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Rectification inversion in oxygen substituted graphyne–graphene-based heterojunctions† Wen-kai Zhao,a Bin Cui,a Chang-feng Fang,b Guo-min Ji,a Jing-fen Zhao,a Xiang-ru Kong,a Dong-qing Zou,a Xiao-hui Jiang,bc Dong-mei Lia and De-sheng Liu*ab Current rectification is found in oxygen-substituted zigzag graphyne nanoribbon/hydrogen-terminated
Received 24th October 2014, Accepted 2nd December 2014
zigzag graphene nanoribbon heterostructure junctions, from the application of nonequilibrium Green’s
DOI: 10.1039/c4cp04859h
the number and location of oxygen atoms in the zigzag graphyne nanoribbon parts, and the rectification
function formalism combined with density functional theory. This behavior could be tuned by varying direction could be reversed due to the parity limitation tunneling effect. Moreover, an obvious negative
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differential resistance behavior is found and may be explained by two different mechanisms.
1. Introduction Investigations on molecular electronic devices have attracted increasing attention and have uncovered several intriguing phenomena and important properties, such as negative differential resistance (NDR),1–4 rectifying behavior,5–7 field-effect characteristics,8–11 and electronic switching properties.12–14 Molecular rectifiers, in particular, have been attracting great attention because they are amongst the most important electronic elements in the design of modern logic and memory circuits. Since Aviram and Ratner proposed a molecular rectifier based donor–acceptor (D–A) that could function as a diode,15 enormous theoretical and experimental efforts have been focused on molecular rectifiers.5–7 From a theoretical viewpoint, any asymmetric junctions may result in rectification. Based on this principle, analogues of metal–semiconductor junctions can be designed as rectifiers. Recently, the two-dimensional carbon allotropes graphene and graphyne have attracted considerable interest and some excellent properties of zigzag graphene nanoribbons (ZGNRs) and zigzag graphyne nanoribbons (ZGYRs) have been discovered.16–20 For instance, Son et al. proposed that ZGNRs are half metallic,17 and Pan et al. predicted that ZGYRs are semiconductors with a band gap of about 1.0 eV.20 The electronic characteristics of a system combining ZGYRs and ZGNRs could satisfy the needs of a rectification model. Although the synthesis of graphyne is still on a
School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, People’s Republic of China. E-mail: [email protected] b Department of Physics, Jining University, Qufu 273155, People’s Republic of China c College of Physics and Engineering, Qufu Normal University, Qufu 273155, People’s Republic of China † Electronic supplementary information (ESI) available. See DOI: 10.1039/ c4cp04859h
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the way, approaches to fabricate its substructures have been developed.18,21 Fortunately, Li et al. have successfully synthesized graphdiyne, which belongs to the same family, on a copper substrate via a cross-coupling reaction using hexaethynylbenzene.22 In addition, first-principles calculations have shown that graphyne is more stable than graphdiyne.18 These two points suggest that graphyne is the more likely to be synthesized in the near future. Moreover, it is well known that the presence of oxygen is widespread and it possesses a similar radius to the carbon atom. The zigzag edges preferred by hydrogen atoms are most likely to be substituted by oxygen atoms.23,24 As a consequence, it is possible to fabricate oxygen-substituted ZGYR/hydrogen-terminated ZGNR heterostructures (O-ZGYR/H-ZGNRs). In this paper, we utilized density-functional theory (DFT) and nonequilibrium Green’s function (NEGF) to investigate how oxygen substitution can affect the electronic transport property of the ZGYR/ZGNR heterostructures. The content of the paper is divided into three parts as follows. The theoretical model and computational method are reported in Section 2. Section 3 contains our results and discussions. Finally Section 4 gives the conclusions. In addition, the width effect is briefly considered in Section S2 (ESI†).
2. Model and method Fig. 1 displays the schematic diagrams of the transport systems of the oxygen-substituted ZGYR/hydrogen-terminated ZGNR heterostructures. The geometric features of the oxygen-substituted ZGYRs are shown in Section S1 (ESI†). The ZGYRs and ZGNRs are joined by acetylenic chains, as the acetylenic chain can connect hexatomic rings flexibly and form various hybrid structures experimentally.25 All of the systems were optimized using the Atomistix
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Fig. 1 Schematic diagrams of the two-probe systems. The rectangular areas indicate the left (L) and right (R) electrodes, between which is the central scattering region. The red, black and gray spheres represent oxygen, carbon and hydrogen atoms, respectively.
