Resonant tunneling transport in highly organized oligoacene assemblies

Organic Electronics 8 (2007) 1–7 www.elsevier.com/locate/orgel

Resonant tunneling transport in highly organized oligoacene assemblies A. Rochefort *, P. Boyer, B. Nacer

1

Department of Engineering Physics, E´cole Polytechnique de Montre´al and Regroupement que´be´cois sur les mate´riaux de pointe (RQMP), Montre´al, Que´., Canada Received 1 May 2006; accepted 7 September 2006 Available online 10 November 2006

Abstract Electronic structure and transport properties of low dimensional organic systems have been theoretically investigated. On isolated molecules, a drastic decrease of the band gap by more than 4.5 eV is observed in acene molecules containing up to 15 members rings. The additional band gap decrease observed upon molecular assembling does not depend on the nature of the molecules but more on the separation between them. Oligoacene assemblies with intermolecular spacing ˚ are characterized by an improved p-electron coupling that facilitates the electrical transport through resonant dmol 6 3.8 A tunneling mechanism. For such molecular arrangement, we have computed significant band dispersion (340 meV), high transmittance (T ðEÞ  1), and relatively high mobility for holes and electrons (0.1–0.9 cm2/V s) in both resonant p-valence and p*-conduction bands.  2006 Elsevier B.V. All rights reserved. PACS: 31.15.Ct; 31.15.Ew; 73.20.At; 73.61.Ph; 73.63.-b Keywords: Resonant tunneling; Electron transport; Organic assembly; Mobility; Band gap; Low dimensional systems

The formation of a highly organized molecular structure constitutes a cornerstone in the technological development of high mobility organic semiconductor devices [1]. Among the numerous methods that favor low dimensional molecular organization, there are techniques such as organic chemistry synthesis exploiting intermolecular hydrogen bonding [2] and approaches exploiting self-assembling on metallic or semiconducting surfaces [3]. Through a *

Corresponding author. E-mail address: [email protected] (A. Rochefort). 1 On leave from University Cadi Ayyad, Faculty of Science and Technology, Department of Physics, Marrakech, Morocco.

judicious choice of the surface, this last technique could lead to the creation of a dense and wellorganized low dimensional nanostructure [3,4]. A surface such as the hydrogenated Si(1 0 0) is charac˚ along the row dimer terized by Si–Si distance of 3.8 A direction on which organic molecules are self-directed assembled by a chain reaction growth mechanism [3,5]. An example of such organized arrangement is shown at Scheme 1A in which styrene molecules were covalently attached to the Si(1 0 0)[2 · 1] surface along the dimer row direction. Once the conjugated molecules are tightly packed into an organized conformation, we may expect a substantial dispersion of low-energy p-band, and a subsequent

1566-1199/$ - see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.orgel.2006.09.006

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A. Rochefort et al. / Organic Electronics 8 (2007) 1–7

Scheme 1. Self-directed assembly of styrene on the reconstructed H–Si(1 0 0)[2 · 1] surface that lead to a well organized structure along the dimer row direction (A). The weak coupling between Si surface states and the low-energy p-electron states which are delocalized over the entire assembly allows the creation of a molecular size conduction channel (B).

improvement of intermolecular electron transport properties [6,7]. This suggests that p-electron transport can be modulated by placing gold electrodes at both ends of the assembly as proposed at Scheme 1B, and where the Si(1 0 0) surface is mainly used as a template to attach and organize molecular species. The simplest and probably the richest existing molecular species to investigate fundamental aspects of p-stacking are small acenes such as naphthalene, anthracene, tetracene, and pentacene assemblies [9]. Most of the previous experimental and theoretical studies on oligoacenes addressed issues related to the electronic structure and transport properties of very good or even perfect crystalline phases in which most of the molecules adopt a herringbone-like structure [9]. Due to the relatively weak intermolecular pelectron coupling, these systems usually have a rather low mobility (106–102 cm2/V s) and demonstrate relatively poor switching abilities [10]. Recent interest for pentacene-based systems originates from the significant improvement in the production of good quality single crystals that give much higher mobility (0.1–10 cm2/V s) than those of polycrystalline samples [10,11]. Although several excellent works have been performed on well-defined crystals, very few

