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Design of Graphene-Nanoribbon Heterojunctions from First Principles Xiao-Fei Li,†,‡ Ling-Ling Wang,† Ke-Qiu Chen,† and Yi Luo*,‡,§ †
School of Physics and Microelectronics Science, Hunan University, Changsha 410082, China Department of Theoretical Chemistry, Royal Institute of Technology, S-106 91 Stockholm, Sweden § Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, 230026, Hefei, China ‡
ABSTRACT:
Graphene nanoribbons with armchair and zigzag edges are known to have very different electronic structure and properties. We show here that the fusion of an armchair and a zigzag graphene-nanoribbon (aGNR|zGNR) can form heterojunctions with remarkable electron transport properties. First-principles calculations reveal that the heterojunction can be either metallic or semiconducting depending on the width of the nanoribbon. A well-defined oscillation of the zero-bias conductance as a function of the ribbon width is observed, which is originated from the resonance and nonresonance of frontier orbitals between aGNR and zGNR. We find that the current/voltage characteristics of the aGNR|zGNR heterojunction possess pronounced rectification effect, and a high rectification ratio can be achieved by tuning the width of the zGNR to minimize the backward current. The unique properties of the proposed heterojunction could be very useful for manufacturing graphene-based electronic devices.
’ INTRODUCTION Graphene heterojunctions or polycrystalline graphenes have attracted considerable attention very recently.14 They have offered an opportunity to study the peculiar properties of the chiral graphene quasi-particles5 and its potential applications in advanced electronic devices.6 It was shown that the formation of grain boundaries is controlled by kinetic factors, for instance, simultaneous nucleation of islands with different orientation.3,7 Lahiri et al. recently discovered1 that by using the Ni(111) surface as a scaffold two simultaneously growing graphene sheets can be connected to each other and lead to the formation of the graphene heterojunction. Scanning tunneling microscopy (STM) measurements and band structure calculations have shown that the produced heterojunctions with one-dimensional extended defects along their central axes are perfect metallic wires.1 Young and Kim2 experimentally studied extremely narrow graphene heterojunction samples and found the magnetic-field-dependent r 2011 American Chemical Society
oscillatory conductance as results of the quantum interference and Klein tunneling effects. Very recently, Yazyev and Louie3 theoretically investigated the topological defects in the graphene sheet and found the energetically favorable symmetric large-angle grain boundaries and the strong tendency toward out-of-plane deformations in the small-angle regimes. Their electronic band structure calculations indicate that the constructed polycrystalline graphene can be either metallic or semiconducting, depending on the angle of the grain boundary,4 which is regarded as a useful property for tuning the transport gap of large-area polycrystalline graphene samples. However, a controllable change of the grain boundary angle in polycrystalline graphene during the growing process is still a challenge with the current technology. Received: March 8, 2011 Revised: May 21, 2011 Published: May 24, 2011 12616
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The Journal of Physical Chemistry C Here, we propose a relatively straightforward way to tune the electronic characteristic of graphene nanoribbon heterojunctions (GNR-HJs) between the metallic and the semiconducting by controlling the width of the nanoribbon at the atomic scale. The designed GNR-HJs can be obtained by cutting a polycrystalline graphene with the largest-angle grain boundary (θ = 30°) growing on the surface of a Ni substrate1,8 or simply be constructed by the fusion of an armchair and a zigzag graphene nanoribbon (aGNR|zGNR). Previous studies912 on semiconductor|semiconductor, semiconductor|metal, and metal|metal heterojunctions have shown that the difference in the work function of the two components can cause electron transfer and lead to a dipole layer presented in the interface of
Figure 1. Fully optimized central scatting region of the heterojunction a25|z14. The interface region between aGNR and zGNR consists of pentagonheptagon pairs. Two zigzag lines (left) and two dimer lines (right) are, respectively, used as surface layers.
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heterojunctions, resulting in pn, pp0 , or nn0 junctions which are primary elements in functional devices. Since it is well-known that GNRs with different edges can have very different electronic property and their work function varied with the increase of their widths,1319 one can thus expect that our designed aGNR|zGNR heterojunctions could have some interesting properties.
