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Electronic transport properties of graphyne and its family
Computational Materials Science 78 (2013) 22–28
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Electronic transport properties of graphyne and its family Yuhang Jing a,b,⇑, Guoxun Wu c, Licheng Guo a, Yi Sun a, Jun Shen b a
Department of Astronautical Science and Mechanics, Harbin Institute of Technology, Harbin 150001, PR China School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China c College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150020, PR China b
a r t i c l e
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Article history: Received 2 August 2012 Received in revised form 21 March 2013 Accepted 19 May 2013 Available online 14 June 2013 Keywords: Graphyne Heterojunction Electronic transport property Rectification behavior
a b s t r a c t Using the non-equilibrium Green’s function method together with the density-functional theory, the electronic transport properties of graphyne and its family have been studied. Unlike graphene, the graphyne and its family display semi-conductive characteristic along zigzag direction and metallic characteristic along armchair direction. The transport properties of graphyne and its family are associated with the length of C link in their structures. With the length of C link increasing, the electrical conductivity decreases. In addition, both the zigzag and armchair graphdiyne nanoribbons display semi-conductive characteristic. The armchair graphene–graphdiyne nanoribbon heterojunction displays symmetrical semi-conductive characteristic. However, the zigzag graphene–graphdiyne nanoribbon heterojunction shows asymmetrical metallic characteristic and displays the superior rectification behavior. Comparison with the previous studies, it can be found that the heterojunction constructed with metallic and semiconductive nanoelements which behave distinct electronic structures can display the rectification behavior, and it can open up opportunities for design of nanodevices. Crown Copyright Ó 2013 Published by Elsevier B.V. All rights reserved.
1. Introduction Graphene is attracting great interest due to its extraordinary mechanical [1,2], thermal [3–5], and electronic properties [6–8], making it one of the most promising new super-materials in nanoelectronics [9,10]. Graphene, a single layer hexagonal lattice of carbon atoms, has very high carrier mobility because of a unique band structure for the itinerant p-electrons near the Fermi energy that behave as massless Dirac fermions. Graphyne, a 2D carbon allotrope, which has the same symmetry as graphene, consists of planar carbon sheets containing sp and sp2 carbon atoms. Theoretical predictions have been performed since the 1980s [11]. Another planar carbon allotrope that is called graphdiyne is proposed by Haley et al. [12], which belongs to the same family as graphyne. Work on synthesis of both graphyne and graphdiyne substructures has been conducted due to their promising electronic properties. Some substructures of graphyne and graphdiyne have been already synthesized [13,14]. Recently, thin film of graphdiyne has been successfully synthesized on a copper substrate by a cross-coupling reaction using hexaethynylbenzene [15]. Future synthesis of single sheet of graphdiyne and graphyne can be expected, though it is a highly challenging work.
⇑ Corresponding author at: Department of Astronautical Science and Mechanics, Harbin Institute of Technology, Harbin 150001, PR China. Tel.: +86 451 86418100; fax: +86 451 86403725. E-mail address: [email protected] (Y. Jing).
Earlier theoretical work has indicated that zigzag graphene nanoribbons (GNRs) always show metallic property [16–18] and armchair GNRs are semi-conductive with direct band gaps [19]. The width dependence of the band gap and transport properties makes GNRs a potentially useful structure for various applications in nanoscale devices. As for carbon allotrope material, previous theoretical and experimental studies have shown that graphdiyne is semiconductor [15,20], which make it as a possible application in the future nanoelectronics. The electronic properties of graphyne and graphdiyne could be found in previous research works [21–23]. Recent research work shows that the electronic properties of graphyne is more amazing than that of graphene due to its directional anisotropy and its nonequivalent Dirac points [24]. Unlike graphene, the mechanical properties of graphyne depend strongly on the direction of applied loading [25]. The stability, elastic modulus, and failure strength of graphynes can be predicted theoretically as a function of acetylene links [26]. However, little information about the electronic transport properties of graphyne or graphdiyne has been reported. In this work, we investigate the electronic transport properties of graphyne and its family using first principles calculations. The density functional non-equilibrium Green’s function method is used to calculate the current–voltage (I–V) characteristics of graphyne and its family. In addition, the electronic transport property of graphene/graphdiyne nanoribbon heterojunction is analyzed, since it is necessary to connect the GNR with GNR or graphdiyne nanoribbon to construct logic circuits.