Toolkit (ATK) program package until the absolute value of the force acting on each atom was less than 0.05 eV Å1. The four cases considered here are denoted A, B, C, and D, which correspond to the different substitution positions of oxygen. The unsubstituted system is labeled as O. The purpose of this study was to provide a necessary understanding of the edge oxidation effects on the electronic transport properties of the heterostructure junction. The quantum transport calculations were performed using the ATK software package based on DFT combined with NEGF formalism.26,27 To improve calculation precision, a double-z plus polarization (DZP) basis set was used for all atoms. Norm-conserving Troullier–Martins pseudo-potentials were used to describe the core
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electrons.28 The exchange–correlation potential was described by the Perdew–Zunger (PZ) parameterization of local density approximation (LDA) function. The Brillouin zone was sampled with 1 1 100 points within the Monkhorst–Pack K-point sampling scheme, and the mesh cutoff was chosen to be 150 Ry. The current ¨ttiker formula:29 was calculated from the Landauer–Bu IðVÞ ¼
ð 2e dETðE; VÞ½ f ðE mL Þ f ðE mR Þ h
where mL and mR are the electrochemical potentials of the left eV eV and right electrodes, mL ¼ EF ; mR ¼ EF þ , and EF is 2 2
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the Fermi energy of the system which was set to be zero in our calculations. The energy region, [mL,mR], that contributes to the total current integral is referred to as the bias window. T(E,V) is the transmission spectrum. The transmission spectrum covers the integrated transmission coefficients T(E,V,k) over the 2D Brillouin 1Ð zone of the incident wave vectors k, TðE; VÞ ¼ ~ dkTðE; V; kÞ, O O where O is the area of the reference unit cell surface. f (E m) = 1/{1 + exp[(E m)/(kBTtemp)]} is the Fermi–Dirac distribution function, kB is Boltzmann constant, and Ttemp is the temperature. Details of the calculation method are available in the literature.30,31
3. Results and discussion The current–voltage (I–V ) characteristic curves of the two-probe systems in the bias region of [0.5 V, 0.5 V] are shown in Fig. 2(a). All of the I–V curves of oxygen-substituted systems exhibit asymmetric features. For a clearer view, the rectification ratio, a ratio of the currents under positive and negative biases
Fig. 2 (a) Refers to the current–voltage curves of the two-probe systems. The rectification ratio R(V) is shown in (b).
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with the same voltage magnitude, was calculated by R(V) = I(V )/|I(V )| as shown in Fig. 2(b). The forward (backward) rectification is defined according to the rectification ratio R(V ) > 1[R(V ) o 1]. For system O, the current is almost zero in the bias range of [0.5 V, 0.5 V]. No rectification occurred in system O, though the structure of the system is asymmetric. This illustrates that an asymmetric structure does not always lead to rectification. For system A, the current is about 2 mA under positive voltages and is almost zero under negative voltages. It displays a forward rectifying performance and shows that the rectification ratio stabilizes at around 10. For system B, the current is always at 1 mA under a positive voltage. Under negative voltages, one NDR response appears at a bias voltage of 0.2 V. Subsequently, the current increases gradually when the bias is beyond 0.2 V. It shows an obviously asymmetric current under positive and negative biases, and the rectification direction is reversed compared with system A. In the case of system C, the current decreases when the negative voltage is enhanced, resulting in an obvious NDR peak in the bias region from 0.1 V to 0.5 V. Interestingly, for system D, the rectification direction is inversed within the bias region of [0.3 V, 0.4 V]. Moreover, the system also shows NDR behavior in the bias range of [0.3 V, 0.5 V]. As we can see, the rectifying performance is different for A to D when different oxygen-substitution occurs on the ZGYRs. To understand the observed I–V characteristics and rectification behavior, we obtained transmission spectra under various bias voltages for each system, shown in Fig. 3, where the Fermi levels are set to zero. Starting with system O at zero bias voltage, there were two broad transmission peaks located in the energy region of [1 eV, 1 eV], and both were far from the Fermi level. When a negative bias was applied, the two broad transmission peaks moved in the direction of higher energy. For a positive bias, a contrary movement for the two transmission peaks occurred in the direction of lower energy. As the voltage increased, none of the transmission peaks could enter the bias window, and did not contribute to tunneling path of the electron. Therefore, no current and rectification behavior was observed in system O. For system A, there was a transmission peak at the Fermi level, and this moved in the direction of lower energy under a positive voltage, and its area only changed slightly. Therefore, the current magnitude of system A under a positive bias was almost constant. When negative biases were applied, the transmission peak near the Fermi level greatly diminished, leading to a negligible current. Therefore, a forward rectifying response was observed. In addition, it was interesting to note that asymmetric Fano-type resonances were displayed at the energy of 1.0 eV in the bias range of [0.3 V, 0.3 V] because of the superposition of a quasi-localized state on a delocalized state.32 For system B, at zero bias, there was also a transmission peak at the Fermi level. Under a positive bias, the transmission peak moved in the direction of lower energy and its area remained constant, after a small decrease, at a bias of 0.1 V. As a result, the positive current remained stable. When a bias of 0.1 V was applied, one transmission peak was present (marked as b1) which was located within the bias window and contributed to the current. At a bias voltage V = 0.2 V,
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Fig. 3
Transmission spectra of all systems at various biases. The red dashed lines indicate the bias window.
