Metal-Independent Coherent Electron Tunneling through Polymerized

Apr 8, 2008 - Coherent electron transmissions of the fullerene wires obtained from ... viewpoint and the orbitals in the real-space viewpoint can prov...
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J. Phys. Chem. C 2008, 112, 7029-7035

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Metal-Independent Coherent Electron Tunneling through Polymerized Fullerene Chains Ga In Lee,† Jeung Ku Kang,*,† and Yong-Hoon Kim*,‡ Department of Materials Science and Engineering, Korea AdVanced Institute of Science and Technology, 373-1 Guseong dong, Yuseong gu, Daejeon 305-701, Korea, and Department of Materials Science and Engineering, UniVersity of Seoul, 90 Jeonnong-dong, Dongdaemun-gu, Seoul 130-743, Korea ReceiVed: August 28, 2007; In Final Form: January 7, 2008

We employ a first-principles computational approach to explore the potential of polymerized one-dimensional [60]fullerene chains as the channel material for improved nanoelectronics applications. Coherent electron transmissions of the fullerene wires obtained from [2+2] cycloaddition are calculated at different numbers of fullerene units (from one to four), electrode materials (Au and Al), and contact configurations (contact distances and symmetries). We find that metal-induced gap states are localized within the first side fullerenes in contact with the electrodes, so conclude that polymerized fullerene wires including more than three units should show a robust device characteristic irrespective of the type of electrode metals and contact configurations. Transmission channels are analyzed in terms of the density of states projected onto each fullerene unit, and for the three-unit chain case they are further characterized via the orbital distributions. We demonstrate that the comparison of the projected density of states in the energy viewpoint and the orbitals in the real-space viewpoint can provide a heuristic approach to understand the charge transport phenomena in the nanoscale junctions.

1. Introduction Various nanoscale materials are currently explored in light of their potential nanoelectronics applications. In particular, carbon nanotubes (CNTs) have been attracting much attention, because of its good electron and thermal conductivities as well as robust mechanical properties.1-4 However, the development of CNT-based transistors is still a difficult task, because the diameter and chirality of CNTs are not easily controlled. Moreover, the characteristics of CNT-based junctions are significantly affected by metal-induced gap states (MIGS) and corresponding Schottky barriers.3-6 Here, we consider a one-dimensional (1D) polymerized [60]fullerene (C60) chain as a potential candidate to overcome the problems originating from MIGS in CNT junctions. Nanoscale devices incorporating a single C60 molecule have been constructed by using a scanning tunneling microscope7 and interesting behaviors such as the single electron tunneling, Coulomb blockade, and nanomechanical oscillation were reported.8,9 Fullerenes were found to make a face-centered-cubic (FCC) crystal structure through weak intermolecular van der Waals bonding,10 and each C60 was observed in Raman spectroscopy experiments to rapidly rotate about its lattice position.11 In particular, photoirradiation of the C60 film with ultraviolet light induces structural transformation12-14 into 1D dumbbell-shaped C60 wires by [2+2] cycloaddition.15-18 Hassanien et al. made a photopolymerized epitaxial C60 film that is composed of parallel 1D polymerized fullerene wire by illuminating the C60 film with a 514.5 nm laser light.14 From 2-unit to around 6-unit polymerized fullerenes were formed according to the illumination temperature. * Corresponding authors. J.K.K.: e-mail [email protected], phone 82-42-869-3338, fax 82-42-869-3310. Y.-H.K.: e-mail [email protected], phone:82-2-2210-5724, fax 82-2-2215-5863. † Korea Advanced Institute of Science and Technology. ‡ University of Seoul.