have investigated the electronic properties of stacked oligoacenes into low dimensional nanostructures to study strong p-electron delocalization [12]. In this paper, we present the results of tight-binding and DFT calculations on the electronic and electron transport properties of perfect p-stacked oligoacene wires that could possibly be synthesized on Si(1 0 0). The individual acene molecules studied are shown in Scheme 2 as well as the stacking direction. The ethyl fragment represents the anchoring group that is usually bounded to the silicon surface when a self-directed reaction has been performed. We previously observed that the formation of a covalent Si–C bond between Si(1 0 0) and such acene molecule is characterized by a charge transfer that is limited to the first Si and C atoms [13]. In addition, we observed no significant mixing between Si surface states and those related to low-lying p-electron of the assembly. We may then confidently assume that the Si surface does not have a significant electronic effect on the remaining conjugated moiety of interest, and we omit the presence of Si in our calculations. Hence, we are focusing on the perfect oligoacene stacking in which the intermolecular distance is fixed for most ˚ which corresponds to the Si–Si discases to 3.8 A tance between surface atoms in the dimer-row direction of the hydrogenated Si(1 0 0) surface. ethylbenzene

eBen

1-ethyl-naphthalene

eNap

9-ethyl-anthracene

eAnt

6-ethyl-pentacene

ePen

y z

stacking direction = z

x

Scheme 2. Acene molecules considered in the formation of an organized wire and their stacking direction.

A. Rochefort et al. / Organic Electronics 8 (2007) 1–7 5.0

5.0

eBen

4.0

Band Gap (eV)

4.5 4.0 3.5

Band Gap (eV)

Most of the electronic structure calculations were performed within the tight-binding extended Hu¨ckel theory (EHT) formalism. The band-like electrical transport properties of 1D structures were computed using Green’s function approach [14] within the Landauer–Bu¨ttiker formalism. The Hamiltonian and overlap matrices used in this formalism were also obtained from the EHT model that explicitly evaluates overlap matrix elements [15]. The transport properties were evaluated in the stacking direction by placing a gold electrode composed of a plane of 29 Au atoms with (1 1 1) crystal arrangement, at both ends of the stack (d(Au-stack) = ˚ ). The metallic contacts consist of a sufficient 2.0 A number of Au atoms to create a large contact area relative to the junction ends, and the short d(Austack) distance was chosen to minimize contact resistance [7]. In contrast to bulk materials [16], the influence of the gold electrodes on the electronic structure of such molecular arrangement occurs within the very first connected molecules. For systems containing ten or more molecules, we can confidently place the Fermi energy at the mid-gap of the p-stacked assembly. The electronic structure calculations within the EHT formalism can reproduce, at least qualitatively, for similar molecular species, the results of more accurate computational techniques, such as density functional theory [7,8]. We also used a different approach to qualitatively evaluate mobility of holes and electrons for each oligoacene assembly at room-temperature (298 K). This hopping-mode technique formally used within the polaronic transport regime was previously derived [17] to include the semiclassical Marcus theory [18], the Einstein Smoluchowski equation of diffusive motion [19], and the Einstein relation [19]. For this case, the reorganization energy was computed with the Gaussian 03 package [20] for negative and positive polarons with the UB3LYP functional and a 6-311G** basis set. Fig. 1 shows the variation of the HOMO–LUMO separation (HLS) or band gap of the different oligoacenes as a function of the number of molecules in the assembly. As a general trend, the HLS decreases as the number of molecules in the assembly increases then reaches a stable value for systems larger than 10 molecular units. This decrease can be easily explained by a progressive evolution from a discrete electronic structure (0D) to a band-like structure (1D) [21]. In addition, a constant decrease of 0.35 eV in HLS from a single molecule to a stable assembly is systematically observed for all the oli-