the magnitude of the transmission peak b1 decreased. At the same time, another transmission peak (marked as b2) started to move into the window and contribute to the current. However, the summation of the peaks b1 and b2 were smaller in area than that of peak b1 at a bias 0.1 V. Therefore, a NDR response was observed. As the bias increased further, the peak b2 increased and moved further into the bias window. Consequently, the current
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value at the negative bias became larger than that under the positive bias, and hence a backward rectification was observed. The behaviour of system C can be understood by a similar explanation. In the case of system D, at a positive bias, a transmission peak appeared within the bias window in the bias range of [0.1 V, 0.3 V] and disappeared in the bias range of [0.4 V, 0.5 V].
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Under a negative bias, in the bias range of [0.1 V, 0.3 V], the transmission peaks were located out of the bias window. This led to forward rectification. As the bias increased further, a small transmission peak emerged near to the Fermi level and this contributed to the current. As a result, a backward rectification was observed. Namely, rectification inversion was observed. In order to understand the mechanism of observed rectification, we present the energy band structures and densities of states (DOSs) of the left and right electrodes of all of the systems in Fig. 4. The nature of the transport properties is due to the energy band structure and DOS of left and right electrodes. In Fig. 4(a), for the left electrode of system O, its energy band gap is about 1 eV, in the middle of which the Fermi level lies. As a result, a transmission gap appears in the same energy range in the transmission spectrum as shown in Fig. 3O. When a positive bias (negative bias) is applied, the energy band of the left electrode moves in the direction of lower energy (higher energy), but the band gap always covers the bias window. Therefore, the magnitude of the I–V curve is almost zero in the calculated bias
Fig. 4 (a) The calculated energy band structure of the left and right electrodes for all of the systems. O–D stand for the energy band structure of the left electrode. ZGNR stands for the energy band structure of the right electrode. (b) The calculated DOSs of the left and right electrodes for all the systems.
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voltage range. Moreover, there is no rectification behavior because of the symmetrical distribution of the energy band structure according to the Fermi level. We can infer that an asymmetrical distribution energy band structure may be the origin of the rectifying behavior, rather than the asymmetrical geometry structure. For the A and B systems, one can see that the energy band of the left electrode has a large variation in comparison with system O. In detail, four subbands (a1, b1, a2 and b2) arise in the vicinity of the Fermi level due to the interaction of the oxygen 2p state and the carbon backbones of the ZGYRs. The a1, b1 and b2 subbands can provide paths for electron tunneling from the left electrode to the right electrode, because the peaks of the DOS (see Fig. 4(b)) of the three subbands are broad. As a result, a broad transmission peak emerges near the Fermi level as shown in Fig. 3(A) and 3(B). However, for the a2 subband, the broadening of DOS is weakly (shown in Fig. 4(b)) and it cannot provide an effective electron tunneling path. Therefore, the transmission peak of system A nearly disappears in the bias range of [0.5 eV, 0 eV] compared with system B. When a positive bias is applied, the energy band of the left electrode moves in the direction of lower energy. There is only one subband (a1, b1) near the Fermi level which contributes to the current. For a negative bias, the energy band of the left electrode moves in the direction of higher energy. The a2 and b2 subbands begin to move into the bias window. Because the a2 subband cannot provide an effective electron tunneling path, the negative current is very low for system A. Therefore, a forward rectification behavior is observed in this system. On the contrary, in system B, the b2 subband can provide an effective electron tunneling path, which leads to the current under the negative bias being larger than that under the positive bias, and hence a backward rectification is observed in this system. For system D, in order to explain the rectification inversion, a series of isosurface plots are shown in Fig. 5 to depict the G-point Bloch wave functions of the d1-, d2-, d3- and d4-subbands of the left electrode. Here, the electrode geometrical structures possess mirror symmetry under the xz midplane mirror operation.
Fig. 5 Isosurface plots of the G-point Bloch wave functions of d1-, d2-, d3- and d4-subbands of the left electrode of system D. Different colors represent different phases.