’ STRUCTURES AND METHODS The aGNR|zGNR heterojunctions we have constructed have pentagonal and heptagonal topological defects at the interface region between two semi-infinitely aGNR and zGNR, as shown in Figure 1. Following previous convention,19,20 GNRs with armchair or zigzag edges on both sides can be labeled as NaGNRs or N-zGNRs, N being the number of dimer lines or zigzag lines across the ribbon width. Here, our N-aGNR|M-zGNR heterojunction is denoted as aN|zM from now on, where N and M are the width of aGNR and zGNR, respectively. Confined by the symmetry, N is an odd number, and M is an even number. To examine width-dependent properties, nine aN|zM heterojunctions with relative smooth edges, namely, a9|z6, a11|z8, a13| z8, a15|z10, a17|z10, a19|z12, a21|z12, a23|z14, and a25|z14, have first been considered in our study. The widest one, a25|z14, is about 3 nm in width, while the narrowest one, a9|z6, is around 1 nm. Furthermore, three groups of heterojunctions aN|z10, a17| zM, and a19|zM with different N or M have been studied to highlight the dependence of the conductance on the width of one side GNR. For each of them, the dangling bonds of carbon atoms at edges are saturated by hydrogen atoms. The geometry optimizations for the central scatting regions, consisting of 122 and 314 carbon atoms for the narrowest and the widest ones, respectively, have been performed using hybrid density functional B3LYP with 6-31G(p,d) basis set as implemented in the Gaussian 09 package.21 During the optimizations, the quadratic convergence was employed, and the residual force
Figure 2. (a) Zero-bias transmission spectra T(E) of aN|zM heterojunctions with N = 9, 11, 13, ..., 25 and M = 6, 6, 8, 8, ..., 14, respectively. From the bottom to the top, each curve is shifted up by 2 units for clarity. The Fermi level is set to zero. (b) The semilog zero-bias conductance (G) of aN|zM heterojunctions as a function of the width (N). (c) The band edges of the aGNR and zGNR in aN|zM heterojunctions with varied width (N), relative to the Fermi level of the zGNRs. The HOMO and LUMO are marked by solid and dotted lines, respectively, while the Fermi level is in red. 12617
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Figure 3. Iso-surface (with iso-value = 0.01) for the wave function of HOMO at the zero bias for heterojunctions (a) a19|z10, (b) a17|z10, (c) a15|z8, and (d) a11|z6, respectively. The dashed line stands for the symmetry axis of the system. At the bottom, the position of the HOMO (solid line) and LUMO (dashed line) of the left and the right electrodes relative to the Fermi level (colored line) of the right electrode are given. The energy gaps of the aGNR electrodes are also given.
was controlled with a tolerance of 106 Hartrees/Bohr. As an example, the optimized structure of a25|z14 is given in Figure 1. After the geometry optimization, we have calculated their electronic transport properties using the ATK package,22 which adopts a nonequilibrium Green’s function method in combination with density functional theory (NEGF-DFT). The Perdew BurkeErnzerhof (PBE) formulation of the generalized gradient approximation (GGA) exchangecorrelation functional is used, together with Double-ζ plus polarization functions (DZP) basis set for the valence electrons, norm-conserving pseudopotentials for core electrons, and a mesh cutoff of 200 Ry.