0927-0256/$ - see front matter Crown Copyright Ó 2013 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2013.05.026
Y. Jing et al. / Computational Materials Science 78 (2013) 22–28
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Fig. 1. The configurations of graphyne family and graphdiyne nanoribbon. (a) Graphdiyne. (b) The acetylene links in different graphyne family structures. (c) Zigzag graphdiyne nanoribbon. (d) Armchair graphdiyne nanoribbon.
Table 1 The optimized bond lengths (Å) (assignation for bonds is same to Ref. [20]).
Graphyne Graphdiyne Graphyne-3 Graphyne-4
1
2
3
4
5
6
1.428 1.434 1.432 1.434
1.413 1.401 1.405 1.402
1.234 1.244 1.245 1.247
– 1.348 1.346 1.341
– – 1.250 1.256
– – – 1.336
Fig. 2. The heterojunctions of (a) zigzag GNR-graphdiyne nanoribbon and (b) armchair GNR-graphdiyne nanoribbon.
2. Computational details The atomic structure and electronic structure properties of graphyne and its family are calculated using SIESTA code [27]. SIESTA is a density functional theory (DFT) program which solves the standard Kohn–Sham equations and has been demonstrated to be very efficient for large atomic systems [27–29]. By means of extensive optimization, a user-defined double zeta plus polarization (DZP) basis set is constructed for the graphyne and its family. The Perdew–Burke–Ernzerhof (PBE) formulation of the generalized gradient approximation (GGA) for the exchange and correlation functional is used in the calculation to account for the electron–electron interactions. The k-grid sampling of 1 4 4 for the graphyne and its family, together with a mesh cutoff of 200 Ry for the system are used in the calculation. Structural geometry optimization is defined in terms of the forces which are smaller than 0.01 eV Å1. On the basis of optimized structures of the graphyne and its family, the I–V characteristics are calculated using the quantum transport code SMEAGOL [30,31] in which the SIESTA is applied as a platform. The code SMEAGOL is a practical implementation of the non-equilibrium Green’s functions (NEGF) and the DFT method. The NEGF provides a sound conceptual basis for the development of atomic-level quantum mechanical simulators and can lead to physically sensible results for a simple short resistor [32], which should be able to capture the essential physics of most nanoscale devices. Recently, the NEGF method has been employed extensively to study the transport characteristics of nanostructures such as molecular wire [33], graphene nanoribbon [34], and molecular device [35]. For the NEGF formalism, the three parts: the left electrode, the right electrode, and the central scattering region, are required. By the Landauer–Büttiker formula [36], the current is calculated from the corresponding Green’s function and the self-energies:
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CRðLÞ
" #, y X X 2 ¼i ðEÞ ðEÞ R;L
ð3Þ
R;L
P where R,L(E) is the self-energy describing the coupling of the left and right electrode to the semi-infinite electrode. 3. Results and discussion 3.1. Geometrical properties Fig. 1 shows the configurations of graphyne family and graphdiyne nanoribbon discussed in our article. Fig. 1a gives the structure of graphdiyne to describe the configuration of graphyne family, and Fig. 1b shows the acetylene links in different graphyne structures. The graphyne-n denotes the structure that contains nacetylenic linkages between the nearest-neighboring carbon hexagons. Fig. 1c and d shows the structures of zigzag and armchair graphdiyne nanoribbons respectively. The optimized bond lengths of graphyne and its family are given in Table 1. Our results are consistent with the previous results [20]. The C–C bond lengths of the graphyne family display different values which imply that the different C–C hybridization in C links of graphyne family. To construct logic circuits based on GNRs or graphyne nanostructures as building block units, it is necessary to joint them and discuss the electronic properties of heterojunctions constructed by the GNR and graphyne nanostructure. Therefore, we construct and relax the heterojunctions of zigzag GNR-graphdiyne nanoribbon (Fig. 2a) and armchair GNR-graphdiyne nanoribbon (Fig. 2b). 3.2. Electron transport properties of graphyne and its family
Fig. 3. The I–V curves of graphene and graphyne family structures. (a) Graphene. (b) Graphyne, graphyne-3, and graphyne-5. (c) Graphdiyne, graphyne-4, and graphyne6.