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In accordance with their symmetric geometry, the d1- and d3-subbands have even parity, and the d2- and d4-subbands have odd parity for the left electrode. For the right electrode, the p*-subbands have even parity, and the p-subbands have odd parity. When a bias of 0.2 V is applied, as shown in Fig. 6(a), electrons from the right electrode p-subband cannot tunnel to the left electrode d1-subband because tunneling between two opposite parities is forbidden.16 As a result, the magnitude of the transmission near the Fermi level is almost zero. However, there are still some transmissions at 0.1 eV because of the coupling of the p*–d1 subbands. At a bias of 0.2 V, there are still some transmissions at 0.1 eV because of the coupling of the p*–d3 and p–d2 subbands. While, the d3- and d2- subbands near the G-point are flat, they are just localized. It cannot provide an effective electron tunneling path, and hence a forward rectification response is observed. When the bias is increased up to 0.4 V, as shown in Fig. 6b, there is only p–d1 coupling in the bias window, which leads to zero transmission. On the other hand, the d3–p* coupling can lead to a weak
Fig. 6 Band structures of both the left and right electrodes for system D: at (a) 0.2 V and (b) 0.4 V. The Fermi level is set to be zero. The dashed lines represent the electrochemical potentials of the left and right electrodes.
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transmission peak at the Fermi level. Therefore, a rectification inversion is observed. The NDR feature has also been found in the B and C systems which belong to another type with a distinct mechanism to system D, and we mainly discuss system C as a representative example. Commonly, the coupling of electronic states from the two ends of the central scattering region play an important role in the electronic transport. The maps of the energy-dependent local density of states (LDOS)33 could depict a direct image of the coupling of states from the two ends and further the electronic path of the central scattering region according to the energy space under a certain bias voltage. At biases of 0.1 V and 0.3 V, the maps of the LDOS are shown in Fig. 7(a) and (b), respectively, in which the horizontal axis shows the horizontal position (the z coordinate of the real space) of the central scattering region, and the vertical axis shows the energy of the electrons. The LDOS is averaged in the plane perpendicular to the current flow,
Fig. 7 The energy-dependent local density of states of system C at a bias of (a) 0.1 V and (b) 0.3 V. The LDOS is averaged in the plane perpendicular to the current. The blue and red colors represent regions of low and high density of states, respectively. The horizontal axis represents the length of the central scattering region. The bias window is indicated by black lines.
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and colors indicate the scale of the density of states. Blue and red colors represent the low and high values, respectively. When the bias is 0.1 V, as shown in Fig. 7(a), the electron density is almost distributed uniformly over the central scattering region within the bias window. As a result, a transmission peak appears at the Fermi level. When the bias voltage is increased, as shown in Fig. 7(b), the energy of the incidence states of the left electrode increases and that of the right electrode decreases, and the original transmission channel disappears gradually within the bias window. Therefore, a NDR response is observed. To investigate the underlying physical reason for the NDR behavior of system C, we depicted the projected density of states (PDOS) of the central scattering region of the left and right parts in Fig. 8. There is one wide PDOS peak near 0.05 eV which stems from the c1 and c2 subbands of the left electrode (see Fig. 4(a)). Meanwhile, there exists one wide PDOS peak near 0.05 eV derived from the edge state of the graphene nanoribbon. When the bias is increased to 0.3 V, the two PDOS peaks near the bias window move away from the Fermi energy, and the overlap between them is reduced. Because this type of NDR does not originate from parity limitation tunneling through the junction, and it is not large enough, systems B and C display NDR effects.
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However there is not a significant rectification inversion such as that shown in system D.
4. Conclusions In summary, we have investigated the electronic transport properties of oxygen-substituted ZGYR/hydrogen-terminated ZGNR heterostructures. The calculations show that the asymmetric structure does not always lead to rectification behavior. Asymmetrical energy band structure is the origin of the rectifying behavior. The rectification direction is sensitive to the position and number of oxygen atoms in the ZGYRs, and the energy band structure and DOSs help to explain the phenomenon. Moreover, a parity limitation tunneling effect can lead to obvious rectification inversion which may be used to design a molecular rectifier. The B, C and D systems show a NDR effect, and the mechanism of NDR has been explained. These findings may be useful for the application of ZGYR/ZGNR-based heterostructure molecular devices.
Acknowledgements This work was supported by the Natural Science Foundation of China (Grant Nos. 11374183, 11404188 and 11404141), the Natural Science Foundation of Shandong Province (Grant No. ZR2012AQ018) and the Doctoral Fund of Ministry of Education of China (Grant No. 20130131110007).
References
Fig. 8 The density of states is projected (PDOS) onto the corresponding two parts of the central scattering region under the biases of 0.1 V (a) and 0.3 V (b). The two horizontal dashed lines highlight the bias window.