’ RESULTS AND DISCUSSION Zero-Bias Conductance Oscillation. The calculated zerobias transmission spectra T(E) of GNR-HJs are illustrated in Figure 2(a), which are all asymmetrical with respect to the Fermi level. This originated from the inherent asymmetry of the topologic structures of the junctions since any defects in GNRs are known to affect the symmetrical transmission spectra of perfect GNRs through the introduction of the localization.2326 It can be seen that there is a wide transmission gap that appears
around the Fermi level of a9|z6, a13|z8, a15|z8, a19|z10, a21|z12, and a25|z14, respectively, suggesting a semiconductor behavior in these systems. A transmission peak, on the other hand, with considerable intensity presents the Fermi level of heterojunctions a11|z6, a17|z10, and a23|z12, demonstrating the metallic property with good conductivity. It is clear that the transmission property of the heterojunction depends strongly on the width of the nanoribbon. On the basis of our model systems, we can find that if the width (N) of an aN|zM heterojunction fulfills the condition of N = 6p þ 5 (where p = 1, 2, 3, ...), it should be metallic, while if it follows N = 6p þ 1 or = 6p þ 3 (where p = 1, 2, 3, ...) it is a semiconductor. In other words, the aGNR|zGNR heterojunction can be tuned to be either metallic or semiconducting by controlling the width of the ribbon at the atomic scale. Such a fascinating characteristic of aGNR|zGNR could be useful for making graphene-based electronic devices. The calculated zero-bias conductance (G) of the aGNR|zGNR with different widths is given in Figure 2 (b), which shows a nice oscillating behavior. It is found that the metallic heterojunctions, N = 6p þ 5 (p = 1, 2, 3, ...), have a zero-bias conductance close to one G0, whereas the semiconducting heterojunction has a small zero-bias conductance below 104 G0 contributed from the long tail of all 12618
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Figure 4. (a) The currentvoltage (IV) characteristics of aGNR|zGNR heterojunctions with different widths. The transmission spectra T(E, Vb) of the heterojunction (b) a19|z10 and (c) a17|z10. The Fermi level is set to zero.
Figure 5. Rectification ratio as a function of the bias. The rectification ratio is between the forward current and the backward current.
delocalized conducting channels.30 A precondition for forming the metallic GNR-HJs is that some eigenstates of the left aGNR can match well with that of the right zGNR in energy space. This can improve the transparence of the line defect at the interface and induce highly delocalized states.2528 It is known that aGNR and zGNR have very different electronic structure.1320,3133 The zGNRs are metallic with peculiar edge states on both sides of the ribbon regardless of the widths, while the aGNRs are semiconductor with the width (N) dependent energy gap. Moreover, it is found that when N = 3p þ 2 (p is a positive integral number) the aGNR has the
narrowest energy gap (even predicted to be metallic in the tightbinding model).19,20 It could be expected that when the aGNR in the aN|zM heterojunction has a width N = 3p þ 2 the band offset at the heterojunction should be very small. The frontier orbitals of the left aGNR could then match better with those of the right zGNR to form resonant channels for the electron transport. To verify this, we have plotted the band edges for both sides of the heterojunctions with different width (N) in Figure 2(c). It can be immediately seen that for the width of N = 11, 17, and 23 (N = 6p þ 5) the band gap of the aGNRs is indeed very narrow, and the valence band offset is very small. In this case, the highest occupied molecular orbital (HOMO) is expected to become a resonant-conducting channel. As representative examples, the iso-surface of the wave function for HOMOs of the a19|z10, a17|z10, a15|z8, and a11|z6 junctions at the zero bias are illustrated in Figure 3(a)(d), respectively. Indeed, one can see from the figure that the HOMOs of the a19| z10 and the a15|z8 are localized within the zGNR part due to the orbital mismatch, while the HOMOs of the a17|z10 and the a11|z6 are completely delocalized and spread over the entire heterojunctions as a result of good orbital match. Such a difference in the HOMO clearly explains why the zero-bias conductance of the a17| z10 and the a11|z6 junction is almost one G0 and why the a19|z10 and the a15|z8 are very small. At the bottom of Figure 3, we give the energy gap of the left and right GNR electrodes, plus the positions of the HOMO (solid line) and LUMO (dashed line) relative to the Fermi level of the right electrode. Apparently, the energy gaps in the ribbons a11 and a17 are much narrower than that in the a15 and the a19. Consequently, the valence band offsets in junctions a11|z6 and the a17|z10 are very small but large in the a15|z8 and the a19|z10 heterojunctions. The energy resonances have resulted in perfect delocalization of HOMOs in the a11|z6 and the a17|z10 junctions and the transmission peak appearing at the Fermi level, as shown in Figure 2(a). On the other hand, the 12619
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Figure 6. Semilog of zero-bias transmission spectra of aN|z10 with N = 9, 11, 13, 15, 17, and 19, respectively, and the structure of a “T”-shaped heterojunction a9|z10.
