Electronic and Quantum Transport Properties of Heterobilayers of

Article pubs.acs.org/JPCC

Electronic and Quantum Transport Properties of Heterobilayers of Graphene Nanoribbons and Zinc-Porphyrin Tapes Hong Seok Kang* Department of Nano and Advanced Materials, College of Engineering, Jeonju University, Hyoja-dong, Wansan-ku, Chonju, Chonbuk 560-759, Republic of Korea

Yang-Soo Kim Korea Basic Science Institute, Suncheon, 540-742, Republic of Korea S Supporting Information *

ABSTRACT: Using the first-principles calculation, we have shown that heterobilayers can be formed between armchair graphene nanoribbons (GNRs) and zinc-porphyrin tapes (ZnPPTs). The PPTs investigated include triply lined (TL) and doubly linked (DL) PPTs. In addition, we have also investigated electronic structures and conductances of these heterobilayers. The bilayer involving the DL Zn-PPT is more stable than its TL correspondents due to stronger electronic coupling, which can be ascribed to the similar dispersion relations of the free-standing GNR and the DL PPT around the Fermi level. Consequently, the bilayer formation of TL Zn-PPT with GNR turns it into a metal, while its DL correspondent remains semiconducting but exhibits an increased on-current at an appropriate gate voltage. Our calculation of the band gap of the GNR as a function of the ribbon width also shows that the band-gap oscillation is reduced upon bilayer formation with DL Zn-PPT.

1. INTRODUCTION Graphene is a novel semimetal with an extremely high electron mobility, which is a consequence of a linear dispersion relation in the band structure of the π and π* states around the charge neutrality point. It is potentially useful in the realization of spin qubits because of its long spin-coherence time and long spinrelaxation time.1 Graphene nanoribbons (GNRs) are strips of graphene with electronic properties that depend on their edge symmetry and width.2,3 Edge states in zigzag GNRs (zGNRs) are spin-polarized, whereas hydrogen-terminated armchair GNRs (aGNRs) do not exhibit such edge-localized states and are not spin-polarized.4−6 In this regard, zGNR-based spintransporting devices were proposed by theoretical calculations.7−10 For practical applications, graphene devices are fabricated on a substrate. Therefore, it is desired that the interaction between the graphene-based material and the substrate does not significantly degrade the electron transport properties and device characteristics. Unfortunately, it was shown that a SiO2 substrate reduces carrier mobility due to surface defects and surface optical phonons.11,12 On the other hand, the mobility is an order of magnitude higher when graphene is deposited on hexagonal boron nitride.13,14 In this respect, understanding the electronic structure and transport properties of graphene- or GNR-adsorbed substrates in comparison with those of the freestanding graphene is quite important. The understanding of bilayer or trilayer formation with other kinds of graphene analogues is also interesting. In this regard, a recent calculation © 2012 American Chemical Society

showed that a graphene bilayer between hexagonal boron nitride sheets exhibits a giant Stark effect.15 While there is a strong electronic coupling between a graphene monolayer and the adjacent metal, Sutter et. al showed that an epitaxial graphene trilayer on Ru(0001) recovers the π-bands of freestanding graphene near the Fermi level.16 Consistent with this observation, measurements of surface-enhancement Raman scattering spectra indicated that the Ag deposition on a graphene monolayer is much stronger than that on a trilayer.17 The specific π−π interaction between an aGNR and a nucleobase of the DNA was also shown to exhibit a characteristic quantum transport, which can be directly applied to a fast DNA sequencing.18 The interaction between graphene and pophyrins is also interesting, because porphyrins are natural light-harvesting systems. Recently, scandium(III)-catalyzed oxidation of meso− meso-linked Zn(II)-porphyrin (Zn-PPH) arrays led to the synthesis of a triply linked (TL) porphyrin tape (Zn-PPT) in which monomers are interlinked by three C−C bonds in such a way that a rigid planar π-conjugated structure extends up to dodecamer porphyrin units.19 A drastic red shift in the electronic spectra is observed as the number of monomers increases. Meanwhile, an oxidation of M(II)-prophyrin produced a doubly linked (DL) porphyrin tape (M-PPT), Received: December 18, 2011 Revised: March 16, 2012 Published: March 16, 2012 8167

dx.doi.org/10.1021/jp212206d | J. Phys. Chem. C 2012, 116, 8167−8173

The Journal of Physical Chemistry C

Article

aGNR-[Zn PPT], was considered, where n (14−26) represents the ribbon width. Coherent electron transport calculations at zero bias were performed using the ATK 2011.02 program,29 in which the transmittance was calculated from the Landauer formula combined with the nonequilibrium Green’s function (NEGF) method30

