J. Phys. Chem. B 2005, 109, 12891-12898
12891
Electronic Structures and Charge Transport Properties of the Organic Semiconductor Bis[1,2,5]thiadiazolo-p-quinobis(1,3-dithiole), BTQBT, and Its Derivatives Jingsong Huang and Miklos Kertesz* Department of Chemistry, Georgetown UniVersity, 37th and O Street, Washington, DC 20057-1227 ReceiVed: March 16, 2005; In Final Form: May 6, 2005
We analyze the correlation between crystal and film structures and charge transport of an important organic semiconductor, bis[1,2,5]thiadiazolo-p-quinobis(1,3-dithiole) (BTQBT), and its derivatives 4,8-bis(1,3-dithiol2-ylidene)-4H,8H-[1,2, 5]selenadiazolo[3,4-f]-2,1,3-benzothiadiazole, 4,8-bis(1,3-diselenol-2-ylidene)-4H,8Hbenzo[1,2-c:4,5-c′]bis[1,2,5]thiadiazole, and tetramethyl-BTQBT. We present first-principles density functional theory (DFT) calculations that agree well with earlier angle-resolved photoelectron spectroscopy (ARPES) experiments on BTQBT films, strongly supporting that the BTQBT films adopt the same layered structure as in the single crystals. Qualitative charge transport properties based on presented DFT results agree with experiments regarding the sign of the charge carriers and the unusually small anisotropy of conductivity. These agreements indicate that accurate electronic structure calculations, when coupled with ARPES, help establish the correlation between intermolecular packing and charge transport, which is one of the central but elusive aspects of organic molecular materials. Predictions are made for derivatives of BTQBT, and calculations agree with available experimental information on the conductivities. Comparisons are made with pentacene, one of the most widely studied organic molecular materials.
Introduction Electroactive organic molecular materials are regaining a great deal of interest because of their potential applications as elements of electronic (nano)devices such as field-effect transistors (FET), light-emitting diodes (LED), and photovoltaic (PV) devices.1,2 New molecules and materials are being developed,3,4,5,6 and scientists are making substantial progress in improving the performance and efficiency of the organic-based devices, for example, in the field of FET.7,8,9 Single crystals and films of the important organic semiconductor bis[1,2,5]thiadiazolo-p-quinobis(1,3-dithiole) (BTQBT; Figure 1) exhibit remarkably high electrical conductivity concomitant with a small anisotropy of the conductivity.10 The field-effect mobility and on/off current ratio of its FET devices5,6,11 are higher than those of many organic semiconductors studied to date and are almost comparable to those of pentacene thin films,5-7,9 one of the most widely studied organic molecular materials for FET application.12,13 By optimization of the device fabrication techniques,4,14 the performance and efficiency of BTQBT-based devices could be even more improved. The similarity between BTQBT and pentacene (and other materials as well) is that these molecules are nearly planar; therefore, a primary delocalization due to conjugation is established within the molecular plane. Both materials adopt π-π packing motives,17 allowing for a secondary delocalization along the packing direction due to intermolecular overlap of the π-electrons providing conduction pathways throughout the material. Intermolecular packing across van der Waals gaps determines the charge transfer (hopping) integrals between neighboring molecules and is responsible for dramatic variations in charge transport properties. Recent calculations for different polymorphs of pentacene by Troisi and Orlandi have shown * Author to whom correspondence should be addressed. E-mail: kertesz@ georgetown.edu.