3

3.0

3.0 2.0 1.0 0.0 0 5 10 Number of Aromatic Ring

eNap

15

2.5 2.0

eAnt

1.5 1.0

ePen

0.5 0.0

0

10

20

30

40

Number of Molecules

Fig. 1. Variation of the band gap as a function of the number of ethyl-benzene (eBen), 1-ethyl-naphthalene (eNap), 9-ethylanthracene (eAnt), 6-ethyl-pentacene (ePen) units in the organic ˚ except for (eNap) wire. Intermolecular distance was fixed to 3.8 A ˚ (open circle – dashed line). The where we also considered 3.5 A inset gives the variation of the HOMO–LUMO separation (band gap) with the number of benzene rings in the isolated molecules.

goacenes considered. A larger variation is calculated (0.65 eV) for 1-ethyl-naphthalene assembly for ˚ ). This result shorter intermolecular distance (3.5 A is directly related to an improved band dispersion that is due to an increasing p-electron overlap between the molecules in the assembly. Finally, the variation of electronic properties of an isolated molecule from ethylbenzene to polyacene is reported in the inset of Fig. 1. From one to eleven benzene rings, we estimate a decrease of 4.45 eV of the HLS value. This change reflects the increasing number of p-electron in longer acene. This variation should progressively converge to the unidimensional band structure limit of polyacene (0.0 eV) if no Peirls distortion occurs [22]. Hence, these results suggest that electronic properties of small oligoacene assemblies can be tailored over a broad range of energy. The electronic structure and transport properties of ethylbenzene (eBen), 1-ethyl-naphthalene (eNap), 9-ethyl-anthracene (eAnt) and 6-ethyl-pentacene (ePen) stacks are compared in Fig. 2. The lower panel shows the density of states of a 10 molecules assembly, while the upper panel gives the calculated transmittance into the different p-resonant channels in the vicinity of Fermi energy (EF), and the middle panel shows similar results but on a logarithmic scale to emphasize the very large modulation (>1015) of the transmittance (conductance) observed in this resonant tunneling transport mechanism. In this mechanism, electrons and holes propagate from

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A. Rochefort et al. / Organic Electronics 8 (2007) 1–7

ePen

T(E)

eAnt eNap eBen

-5 -10

en eB

ap

eA

-15

eN

nt

ePen

ePen

DOS(E) (a.u.)

log 10 [T(E)]

0

eAnt eNap eBen -13

-12

-11

-10

-9

-8

-7

Energy (eV) Fig. 2. Electron transport and electronic structure properties of 10 molecules assemblies, ethyl-benzene (eBen), 1-ethyl-naphthalene (eNap), 9-ethyl-anthracene (eAnt), and 6-ethyl-pentacene ˚ . The (ePen) where the intermolecular distance was fixed to 3.8 A upper panel shows the variation of the transmittance while the middle panel shows the results in logarithmic scale. The lower panel gives the density of states (DOS) of the different oligoacene assemblies. Fermi level is indicated by the long vertical dashed line, and is defined with respect to the mid-gap of the assemblies.

a molecule to the next one through a conduction channel which is formed from the combination of p-electron of individual molecules. Hence, molecular p-orbitals combine to form a valence p-stacked band in which the HOMO (top-band) will be an anti-bonding p  p = p* orbital. Conversely, molecular p* orbitals mix to form a conduction p-stacked band where the LUMO (bottom-band) is a bonding orbital (p* + p* = p). Since the molecules in the assembly are not chemically connected but sepa˚ , and the fact that the only conducrated by 3.8 A tion channels available are the p-resonant bands, we can easily understand the very low calculated transmittance at EF. At this level, the oligoacene assemblies can be considered as a series of individ˚ vacuum barrier. ual conductor separated by a 3.8 A The number and the position of the resonant pbands are consistent with the calculated density of states (DOS) for the finite 10 units stacks (see