IðVÞ ¼ 2e=h
Z
þ1
1
dE fl ðE ll Þ fr ðE lr Þ TðE; VÞ
ð1Þ
where e is the electronic charge, h is the Planck constant, ll and lr are the electrochemical potentials of the left and right electrodes, respectively, and fr and fl are the corresponding Fermi distributions of the two electrodes. T(E, V) is the transmission coefficient at energy E and bias voltage V, which can be expressed as:
h i TðE; VÞ ¼ Tr CR GR ðEÞCL GA ðEÞ
ð2Þ
where GR(E) and GA(E) are the retarded and advanced Green’s function of the conductor, respectively, and CR(L) is the coupling matrices from the conductor to the right (left) lead; they are given by:
Fig. 3 gives the calculated I–V characteristics of the structures including graphene and different graphyne family structures. It can be seen that graphene and different graphyne family structures display different I–V curves in the different current transport directions. For a single layer graphene structure, it shows the superior metallic characteristic along the zigzag direction. However, along the armchair direction the graphene shows semi-conductive properties obviously (Fig. 3a). The zigzag graphene shows the negative differential resistance (NDR) characteristic around 1.6 V. The truncation voltage of the armchair semi-conductive graphene is about 2.0 V and the current is about 0.03 lA. The current rises sharply when the bias voltage exceeds the truncation voltage. For the graphyne family structures, the I–V curve characteristics also display the different transport properties along the different directions (Fig. 3b and c). We define the style of the graphyne family according to the shape of the C hexagon structure. The graphyne family structure is zigzag configuration when the C hexagon structure is along the zigzag direction as in the graphene. Otherwise, the graphyne family structure is considered as armchair configuration. Interestingly, the graphyne family structures show the opposite transport properties compared with graphene in the same transport directions. Graphyne family structures show metallic properties along armchair direction and show semi-conductive characteristic along zigzag direction. Compared with the I–V curve of the graphene, the metallic graphyne family structures show a current suppression region with the width around 0.6 V and the semi-conductive graphyne family structures display the different truncation voltages, which are related with the unique configurations of the graphyne family. The conductivities of the metallic graphyne family structures are smaller than that of the metallic graphene. The C atomic links in the graphyne family structures may be responsible for significant reduction in the superior
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Fig. 4. The PDOS spectrums of C atoms at different positions in graphyne family, graphene, and 8-C atomic link structures. (a) Graphene. (b) 8-C atomic link. (c) Graphyne-3.
electronic transport properties of graphene. In addition, the conductivities of metallic graphyne family structures decrease with the increasing of the length of the C atomic link. From Fig. 3b and c, we can find the I–V curves present regular changes with the increase of the C amounts of the C atomic links in graphyne family structures. Graphyne with 2 C atoms link, graphyne-3 with 6 C atoms link, and grahpyne-5 with 10 C atoms link display the similar transport properties (Fig. 3b). Graphdiyne with 4 C atoms link, graphyne-4 with 8 C atoms link, and graphyne-6 with 12 C atoms link show the similar transport properties (Fig. 3c). The armchair graphyne, graphyne-3, and graphyne-5 structures show the similar metallic characteristics though the current is lower than that of the zigzag graphene. The zigzag graphyne, graphyne-3, and graphyne-5 display the similar semiconductive properties like the armchair graphene I–V curve. They can be considered as good semi-conductive materials and the truncation voltages for the three structures are around 2.0, 1.4, and 1.2 V, respectively. The armchair graphdiyne and graphyne-4 structures show the similar metallic characteristics, and the NDR phenomenon appears under 2.0 V like graphene. The zigzag graphdiyne and graphyne-4 display the similar transport properties which show narrow current suppression region around 0.6 V. The zigzag graphyne-6 structure shows little increasing of the current around 1.0 V, which is similar with graphyne-4. The armchair graphyne-6 structure makes a lower conductivity than graphyne4 and the NDR phenomenon appears obviously. When the bias voltage surpasses the truncation voltage, the current does not rise sharply as the zigzag graphene. The conductivities are below 20, 10, and 10 lA for the zigzag graphdiyne, graphyne-4, and graphyne-6 structures respectively when the voltage is below 2.4 V.