Figure 1. Molecular structures of bis[1,2,5]thiadiazolo-p-quinobis(1,3dithiole) (BTQBT) and its derivatives TSQBT, BTQBS, and TMBTQBT.15,16
that the bandwidth can differ by a factor of 4, and the hole mobility tensors are accordingly quite different.18 It is widely accepted that the charge transport properties of conjugated molecules are intrinsically correlated with their structures. However, such structure-property correlations are still an elusive aspect of organic materials.9,13,19 The present work is motivated by the challenge to understand the properties of a specific promising material (BTQBT) as well as to gain further insights into these structure-property correlations. Generally speaking, a broader energy band leads to a lower effective mass, which, in turn, leads to a higher mobility and higher conductivity. Therefore, electronic band structures are usually used to rationalize the correlation between crystal structures and charge transport properties.18,20-22 Electronic band structure calculations for various organic molecular materials have been performed at a various levels of theory, including extended Hu¨ckel theory (EHT),20,22,23 Zerner’s intermediate neglect of differential overlap (ZINDO/S),21,24-27 and density functional theory (DFT).18,28-31 The agreement between ab initio calculations and experiments is usually satisfactory.31,32 At the same time, quantitative and sometimes even qualitative dis-
10.1021/jp0513869 CCC: $30.25 © 2005 American Chemical Society Published on Web 06/09/2005
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crepancies between semiempirical calculations and experiments are common. The relevant key parameters governing charge transport in organic molecular materials are the intermolecular transfer integrals, βn, 24,33 which describe the strength of the electronic coupling between the nth molecular orbitals (MO). βn is related to the following matrix element
β′n ) 〈ψn,A|H ˆ |ψn,B〉
(1)
where ψn,A refers to the nth MO of molecule A in the vicinity of molecule B and H ˆ is the crystal Hamiltonian. (The prime in eq 1 indicates that the transfer integrals, βn, are actually not equal to these matrix elements; see below.) The connection between the nth energy band, En(k), of a one-dimensional stack of molecules and the nth transfer integral is approximately
En(k) ) Rn + 2βn cos ka
(2)
where a is the lattice constant, k is the reciprocal lattice wave vector, and Rn is the MO energy. This approximation is valid when the molecular orbitals are isolated from one another and the overlap is neglected. In such a case, the nth bandwidth (BWn) is about 4βn
BWn ) 4|βn|
(3)
Dimers are useful in calculations for obtaining accurate values for βn. An energy-scale-independent definition of βn is based on the energy level splitting of the dimer
|βn| ) 0.5(En,+ - En,-)
(4)
where En,( are the dimer orbital energies originating in the nth MO energy of the monomer. The sign of βn can be obtained by inspecting the bonding-antibonding interactions between the MOs in the dimer. The advantage of this approximation is that it is free from the choice of the origin of the energy scale, while the matrix elements in eq 1 are not.32b This allows systematic comparisons of transfer integrals across various methods and basis sets. For instance, our previous systematic studies of transfer integrals have shown that transfer integrals depend on the basis set and the level of theory.32 By comparing theoretical transfer integral values with experimental data, we found that DFT in the generalized-gradient approximation (GGA) in conjunction with either a sufficient plane-wave basis set or Pople-style Gaussian basis sets of at least 6-31G* provides a reliable model chemistry for transfer integral (and so electronic band structure) calculations of π-stacked organics containing first row elements. From the experimental perspective, angle-resolved photoelectron spectroscopy (ARPES) is a very powerful tool to probe the electronic structures of solids. Many ARPES experiments are performed on thin films, because there is no sample charging effect with films usually observed on single crystals of organic semiconductors.34,35 Electronic structures can be probed along two directions, denoted in terms of the wave vector by k| and k⊥, meaning the direction parallel or perpendicular to the surface, respectively. For the former one, the emission angles of the photoelectrons are resolved, and for the latter one, the incident photon energies are varied. For conductivity, usually the most relevant n values correspond to the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), but ARPES provides no information for the LUMO band. In this paper, we look at the HOMO and HOMO - 1
bands, because there is direct experimental information available from ARPES. Typical ARPES experiments inform about the effects of interlayer interactions on the energy bands in graphite and the similarly weak intermolecular interactions in organics. ARPES studies of organic semiconductor materials have been performed for various π-stacked materials including films of BTQBT,36 films of 3,4,9,10-perylenetetracarboxylic dianhydride (PTCDA),37 films of the discotic molecule hexakis(hexylthio)diquinoxalino[2,3-a:2′,3′-c]phenazine (HATNA-SC6),27 graphite,38,39 and C60.34,40 In this work, we first compare the calculated electronic structure of BTQBT with that of BTQBT films deposited on the substrate of cleaved highly oriented pyrolytic graphite (HOPG) probed by ARPES.36 The comparison is made possible by analyzing the normal emission direction of photoelectrons as shown in the next section and the fact that the BTQBT molecules in the films are aligned similar