(M = Ni, Zn, Cu, and Pd) in which two adjacent units are interlinked by two C−C bonds.20,21 In the longest tape synthesized, a rigid planar π-conjugated structure extends up to heptamer units along one direction. These procedures involve bottom-up syntheses of porphyrin-based one-dimensional nanosystems. One of the most important features of these tapes is the diversity in metal ions that can be located at the center of the porphyrin ring. In the previous work, we investigated the electronic structures of infinite TL M-PPTs and DL M-PPTs with various divalent metal ions M using a calculation based on the density functional theory.22 The calculation showed that PPTs with a broad range of electronic properties can be engineered from semiconductors to metals, and even half-metals, by a simple variation of the central metal ion M and the method of linkage between the monomers. Afterward, the TL Cr-PPT was also shown to exhibit the halfmetallicity.23 These findings suggest that porphyrin-based one-dimensional tapes can be as useful for nanoelectronics as other types of nanomaterials. In this work, we investigate the possibility of forming heterobilayers between aGNRs of various ribbon widths and Zn-PPTs; we also investigate the electronic structures and quantum transport properties of the heterobilayers. A detailed comparison is made of bilayer properties involving TL and DL Zn-PPTs.

T (E , V = 0) = Tr(ΓR GR ΓLG A )

(1)

where T(E, V = 0), ΓL, G , and G are the transmittance of an incident electron with energy E at zero bias, the coupling strength to the right electrode, the retarded Green’s function of the scattering region, and the advanced Green’s function of the scattering region, respectively. A double-ζ plus polarization (DZP) basis set was adopted for all atoms. R

A

3. RESULTS AND DISCUSSION We first consider a heterobilayer of 16-aGNR and TL Zn-PPT. To investigate the possibility of the bilayer formation, we calculated the binding energy (Eb) of the process GNR + ZnPPT → GNR-(Zn-PPT) for the various configurations shown in Figure 1. Table 1 shows that Eb obtained from the PBE-D2

2. COMPUTATIONAL METHODS Geometric optimizations were carried out using the Vienna Ab initio Simulation Package (VASP).24,25 Electron−ion interactions were described by the projector-augmented wave (PAW) method, which is basically a frozen-core all-electron calculation.26 Calculations were performed using the PBE-D2, which represents the PBE that empirically includes van der Waals interaction using Grimme’s approach.27,28 For structure optimization, the atoms were relaxed in the direction of the Hellmann−Feynman force using the conjugate gradient method until a stringent convergence criterion (0.03 eV/Å) was satisfied. Our previous calculation shows that the optimized lattice constants for DL and TL Zn-PPTs are 8.93 and 8.42 Å, respectively.22 These constants are within 4% and 2%, respectively, of the lattice constant of two primitive cells of a hydrogen-terminated 16-armchair GNR (16-aGNR), which is 8.572 Å, where 16-aGNR includes 16 carbon dimers along the ribbon width and two primitive cells along the ribbon axis. We adopt the lattice constant of the hydrogen-terminated GNR as that of GNR-(M-PPT) heterobilayers, where M is a divalent metal ion. k-point sampling was performed with nine k-points in the first Brillouin zone. For the calculation of quantum conductance, a semi-infinite replica of a primitive cell of an appropriate heterobilayer was used for the electrode, while one primitive cell was adopted for the scattering region. We adopt the LDA instead of the PBE-D2 as the exchange-correlation function. To be consistent with the conductance calculation, the band structure was also calculated using the LDA. In this calculation, we also employ the LDAoptimized lattice constant (8.493 Å) of the GNR as that for the heterobilayers. Full structure optimization was again performed for the heterobilayers. As is described in the next section, optimized geometries of the bilayers calculated with those two exchange-correlation functions are almost the same. To investigate the effect of the GNR width on the electronic structure of the heterobilayer, a set of heterobilayers, that is, n-