The graphyne-6 shows smallest conductivity among the graphyne family structures due to the increasing of the C atom amounts in the C links. In order to gain a deep insight into the unique transport properties of the graphyne family, the partial density of states (PDOS) of the graphyne family structures are shown in Fig. 4. Because graphyne family structures are constructed with benzene rings and C atomic links, we show the PDOS of graphene and 8-C atomic link structures in Fig. 4a and b respectively in order to understand the electronic structures of graphyne family structures. Graphene shows the sp2 hybridization configuration which can be seen from the PDOS spectrum (Fig. 4a). The wave around Fermi energy is supplied by the 2p-y orbital which is seen as p orbital. The 2s and other 2p orbitals showing the similar flat zero wave shapes around Fermi energy are supposed to be r orbital. The unique transport property of graphene is due to the electronic transport through p orbital and the r orbital constructs the r bonds which make the graphene behave the strongest mechanic characteristic. For the 8-C atomic link structure, 2s and 2p-z orbitals display the similar wave shape with the value of 0 around Fermi energy, and 2p-x and 2p-y orbital show the same spectrum around Fermi energy (Fig. 4b). From the PDOS spectrum of the 8-C link structure, it can be seen that its transport property is weaker than that of the graphene. However, when the link structure is connected to the benzene ring to construct the graphyne family structure, the electronic structures of C atoms are changed and the brand new transport properties of graphyne family are obtained. We define the C atom at the position of the benzene in the graphyne family structures as C-0 atom, and the C atoms in the atomic link from the near to the distant as C-1, C-2, C-3, and C-4
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Fig. 6. The (a) I–V curves and (b) average DOS for per C atom of the graphdiyne nanoribbons and graphdiyne.
Fig. 5. The total transmission spectrums of graphene and graphyne family structures. (a) Graphene. (b) Graphyne and graphyne-3. (c) Graphdiyne and graphyne-4.
atoms (Fig. 1b). Because the electronic structures for graphyne family show the similar effect from C atomic link structure, only the different PDOS spectrums of the C atoms at different positions in graphyne-3 structure are shown in Fig. 4c for brevity. For the PDOS spectrum of each graphyne family structure, the 2p-y orbital shows the similar wave shape no matter what position the C atom is, however, the 2p-x orbital displays the different PDOS spectrum. For C-0 atoms in graphyne family structures, the 2p-y orbital shows the small wave shape around Fermi energy which is just like the p orbital in graphene and other orbitals show flat zero wave
shape just like r orbital. Therefore, the benzene rings in graphyne family structures have sp2 hybridization configuration. The C atoms at the positions of the C atomic link in graphyne family structures show different PDOS spectrum for the 2p-x orbital though the 2p-y orbitals display the similar spectrum as the C-0 atoms. Since all the C atoms show the similar p orbital like spectrum, the graphyne family structures may have the similar transport properties as graphene in which the 2p-y orbital is in charge of electronic transporting. The spectrums of the C atoms in C atomic links show high peaks of wave in a long distance more than 1.5 eV around Fermi energy. Thus, the transport properties have little relationship with the 2p-x orbital. Because the PDOS spectrum of the C atoms in the atomic links in graphyne family structures are different from the 8-C atomic link structure, the electronic structures of the C atoms can be affected by the benzene ring and have the brand new hybridization configuration which is different from the ethylenic or acetylenic configuration. The PDOS spectrum results show that the p orbitals still exist in graphyne family structures to supply the electronic transport paths and make graphyne family structures have unique transport properties just like graphene. Fig. 5 shows the total transmission curves at zero voltage (T(E, V = 0)) of the graphene and graphyne family structures corresponding to the I–V curves (Fig. 3). It can be seen from Fig. 5a that the zigzag graphene displays great metallic characteristic due to the broad peak of wave around Fermi energy. The armchair graphene displays good semi-conductive characteristic because of the 0 energy band with the width about 2 eV around Fermi energy. They are consistent with the I–V curves of the graphene (Fig. 3a). The
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DOS for per C atom of the zigzag graphdiyne nanoribbon, armchair graphdiyne nanoribbon, and graphdiyne. The wave shapes of the DOS are similar for these three different structures and the DOS spectrum of armchair graphdiyne nanoribbon and graphdiyne are almost same. Because of the similar electronic structures for graphdiyne nanoribbons and graphydiyne, the graphdiyne nanoribbons should have the similar transport properties with the graphdiyne. The reduction of the width of the nanoribbons makes the conductivity of the graphdiyne reduce. The different transport properties of zigzag and armchair graphdiyne nanoribbons should be associated with the transport directions and have less relationship with the H atoms. The electronic structures of the graphdiyne nanoribbons are less affected by the H atoms at the edge, which is quite different from the properties of GNRs. Since the transport properties of graphyne family structures are not sensitive to the H atoms at the edges, it may be easier to design the future nanodevices with graphdiyne nanoribbons rather than the GNRs with complex transport properties depending on the chirality and width. 3.4. Electron transport properties of the heterojunctions
Fig. 7. The I–V curves of the heterojunctions of (a) armchair GNR-graphdiyne nanoribbon and (b) zigzag GNR-graphdiyne nanoribbon. The inset in Fig. 7a shows the I–V curve between the truncation voltages. The inset in Fig. 7b shows the rectification ratio changing with bias voltages.