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Rectification inversion in oxygen substituted graphyne–graphene-based heterojunctions† Wen-kai Zhao,a Bin Cui,a Chang-feng Fang,b Guo-min Ji,a Jing-fen Zhao,a Xiang-ru Kong,a Dong-qing Zou,a Xiao-hui Jiang,bc Dong-mei Lia and De-sheng Liu*ab Current rectification is found in oxygen-substituted zigzag graphyne nanoribbon/hydrogen-terminated
Received 24th October 2014, Accepted 2nd December 2014
zigzag graphene nanoribbon heterostructure junctions, from the application of nonequilibrium Green’s
DOI: 10.1039/c4cp04859h
the number and location of oxygen atoms in the zigzag graphyne nanoribbon parts, and the rectification
function formalism combined with density functional theory. This behavior could be tuned by varying direction could be reversed due to the parity limitation tunneling effect. Moreover, an obvious negative
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differential resistance behavior is found and may be explained by two different mechanisms.
1. Introduction Investigations on molecular electronic devices have attracted increasing attention and have uncovered several intriguing phenomena and important properties, such as negative differential resistance (NDR),1–4 rectifying behavior,5–7 field-effect characteristics,8–11 and electronic switching properties.12–14 Molecular rectifiers, in particular, have been attracting great attention because they are amongst the most important electronic elements in the design of modern logic and memory circuits. Since Aviram and Ratner proposed a molecular rectifier based donor–acceptor (D–A) that could function as a diode,15 enormous theoretical and experimental efforts have been focused on molecular rectifiers.5–7 From a theoretical viewpoint, any asymmetric junctions may result in rectification. Based on this principle, analogues of metal–semiconductor junctions can be designed as rectifiers. Recently, the two-dimensional carbon allotropes graphene and graphyne have attracted considerable interest and some excellent properties of zigzag graphene nanoribbons (ZGNRs) and zigzag graphyne nanoribbons (ZGYRs) have been discovered.16–20 For instance, Son et al. proposed that ZGNRs are half metallic,17 and Pan et al. predicted that ZGYRs are semiconductors with a band gap of about 1.0 eV.20 The electronic characteristics of a system combining ZGYRs and ZGNRs could satisfy the needs of a rectification model. Although the synthesis of graphyne is still on a
School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, People’s Republic of China. E-mail: [email protected] b Department of Physics, Jining University, Qufu 273155, People’s Republic of China c College of Physics and Engineering, Qufu Normal University, Qufu 273155, People’s Republic of China † Electronic supplementary information (ESI) available. See DOI: 10.1039/ c4cp04859h
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the way, approaches to fabricate its substructures have been developed.18,21 Fortunately, Li et al. have successfully synthesized graphdiyne, which belongs to the same family, on a copper substrate via a cross-coupling reaction using hexaethynylbenzene.22 In addition, first-principles calculations have shown that graphyne is more stable than graphdiyne.18 These two points suggest that graphyne is the more likely to be synthesized in the near future. Moreover, it is well known that the presence of oxygen is widespread and it possesses a similar radius to the carbon atom. The zigzag edges preferred by hydrogen atoms are most likely to be substituted by oxygen atoms.23,24 As a consequence, it is possible to fabricate oxygen-substituted ZGYR/hydrogen-terminated ZGNR heterostructures (O-ZGYR/H-ZGNRs). In this paper, we utilized density-functional theory (DFT) and nonequilibrium Green’s function (NEGF) to investigate how oxygen substitution can affect the electronic transport property of the ZGYR/ZGNR heterostructures. The content of the paper is divided into three parts as follows. The theoretical model and computational method are reported in Section 2. Section 3 contains our results and discussions. Finally Section 4 gives the conclusions. In addition, the width effect is briefly considered in Section S2 (ESI†).
2. Model and method Fig. 1 displays the schematic diagrams of the transport systems of the oxygen-substituted ZGYR/hydrogen-terminated ZGNR heterostructures. The geometric features of the oxygen-substituted ZGYRs are shown in Section S1 (ESI†). The ZGYRs and ZGNRs are joined by acetylenic chains, as the acetylenic chain can connect hexatomic rings flexibly and form various hybrid structures experimentally.25 All of the systems were optimized using the Atomistix
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Fig. 1 Schematic diagrams of the two-probe systems. The rectangular areas indicate the left (L) and right (R) electrodes, between which is the central scattering region. The red, black and gray spheres represent oxygen, carbon and hydrogen atoms, respectively.
