijing Municipal Commission of Education, China Postdoctoral Science Foundation (20090460210), and University of Science and Technology Beijing is gratefully acknowledged. We are also grateful to the Shandong Province High Performance Computing Center for a grant of computer time.
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