In this work, we theoretically consider junctions comprised of these dumbbell-shaped 1D polymerized C60 chains sandwiched between Au and Al metal electrodes. We particularly focus on the coherent electron tunneling behaviors attributed to MIGS and intrinsic C60 wire channel. The organization of the paper is as follows. In section 2, we first describe the computational details to determine the molecular structures, device models, electron transmissions, and current versus bias voltage (I-V) curves. Section 3 describes the interplay between MIGS and intrinsic C60 orbital states in the coherent electron transmission of the device models. Transmission properties of the C60 chains with different numbers of C60 units (1-4) at different contact distances are analyzed by the projected density of states (PDOS) of side and central C60s to distinguish the contribution of the intrinsic C60 orbitals and MIGS. The transmission channel is further analyzed within the real-space molecular-orbital picture for the three-unit case, which will complement the PDOS analysis in the energy point of view. The effects of contact configurations and metal electrodes on the electron transmission are also studied. Section 4 summarizes the present paper. 2. Computational Details Before studying the device transport characteristics, we performed full geometry optimizations using the Gaussian program19 for the C60 wires without metal electrodes. We used the density functional theory (DFT) method with the PerdewBurke-Enzhrof (PBE) parametrization of exchange-correlation functional20 and a split basis set of 6-31G21 valence double-ζ. We also tested the B3LYP functional and found similar orbital ordering and orbital shapes as in the PBE case. Next, we constructed device models by sandwiching the C60 wires between FCC(111) metal electrodes at the contact distances of d ) 2.0, 2.5, and 3 Å. We then performed twodimensional (2D) DFT calculations using a modified version

10.1021/jp076879n CCC: $40.75 © 2008 American Chemical Society Published on Web 04/08/2008

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Figure 1. Schematic view of the device model based on a three-unit C60 chain in contact with the FCC (111) metal electrodes. Among the three contact points, A (on-top), B (FCC hollow), and C (HCP hollow), we chose the symmetric (A-chain-A) and the asymmetric (A-chain-B) device configurations. Three contact distances (d ) 2.0, 2.5, and 3.0 Å) were considered.

of the SeqQuest program22 to determine the electronic structures of the C60 wire in contact with Au(111) or Al(111) slabs. Here, we used the PBE functional, norm-conserving pseudopotentials,23,24 and the corresponding double-ζ-polarization and singleζ-polarization quality Gaussian basis sets for the C, Au, and Al atoms, respectively. Subsequently, we computed the charge transport properties of the device models using our in-house code25-27 that implements the matrix Green’s function (MGF) approach for the transmission function,28

T(E) ) Trace[Γ1(E)GM(E)Γ2(E)GM+(E)]

(1)

GM(E) ) [ESM - HM + Σ1 + Σ2]-1

(2)

Γ1,2 ) i

[∑

1,2

-

∑1,2+

]

Σ1,2 ) x1,2gS1,2x1,2+

(3) (4)

where SM and HM are the overlap and Hamiltonian matrices of the molecular channel region, respectively, and x1,2 are the channel-electrode 1 or 2 contact parts of the total ES - H matrices. The self-energies Σ provide the accurate descriptions of the broadening and shift of channel energy levels, which result from the coupling between the C60 wires and metal electrodes. The surface green functions gS were extracted from two independent bulk DFT calculations for the unit cells corresponding to the top and bottom electrodes with the single Γ k||-point sampling along the electrode-surface direction and the four k⊥-point sampling along the electrodesurface-normal direction. The energy was scanned around the Fermi level (EF), using the 0.01 eV step. To analyze the nature of transmission channels, we used the atomic projection of density of states,

DOS )

1 2πΩ

∫Ω˜ dk Tr[AM(E)SM]

(5)

where AM ) i(GM - G+ M) is the spectral function corresponding to the molecular channel, and Ω ˜ is the area of the reference unit cell. Finally, the current under a bias voltage (V) was calculated via a Landauer-Bu¨ttiker-type formula,

I(V) )

2e h

∫µµ 1

2

dET(E,V) [f(E - µ1) - f(E - µ2)]

