Giant Rectification Ratios of Azulene-like Dipole Molecular Junctions

Jul 25, 2014 - College of Physics and Electronics, Shandong Normal University, Jinan 250014, China. J. Phys. Chem. ... of the molecular junctions. Gia...
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Giant Rectification Ratios of Azulene-like Dipole Molecular Junctions Induced by Chemical Doping in Armchair-Edged Graphene Nanoribbon Electrodes Yang Song, Zhen Xie, Yong Ma, Zong-liang Li, and Chuan-Kui Wang* College of Physics and Electronics, Shandong Normal University, Jinan 250014, China S Supporting Information *

ABSTRACT: Electron transport properties of an azulene-like dipole molecule anchored with carbon atomic chains sandwiched between two graphene nanoribbon (GNR) electrodes are theoretically investigated at the ab initio level. The molecular junctions are constructed with a strategy of modulating symmetry of Bloch wave functions. The chemical doping in an armchair-edged GNR is shown to play a significant role in determining the conductance behavior and rectifying performance of the molecular junctions. Giant rectification ratios up to 104 at low bias voltages are obtained for the molecular junctions with asymmetric arrangement of undoped zGNR and doped aGNR electrodes. The boron (aluminum) dopants in the aGNR electrode induce a better rectifying performance for the molecular junctions than the respective nitrogen (phosphorus) dopants. Moreover, the boron or nitrogen doping is more advantageous than the respective aluminum or phosphorus doping in view of improving rectifying behaviors of the molecular junctions. Taking double doping in the aGNR electrode, we just demonstrate that the double boron-doping displays an improvement of rectifying features in comparison with the single case. The observed results are understood in terms of the transmission spectrum and the molecular projected self-consistent Hamiltonian as well as band structures of the electrodes with applied bias combined with symmetry analyses of Bloch wave functions of the corresponding subbands.

1. INTRODUCTION Single molecule devices with advanced functions have been attracting considerable attention owing to their remarkable electronic properties and their possible applications in integrated circuit areas.1 As analogues to traditional diodes, molecular diodes play an essential role in the formation of integrated circuits. It is observed that a lot of work on molecular rectifiers has been performed in experimental designs2−6 and theoretical predictions.7−11 As one knows, a high quality rectifier is generally characterized by two points. First, it should have a giant rectification ratio, namely, current values are large at one bias direction, whereas they are very small at the other direction. Second, rectifying properties should be fairly stable under a region of bias. At present, the available molecular diodes are not satisfying in view of approaching applicable level. Thus, synthesis of high characteristic molecular diodes and theoretical investigation on their rectifying mechanisms are important tasks to be pursued.3,8,12,13 With the improvement of experimental technology, various kinds of two-dimensional (2D) layered nanomaterials have been formed, which would be helpful for development of molecular electronics. In particular, graphene, showing a vast array of outstanding properties, such as quantum Hall effect,14 peculiar topological behavior,15 spontaneous magnetization,16 and zitterbewegung characteristics,17 was used to fabricate lots of prototype devices.18−21 Furthermore, various approaches © 2014 American Chemical Society

were developed to fabricate graphene nanoribbons (GNRs) on the basis of graphene. GNRs’ electrical properties were found extremely sensitive to their edge geometries, namely, zigzag edged graphene nanoribbons (zGNRs) are shown to be metallic, whereas those ribbons with armchair edges (aGNRs) generally display as semiconductors with energy gaps shrinking with the ribbon widen.22−24 These nanostructures are potential building blocks for molecular devices, displaying various interesting physical properties, such as rectification,12,25 switching,12,26 negative differential resistance (NDR),8,27−29 spin filtering,26,27 and field-effect characteristic.30,31 When GNRs are used as electrodes, their electronic symmetry plays a critical role on charge transport properties. Namely, the tunneling between them will be forbidden if two subbands have an opposite symmetry.32−34 Thus, modifying electronic symmetry of the two subbands is expected to be a valid strategy for controlling charge transportation of a molecular device. As one of the most frequently adopted ways, chemical doping in GNRs was found to modify their electronic structures effectively, and the electronic transport properties of devices based on doped GNRs are correspondingly tuned.25,35−38 Therefore, one would design molecular Received: May 6, 2014 Revised: July 17, 2014 Published: July 25, 2014 18713