transmission spectrums shown in Fig. 5b and c display the similar wave shape respectively, which are also consistent with the results that graphyne and graphyne-3 have the similar transport properties (Fig. 3b), and graphdiyne and graphyne-4 have the similar transport properties (Fig. 3c). With the length of the C atomic links increasing, the height of the transmission spectrum around Fermi energy decreases resulting in the decrease of the conductivities of the graphyne family structures. The little 0 energy band about 0.5 eV explains the current suppression phenomenon in the graphyne family structures. 3.3. Electron transport properties of graphdiyne nanoribbons Fig. 6a shows the I–V curves of the graphdiyne nanoribbons in different directions (Fig. 1c and d), and the I–V curves of the graphdiyne for comparison. The zigzag and armchair graphdiyne nanoribbons display semi-conductive properties which are different from graphdiyne structure. The truncation voltages of zigzag and armchair graphdiyne nanoribbons are 1.2 eV. When the bias surpasses the truncation voltage, the current of both two nanoribbons increases sharply. However, the I–V curve of zigzag nanoribbon declines under 2.0 V. As shown in Fig. 6a, the graphdiyne structure and graphdiyne nanoribbons show the similar wave shape of the I–V curves, but the graphdiyne nanoribbons display the lower conductivity than the graphdiyne structure. Fig. 6b shows the average
Fig. 7 shows the I–V curves of the heterojunctions of armchair GNR-graphdiyne nanoribbon and zigzag GNR-graphdiyne nanoribbon (Fig. 2). It can be seen that the armchair and zigzag GNRgraphdiyne nanoribbon heterojunctions show different I–V curves. The armchair GNR-graphdiyne nanoribbon heterojunction shows the symmetrical wave shape and displays the semi-conductive characteristic. However, the zigzag GNR-graphdiyne nanoribbon heterojunction shows the asymmetric I–V curve and displays the metallic characteristic. The truncation voltages of the semi-conductive junction are 0.9 and 0.9 V (Fig. 7a (inset)). The current in this region is below 2.2 105 lA. The current increases sharply when the voltage surpasses the truncation voltage and the biggest value of the current can reach 99 lA. The current suppression region of the metallic junction is from 3.6 to 1.8 V and the current in the region is below 12 lA. The biggest conductivities under positive and negative bias voltage are 110 and 88 lA respectively. The NDR phenomenon appears under 3.5 V and the current increases again under 4.1 V. The transport properties of the heterojunctions are determined by the nanoelements constructing them. Because the armchair heterojunction is constructed by the semi-conductive GNR and graphdiyne nanoribbon, it shows the symmetrical semi-conductive characteristic. The zigzag heterojunction is constructed by metallic GNR and semi-conductive graphdiyne nanoribbon, and it displays the asymmetric metallic characteristic. Because of the asymmetry of the I–V curve for the zigzag heterojunction, it displays the superior rectification behavior. The biggest ratio of the current under the same absolute value of bias voltage can reach around 7.3 (Fig. 7b (inset)). Comparison with our previous study of zigzag and armchair GNR heterojunction [37], the junction constructed with the semi-conductive armchair GNR and metallic zigzag GNR also displays very superior rectification behavior. The similar rectification behavior also occurs for CNT heterojunction constructed with semi-conductive and metallic CNTs [38]. Therefore, it can be expected that the heterojunction constructed with metallic and semi-conductive nanoelements which behave distinct electronic structures can display the asymmetric rectification behavior, and it can open up opportunities for design of nanodevices. 4. Conclusions In this work, the electronic transport properties of graphyne family, graphdiyne nanoribbons and the heterojunctions constructed with the GNR-graphdiyne nanoribbon have been investi-