Toolkit (ATK) program package until the absolute value of the force acting on each atom was less than 0.05 eV Å1. The four cases considered here are denoted A, B, C, and D, which correspond to the different substitution positions of oxygen. The unsubstituted system is labeled as O. The purpose of this study was to provide a necessary understanding of the edge oxidation effects on the electronic transport properties of the heterostructure junction. The quantum transport calculations were performed using the ATK software package based on DFT combined with NEGF formalism.26,27 To improve calculation precision, a double-z plus polarization (DZP) basis set was used for all atoms. Norm-conserving Troullier–Martins pseudo-potentials were used to describe the core
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electrons.28 The exchange–correlation potential was described by the Perdew–Zunger (PZ) parameterization of local density approximation (LDA) function. The Brillouin zone was sampled with 1 1 100 points within the Monkhorst–Pack K-point sampling scheme, and the mesh cutoff was chosen to be 150 Ry. The current ¨ttiker formula:29 was calculated from the Landauer–Bu IðVÞ ¼
ð 2e dETðE; VÞ½ f ðE mL Þ f ðE mR Þ h
where mL and mR are the electrochemical potentials of the left eV eV and right electrodes, mL ¼ EF ; mR ¼ EF þ , and EF is 2 2
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the Fermi energy of the system which was set to be zero in our calculations. The energy region, [mL,mR], that contributes to the total current integral is referred to as the bias window. T(E,V) is the transmission spectrum. The transmission spectrum covers the integrated transmission coefficients T(E,V,k) over the 2D Brillouin 1Ð zone of the incident wave vectors k, TðE; VÞ ¼ ~ dkTðE; V; kÞ, O O where O is the area of the reference unit cell surface. f (E m) = 1/{1 + exp[(E m)/(kBTtemp)]} is the Fermi–Dirac distribution function, kB is Boltzmann constant, and Ttemp is the temperature. Details of the calculation method are available in the literature.30,31
3. Results and discussion The current–voltage (I–V ) characteristic curves of the two-probe systems in the bias region of [0.5 V, 0.5 V] are shown in Fig. 2(a). All of the I–V curves of oxygen-substituted systems exhibit asymmetric features. For a clearer view, the rectification ratio, a ratio of the currents under positive and negative biases
Fig. 2 (a) Refers to the current–voltage curves of the two-probe systems. The rectification ratio R(V) is shown in (b).
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with the same voltage magnitude, was calculated by R(V) = I(V )/|I(V )| as shown in Fig. 2(b). The forward (backward) rectification is defined according to the rectification ratio R(V ) > 1[R(V ) o 1]. For system O, the current is almost zero in the bias range of [0.5 V, 0.5 V]. No rectification occurred in system O, though the structure of the system is asymmetric. This illustrates that an asymmetric structure does not always lead to rectification. For system A, the current is about 2 mA under positive voltages and is almost zero under negative voltages. It displays a forward rectifying performance and shows that the rectification ratio stabilizes at around 10. For system B, the current is always at 1 mA under a positive voltage. Under negative voltages, one NDR response appears at a bias voltage of 0.2 V. Subsequently, the current increases gradually when the bias is beyond 0.2 V. It shows an obviously asymmetric current under positive and negative biases, and the rectification direction is reversed compared with system A. In the case of system C, the current decreases when the negative voltage is enhanced, resulting in an obvious NDR peak in the bias region from 0.1 V to 0.5 V. Interestingly, for system D, the rectification direction is inversed within the bias region of [0.3 V, 0.4 V]. Moreover, the system also shows NDR behavior in the bias range of [0.3 V, 0.5 V]. As we can see, the rectifying performance is different for A to D when different oxygen-substitution occurs on the ZGYRs. To understand the observed I–V characteristics and rectification behavior, we obtained transmission spectra under various bias voltages for each system, shown in Fig. 3, where the Fermi levels are set to zero. Starting with system O at zero bias voltage, there were two broad transmission peaks located in the energy region of [1 eV, 1 eV], and both were far from the Fermi level. When a negative bias was applied, the two broad transmission peaks moved in the direction of higher energy. For a positive bias, a contrary movement for the two transmission peaks occurred in the direction of lower energy. As the voltage increased, none of the transmission peaks could enter the bias window, and did not contribute to tunneling path of the electron. Therefore, no current and rectification behavior was observed in system O. For system A, there was a transmission peak at the Fermi level, and this moved in the direction of lower energy under a positive voltage, and its area only changed slightly. Therefore, the current magnitude of system A under a positive bias was almost constant. When negative biases were applied, the transmission peak near the Fermi level greatly diminished, leading to a negligible current. Therefore, a forward rectifying response was observed. In addition, it was interesting to note that asymmetric Fano-type resonances were displayed at the energy of 1.0 eV in the bias range of [0.3 V, 0.3 V] because of the superposition of a quasi-localized state on a delocalized state.32 For system B, at zero bias, there was also a transmission peak at the Fermi level. Under a positive bias, the transmission peak moved in the direction of lower energy and its area remained constant, after a small decrease, at a bias of 0.1 V. As a result, the positive current remained stable. When a bias of 0.1 V was applied, one transmission peak was present (marked as b1) which was located within the bias window and contributed to the current. At a bias voltage V = 0.2 V,
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Fig. 3
Transmission spectra of all systems at various biases. The red dashed lines indicate the bias window.