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the periodic doping adds a new energy subband locating inside the energy gap. It is understandable that the symmetry of the corresponding wave functions is closely related to position of the dopants. On the basis of density functional theory (DFT) calculation and nonequilibrium Green’s function (NEGF) technique, the electronic transport properties of these molecular devices are investigated. We present a most interesting result that the giant rectifying behaviors with rectification ratios up to the order of 105 can be obtained by applying doping to the aGNR electrodes. Moreover, in view of the rectifying performance, the boron doping in the aGNR is a more useful method than the nitrogen doping. In addition, improvement of rectifying behaviors is found in the configuration with double boron-doping. The transmission spectra and band structures are analyzed to give insight into different rectification properties of junctions, which demonstrates that the overlapping between the even parity subbands of the electrodes is a dominating factor for deciding the rectifying performance.

Figure 1. Typical molecular junctions with different electrodes: blue, pristine zGNR; yellow, single atom doped aGNR; fuchsia, pair atoms doped aGNR. (a) Molecular junctions with symmetric electrodes, denoted as S1, S2, and S3. (b) Molecular junctions with a zGNR electrode and a single-doped aGNR electrode, denoted as B1, N1, A1, and P1 with boron, aluminum, nitrogen, and phosphorus atoms, respectively, and B2 (N2) with exchanged electrodes in B1 (N1). (c) Molecular junctions with a zGNR electrode and a double-doped aGNR electrode, denoted as B3 and N3 with boron and nitrogen atoms.

2. THEORETICAL MODEL AND CALCULATION METHOD The typical molecular junctions, consisting of an azulene-like molecule anchored with carbon atomic chains between two GNR electrodes, are illustrated in Figure 1. In detail, two kinds of symmetric arrangement of electrodes, one is with undoped zGNRs and the other is with doped aGRNs, are considered at first (Figure 1a). Then, the combination of metallic zGNR and doped aGNR electrodes is proposed for constructing molecular junctions (Figure 1b). Four elements in groups III and V, boron, aluminum, nitrogen, and phosphorus, are used as dopants, and they are located on the center positions, in which one center carbon atom per two carbon unit cells is substituted by a doping atom. In this doping configuration, even parity of wave functions of the impurity-subband under the central xz midplane mirror operation is observed. Moreover, substitution of two carbon atoms per two carbon unit cells in an aGNR electrode by two B or N atoms is considered in Figure 1c. As shown in Figure 1, the entire molecular junctions are divided

devices with specific functions by using doped GNRs as electrodes. As an asymmetry molecule, the azulene-like molecule constructed by fusing a naphthalene between the heptagon and pentagon rings has been reported to exhibit obvious rectification performance with gold electrodes.39,40 Moreover, when GNRs serve as electrodes, carbon atomic chains were expected to be better interconnects than traditional anchoring groups.11,22,41,42 Motivated by the discussion above, we design a molecular junction constructed by an azulene-like molecule capped with carbon atom chains between two GNR electrodes in this work. To obtain obvious rectifying characteristics, the aGNR electrodes are doped by elements of groups III and V, where

Figure 2. Current−voltage curves for molecular junctions S1(a), S2(b), and S3(c), and the corresponding rectification ratio curves for S1(d), S2(e), and S3(f). 18714

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Figure 3. Bias-dependent transmission spectra and band structures of both electrodes for S1 at ±0.3 V (a, b), S2 at ±0.4 V (c, d), and S3 at ±0.4 V (e, f). The dashed lines in the transmission spectra indicate the bias window, and the triangle and square symbols point to MPSH eigenvalues around the Fermi level.

approximation (GGA) in calculating carbon based materials.45 Numerical atomic orbitals are employed as the basis set, and the core electrons are represented by Troullier−Martin-type norm-conserving pseudopotentials for the computation.46 A single-ζ plus single polarization (SZP) basis set is adopted for all atoms tested in previous work.33 The Brillouin zone has been sampled with a 1 × 1 × 100 k-point grid using the Monkhorst−Pack scheme. An energy shift parameter of 100 meV is used for generating the cutoff radii of the pseudoatomic orbitals, and a 300 Ry mesh cutoff is set for the grid sampling to achieve a balance between the calculation time and the accuracy. The convergent criterion for the density matrix is chosen as 10−4. The current through the junctions is calculated by the Landauer−Büttiker formula, which is written as