Figure 1. Molecular structure of various configurations of the heterobilayer of 16-aGNR-(TL Zn-PPT): configurations Z (a, b), C (c), and A (d). For configuration Z, two different views are shown for a better understanding.

calculation is −1.49 eV for the most stable configuration (Z), indicating that the bilayer formation is quite strong. Figure 1c,d shows two other configurations “C” and “A” of the heterobilayer considered in this work, which are 0.05 and 0.19 eV less stable than configuration “Z”. In configuration Z, diagonal N−Zn−N bonds are located on top of a zigzag bond of the GNR, where the zigzag bond indicates the CC bond of 8168



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Table 1. Binding Energy (Eb) and the Metal Ion−Graphene Plane Distance [l(M−GNR)] Obtained from the PBE-D2 Calculation for the Optimized Structure of the Most Stable Configuration of 16-aGNR-(M-PPT) Heterobilayers Eb (eV) l(M−GNR) (Å)

16-aGNR-(TL Zn-PPT)

16-aGNR-(DL Zn-PPT)

−1.49 3.18(3.19)a

−1.60 3.15(3.20)a

a

The number inside the parentheses denotes corresponding distance obtained from the calculation using the LDA exchange correlation function.

the GNR, which lies at 60° with respect to the crystal axis. The GNR adopts a slightly convex geometry with respect to the planar Zn-PPT. Namely, the Zn−GNR interlayer distance, l(Zn−GNR) (3.18 Å), is 0.06 Å longer than the HPPT−GNR distance, where HPPT denotes a terminal hydrogen atom of the Zn-PPT. It is worth mentioning that a comparison of the Eb value for configuration Z with that (−0.02 eV) from our separate PBE calculation indicates a dominant role of the van der Waals interaction in the bilayer formation. Next, we investigate zero-bias transmittance of the heterobilayer. For computational simplicity, we adopt 14aGNR instead of 16-aGNR. As was mentioned in the previous section, the LDA exchange-correlation was employed instead of the PBE-D2 for the transmittance calculation. Structure optimization with the LDA exchange-correlation function indicates that the GNR also adopts a slightly convex geometry. In addition, l(Zn−GNR) (3.19 Å) is very close to that from the PBE-D2 calculation (3.18 Å), as shown in Table 1. Figure 2 shows the band structure of the 14-aGNR-(TL ZnPPT) heterobilayer in comparison with those of the freestanding 14-aGNR and TL Zn-PPT. The free-standing 14aGNR and TL Zn-PPT are quasi-semimetals with small band gaps (0.09 and 0.08 eV, respectively) at the Γ-point and the zone boundary, respectively. The valence band (n = 175) of the bilayer has a dispersion relation similar to that of 14-aGNR to three-fourths of the zone boundary. It crosses the Fermi level near the Γ-point, while the valence band of the free-standing GNR is located 0.05 eV below the Fermi level at the Γ-point. The conduction band (n = 176) of the bilayer crosses the Fermi level near the zone boundary, which indicates a small charge transfer from the GNR to the PPT. It is an admixture of the conduction band of the free-standing GNR (n = 117 in Figure 2a) and that of the free-standing Zn-PPT (n = 60 in Figure 2b). Our separate analysis of electron density indicates that the band is like the conduction band of the GNR at the Γ-point, while it resembles that of Zn-PPT at the zone boundary. Figure 3 shows the zero-bias transimittance T(E, V = 0) of configurations Z and C of the heterobilayer in comparison to that of TL Zn-PPT as a function of the energy of the incident electron. First, we focus on configuration Z. Consistent with the band structure shown in Figure 2b, we find zero transmittance around E = 0 for the free-standing Zn-PPT. On the other hand, we observe metallic behavior for the bilayer. Around E = 0, the transmittance spectrum exhibits a narrow peak with a T(E) of 2.0, indicating that the zero-bias conductance or the linear response conductance will be 2G0. [Note that G0 = 2e2/h, and the linear response conductance is given by the relation, G = G0·T(E = 0), where e, h, and T(EF) are electron charge, Planck constant, and the transmittance at the Fermi energy.] Our separate analysis shows that the transmittance originates from the ballistic transport through