the magnitude of the transmission peak b1 decreased. At the same time, another transmission peak (marked as b2) started to move into the window and contribute to the current. However, the summation of the peaks b1 and b2 were smaller in area than that of peak b1 at a bias 0.1 V. Therefore, a NDR response was observed. As the bias increased further, the peak b2 increased and moved further into the bias window. Consequently, the current
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value at the negative bias became larger than that under the positive bias, and hence a backward rectification was observed. The behaviour of system C can be understood by a similar explanation. In the case of system D, at a positive bias, a transmission peak appeared within the bias window in the bias range of [0.1 V, 0.3 V] and disappeared in the bias range of [0.4 V, 0.5 V].
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Under a negative bias, in the bias range of [0.1 V, 0.3 V], the transmission peaks were located out of the bias window. This led to forward rectification. As the bias increased further, a small transmission peak emerged near to the Fermi level and this contributed to the current. As a result, a backward rectification was observed. Namely, rectification inversion was observed. In order to understand the mechanism of observed rectification, we present the energy band structures and densities of states (DOSs) of the left and right electrodes of all of the systems in Fig. 4. The nature of the transport properties is due to the energy band structure and DOS of left and right electrodes. In Fig. 4(a), for the left electrode of system O, its energy band gap is about 1 eV, in the middle of which the Fermi level lies. As a result, a transmission gap appears in the same energy range in the transmission spectrum as shown in Fig. 3O. When a positive bias (negative bias) is applied, the energy band of the left electrode moves in the direction of lower energy (higher energy), but the band gap always covers the bias window. Therefore, the magnitude of the I–V curve is almost zero in the calculated bias
Fig. 4 (a) The calculated energy band structure of the left and right electrodes for all of the systems. O–D stand for the energy band structure of the left electrode. ZGNR stands for the energy band structure of the right electrode. (b) The calculated DOSs of the left and right electrodes for all the systems.
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voltage range. Moreover, there is no rectification behavior because of the symmetrical distribution of the energy band structure according to the Fermi level. We can infer that an asymmetrical distribution energy band structure may be the origin of the rectifying behavior, rather than the asymmetrical geometry structure. For the A and B systems, one can see that the energy band of the left electrode has a large variation in comparison with system O. In detail, four subbands (a1, b1, a2 and b2) arise in the vicinity of the Fermi level due to the interaction of the oxygen 2p state and the carbon backbones of the ZGYRs. The a1, b1 and b2 subbands can provide paths for electron tunneling from the left electrode to the right electrode, because the peaks of the DOS (see Fig. 4(b)) of the three subbands are broad. As a result, a broad transmission peak emerges near the Fermi level as shown in Fig. 3(A) and 3(B). However, for the a2 subband, the broadening of DOS is weakly (shown in Fig. 4(b)) and it cannot provide an effective electron tunneling path. Therefore, the transmission peak of system A nearly disappears in the bias range of [0.5 eV, 0 eV] compared with system B. When a positive bias is applied, the energy band of the left electrode moves in the direction of lower energy. There is only one subband (a1, b1) near the Fermi level which contributes to the current. For a negative bias, the energy band of the left electrode moves in the direction of higher energy. The a2 and b2 subbands begin to move into the bias window. Because the a2 subband cannot provide an effective electron tunneling path, the negative current is very low for system A. Therefore, a forward rectification behavior is observed in this system. On the contrary, in system B, the b2 subband can provide an effective electron tunneling path, which leads to the current under the negative bias being larger than that under the positive bias, and hence a backward rectification is observed in this system. For system D, in order to explain the rectification inversion, a series of isosurface plots are shown in Fig. 5 to depict the G-point Bloch wave functions of the d1-, d2-, d3- and d4-subbands of the left electrode. Here, the electrode geometrical structures possess mirror symmetry under the xz midplane mirror operation.
Fig. 5 Isosurface plots of the G-point Bloch wave functions of d1-, d2-, d3- and d4-subbands of the left electrode of system D. Different colors represent different phases.