(6)

where µ1 and µ2 are the chemical potentials of electrodes 1 and 2, respectively, and f is the Fermi-Dirac distribution function. Because we restrict ourselves to the low bias regime, we approximated the transmission function T(E,V) by the zero-bias transmission function, T(E,0). Via performing DFT calculations with the periodic boundary condition for the device and electrode models, we faithfully reproduce their bulk nature and achieve numerically negligible band gaps for each of them. This represents an important merit of our method in that we can avoid the ambiguity in aligning bands of three models. More detailed descriptions of our computation scheme can be found elsewhere.26,27 3. Results and Discussions 3.1. Geometries of Fullerene Wires and Device Models. From the geometry optimization of the three-unit polymerized C60 chains (Figure 1), we determined the length of intermolecular bonds connecting two neighboring C60 units as 1.60 Å. This gives the C60-C60 center-of-mass distance of 9.144 Å, which is in good agreement with other theoretical and experimental data.14-17 The lengths of optimized C60 wires (l) are then 6.96, 16.12, 25.27, and 34.41 Å for the 1-, 2-, 3-, and 4-unit chains, respectively. In constructing device models, we considered several possibilities of contact geometry to check the reliability of our conclusion. For the contact points, we chose the on-top (A) and the FCC-hollow (C) sites, and formed the symmetric contact geometry corresponding to the A-C60 chain-A configuration and the asymmetric contact geometry corresponding to the A-C60 chain-C configuration. For the contact distances between the

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Figure 2. Differential charge density of a single-fullerene under asymmetric Au(111) contacts averaged along the electrode-surface direction for the contact distance d ) (a) 2.0 , (b) 2.5, and (c) 3.0 Å. Open triangles indicate the location of the electrode surface Au atoms and the closed triangles indicate the position of the C60 boundary C atoms. Transmission coefficients (T) of a single C60 under asymmetric Au (111) contacts at d ) (d) 2.0, (f) 2.5, and (h) 3.0 Å and (e, g, i) the corresponding PDOS and (j) I-V curves.

side C60s and the metal electrodes (d), we considered three cases: d ) 2.0, 2.5, and 3.0 Å. Geometry optimization of a C60 molecule located on top of the three-layer 6 × 6-cell Au(111) slab resulted in d ) 3.2 Å and that of the C60 on top of the three-layer 6 × 6-cell Al(111) slab resulted in d ) 3.4 Å. However, the energy difference between the Au-electrode d ) 2.5 and 3.2 Å cases is only 44 meV, which implies that the C60-metal distance could be easily modified. So, the contact distances d ) 2.0-3.0 Å approximately correspond to the situations where metal electrode atoms are tightly or optimally deposited situations. 3.2. Transmission Coefficients and PDOS of Au-Contacted Fullerene Wires. First, we consider a single C60 molecule asymmetrically contacted to Au(111) electrodes. Its transmissions and the resulting I-V curves are shown in Figure 2. Because the ionization potential of C60 clusters (∼7.6 eV)29 is

larger than the work function of Au surfaces (∼5.1 eV), the C60 molecule attracts electrons from the Au electrodes, which results in the n-type character of the composite system. The transferred electrons occupy MIGS, which originate from the hybridization between the metallic electrode states and C60 molecular orbitals. The specific amount of charge transfer differs according to the contact distances or the strength of orbital hybridizations: Our Mulliken population analysis gives about -0.51 e, -0.16 e, and -0.04 e C60 charge for the d ) 2.0, 2.5, and 3.0 Å cases, respectively. To further understand the nature of this charge transfer, we analyze the charge density differences [)F(Au + C60 wire) - F(Au) - F(C60 wire)] plotted in panels a, b, and c of Figure 2 for the d ) 2.0, 2.5, and 3.0 Å cases, respectively. Transferred charges are concentrated around the metal-C60 contact regions and their amount rapidly decreases as d increases (as indicated by the Mulliken population analysis),

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Figure 3. (a, c, e) Transmissions and (b, d, f) PDOS of a two-unit C60 wire under asymmetric Au(111) contacts at d ) 2.0, 2.5, and 3.0 Å, respectively.