Figure 7. Semilog zero-bias transmission spectra of a17|zM (a) and a19|zM (b) with M = 6, 8, 10, 12, and 14, respectively.
energy mismatching makes the HOMO of the a19|z10 and the a15|z8 localized at the zGNR part. It is clear that the change of the ribbon width can shift relative position of the left and the right GNRs’ orbitals, hence to control the conductivity of the heterojunction. The orbital matching or mismatching is the source of the zero-conductance oscillation. Rectification Behavior. Rectification at the molecular scale is an attractive device function, which was first proposed by Aviram and Ratner.34 To date many experimental studies of the rectification behavior have been carried out for LangmuirBlodgett films,35 self-assembled monolayers,36 and even single molecules37,38 but not yet widely studied for the graphene-based devices.39,40 We have found that our designed aGNRs|zGNRs heterojunctions have pronounced rectifying effects that can be even controlled accurately by the width of the nanoribbon. The calculated currentvoltage (IV) characteristics of the aGNR|zGNR heterojunctions with different widths are summarized
in Figure 4(a). For all junctions, IV curves are asymmetry with striking rectification behaviors. It can be at least concluded that the rectifying is an intrinsic property of the aGNR|zGNR heterojunction, and the rectifying direction can also be tuned by the width of the junction. As for the conductance, the general character of the rectification is oscillating with the width of the ribbon. The rectifier works for the forward current flow in the direction of aGNRzGNR when the width is N = 6p þ 5 (p = 1, 2, 3, ...), and for the backward current flow when the width fulfills N = 6p þ 1 or = 6p þ 3 (p = 1, 2, 3, ...). In other words, one can find the forward rectifying (from þ to ) in the metallic heterojunctions and the backward rectifying in the semiconducting heterojunctions. The width-dependent rectifying effect observed here is very unique, and to the best of our knowledge it has never been reported before. The asymmetry of the IV characteristic could be understood by analyzing the bias-dependent transmission spectra. Figure 4b 12620
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Figure 8. (a) and )b) are the semilog currentvoltage (IV) characteristic and rectification ratio of “T”-shaped heterojunction a17|zM with M = 6, 8, 12, and 14, respectively. (c) and (d) are the Semilog currentvoltage (IV) characteristic and semilog rectification ratio of “T”-shaped heterojunction a19|zM with M = 6, 8, 12, and 14, respectively. The IV curve and rectification ratio of a19|z10 with relative smooth edges have also been plotted for comparison. In (a) and (c) the currents at the negative have been reversed.