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In accordance with their symmetric geometry, the d1- and d3-subbands have even parity, and the d2- and d4-subbands have odd parity for the left electrode. For the right electrode, the p*-subbands have even parity, and the p-subbands have odd parity. When a bias of 0.2 V is applied, as shown in Fig. 6(a), electrons from the right electrode p-subband cannot tunnel to the left electrode d1-subband because tunneling between two opposite parities is forbidden.16 As a result, the magnitude of the transmission near the Fermi level is almost zero. However, there are still some transmissions at 0.1 eV because of the coupling of the p*–d1 subbands. At a bias of 0.2 V, there are still some transmissions at 0.1 eV because of the coupling of the p*–d3 and p–d2 subbands. While, the d3- and d2- subbands near the G-point are flat, they are just localized. It cannot provide an effective electron tunneling path, and hence a forward rectification response is observed. When the bias is increased up to 0.4 V, as shown in Fig. 6b, there is only p–d1 coupling in the bias window, which leads to zero transmission. On the other hand, the d3–p* coupling can lead to a weak
Fig. 6 Band structures of both the left and right electrodes for system D: at (a) 0.2 V and (b) 0.4 V. The Fermi level is set to be zero. The dashed lines represent the electrochemical potentials of the left and right electrodes.
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transmission peak at the Fermi level. Therefore, a rectification inversion is observed. The NDR feature has also been found in the B and C systems which belong to another type with a distinct mechanism to system D, and we mainly discuss system C as a representative example. Commonly, the coupling of electronic states from the two ends of the central scattering region play an important role in the electronic transport. The maps of the energy-dependent local density of states (LDOS)33 could depict a direct image of the coupling of states from the two ends and further the electronic path of the central scattering region according to the energy space under a certain bias voltage. At biases of 0.1 V and 0.3 V, the maps of the LDOS are shown in Fig. 7(a) and (b), respectively, in which the horizontal axis shows the horizontal position (the z coordinate of the real space) of the central scattering region, and the vertical axis shows the energy of the electrons. The LDOS is averaged in the plane perpendicular to the current flow,
Fig. 7 The energy-dependent local density of states of system C at a bias of (a) 0.1 V and (b) 0.3 V. The LDOS is averaged in the plane perpendicular to the current. The blue and red colors represent regions of low and high density of states, respectively. The horizontal axis represents the length of the central scattering region. The bias window is indicated by black lines.
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and colors indicate the scale of the density of states. Blue and red colors represent the low and high values, respectively. When the bias is 0.1 V, as shown in Fig. 7(a), the electron density is almost distributed uniformly over the central scattering region within the bias window. As a result, a transmission peak appears at the Fermi level. When the bias voltage is increased, as shown in Fig. 7(b), the energy of the incidence states of the left electrode increases and that of the right electrode decreases, and the original transmission channel disappears gradually within the bias window. Therefore, a NDR response is observed. To investigate the underlying physical reason for the NDR behavior of system C, we depicted the projected density of states (PDOS) of the central scattering region of the left and right parts in Fig. 8. There is one wide PDOS peak near 0.05 eV which stems from the c1 and c2 subbands of the left electrode (see Fig. 4(a)). Meanwhile, there exists one wide PDOS peak near 0.05 eV derived from the edge state of the graphene nanoribbon. When the bias is increased to 0.3 V, the two PDOS peaks near the bias window move away from the Fermi energy, and the overlap between them is reduced. Because this type of NDR does not originate from parity limitation tunneling through the junction, and it is not large enough, systems B and C display NDR effects.
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However there is not a significant rectification inversion such as that shown in system D.
4. Conclusions In summary, we have investigated the electronic transport properties of oxygen-substituted ZGYR/hydrogen-terminated ZGNR heterostructures. The calculations show that the asymmetric structure does not always lead to rectification behavior. Asymmetrical energy band structure is the origin of the rectifying behavior. The rectification direction is sensitive to the position and number of oxygen atoms in the ZGYRs, and the energy band structure and DOSs help to explain the phenomenon. Moreover, a parity limitation tunneling effect can lead to obvious rectification inversion which may be used to design a molecular rectifier. The B, C and D systems show a NDR effect, and the mechanism of NDR has been explained. These findings may be useful for the application of ZGYR/ZGNR-based heterostructure molecular devices.
Acknowledgements This work was supported by the Natural Science Foundation of China (Grant Nos. 11374183, 11404188 and 11404141), the Natural Science Foundation of Shandong Province (Grant No. ZR2012AQ018) and the Doctoral Fund of Ministry of Education of China (Grant No. 20130131110007).
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Fig. 8 The density of states is projected (PDOS) onto the corresponding two parts of the central scattering region under the biases of 0.1 V (a) and 0.3 V (b). The two horizontal dashed lines highlight the bias window.
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