Figure 2. Band structures of 14-aGNR (a), TL Zn-PPT (b), and configuration Z (c) of 14-aGNR-(TL Zn-PPT) obtained from the LDA calculations.

two perfectly transmitting eigenchannels. As can be expected from the band structure analysis, those eigenchannels correspond to two (n, k) states crossing the Fermi level, where n and k denote the band index and the crystal momentum, respectively. Figure 2c shows that those bands are the valence band of the GNR (n = 175) and the conduction band of the Zn-PPT (n = 176). Therefore, one-half of the total electron conduction will occur through the 72-GNR and the other half through the Zn-PPT in the linear regime. As shown in Figure S1 (Supporting Information), this observation can be further clarified by a comparison of the π-component of PDOS plots for the GNR and the Zn-PPT in the bilayer at the Fermi level. (Although not explicitly shown here, this is also the case for configuration C.) Transmittance at other energies can also be understood from the band structure. For example, the transmittance at E = −0.01 eV occurs through a single eigenchannel; that is, the valence band of the GNR and that at 8169



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Figure 3. Zero-bias transmittances of the 14-aGNR (a), TL Zn-PPT (b), configuration Z of 14-aGNR-(TL Zn-PPT) (c), and configuration C of 14aGNR-(TL Zn-PPT) (d) obtained from LDA calculations.

E = −0.15 eV can be ascribed to one more eigenchannel, that is, the valence band of the Zn-PPT (n = 174). Similar arguments hold for configuration C. Next, we investigate the possible formation of a heterobilayer of 16-GNR and DL Zn-PPT. For the most stable configuration (Z), we find that the binding energy, Eb (−1.60 eV), of the heterobilayer is larger than that involving the TL Zn-PPT. Figure 4 shows configuration Z, which is defined in such a way that diagonal N−Zn−N bonds are located on top of a zigzag bond of the GNR. As in the case of the free-standing DL ZnPPT, the PPT adopts a twisted geometry. The GNR adopts a slightly convex geometry upon bilayer formation. The configuration is found to be more stable than the other two configurations (E and C) shown in Figure 4 by 0.07 and 0.18 eV, respectively. A comparison of the Eb value for configuration Z with that (−0.03 eV) from the PBE calculation also confirms the dominant role of the van der Waals interaction in the bilayer formation. It is also worth mentioning that the fact that the binding energy of the bilayer involving the DL Zn-PPT is larger than the TL Zn-PPT may be attributed to the larger interface area of the bilayer involving the DL Zn-PPT. Figure 5 gives a comparison of the band structure of the 14aGNR-(DL Zn-PPT) bilayer with that of the DL Zn-PPT, for which the LDA exchange-correlation function was used. We note that l(Zn−GNR) is 3.20 Å, also indicating that the LDA-optimized geometry is similar to the PBE-D2-optimized one. Different from the case of the bilayer involving the TL ZnPPT, we find that the heterobilayer remains semiconducting, with a band gap of 0.19 eV. The gap is slightly larger than that of the free-standing 14-aGNR (0.14 eV), while smaller than that of DL Zn-PPT (0.41 eV). Different from the case of its TL correspondent, this observation suggests that there is more than a simple charge transfer between the GNR and the DL PPT. It can be understood if we note that band gaps of both the freestanding GNR and the free-standing DL Zn-PPT are commonly located at the Γ-point, which is different from the

case of its TL correspondent. (On the other hand, band structures of the free-standing TL Zn-PPT and DL Zn-PPT exhibit opposite dispersion relations around the Fermi level.)

Figure 4. Molecular structure of various configurations of the heterobilayer of 16-aGNR-(TL Zn-PPT): configurations Z (a, b), E (c), and C (d). For configuration Z, two different views are shown for a better understanding. 8170



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Figure 5. Band structures of DL Zn-PPT (a) and configuration Z of 14-aGNR-(DL Zn-PPT) (b) obtained from LDA calculations.