into three regions, a left electrode, an extended molecule, and a right electrode. The extended molecule includes the carbon atomic chains anchored in an azulene-like molecule and several layers of GNRs, in which the screen effect is taken into account. Considering the carbon chain hybridization influence on molecular junction structure,11 we choose a three-carbonatom-chain anchoring group for the zGNR electrode and a twocarbon-atom-chain anchoring group for the aGNR electrode. The zGNR electrode is simulated by a unit cell with six layers of carbon atoms, and the aGNR one is modeled by a four layered unit cell. The electrodes are computed with periodic boundary conditions to ensure their semi-infinite feature. In this work, the geometric and electronic structures of devices are calculated in the SIESTA code.43 The corresponding electronic transport properties are investigated in the TranSIESTA module.44 The exchange−correlation potential resorts to the local density approximation (LDA), which have been proved to be a better choice than the generalized gradient

I= 18715

2e h

∫ T(E ,V )[f (E − μL ) − f (E − μR )] dE

(1)

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consider the case of doped aGNR electrodes. In view of comparison, the molecular junction with symmetric zGNR electrodes is also considered. Electronic transport properties of the molecular junctions shown in Figure 1a are presented in Figure 2. For the purpose of characterizing the rectifying behaviors of the devices, we define the bias dependent rectification ratio as RR(V) = |I(V)/I(−V)|. From Figure 2, one can notice that these molecular junctions display rectifying behavior. Molecular junctions with B- and N-doped aGNRs not only have larger current values but also show more obvious rectifying behavior. The maximum rectification ratios (MRR) of S1, S2, and S3 are 3.4, 12.5, and 19.6, respectively, presenting a larger MRR compared to those junctions with gold electrodes.40 Although the MRR of the N-doped junction is larger than that of the B-doped one, the latter has a broader rectifying region in the calculated bias regime. Furthermore, inversion of the rectifying direction of S2 and S3 is observed. To give insight into different rectification properties of junctions with symmetric electrodes, we plot transmission spectra under the bias related to the MRRs and band structures of both semi-infinite electrodes in Figure 3. For each studied molecular junction, there are two frontier molecular orbitals around the Fermi energy analyzed by a molecular projected self-consistent Hamiltonian (MPSH) calculation, which are responsible for the electronic transmission under low bias voltages. The spatial distributions of these orbitals are shown in Figure 4a. It is observed that orbital h labeled with a green triangular symbol and orbital l with a red square symbol have even (π*) and odd (π) parities under the central xz midplane mirror operation. Moreover, orbital h shows a well delocalized feature, serving for a charge transfer channel with higher conductivity, and orbital l localized on the four ring backbone provides lower conductivity. Thus, we just focus on orbital h in the following analysis. Accordingly, tunneling between the electronic states with even parities in both electrodes is allowed. In Figure 4b, we give the isosurface plots of the Γ-point wave functions of two subbands (π* and π) of the zGNR electrodes, and one impurity subband (1π*) and two subbands (2π and 3π*) of the B- and N-doped aGNR electrodes. These subbands are around the Fermi energy and are responsible for the charge transportation in the studied bias regime. It is clearly demonstrated that the impurity subband of the B-doped/ N-doped aGNR electrode is near the valence/conduction band

Figure 4. (a) Spatial distribution of the two frontier molecular orbitals noted in transmission spectra. (b) Isosurface plots of Bloch wave functions of subbands for different GNR electrodes. The dotted line is the symmetry axis of mirror operation.

where T(E,V) is the bias-dependent electron transmission coefficient defined as T(E,V) = Tr[ΓLGMΓRG†M], where GM is the retarded Green’s function of the extended molecule, ΓL(R) is the coupling matrix between the scattering region and the left (right) electrode, f is the Fermi−Dirac distribution function, and μL(R) is the electrochemical potential of the left (right) electrode.

3. RESULTS AND DISCUSSION 3.1. Symmetric Arrangement of Boron- or NitrogenDoped aGNR Electrodes. The current of molecular junctions with aGNR electrodes is expected to be very small in the low bias region because of their semiconductor features. We thus

Figure 5. Current−voltage curves for molecular junctions B1 (a), B2 (b), N1 (c), and N2 (d), and the rectification ratio curves for B1 (e), B2 (f), N1 (g), and N2 (h). 18716