to those in the singlecrystal structure as deduced earlier from ARPES36,41 and X-ray diffraction data.10 However, this is not always the case, because films often display intermolecular packing different from the bulk.27,42 This favorable situation offers us the opportunity to compare the theoretical band structure with the ARPES and other experimental data for BTQBT single crystals and films by using the single-crystal structure for the calculations. Detailed analysis of the electronic structure of BTQBT is then presented to further establish the connection between charge transport and intermolecular packing, one of the central but elusive aspects of organic conductors. The excellent agreement obtained points toward further opportunities for this particular level of theory and ARPES experiments in elucidating the electronic and transport properties of organic materials. Results and Discussion Direct and Reciprocal Space Structures of BTQBT Crystal and Film. The crystal structure of BTQBT belongs to the C2/m space group. There are two molecules in the unit cell, and the asymmetric unit is a quarter of a molecule (Table 1).16,43 Figure 2 shows the direct space crystal structure of BTQBT viewed along b. The molecules pack in such a way that a twodimensional network sheet of molecules in the (201) plane repeat along c with an intermolecular stacking separation of 3.465 Å. Each molecule in the (201) plane is inclined by ∼5° with respect to the (201) plane. The inset shows the close S‚‚‚S contact of 3.262 Å in the network of BTQBT molecules of the (201) plane. This distance is much shorter than the van der Waals distance of 3.70 Å, leading to strong intermolecular interaction through the heteroatoms.44 Short S‚‚‚S contacts are common in highly conducting sulfur-containing organics.45 The S‚‚‚S intermolecular contacts present in BTQBT and some of its derivatives are sufficiently strong to maintain planar networks of the molecules in films and in the crystal allowing the use of the crystal structure in modeling the behavior of films. In the film of BTQBT deposited on the substrate of HOPG, the network sheets were deduced by Ueno et al. to be parallel to the HOPG surface, and the molecular inclination angle is e10° based on the emission angle dependence of the photoelectron spectra.41,46 The periodicity of the electronic band structure observed along the direction normal to the substrate surface, k⊥, indicates periodicity in direct space with the period of |a⊥|, in agreement with the separation between the (201) planes of the crystal.47 X-ray diffraction of the film also verifies that d201 ) 3.30 ( 0.01 Å.10 These agreements confirm that the BTQBT molecules are aligned similarly in the film and in
Charge Transport Properties of BTQBT
J. Phys. Chem. B, Vol. 109, No. 26, 2005 12893
TABLE 1: Crystal Data for BTQBT, TSQBT, and TMBTQBT BTQBTa,b
TSQBTa
TMBTQBTa
volume (Å3)
monoclinic C2/m 0.25 2 a ) 16.226(4) Å b ) 11.191(2) Å c ) 3.833(1) Å R ) 90° β ) 96.88(2)° γ ) 90° 691.004
monoclinic C2/m 0.25 2 a ) 16.244(19) Å b ) 11.169(19) Å c ) 3.848(3) Å R ) 90° β ) 96.75(9)° γ ) 90° 693.301
monoclinic C2/m 0.25 2 a ) 12.166(6) Å b )18.968(4) Å c ) 3.915(4) Å R ) 90° β ) 94.69(8)° γ ) 90° 900.419
intermolecular separationc d along c (Å) intermolecular offsetc,d (Å) short S‚‚‚S contact in (201) planec (Å)
3.465 L ) 1.640 3.262
3.510 L ) 1.578 3.256
3.525 T ) 1.703 no short contact
crystal system space group Z′ Z unit cell dimensions
a
From ref 16. b From ref 43. c Derived from the published structures. d L: longitudinal, and T: transverse offset parallel to the molecular plane.
c′* in the reciprocal space is determined by the following relationship
a′ × b′ c′* ) 2π c′•a′ × b′
Figure 2. Direct space structure of a monoclinic BTQBT crystal (also of film) viewed along b. The reciprocal space vectors are distinguished by an asterisk. The primitive unit cells in reciprocal space are indicated as the 1st and the 2nd Brillouin zones (BZs). The origin of the direct space is o, and that of the reciprocal space is Γ (0,0,0). Special reciprocal space points are Z (0,0,0.5) and K (1,0,0.5), respectively, and are equivalent. The dashed lines define a new unit cell, where vector a′ is shown by a green broken arrow, c′ is identical to c, and the corresponding reciprocal lattice vector a′* is identical to a* and c′* in the direction of k⊥, the direction of the emitted photoelectron. The distance between the (201) planes is d201 with a length of 3.292 Å. The inset shows a sheet of BTQBT molecules in the (201) plane with close S‚‚‚S contacts of 3.262 Å indicated by red dashed lines (Table 1).
the single crystal; therefore, the single-crystal structure of BTQBT was used for all calculations. In Figure 2, we also show the reciprocal space to help understand the normal emission direction of the photoelectrons. The ARPES observation direction is k⊥, normal to the HOPG substrate surface, therefore normal to the (201) plane. It starts from the zone center, Γ ) (0,0,0), of the first Brillouin zone, then exits the second Brillouin zone at the K point, at (1,0,0.5). One sees periodicity of the photoelectron energy as a function of |k⊥|, because the k⊥ direction passes through a third Brillouin zone and then the zone center of a fourth zone with the k-space coordinates (2,0,1), which is equivalent to the Γ point. Another way to see this is to define a new unit cell by using the vector (a - 2c) as the new vector a′, which is in the (201) plane. Suppose one keeps b′) b and c′) c; this leads to a new unit cell with a′ of 18.758 Å, β′ ) 120.81°, and the rest of unit cell parameters being the same as before. With this new unit cell,
(5)