while the charge transfer is almost negligible for the C60 region. This behavior results from the extremely reactive/inert nature of the exterior/interior part of C60. This also indicates that the electronic structure of a C60 on metal surfaces is dominated by the MIGS localized between C60 and metal surfaces. Below, we will show that this feature will endow C60 wires with unique metal-independent charge transport properties. Next, we consider the transmission and PDOS of the oneunit C60 devices. Upon observing PDOS, we find that MIGS around the system Fermi level (EF) energetically originate from the orbitals around the lowest unoccupied molecular orbital (LUMO) rather than the highest occupied molecular orbital (HOMO), because the former (located around EF +0.5 eV) is closer to EF than the latter (located around EF -1 eV). For the d ) 2.0 Å case, we find that the MIGS completely dominate the transmission (Figure 2d), and result in a metallic I-V behavior (Figure 2g). As d increases, however, the transmission near EF rapidly decreases (Figure 2e,f), because the contribution of MIGS (or the amount of charge transfer) decreases. This results in a significant variation of device I-V characteristics as shown in Figure 2j. Discrete transmission characters for d ) 3.0 Å indicate the reduction of MIGS effects and the conduction through the original fullerene orbital states. The main focus of this study is to understand how MIGS and the intrinsic C60 orbital channels affect the device transmissions as the number of C60 units increases and as the contact configurations are varied. Figure 3 shows electron transmission coefficients and PDOS for a two-unit C60 wire in asymmetric Au contacts at different contact distances. Both C60s are in contact with Au(111) electrodes, so the overall behavior is similar to that of the oneunit case: At d ) 2.0 Å, significant MIGS (yet smaller than those in the one-unit case) arise right above EF, and they rapidly disappear with increasing d. Transmission functions closely follow this behavior, and thus result in a large change in the I-V characteristics with varying d as in the one-unit case. We next consider three-unit C60 chains asymmetrically contacted to the Au(111) electrodes. This is the first case when

Lee et al. a C60 that is not in contact with the metal electrodes (“central” C60) enters into our consideration. Calculated transmissions and PDOS of side and central C60s are shown in Figure 4. Whereas the characteristics of side C60 PDOS are similar to those in the two-unit case (Figure 4b,e,h), we find that the PDOS of the central C60 strongly preserves its molecular character and does not change much with increasing d (Figure 4c,f,i). The transmission arising from MIGS between EF and EF + 0.5 eV, which are mainly located at the side fullerenes, is now significantly decreased even at d ) 2.0 Å (Figure 4a). Thus, except for a small transmission peak at ∼EF +0.2 eV, we obtain a relatively uniform transmission behavior near EF for all three device models. For the three-unit case, we next analyze the transmission channels from the real-space orbital point of view, which should provide a heuristic picture by complementing the above analysis based on PDOS in the energy domain. We emphasize that this is possible because the transmission functions manifest a rather strong signature of the molecular identity for the three-unit case unlike the one-unit and two-unit cases. We also caution that this mapping between molecular orbitals (of the isolated chain) and the transmission peaks (of the chain sandwiched between metal electrodes) is not completely exact, as some of the neardegenerate orbitals can intermix with each other with the charge transfer between the side C60s and metal electrodes. Representative unoccupied molecular orbitals identified for the isolated three-unit C60 chain are shown in Figure 5, together with their assignment to the LUMO-region transmission and PDOS peaks of the chain between metal electrodes. The oribtals of the threeunit C60 chains can be categorized into three types: (i) delocalized throughout the chain, (ii) localized at the central C60, and (iii) localized at the side C60s. For the orbitals shown in Figure 5, orbitals 1, 4, 6, and 9 correspond to type (i), orbitals 2 and 8 correspond to type (ii), and orbitals 3, 5, and 7 correspond to type (iii). One can intuitively expect that type (i) orbitals will be a good transmission channel, whereas types (ii) and (iii) will be relatively poor transmission channels. We indeed find that delocalized orbitals 1, 4, 6, and 9 lead to the strong transmission peaks. Moreover, we note that the degree of delocalization (6 ≈ 9 > 4 > 1) corresponds to the height of the transmission peaks. Orbitals localized at the central or side C60s (e.g., orbitals 2 and 3) result in smaller transmissions. However, for some localized orbitals (orbtials 5, 7, and 8), because there exist other orbtials close in energy and they are strongly hybridized with metal electrodes (as manifested in the strongly broadened PDOS and transmission peaks), we observe relatively strong transmissions. This is especially noticeable for orbital 7 localized at the side C60s, for which we find a transmission peak that is even higher than that of the delocalized orbital 1. Similar orbital characterization of the HOMO region (Figure S1) is provided in the Supporting Information. We now consider the four-unit case, whose transmissions and PDOS shown in Figure 6 can be similarly characterized as for the three-unit case. At d ) 2.0 Å, the side C60s show significant MIGS at the energy range between EF and EF + 0.5 eV that results from the strong coupling with Au electrodes (Figure 6b). The MIGS and the coupling strength rapidly decrease as d increases to 2.5 and 3.0 Å (Figure 6, panels e and h). On the other hand, although slight variation exsits, the central two C60s strongly perserve their molecular identity (Figure 6c,f,i). Considering the interplay of these side and central C60s on the total transmission, we find very small contribution from the MIGS of side fullerens even at d ) 2.0 Å (Figure 6a). This results in similar transmissions with well-defined HOMO-