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because boron/nitrogen atoms are acceptor/donor impurities. When a bias voltage V is applied, we assume that the energy bands of the left (right) electrode are shifted by eV/2 (−eV/2). The bias-dependent transmission spectra of S1 at +0.3 and −0.3 V are given in Figure 3a,b, respectively. It is noted that there exists fluctuation of the Van Hove singularity13 in the energy bands of zGNRs, which is attributed to interaction between the edge states on one side and those on the other side. As one knows, the edge states decay gradually from the edge to the inner in zGNRs15 thus, interaction becomes more obvious as the zGNRs are narrower. When a bias is applied, π*(π) subbands of the zGNR electrodes simultaneously lie in the bias window because of the fluctuation of Van Hove singularity. As a consequence, charge transmission may be possible. As shown in Figure 3a,b, one can see a larger transmission peak under the positive bias compared with that at the negative bias. The reason is that molecular orbital h at positive bias is much closer to the tunneling energy around the Van Hove singularity, resulting in a larger tunneling probability. In Figure 3c,d for S2, one can see that the 1π* subband for each B-doped aGNR appears in the bias window. Because molecular orbital h locates out of the overlapping region of the two 1π* subbands, the transmission probability is weak at the positive bias. However, for the negative bias, h is inside the overlapping region, and the transmission probability is accordingly large, showing inversion of the rectifying direction compared to that for S1. The similar discussion goes to the case of N-doped aGNRs as shown in Figure 3e,f. 3.2. Asymmetric Arrangement of zGNR and SingleDoped aGNR Electrodes. Asymmetric arrangement of electrodes was demonstrated to enhance rectification behaviors of molecular junctions. Thus, we construct molecular junctions with the combination of undoped zGNR and single-doped aGNR electrodes and study their charge transport properties. In Figure 5, we present the current−voltage (I−V) characteristics and the bias dependent rectification ratios for B1, B2, N1, and N2. It is clear that obvious rectifying behaviors are observed in these curves. The currents at positive bias voltages are markedly larger than those at negative bias voltages for B1 and N1. The reverse situation is for B2 and N2 because the electrodes are interchanged. As a result, giant MRRs up to 104 are obtained in these junctions. Especially, the giant rectifying characteristic is observed in a wider bias range for the molecular junctions with B doping. It is clear that the molecular junction with the combination of undoped zGNR and aGNR electrodes has no current at low bias regime because of the semiconductor feature of aGNR. It is thus concluded that the large current values and obvious rectifying behaviors originate from the chemical doping. To illustrate the mechanism of the obvious rectifying behavior, taking B1 and N1 as examples, we present the bias dependent transmission spectra and band structures of both left and right electrodes at the bias voltages corresponding to their MRRs in Figure 6. From Figure 6, it is found that the half-filled impurity-band 1π* cutting the Fermi level induces significantly different transmission spectra. At 0.9 V in Figure 6a for B1, one can see that 1π* of the left electrode has partly overlapping with π* of the right electrode in the bias window. As a result, there exists a high transmission peak because of location of molecular orbital h inside the overlapping region. However, there is no overlapping between subbands with the even parity in the bias window (−0.45, +0.45 V) as shown in Figure 6b at −0.9 V, resulting in zero transmission probability. Moreover, one can see that overlapping between subbands with the even

Figure 6. Bias-dependent transmission spectra and band structures of both electrodes for B1 at ±0.9 V (a, b) and N1 at ±0.4 V (c, d). The dashed lines in the transmission spectra indicate the bias window, and the triangle and square symbols point to MPSH eigenvalues around the Fermi level.

parity in the bias window is absent for a range of applied negative bias. Therefore, the giant rectifying characteristic of the molecular junctions with B-doping is kept in a wide bias region. For the case of N-doping in Figures 6c at 0.4 V, one can see a high transmission peak in the bias window (−0.2, +0.2 V). Nevertheless, the transmission probability in the bias window (−0.2, +0.2 V) as shown in Figures 6d is zero because there is no overlapping between π* subbands of the electrodes. The position of the impurity-subband in the energy gap is an important factor for influencing the rectifying behavior of these molecular junctions. For the B-doped aGNR electrode, the impurity-subband 1π* is near the valence bands. As a positive bias voltage is increased, the subband 3π* would enter into the bias window, resulting in an increased current. For the N-doped aGNR electrode, the impurity-subband 1π* is near the

Figure 7. Current−voltage curves for molecular junctions A1(a) and P1(b), and the corresponding rectification ratio curves. 18717