The new reciprocal space vector, c′*, points in the direction normal to the (201) plane, and its length is 2π/d201. This indicates that it passes through the Γ′ point (0,0,0) and Z′ point (0,0,0.5), where Γ′ is the same as Γ and Z′ is the same as K. This analysis indicates that the ARPES observation direction passes through the Γ and K points, greatly simplifying the analysis of the theoretical and experimental electronic structures. The direct comparison between theoretical electronic structure and the one probed from ARPES is thus made possible. Electronic Structure and Charge Transport of BTQBT. Solid-state calculations were performed using the Vienna ab initio simulation package (VASP).48 Density functional theory with the PW91 exchange-correlation functionals49 were used together with Vanderbilt-type50 ultrasoft pseudopotentials.51 The kinetic energy cutoff on the wave function expansion was 348.1 eV. A single-crystal structure16,43 of BTQBT and a 10 × 8 × 20 k-point mesh were used for the solid-state calculations. Comparison of the theoretical electronic structure for the HOMO and the HOMO - 1 bands (two each) with the experimental data obtained from ARPES measurement along the Γ-K direction is shown in Figure 3. Although the two HOMO and two HOMO - 1 valence bands were each treated as one band in the experimental and early theoretical work,36,52 the present DFT calculations show two bands for each as dictated by the presence of the two molecules in the unit cell. For the pair of HOMO-derived bands, experimental data exhibit two values for each k-vector near Γ and K. Halfway down the Γ-K line, both experiments and our calculations indicate near degeneracy. We will address this near degeneracy further when showing the full band structure. The calculated and experimental bands agree reasonably well. It is worth noting that the calculated HOMO BW is too large at this level of theory by about 0.2-0.3 eV for a total calculated BW of 0.84 eV. The earlier EHT calculations52 produced a single HOMO band with a BW of ∼0.49 eV, which is lower than the experimental value of ∼0.6 eV. This comparison appears to be favorable for EHT; however, it is based on a single band model and is therefore qualitatively incorrect. Similarly, the experiments were analyzed by a single band fit, and therefore the transfer integral in ref 36 is probably underestimated. The two (HOMO - 1)-derived bands run upward along Γ-K with a small dispersion, in good agreement with the experimental
12894 J. Phys. Chem. B, Vol. 109, No. 26, 2005
Figure 3. HOMO- and (HOMO - 1)-derived electronic band structure of BTQBT in the direction of k⊥ along Γ (0,0,0) to K (1.0,0,0.5) compared with the data (filled circles) obtained from the ARPES experiments in ref 36. The binding energy of the theoretical bands was obtained by setting the (HOMO - 1)-derived bands to have the same binding energy as the experimental value at the Γ point.
measurements. The experimental data do not resolve the two bands. Assuming a single band fit, Hasegawa et al. obtained a bandwidth of 0.08 eV for this narrow band, corresponding to an approximate transfer integral of -0.02 eV as estimated by using eq 2.36 In comparison, EHT provides a transfer integral of -0.084 eV,36 which overestimates the BW to ca. 4 × 0.084 ≈ 0.34 eV. Generally, double-ζ EHT (DZEHT) provides intermolecular transfer integrals that are in reasonable agreement with DFT calculations;32b however, basis set information was not reported in refs 36 and 52. A ZINDO/S estimate based on dimers provides a transfer integral of +0.042 eV,53 which implies a band running downward along Γ-K, qualitatively contradicting the experimental and the more accurate DFT results. The gap between the two HOMO bands and the two HOMO - 1 bands also agrees well with the experiments at Γ, albeit the agreement is not as good at K. The general feature of the electronic band structure is reproduced with DFT very well. It is worth pointing out that the energy error and k-vector error are coupled through the band dispersion, as discussed, for example, for the discotic liquid crystal material HATNA-SC6.27 The energy uncertainty is not reported in the experimental work on BTQBT.36 Considering a typical energy uncertainty of (0.2 eV,27,39 the agreement between the ARPES experiments and the presented DFT calculations for BTQBT is excellent. The electronic band structure of BTQBT along several directions is shown in Figure 4. As one can see, the top of the valence bands is located at the Γ point, and the bottom of the conduction bands is located at the Z point. The direct gap at Γ point is 1.166 eV, very close to the indirect gap of 1.140 eV between Γ and Z points. All bands are degenerate in pairs in the (x,0.5,z) plane, which includes the A-Y line. There are two bands associated with each MO due to the presence of two molecules in the unit cell, similar to other molecular crystals with two molecules (Z ) 2) in the unit cell, such as pentacene.28 The bands are still similar to those in eq 2, but the orbital energies are split by the interactions of the two molecules in the unit cell.54 The near degeneracy of the HOMO-derived bands along Γ-K discussed previously can be understood as follows. As shown in Figure 4, there is a near degeneracy along the B-X line for the top two HOMO-derived valence bands. Near the point where
Huang and Kertesz
Figure 4. Electronic band structure of BTQBT in the energy window of -1.5 to 2.0 eV with the top of the valence band set to 0 eV. The coordinates of the reciprocal space points are Z (0,0,0.5), B (0.5,0,0.5), X (0.5,0,0), Γ (0,0,0), A (0,0.5,0.5), and Y (0,0.5,0). (See Figure 1S of the Supporting Information for these reciprocal space points.)