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Figure 4. Transmissions of a three-unit C60 wires under asymmetric Au(111) contacts at d ) (a) 2.0, (d) 2.5, and (g) 3.0 Å. PDOS of the side and the central fullerenes at d ) (b, c) 2.0, (e, f) 2.5, and (h, i) 3.0 Å, respectively.

Figure 5. The LUMO-region transmission and PDOS of the three-unit C60 chain between metal electrodes at d ) 3.0 Å (Figure 4g,h,i) reproduced in a higher resolution. For each transmission or PDOS peak, corresponding orbitals of the three-unit fullerene wire without contact metals are presented. Brackets represent nearly degenerate orbitals.

LUMO gaps of about 1.4 eV (and the resulting I-V characteristics) throughout the d ) 2.0, 2.5, and 3.0 Å cases (Figure 6a,d,g). We also calculated the 5-unit C60 chain under asymmetric contacts, and the results were similar to those of the fourunit case (not shown). We finally check the robustness of our findings with respect to the changes in contact configurations and the type of metal electrodes. The transmission and PDOS of the three-unit C60 chain that is symmetrically contacted in the A-chain-A configuration (see Figure 1 and the comments in section 3.1) between Au(111) electrodes at d ) 2.5 Å are shown in Figure 7. Similar

results are obtained for the C-chain-C configurations. Comparing with panels d, e, and f of Figure 4, we find more degenerate central C60 PDOS (Figure 4c) and more broadened side C60 PDOS (Figure 4b) and transmission (Figure 4a), which implies a stronger hybridization between the C60 states and the electrode states. In sptie of such differences, the energetic locations of the HOMO and LUMO transimission peaks is similar to those of the asymmetric contact case. The difference in the transmission functions becomes even smaller for the four-unit case (see below). We also simulated the thermal vibration of molecules by slightly perturbing the molecular geometry of the three-unit

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Figure 6. Transmissions of four-unit C60 wires under asymmetric contacts at d ) (a) 2.0, (d) 2.5, and (g) 3.0 Å. PDOS of the side and the central fullerenes at d ) (b, c) 2.0 Å, (e, f) 2.5, and (h, i) 3.0 Å, respectively.

Figure 7. (a) Transmission, (b) PDOS for the side C60s, and (c) PDOS of the central C60 of a three-unit C60 wire under symmetric Au(111) contacts at d ) 2.5 Å.