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gated systematically. It is found that the graphyne and its family display semi-conductive characteristic along zigzag direction and metallic characteristic along armchair direction, which is different from the graphene transport property. The transport properties of graphyne and its family are associated with the length of C links in the graphyne family structures. Graphyne, graphyne-3, and graphyne-5 show similar transport properties, and graphdiyne, graphyne-4, and graphyne-6 show similar transport properties. With the length of C links increasing, the conductivity of graphyne family decreases obviously. It is further found out that the C atoms in the C links behave p orbital PDOS spectrum. The C–C bonds in the C links display the brand new connection different from ethylene or acetylene bonds. In addition, both the zigzag and armchair graphdiyne nanoribbons display semi-conductive characteristic. From the results of the PDOS spectrum, the H atoms make little effect on the electronic structures of the graphdiyne nanoribbons. The armchair GNR-graphdiyne nanoribbon heterojunction displays symmetrical semi-conductive characteristic. However, the zigzag GNR-graphdiyne nanoribbon heterojunction shows asymmetrical metallic characteristics and displays the superior rectification behavior. The implication of this work is tremendously useful in understanding the electronic transport properties of graphyne and its family. The interesting electronic transport properties that differ from those of graphene in important aspects make graphyne and its family promising candidates for future applications in novel nanoelectronics and molecular devices. The rectification properties of heterojunctions constructed with metallic and semi-conductive nanoelements may open up opportunities for design of nanodevices.
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Acknowledgements The work is supported by NSFC (11072067), NCET (08-0151), China Postdoctoral Science Foundation, Fundamental Research Funds for the Central Universities under Grant No. HIT.NSRIF.2013031 and Science Funds for Distinguished Young Scholar of Heilongjiang Province, China. Thanks also to Prof. Stefano Sanvito for his kindly supply of SMEAGOL code.
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Electronic transport properties of graphyne and its family Yuhang Jing a,b,⇑, Guoxun Wu c, Licheng Guo a, Yi Sun a, Jun Shen b a
Department of Astronautical Science and Mechanics, Harbin Institute of Technology, Harbin 150001, PR China School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China c College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150020, PR China b
a r t i c l e
i n f o
Article history: Received 2 August 2012 Received in revised form 21 March 2013 Accepted 19 May 2013 Available online 14 June 2013 Keywords: Graphyne Heterojunction Electronic transport property Rectification behavior
a b s t r a c t Using the non-equilibrium Green’s function method together with the density-functional theory, the electronic transport properties of graphyne and its family have been studied. Unlike graphene, the graphyne and its family display semi-conductive characteristic along zigzag direction and metallic characteristic along armchair direction. The transport properties of graphyne and its family are associated with the length of C link in their structures. With the length of C link increasing, the electrical conductivity decreases. In addition, both the zigzag and armchair graphdiyne nanoribbons display semi-conductive characteristic. The armchair graphene–graphdiyne nanoribbon heterojunction displays symmetrical semi-conductive characteristic. However, the zigzag graphene–graphdiyne nanoribbon heterojunction shows asymmetrical metallic characteristic and displays the superior rectification behavior. Comparison with the previous studies, it can be found that the heterojunction constructed with metallic and semiconductive nanoelements which behave distinct electronic structures can display the rectification behavior, and it can open up opportunities for design of nanodevices. Crown Copyright Ó 2013 Published by Elsevier B.V. All rights reserved.