the Γ-K line crosses the B-X line, a near degeneracy is then expected as indicated by the Brillouin zone shown in Figure 1S of the Supporting Information. Figure 4 shows that the two valence bands run downward parallel along Γ-Z, and since the K point is equivalent to the Z point, these two bands cannot cross along Γ-K either. The two HOMO-derived valence bands have significant dispersions of 0.49 and 0.57 eV and run downward parallel along the Γ-Z line. The two LUMO-derived conduction bands have very small dispersions. This indicates that the electrons should be much less mobile than the holes and the charge transport should be primarily hole transport in BTQBT. This band-theory-based conclusion agrees with the experimental observation that the sign of the dominant charge carriers is positive.5,6,55,56 In contrast, EHT calculations provide comparable dispersions for both valence and conduction bands,52 which would imply that the electron and hole mobilities should be similar assuming a band conduction mechanism. It should be pointed out that the charge transport of organic molecular materials also depends on a number of factors and mechanisms of charge transport.25,26,33 ZINDO/S calculations indicate that the electron and hole mobilities should be similar for pentacene, assuming a band conduction mechanism.25 This issue needs further analysis because there is earlier evidence that the holes dominate transport in pentacene.57 The success of theoretical predictions for BTQBT indicates the validity of the band model for this organic molecular semiconductor. The Hall mobility on the order of 2-6 cm2 V-1 s-1 together with its inverse power law temperature dependence56 also point toward band conduction.58,59 As one can also see from Figure 4, the band structure along Γ-X and Γ-Y are back-folded, and the largest splitting along Γ-X and Γ-Y for the two HOMO-derived bands is 0.27 eV at the Γ point. This splitting reflects the band dispersion in the (201) plane, because b is in the (201) plane, the reciprocal lattice vector a* is the same as a′*, and the corresponding direct space vector a′ is in the (201) plane. This dispersion is about half of the valence band dispersion along the Γ-Z stacking direction on the order of 0.5-0.6 eV. The electrical conductivity of BTQBT exhibits unusually small anisotropy of conductivity. The ratio of σ⊥/σ| is ∼2 for single crystals55 and ∼1.6 for films,10 where σ⊥ and σ| are the conductivities along the stacking direction and in the (201) plane. This agreement between band dispersion ratio and conductivity ratio suggests again that the conduction mechanism in BTQBT is band transport. Recent
Charge Transport Properties of BTQBT
Figure 5. Electronic band structure of TSQBT in the energy window of -1.5 to 1.98 eV with the top of the valence band set to 0 eV. Instead of sampling along Γ-Z, the bands along k⊥ normal to the (201) plane (Γ-K) are shown. The coordinates of the reciprocal space points are the same as in Figures 3 and 4.
measurements indicate the band-like transport in pentacene up to room temperature.60 The small conductivity anisotropy of BTQBT is in sharp contrast to the high anisotropy of conductivity of pentacene. The layered crystal structure of pentacene and theoretical studies based on that structure indicate a rather twodimensional charge transport in pentacene.28 Due to this difference, charge transport in the channel of an FET likely occurs in more layers of a BTQBT film than in a pentacene film. Electronic Structures of TSQBT, BTQBS, and TMBTQBT. We discuss how substitutions modify the electronic structures of three derivatives of BTQBT, showing the effects of Se substitution in some of the S sites and the effects of methyl substitutions. The computational details are the same as those for BTQBT. Figure 5 shows the electronic band structure of TSQBT calculated with a 10 × 8 × 20 k-point mesh. The reported crystal structure is disordered,16 but in our calculations we assume a fully ordered periodic structure. The electronic band structure is very similar to that of BTQBT as a result of their isomorphous crystal structures (Table 1). Due to the larger atomic radius of Se compared to S, the vector c is larger in TSQBT than in BTQBT, and the intermolecular separation is also larger (3.510 Å compared with 3.465 Å). As can be seen from the electronic band structure along Γ-K, the two HOMO-derived valence bands have dispersions of 0.59 and 0.65 eV, larger than the corresponding BTQBT values, consistent with the fact that the conductivity of TSQBT single crystals is higher than that of BTQBT along the stacking direction (σ⊥).16 This is related to the more diffuse p atomic orbitals of Se, leading to a more effective electronic coupling between molecules and to a larger dispersion along the stacking direction. These large dispersions indicate hole transport character also for TSQBT, in agreement with recent experiments.5 The band dispersion in the (201) plane is 0.28 eV at the Γ point, just slightly larger than that of BTQBT. There is no significant selenium effect in the (201) plane, because the neighboring TSQBT molecules in that plane still overlap through short S‚‚‚S contacts at 3.256 Å. To cause an increase in the in-plane conductivity, the sulfur atoms in the 1,3-dithiole rings of BTQBT might be replaced with selenium atoms. We tested this idea by performing a band calculation for BTQBS. For this calculation, we replaced all four sulfur atoms in the two dithiole rings of BTQBT by selenium atoms and kept the structure otherwise unchanged. The model structure thus generated has too short Se‚‚‚Se contacts due to the larger size of Se. The
J. Phys. Chem. B, Vol. 109, No. 26, 2005 12895
Figure 6. Electronic band structure of TMBTQBT in the energy window of -1.5 to 2.25 eV with the top of the valence band set to 0 eV. The coordinates of the reciprocal space points are the same as in Figure 4.