Fig. 2) as well as with the periodic 1D band structure (not shown). The upper panel in Fig. 2 shows that the LUMO (conduction) bands give much broader and intense transmittance peaks than the HOMO (valence) bands. The bandwidth of LUMO transmittance peaks is much larger than kT and phonon frequencies. This result suggests that an oligoacene stack would be a better n-type than p-type semiconductor, and where fast band transport can be significant. In addition, the widths of the transmittance peaks of HOMO bands do not appear sufficiently large to expect an efficient band transport: carriers would be strongly perturbed by thermal and vibronic effects [23]. At first glance, this trend sounds surprising since most of experimental works in the field show that active organic materials are hole or p-type semiconductors [24]. Nevertheless, recent works in which specific efforts were deployed to control the chemistry of interfaces show a significantly improved n-type behavior for several organic semiconductors [25]. On the other hand, we are also interested in comparing the band mode conduction to the phononassisted hopping mode. In this context, Table 1 gives the calculated values of the interchain transfer integral describing the interaction between adjacent molecules [18], the reorganization energy of negative and positive polarons [27], and the holes and electrons mobilities. The interchain transfer integral which is related to the splittings of the HOMOs for holes (0.4–0.6 eV) and the LUMOs for electrons (0.4–0.5 eV) predicts that holes and electrons might have comparable mobilities in one dimentional stack. The computed reorganization energy for 9-ethylanthracene and 6-ethyl-pentacene are in good agreement with those calculated by Coropceanu et al. [17] for anthracene and pentacene molecules. We find that the room-temperature mobility of holes (electrons) increases remarkably from 1.30 · 104 cm2/V s (0.25 · 104 cm2/V s) for ethyl-benzene to 0.91 cm2/ V s (0.68 cm2/V s) for 6-ethyl-pentacene. The two remaining molecules, 1-ethyl-naphthalene and 9ethyl-anthracene, have intermediate mobilities. We should emphasized that the calculated mobilities remain a qualitative description of transport properties. Nevertheless, although we have used two different theoretical approaches, both predict very promising transport properties for these small oligoacene assemblies. In addition to the hopping mode where intramolecular deformations contribute to the transport mechanism, more specifically through a polaronic

A. Rochefort et al. / Organic Electronics 8 (2007) 1–7

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Table 1 Estimated values of transfer integrals, reorganization energies, and mobilities for ethyl-benzene, 1-ethyl-naphthalene, 9-ethyl-anthracene and 6-ethyl-pentacene Transfer integral (eV)

Mobility (cm2/V s)

Polaron reorganization energy (eV)

Molecule

Hole

Electron

Positive

Negative

Hole

Electron

Ethyl-benzene (eBen) Ethyl-naphthalene (eNap) Ethyl-anthracene (eAnt) Ethyl-pentacene (ePen)

0.06 0.05 0.05 0.04

0.04 0.04 0.05 0.04

0.98 0.18 0.16 (0.14) 0.10 (0.10)

1.06 0.26 0.20 (0.20) 0.12 (0.13)

0.13 · 103 0.48 0.62 0.91

0.25 · 104 0.12 0.38 0.68

The values from the work of Coropceanu et al. [17] are in parenthesis.

observed in the deformed eNap assembly but with smaller intensities and narrower peaks. We can interpret these changes by noting that individual 3.1 3.0

deformed

Band Gap (eV)