The stronger electronic coupling between the GNR and the DL Zn-PPT is manifested in the binding energy, which is larger than that of the bilayer involving the TL Zn-PPT. Consistent with this observation, l(Zn−GNR) (3.15 Å) is slightly shorter than that of its TL correspondent. In fact, both its conduction band (n = 177) and its valence band (n = 176) are admixtures of corresponding bands of the 72-GNR and DL Zn-PPT. Our separate analysis of electron density indicates that they resemble the corresponding bands of the free-standing 14aGNR near the Γ-point, while they are like the corresponding bands (n = 60 and 61 in Figure 5a) of the free-standing DL ZnPPT near the zone boundary. To investigate how the band gap of the heterobilayer is affected by the width of the GNR, we have also investigated the electronic structure of the bilayer of 22-aGNR and Zn-PPT. Comparison of panels a−c in Figure 6 indicates that the same conclusion can be drawn. Namely, the bilayer of 22-aGNR and the TL Zn-PPT is again metallic, where the valence band and the conduction band of the free-standing TL Zn-PPT are largely preserved in one-third of the whole irreducible region of the first Brillouin zone. On the other hand, the band structure of the bilayer involving the DL Zn-PPT is similar to that of the bilayer of 14-aGNR-[DL Zn-PPT], again indicating that the bilayer is a semiconductor. Figure 7 shows the band-gap variation of the bilayer of n-aGNR-(DL Zn-PPT) in comparison with those of the free-standing and bent naGNRs, where n = 14−26.31 Here, the bent aGNR denotes the aGNR taken from the corresponding bilayer. As was noted for the free-standing GNR,5 the figure clearly shows a periodicity of n = 3 for the bilayer. Band gaps of the bent aGNR are almost the same as those of the free-standing aGNR, indicating that the bending effect is insignificant. However, the band-gap variation of the bilayer is smaller than that of the free-standing GNR. Similar to the case of the bilayer of 14-aGNR-(Zn PPT), the band gaps of 20- and 26-aGNR-(DL Zn-PPT) are larger than those of free-standing aGNR. For example, the gap of 26-

Figure 6. Band structures of 22-aGNR (a), configuration Z of 22aGNR-(TL Zn-PPT) (b), and configuration Z of 22-aGNR-(DL ZnPPT) (c) obtained from LDA calculations.

aGNR-(DL Zn-PPT) is 0.11 eV, whereas that of 26-aGNR is 0.08 eV. Considering that their ribbon widths are ∼2.81 nm, the heterobilayer formation of the GNR with the DL Zn-PPT can be a new way of introducing an appreciable band gap in the armchair GNR of ∼3 nm wide. Figure 8a−c compares the zero-bias transmittance of the configurations Z and E of the heterobilayer with that of the free-standing DL Zn-PPT. Consistent with the band structure analysis, there is a transmission gap around the Fermi level for configuration Z, which is larger than that of 14-aGNR, but smaller than that of DL Zn-PPT. At other energies, the figures also indicate ballistic transport through various eigenchannels, which can be easily identified from the band structure previously mentioned. For example, the transmittances at −0.1 and 0.1 eV of configuration Z can be ascribed to the 8171



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low bias will occur predominantly through the GNR, which can be further clarified by a comparison of the π-component of the PDOS of the GNR in the bilayer with that of the Zn-PPT in the bilayer shown in Figure S2 (Supporting Information). The increased transmittance at E = 0.2 eV is due to an additional eigenchannel associated with k-states of the conduction band of the Zn-PPT, which is located within [0, 0.1] eV in the band structure shown in Figure 5b. Meanwhile, the higher transmittance of the bilayer than those of the free-standing GNR and the DL Zn-PPT at E ≥ ± 0.1 eV, which can be easily identified from comparing Figures 3a and 8a,b, ensures a larger on-current upon application of an appropriate gate voltage. Similar arguments hold for configurarion E, for which there is a transmission gap of 0.11 eV. Therefore, the bilayer can be a promising channel material in a field-effect transistor (FET) working at low voltage.