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aluminum or phosphorus doping is disadvantageous to improve the rectifying behavior of the molecular junctions. 3.3. Asymmetric Arrangement of zGNR and DoubleDoped aGNR Electrodes. The recent studies have shown that nitrogen dopants in pairs of neighboring atoms of the same sublattice are possible.38,47 We thus consider doping configurations of substitution of two carbon atoms per two carbon unit cells in an aGNR electrode by two B or N atoms as shown in Figure 1c, ensuring wave functions of the impurity-subband have even parity under the central xz midplane mirror operation. In Figure 8, we present the I−V curves of B3 and N3. It is clear that B3 has a better rectifying feature than N3. Furthermore, in comparison with B1, B3 has a larger MRR and a more stable rectifying performance in a bias region, indicating improvement of rectifying behaviors for the configuration with double B-doping. However, the double N-doping in N3 does not show a better improvement of the rectifying performance in comparison with the single N-doping in N1. In Figure 9, we further give the transmission spectra and band structures of both left and right electrodes at the bias voltages corresponding to their MRRs. Two impurity bands (1π and 2π*) are observed in Figure 9 due to the periodic double doping. It is noted that 1π has little contribution to the transmission probability. One can also see that the parity of the first valence or conduction subband is changed from odd to even as the chemical doping is taken from single to double. This variation for B3 would be advantageous for improving the rectifying performance. At 0.9 V in Figure 9a for B3, one can see that 2π* and 3π*of the left electrode has partly overlapping with π* of the right electrode in the bias window, which brings an obvious transmission spectra through the molecular orbital h. Nevertheless, zero transmission probability is observed as shown in Figure 9b at −0.9 V because the overlapping between subbands with the even parity in the bias window (−0.45, +0.45 V) is absent.

Figure 8. Current−voltage curves for molecular junctions B3(a) and N3(b), and the corresponding rectification ratio curves.

conduction bands. Therefore, the subband 3π* cannot locate inside the bias window for any value of the positive bias voltage. In short, it is understandable that B1 has better rectifying performance than N1. In Figure 7, we also give electron transport properties of Al- and P-doped junctions to show the role playing by other elements in groups III and V. In view of the rectifying behavior, it is observed that A1 has a better performance than P1. In detail, the RR for A1 still takes 104 and is in a wide bias region, whereas the RR for P1 decreases to 103 and locates in a narrow bias region. The results seem to demonstrate that, in comparison with the respective boron or nitrogen doping, the

Figure 9. Bias-dependent transmission spectra and band structures of both electrodes for B3 at ±0.9 V (a, b) and N3 at ±0.9 V (c, d). The dashed lines in the transmission spectra indicate the bias window, and the triangle and square symbols point to MPSH eigenvalues around the Fermi level. 18718

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Turning to the case of N-doping as shown in Figure 9c at 0.9 V, we see that there only exists overlapping between 2π* and π*. As a result, there exist transmission probabilities in the bias window. But, at −0.9 V in Figure 9d, the transmission probabilities in the bias window are zero with the same reason as discussion above.

4. CONCLUSION We have proposed a series of molecular diodes constructed by an azulene-like dipole molecule embedding in a carbon atomic chain sandwiched between two GNR electrodes. The influence of chemical doping on transport properties of the molecular diodes has been investigated. The I−V characteristics of the molecular junctions with asymmetric arrangement of undoped zGNR and doped aGNR electrodes exhibit marked rectifying behaviors, which are dependent on the property and the concentration of the dopants. The boron (aluminum) dopants give rise to a better rectifying performance than the respective nitrogen (phosphorus) dopants. Moreover, the molecular junction with the double B-doping displays advantaged rectifying behaviors in the interesting bias regime, with giant rectification ratios and stable rectifying performance. The position of the impurity-subband in the energy gap, and symmetry of the Bloch wave functions and the molecular orbitals are important factors for determining the rectifying behavior of these molecular junctions. This work provides a method to significantly modulate the rectifying behaviors of molecular diodes by chemical doping in an armchair-edged GNR.

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ASSOCIATED CONTENT

S Supporting Information *

Band structures of the electrodes and bias-dependent transmission spectra. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*C.-K. Wang. Phone: +86 531 86180892. E-mail address: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (Grant No. 11374195), and the Nature Science Foundation of Shandong Province (Grant No. ZR2013FM006). Part of the computation is carried on the HPC supported by CETV and guoshi.com.

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REFERENCES

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dx.doi.org/10.1021/jp504448n | J. Phys. Chem. C 2014, 118, 18713−18720