and 4c present the transmission spectra T(E, Vb) of heterojunctions a19|z10 and a17|z10 in the region of 0.5 to 0.5 V, respectively. For the semiconducting a19|z10 in Figure 4b, under both the positive and the negative biases, the occupied molecular orbiatls are affected by the voltage more than unoccupied orbitals. The HOMOs move away from the Fermi level under the positive bias but close to the Fermi level under the negative bias, leading to larger current changes for the backward current. For the metallic junction like the a17|z10, it is the LUMOs that are sensitive to the external bias, resulting in the rectifying for the forward current. In a way, the resonance channels can asymmetrically move with respect to the applied bias because of the inherent asymmetry of the heterojunction, which is the root of such rectifying behavior. One can notice in Figure 5 that the rectification takes place at very low bias for the metallic junctions, while it becomes visible at relatively larger bias (>0.2 V) for the semiconducting junctions. The rectification ratio of the heterojunction shows noticeable width dependence with a value of less than 100, as often observed
for single molecular rectifiers.4144 On the basis of the barrier tunneling model, it was suggested that the rectification ratio of a single molecular device should be small (never be greater than 100),45 while recently Andrews et al. suggested that the multiple interference effect can induce very large rectification ratios in the cross-conjugated molecules.46 The GNRs are typical conjugated molecules, and the interference effect should be possible to induce large rectifying effects in some well-designed devices based on GNRs. “T”-Shaped aGNR|zGNR. We can notice from the results of the a19|z10 and the a17|z10 heterojunctions that the electronic characteristic of an aN|zM heterojunction is only dependent on the width of aGNR. In other words, the electron transport properties of the entire aGNR|zGNR junction might be totally controlled by the width of aGNR. To clarify this, we have investigated three groups of “T”-shaped heterojunctions, namely, aN|z10, a17|zM, and a19|zM, in which the width of only one side of the GNR varies. Their zero-bias transmission spectra are collected in Figure 6 and Figure 7, respectively. The general 12621
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Figure 9. Zero-bias transmission spectra T(E) of the ideal GNRs, a11 and z6, and homojunctions, a11|a11 and z6|z6. The curves for the a11| a11 and z6|z6 are shifted up by 5 units for clarity. The Fermi level is set at zero. The energy gap of a11 is about 0.14 eV.
structure of a T-shaped heterojunction is represented by a a9|z10 junction shown in Figure 6 . It is already known that the Fermi level of N-GNR changes with the width N.19,20 We have also shown that in the aN|z10 heterojunctions the HOMOs of the a17 and the z10 are resonant with good orbital matching. Obviously, the HOMO of other junctions with N 6¼ 17 could not match well with the HOMO of the z10, due to the change of the Fermi level. This explains why only the a17|z10 heterojunction has a high transmission peak right at the Fermi level in Figure 6. The a11 also has a narrow energy gap, but the transmission probability near the Fermi level is still quite small in the a11|z10 junction. In this case, the Fermi level of the a11 is shifted up about 0.12 eV with respect to the z10, resulting in the nonresonance between the orbitals of the a11 and the z10 near the Fermi level. Following the same resonance (orbital matching) argument, one can also understand the transmission spectra of the a17|zM and the a19|zM junction series as given in Figure 7. For the results of the a17|zM junctions in Figure 7a, it can be seen that the a17|z14 and the a17|z12 are semiconducting. It is noted that the widths of the z12 and the z14 are larger than that of the a17. The energy position of their HOMO is therefore lower than that of the a17, thus the HOMOs of the junctions a17|z12 and a17|z14 are nonconductive. The a17|z6 and the a17|z8 junctions show obvious metallic behavior because the Fermi levels of z6 and z8 shift up to across over the Fermi level of a17, so that the LUMOs of the a17 can be matched to the HOMOs of the z6 and the z8, and the wider transmission peaks appear around the Fermi levels of the heterojunctions. For the “T”-shaped junctions a19|zM (M = 6, 8, 12, 14), although the Fermi level of the zGNR has changed with the width, it remains to locate in the wide energy gap (0.54 eV) of the a19. In this case, the frontier orbitals of the zGNR are also localized due to the energy mismatch, and only very small transmissions are presented around the Fermi level of the system. It can be concluded that the change of the width of each ribbon can significantly alter the zero-bias transport property in metallic heterojunctions. We have calculated the IV characteristics and rectification ratios of two groups of “T”-shaped heterojunctions, a17|zM and
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a19|zM. The results are presented in Figure 8. To compare the “almost zero” currents around zero bias, the IV curves have been plotted on semilog scale with the negative bias currents reversed. One can immediately notice that all IV curves are asymmetric with intrinsic rectifying property. Most strikingly, a very high rectification ratio can be achieved in semiconducting “T”-shaped a19|zM junctions (M = 6, 8, 12, and 14). It can be as high as 104, which is comparable to that in solid-state rectifiers. Previous studies have already shown that the current rectification can be induced by the asymmetrical electrode materials47 or by the asymmetrical moleculeelectrode contacts,48 with relative small ratios (