molecular geometry was not minimized. The purpose was to see how the Se substitutions will affect the BW in the (201) plane. These calculations did provide slightly larger BW values in the (201) plane (0.30 eV), in addition to larger BW values along the stacking direction (0.55 and 0.66 eV) compared to those of BTQBT (Figure 3S of the Supporting Information). These Se effects turned out to be minor because the in-plane π-π overlap is much smaller than the corresponding stacking overlap. The electronic band structure of the experimentally synthesized TMBTQBT crystal was calculated with an 8 × 8 × 16 k-point mesh using its single-crystal structure16 and is presented in Figure 6. A striking difference of single-crystal structures between TMBTQBT with BTQBT (also TSQBT) is that BTQBT stacks along c with a longitudinal offset of 1.640 Å, while TMBTQBT stacks along c with a transverse offset of 1.703 Å. This difference is reflected in the electronic band structure of TMBTQBT. The two valence bands derived from HOMO are almost nondispersive, losing the hole transport feature of BTQBT and TSQBT. Since the two conduction bands derived from the LUMO have small dispersions too, it is no wonder that the conductivity of a TMBTQBT single crystal is significantly smaller than that of a BTQBT single crystal.16 The dependence of band dispersion on both longitudinal and transverse offsets has been studied by Kazmaier and Hoffmann for the case of 3,4,9,10-perylenetetracarboxylic diimide (PTCDI).61 The dependence of transfer integrals and band dispersions on the offset parameter exhibits oscillations in accordance with the nodal structure of the relevant orbitals. Thus, the HOMO-derived valence bands of TMBTQBT can be understood to be near a level crossing along transverse offset (Figure 5S of the Supporting Information). Similar observations are reported as a function of longitudinal offset for R-hexathienyl (R-6T)24 and tetracyanoquinodimethane (TCNQ)32 and as a function of rotational angle for phthalocyanine (Pc)62 and discotic liquid crystal materials.26,30 Additionally, the intermolecular separation, 3.525 Å, is now somewhat larger due to the replacements of hydrogen atoms by the bulkier methyl groups. This may further reduce bandwidths, but it is not the dominant reason for the narrow valence bands of TMBTQBT, as indicated by the slight increase of the bandwidths of the (HOMO - 1)- and LUMOderived bands. Experimental and Theoretical Band Gaps. Experimental and theoretical band gaps are shown in Table 2. A straight comparison is not possible due to the common problem of
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TABLE 2: Experimental and Theoretical Band Gaps for BTQBT and Its Derivatives optical gap (eV)a calculated gap (eV)
TMBTQBT
BTQBT
TSQBT
BTQBS
1.369
2.29b, 2.1c 1.166
2.23b 1.151
2.00b 1.132
a Estimated from optical absorption data from the references as indicated. b Reference 16. (Low-energy absorption shoulder.) c Reference 10. (Low-energy absorption edge.)
underestimating band gaps by nonhybrid DFT. As mentioned before, the calculated direct band gap of BTQBT is 1.166 eV. The calculated band gaps of TSQBT and TMBTQBT are 1.151 eV (direct gap at Γ) and 1.369 eV (direct gap at Z), respectively. The calculated band gap of BTQBS is 1.024 eV (indirect gap between Γ and Z) and 1.132 eV (direct gap at Γ). For TMBTQBT, the band gap is the largest, since the molecular orbital levels are not much affected by the methyl substitution, and under these circumstances, the smaller the band dispersion, the larger the corresponding gap. The rest of the systems show very similar gaps, due to a partial compensation of MO level changes due to the Se substitutions and BW changes as well. This trend of the gaps is not related to the observed activation energies of the conductivity, Ea, which are 0.42, 0.21, and 0.17 eV for TMBTQBT, BTQBT, and TSQBT, respectively.16 The smaller experimental Ea values compared with the optical band gaps are due to the fact that these materials are extrinsic conductors, as pointed out by Xue and Forrest.10 Electronic Structures of Organic Semiconductor Films. Thin films of organic semiconductors are grown as active organic layers on solid substrates for applications in organic electronics.63 Although studies of single crystals as elements of FETs are actively being pursued by a number of groups,9,64 their main purpose is to eliminate grain boundaries and to minimize trap concentration to obtain intrinsic electrical properties of organic materials. In terms of practicability, thin films have advantages over single crystals.8,58 Epitaxial organic molecular films typically adopt structures different from their single crystals. For example, pentacene