Figure 8. Transmission of a four-unit C60 wire under asymmetric Al(111) contacts at d ) 2.5 Å. Corresponding PDOS of the (b) side and (c) central fullerenes.

fullerene device models and found that their effects on the transmission behavior around EF are negligble as shown in the Supporting Information. We next consider the case of a different metal electrode type. The transmission and PDOS of the four-unit C60 wire that is asymmetrically sandwiched between Al(111) electrodes at d ) 2.5 Å are shown in Figure 8. When Figures 8b and 6e are compared, the differences in the PDOS of the side C60s contacted at the Al and Au electrodes are significant. However, the strong molecular identity of the central C60s is maintained (Figure 8c) as in the Au-electrode case (Figure 6f), and we obtain a transmission function (Figure 8a) that is very similar to that of the Au-electrode case (Figure 6d). Considering a large difference in the work functions of the Au (5.10 eV) and Al surfaces (4.26 eV), the similar energetic positioning of the HOMO and LUMO transmission peaks in the C60-wire devices is noticeable. This suggests that employing C60 wires as the channel material

possibly resolves the problems arising from MIGS in the nanoscale junctions. 4. Summary In this work, we assessed the electron transmission properties of 1D C60 chains with varying lengths, contact distances, contact symmetries, and types of metal electrodes. We found that significant MIGS and charge transfer arise at the side C60s for short contact distances (d ) 2.0 Å), and they rapidly disappear as d increases (d ) 2.5 and 3.0 Å). These MIGS dominated the transmissions of one-unit and two-unit C60 chains and resulted in significantly different I-V curves with varying d. However, the contribution of MIGS on the transmission rapidly disappeared as the number of C60 units increased further, and even for the four-unit C60 chains we found a rather uniform transmission character that does not sensitively depend on the contact configurations. We thus expect that polymerized C60

Metal-Independent Coherent Electron Tunneling chains could be adopted in the contact engineering of nanoscale devices as a method to minimize the effect of MIGS. Acknowledgment. G. I. Lee and J. K. Kang were supported by the Korea Science and Engineering Foundation (KOSEF) (grant no. R0A-2007-000-20029-0) and by the Korea Research Foundation Grant (grant no. KRF-2005-005-J09703). They were also supported in part by the Hydrogen Energy R & D program oftheMinistryofScience&Technology(grantno.M103KW01001706K2301-01720). Y.-H. Kim was supported by the University of Seoul (2007 Academic Research grant). Supporting Information Available: Figure showing the HOMO-region transmission, PDOS peaks for the three-unit fullerene chan sandwiched between metal electrodes, and realspace orbital diagrams of the corresponding fullerene wire without contact metals. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Tans, S. J.; Verschueren, A. R. M.; Dekker, C. Nature 1998, 393, 49. (2) Nygard, J.; Cobden, D. H.; Bockrath, M.; McEuen, P. L.; Lindelof, P. E. Appl. Phys. A 1999, 69, 297. (3) Javey, A.; Guo, J.; Wang, Q.; Lundstrom, M.; Dai, H. Nature 2003, 424, 654. (4) Chen, Z.; Appenzeller, J.; Knoch, J.; Lin, Y. M.; Avouris, P. Nano Lett. 2005, 5, 1497. (5) Pomorski, P.; Roland, C.; Guo, H. Phys. ReV. B 2004, 70, 115408. (6) Wang, D.; Chang, Y.-L.; Wang, Q.; Cao, J.; Farmer, D. B.; Gordon, R. G.; Dai, H. J. Am. Chem. Soc. 2004, 126, 11602. (7) Tersoff, J.; Hamann, D. R. Phys. ReV. B 1985, 31, 805. (8) Li, B.; Zeng, C.; Zhao, J.; Yang, J.; Hou, J. G.; Zhu, Q. J. Chem. Phys. 2006, 124, 064709. (9) Likharev, K. K. Proc. IEEE 1999, 87, 606. (10) Kroto, H. W.; Heath, J. R.; O’Brien, S. C.; Curl, R. F.; Smalley, R. E. Nature 1985, 318, 162. (11) Dresselhaus, M. S.; Dresselhaus, G.; Ekland, P. C. J. Raman Spectrosc. 1996, 27, 351. (12) Rao, A. M.; Zhou, P.; Wang, K. A.; Hager, G. T.; Holden, J. M.; Wang, Y.; T.;, L. W.; Bi, X. X.; Ekland, P. C.; Cornett, D. S.; Duncan, M.

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