Figure 7. Band-gap variation of bilayers (solid line) of n-aGNR-(DL Zn-PPT) (square) in comparison with those of the free-standing naGNRs (circle) and the bent n-aGNR (diamond) in the bilayer, where n = 14−26.

eigenchannels associated with k-states of the valence band and the conduction band of the bilayer with those specific energies. Therefore, we can conjecture that the electric conduction at a

4. CONCLUSION We have shown that heterobilayers can be formed between armchair 16-aGNR and two types of Zn-PPTs. The ZN-PPTs investigated include TL Zn-PPT and DL Zn-PPT. While the free-standing GNR and the TL PPTs exhibit an opposite dispersion relation around the Fermi level, the free-standing GNR and the DL PPTs have similar dispersion relations. As a consequence, there is stronger electronic coupling between the latter, which is manifested in the electronic structures and zerobias transmittances of their heterobilayer. While n-aGNR can be a semiconductor with an appreciable gap depending upon the ribbon width, the heterobilayer of n-aGNR-(TL Zn-PPT) is always a metal or quasi-semimetal irrespective of the ribbon width. In fact, our separate calculation shows that TL bilayers are quasi-semimetals with a constant band gap of 0.06 eV at the zone boundary, when band gaps of the free-standing GNRs exhibit maxima, as shown in Figure 7. For example, the bilayer formation of 16-GNR with the TL Zn-PPT drastically decreases the band gap from 0.73 to 0.06 eV. Therefore, the bilayer will be useful as a conducting wire in nanoelectronics, in which the low-bias conductance is approximately twice as large as those of individual components. On the other hand, the heterobilayer of GNR-(DL Zn-PPT) remains semiconducting. As the ribbon width increases, we find that the band gap of the bilayer oscillates with a smaller amplitude than the free-standing aGNR. Specifically, bilayer formation slightly increases the band gap for n = 3k + 2, where the gap minima occur. Meanwhile, the bilayers are still semiconductors with appreciable band gaps for n = 3k + 1, where the gap maxima are observed. For example, the gap (0.40 eV) is appreciable when n = 16, which can be compared with the corresponding gap (0.06 eV) for the bilayer involving the TL Zn-PPT. In addition, the transmittance spectrum of GNR(DL Zn-PPT) shows that the bilayer formation does not deteriorate the ballistic transport of the GNR. Rather, the π−π interaction of the bilayer is expected to increase the on-current under gate voltage. Although our conclusion was drawn on the basis of the transmission calculation at zero bias, we expect that it will not be affected very much by the calculation at a finite bias. Therefore, the bilayer will be quite promising in the FET working at low voltage. Noting that the ribbon widths (1.6−3.1 nm) of n-aGNRs (n = 14−26) investigated in this work can be lithographically accessible, we expect that our calculation would stimulate application of those heterobilayers in nanoelectronic devices.

Figure 8. Zero-bias transmittances of the DL Zn-PPT (a), configuration Z of 72-GNR-(DL Zn-PPT) (b), and configuration E of 72-GNR-(DL Zn-PPT) (c) obtained from LDA calculations. 8172



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(27) Grimme, S. J. Comput. Chem. 2006, 27, 1787−1799. (28) Bucko, T.; Hafner, J.; Lebegue, S.; Angyan, J. G. J. Phys. Chem. A 2010, 114, 11814−11824. (29) Atomistix Toolkit, version 2008.10; Quantumwise A/S: Copenhagen, Denmark. www.quantumwise.com. (30) Datta, S. Electron Transport in Mesoscopic Systems; Cambridge University Press: Cambridge, England, 1995. (31) Our separate calculation using 13 k-points for the electron density calculation shows that band gaps are the same as those from the calculation using 9 k-points for 17- and 23-aGNRs.

ASSOCIATED CONTENT

S Supporting Information *

A full list of ref 13 and Figures S1 and S2. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant 2010-0007815). Computations were performed using a supercomputer at the Korea Institute of Science and Technology Information (KSC-2011-C1-11).

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REFERENCES

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Electronic and Quantum Transport Properties of Heterobilayers of

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