crystallizes in four polymorphs characterized by their interlayer spacing d001. Single crystals have d001)14.1 or 14.5 Å,65 while the thin film polymorphs have d001 values of 14.1, 14.4, 15.0, and 15.4 Å.66 Since the intermolecular packing is closely correlated with charge transport properties, it is important to study the electronic structures of the organic thin films, which provides insight into the performance of the organic-based devices.67 The structures of epitaxial organic molecular films are typically strongly influenced by the substrate lattice. It was found that for PTCDA and Pc films the competition between substratefilm interaction and the intralayer interaction within the organic films plays a very important role in the organic film structures.68 In the BTQBT film deposited on HOPG, the strong intermolecular interactions within the BTQBT film through the short S‚‚‚S contacts determine the film structure to be similar to that of the single crystal. Although the packing of the very first layer is found by scanning tunneling microscopy (STM) to be still slightly affected by the HOPG substrate,69 the film structure can relax to its single-crystal structure of BTQBT after 1-5 molecular layers.68 Similar to BTQBT, TSQBT has close S‚‚‚S contacts of 3.256 Å in the (201) plane, implying strong intermolecular interactions. Through the choice of an appropriate substrate, the film structure of TSQBT could be similar to its single crystal too. As for the TMBTQBT film, STM of a monolayer on HOPG has indicated that its lattice is slightly different from that of the single crystal.69
TMBTQBT film, as compared to BTQBT, is expected to relax to its single-crystal structure after a larger number of molecular layers due to weaker van der Waals interaction as shown by the absence of short S‚‚‚S contacts in its single crystal. Thus, the electronic band structures of TSQBT and TMBTQBT presented in this work would serve as a guide if the ARPES measurements of these two organic films were to be performed. An additional problem is the surface relaxation effect relative to the bulk structure due to the termination of periodicity on the vacuum side of thin films or single crystals. The valence band dispersion of a tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) film close to the Fermi level is nearly identical to that of an in situ cleaved single crystal.70 The ARPES of its single crystal shows larger bandwidth values by a factor of ∼2 compared to the bulk bandwidth values71 and the theoretical calculations within the DFT framework.72,73 The probing depth of ARPES is comparable to the thickness of a single molecular layer of TTF-TCNQ, ∼9 Å. The discrepancy between the ARPES bandwidths and the DFT calculations for TTF-TCNQ led to the speculation of a significant surface relaxation72 at the vacuum side of TTF-TCNQ single crystals. Sing et al.72 argued that larger tilting angles with respect to the (010) plane would lead to reduced separation between molecules within the surface layer and this, in turn, would lead to an increase in band dispersion and would explain the larger experimental ARPES bandwidth. But the STM observation made on TTF-TCNQ film sublimed onto mica indicates that the tilting angles of TTF and TCNQ in a new phase of the film are smaller with respect to the (010) plane.74 In fact, π-π overlaps are more efficient between TTF molecules and between TCNQ molecules if they can adopt a direct face-to-face packing motive with a close to zero longitudinal offset. Thus, it is expected that the band dispersion of TTF-TCNQ would be enhanced along k| if TTF and TCNQ adopt smaller tilting angles with respect to the (010) plane. Our previous theoretical study of the transfer integrals as a function of the longitudinal offset for TCNQ stacks points to a factor on the order of 2 when the offset decreases from 2 to 0 Å.32 In contrast, the excellent agreement between ARPES and DFT calculations for BTQBT indicates no such surface effects. This can be ascribed to the strong intermolecular interaction between molecules in the (201) plane through short S‚‚‚S contacts, which do not allow the molecules to change their tilting angles. TTF-TCNQ also has sulfur atoms in the TTF moiety, but there is no network of S‚‚‚S short contacts to prevent the surface from relaxation. Conclusion In this work, we calculated the electronic structures of an important organic semiconductor BTQBT and its derivatives using DFT. We compared the electronic structure of BTQBT with ARPES measurements along the k⊥ direction, which is the emission direction of the photoelectrons normal to the BTQBT films deposited on HOPG substrate. The good agreement between theoretical and experimental electronic structures of BTQBT films strongly supports that the BTQBT films adopt the same structures as its single crystals. Charge transport properties based on presented DFT results agree with experiments in terms of the sign of the charge carriers and the unusually small anisotropy of conductivity. The conduction mechanism of BTQBT is likely band transport up to room temperature. The calculations also rationalize available experimental information on the conductivities of BTQBT derivatives. In comparison to probing the electronic structures of organic thin films experimentally, accurate ab initio calculations at the