2.9 2.8

3.8 A

2.7 2.6

perfect 2.5

3.5 A

2.4 2.3

0

5

10

15

20

Number of Molecules

Transmittance

3.8 A deformed

perfect

3.5 A

Transmittance

defect, we have investigated the influence of the internal structure of the assembly on the band-like transport. For the eNap assembly, we studied the influence of both intermolecular spacing and molecular arrangement within the assembly on their electronic and transport properties. For an assembly of ten molecules, Fig. 3 shows the variation of the band gap in the upper panel, and the fluctuation of transmittance in the lower panel. First, we can clearly see that a compression of the molecular stack contributes to improve p-electron overlap, to increase the dispersion of the p-bands, and to dramatically decrease the HLS. Hence, a compression of 10% within the assembly improves significantly the band dispersion and decreases the band gap by a factor of approximately 2. This result is in agreement with our previous findings on molecular pstacked system [7], and with other theoretical works on compressed organic crystal [26]. Consequently, these electronic structure changes have a profound impact on the transport where the width and intensity of transmittance peaks drastically increase, more especially for a perfect stacking arrangement. Besides what is previously shown, more drastic changes are observed when different stacking patterns are considered. In the deformed eNap assembly (see Fig. 3), the molecules were rotated from one to the next by 180 relatively to the ethyl–naphthalene bond or the y-axis (see Scheme 1). In this conformation, only one of the two benzene rings is well-aligned along the stacking direction. As a consequence, the p-coupling between molecules decreases as well as the variation in HLS with the number of stacked molecules. It is interesting to note from Fig. 3 that the change in HLS for this deformed eNap stack (0.12 eV) is significantly smaller than the calculated one for an eBen stack (0.35 eV), even though both stacked assemblies have a benzene ring aligned in the stacking direction. A similar picture can be drawn from the transport calculations where three transmission peaks are still

deformed

perfect -14

-13

-12

-11

-10

-9

-8

-7

-6

Energy (eV) Fig. 3. Influence of molecular conformation and packing density on the electronic and electron transport properties of 1-ethylnaphthalene assembly. Deformed structure is an assembly in which a successive 180 molecular rotation was considered. The upper panel shows the variation of the band gap as a function of the number of molecular units in the wire. The lower panel gives transmittance for a 10 molecules stack in which the intermolecular distance and the internal structure have been modified.

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A. Rochefort et al. / Organic Electronics 8 (2007) 1–7

molecular wavefunction are not drastically perturbed by intermolecular coupling. Delocalized p-wavefunction in isolated molecule remains strongly delocalized once molecules are stacked. It is then clear that a good portion of p-electron in LUMO (HOMO) is not directly participating in the formation of a well-delocalized intermolecular wavefunction over the entire assembly. We may then anticipate the existence of a relatively weak p-electron coupling due to the weak and partial orbital overlap, and finally to a weak dispersion of p-bands in extended systems with such molecular conformation. In summary, a systematic decrease of 0.35 eV in the band gap is observed in highly organized 1D stacked oligoacene assemblies, independently of the molecular unit. The intermolecular p-electron coupling provides new conduction channels where fast band transport could occur through resonant tunneling mechanism. The agreement found between band-like and charge-hopping results in the transport calculations shows that small oligoacene assemblies would present an interesting source of organic semiconductor. The electronic structure properties can be tailored through the chemical composition of the oligoacene assembly. In highly organized molecular arrangement, we have computed significant band dispersion (340 meV), high transmittance (T ðEÞ  1), and relatively high mobility for holes and electrons (0.1–0.9 cm2/V s). Acknowledgements This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), and the Ministe`re du De´veloppement e´conomique et re´gional (MDER). We are grateful to the Re´seau que´be´cois de calcul haute performance (RQCHP) for providing computational facilities. PB thanks NSERC, GCM and E´cole Polytechnique for financial support during this work. BN acknowledges the financial support provided by GCM-RQMP during his sabbatical. References [1] D.R. Gamota, P. Brazis, K. Kalyanasundaram, J. Zhang, Printed Organic and Molecular Electronics, Kluwer Academic, Boston, 2004. [2] (a) M.L. Bushey, A. Hwang, P.W. Stephens, C. Nuckolls, J. Am. Chem. Soc. 123 (2001) 8157; (b) M.L. Bushey, T.-Q. Nguyen, C. Nuckolls, J. Am. Chem. Soc. 125 (2003) 8264;

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