Charge Transport Properties of BTQBT DFT level have the advantage of sampling the electronic structures along various directions, some of which may not be probed by ARPES, but which may be important in understanding the charge transport properties. However, calculations of film electronic structures are hampered by the limited availability of intermolecular packing information for the films. Various force-field-based energy minimizations of film structures can be performed,18,75 but the molecules are mainly held together by weak van der Waals forces, so the accuracy of the structures obtained by such energy minimizations is to be further validated. Accurate electronic structure calculations coupled with ARPES measurements will help to establish correlations between intermolecular packing and charge transport properties in organic solids. Acknowledgment. Financial support from the National Science Foundation (Grant No. DMR-0331710) is gratefully acknowledged. We thank Dr. K. Travis Holman (Department of Chemistry, Georgetown University) for discussions on crystal structures of BTQBT and its derivatives and Dr. James Long (Naval Research Lab) for discussions on ARPES measurements. Supporting Information Available: The Brillouin zone of BTQBT, electronic band structure of a model BTQBT crystal with Z ) 1 and of BTQBS, schematic diagram of a TMBTQBT (001) dimer excised from its single-crystal structure, and the dependence of dimer orbital energies and transfer integrals as a function of transverse offset T for TMBTQBT. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Pope, M.; Swenberg, C. E. Electronic Processes in Organic Crystals and Polymers; Oxford University Press: New York, 1999. (2) Sworakowski, J.; Ulan´ski, J. Annu. Rep. Prog. Chem., Sect. C: Phys. Chem. 2003, 99, 87. (3) For example, see: (a) Sakamoto, Y.; Suzuki, T.; Kobayashi, M.; Gao, Y.; Fukai, Y.; Inoue, Y.; Sato, F.; Tokito, S. J. Am. Chem. Soc. 2004, 126, 8138. (b) Pappenfus, T. M.; Chesterfield, R. J.; Frisbie, C. D.; Mann, K. R.; Casado, J.; Raff, J. D.; Miller, L. L. J. Am. Chem. Soc. 2002, 124, 4184. (c) Facchetti, A.; Mushrush, M.; Katz, H. E.; Marks, T. J. AdV. Mater. 2003, 15, 33. (4) Meng, H.; Bendikov, M.; Mitchell, G.; Helgeson, R.; Wudl, F.; Bao, Z. N.; Siegrist, T.; Kloc, C.; Chen, C.-H. AdV. Mater. 2003, 15, 1090. (5) Takada, M.; Yamashita, Y.; Tada, H. Mater. Res. Soc. Symp. Proc. 2002, 725, 143. (6) Takada, M.; Graaf, H.; Yamashita, Y.; Tada, H. Jpn. J. Appl. Phys. 2002, 41, L4. (7) (a) Dimitrakopoulos, C. D.; Malenfant, P. R. L. AdV. Mater. 2002, 14, 99. (b) Katz, H. E. Chem. Mater. 2004, 16, 4748. (c) Kelley, T. W.; Baude, P. F.; Gerlach, C.; Ender, D. E.; Muyres, D.; Haase, M. A.; Vogel, D. E.; Theiss, S. D. Chem. Mater. 2004, 16, 4413. (8) Horowitz, G. J. Mater. Res. 2004, 19, 1946. (9) Sun, Y. M.; Liu, Y. Q.; Zhu, D. B. J. Mater. Chem. 2005, 15, 53. (10) Xue, J. G.; Qin, J. G.; Bedworth, P. V.; Kustedjo, K.; Marder, S. R.; Forrest, S. R. Org. Electron. 2001, 2, 143 and the comparison of conductivities between single crystals and thin films therein. (11) Xue, J. G.; Forrest, S. R. Appl. Phys. Lett. 2001, 26, 3714. (12) Bendikov, M.; Wudl, F.; Perepichka, D. F. Chem. ReV. 2004, 104, 4891. (13) Ruiz, R.; Choudhary, D.; Nickel, B.; Toccoli, T.; Chang, K.-C.; Mayer, A. C.; Clancy, P.; Blakely, J. M.; Headrick, R. L.; Iannotta, S.; Malliaras, G. G. Chem. Mater. 2004, 16, 4497. (14) Ling, M. M.; Bao, Z. N. Chem. Mater. 2004, 16, 4824. (15) For brevity, we use acronyms of these materials throughout the work: 4,8-bis(1,3-dithiol-2-ylidene)-4H,8H-benzo[1,2-c:4,5-c′]bis[1,2,5]thiadiazole (BTQBT); 4,8-bis(1,3-dithiol-2-ylidene)-4H,8H-[1,2, 5]selenadiazolo[3,4-f]-2,1,3-benzothiadiazole (TSQBT); 4,8-bis(1,3-diselenol-2ylidene)-4H,8H-benzo[1,2-c:4,5-c′]bis[1,2,5]thiadiazole (BTQBS); tetramethylBTQBT (TMBTQBT). (16) Yamashita, Y.; Tanaka, S.; Imaeda, K.; Inokuchi, H.; Sano, M. J. Org. Chem. 1992, 57, 5517. (17) Generally, two types of packing motives featuring π-π overlap can be observed: herringbone (also called edge-to-face) motif, for example,
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