1. Introduction Graphene is attracting great interest due to its extraordinary mechanical [1,2], thermal [3–5], and electronic properties [6–8], making it one of the most promising new super-materials in nanoelectronics [9,10]. Graphene, a single layer hexagonal lattice of carbon atoms, has very high carrier mobility because of a unique band structure for the itinerant p-electrons near the Fermi energy that behave as massless Dirac fermions. Graphyne, a 2D carbon allotrope, which has the same symmetry as graphene, consists of planar carbon sheets containing sp and sp2 carbon atoms. Theoretical predictions have been performed since the 1980s [11]. Another planar carbon allotrope that is called graphdiyne is proposed by Haley et al. [12], which belongs to the same family as graphyne. Work on synthesis of both graphyne and graphdiyne substructures has been conducted due to their promising electronic properties. Some substructures of graphyne and graphdiyne have been already synthesized [13,14]. Recently, thin film of graphdiyne has been successfully synthesized on a copper substrate by a cross-coupling reaction using hexaethynylbenzene [15]. Future synthesis of single sheet of graphdiyne and graphyne can be expected, though it is a highly challenging work.
⇑ Corresponding author at: Department of Astronautical Science and Mechanics, Harbin Institute of Technology, Harbin 150001, PR China. Tel.: +86 451 86418100; fax: +86 451 86403725. E-mail address: [email protected] (Y. Jing).
Earlier theoretical work has indicated that zigzag graphene nanoribbons (GNRs) always show metallic property [16–18] and armchair GNRs are semi-conductive with direct band gaps [19]. The width dependence of the band gap and transport properties makes GNRs a potentially useful structure for various applications in nanoscale devices. As for carbon allotrope material, previous theoretical and experimental studies have shown that graphdiyne is semiconductor [15,20], which make it as a possible application in the future nanoelectronics. The electronic properties of graphyne and graphdiyne could be found in previous research works [21–23]. Recent research work shows that the electronic properties of graphyne is more amazing than that of graphene due to its directional anisotropy and its nonequivalent Dirac points [24]. Unlike graphene, the mechanical properties of graphyne depend strongly on the direction of applied loading [25]. The stability, elastic modulus, and failure strength of graphynes can be predicted theoretically as a function of acetylene links [26]. However, little information about the electronic transport properties of graphyne or graphdiyne has been reported. In this work, we investigate the electronic transport properties of graphyne and its family using first principles calculations. The density functional non-equilibrium Green’s function method is used to calculate the current–voltage (I–V) characteristics of graphyne and its family. In addition, the electronic transport property of graphene/graphdiyne nanoribbon heterojunction is analyzed, since it is necessary to connect the GNR with GNR or graphdiyne nanoribbon to construct logic circuits.
0927-0256/$ - see front matter Crown Copyright Ó 2013 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2013.05.026
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Fig. 1. The configurations of graphyne family and graphdiyne nanoribbon. (a) Graphdiyne. (b) The acetylene links in different graphyne family structures. (c) Zigzag graphdiyne nanoribbon. (d) Armchair graphdiyne nanoribbon.
Table 1 The optimized bond lengths (Å) (assignation for bonds is same to Ref. [20]).
Graphyne Graphdiyne Graphyne-3 Graphyne-4
1
2
3
4
5
6
1.428 1.434 1.432 1.434
1.413 1.401 1.405 1.402
1.234 1.244 1.245 1.247
– 1.348 1.346 1.341
– – 1.250 1.256
– – – 1.336
Fig. 2. The heterojunctions of (a) zigzag GNR-graphdiyne nanoribbon and (b) armchair GNR-graphdiyne nanoribbon.
2. Computational details The atomic structure and electronic structure properties of graphyne and its family are calculated using SIESTA code [27]. SIESTA is a density functional theory (DFT) program which solves the standard Kohn–Sham equations and has been demonstrated to be very efficient for large atomic systems [27–29]. By means of extensive optimization, a user-defined double zeta plus polarization (DZP) basis set is constructed for the graphyne and its family. The Perdew–Burke–Ernzerhof (PBE) formulation of the generalized gradient approximation (GGA) for the exchange and correlation functional is used in the calculation to account for the electron–electron interactions. The k-grid sampling of 1 4 4 for the graphyne and its family, together with a mesh cutoff of 200 Ry for the system are used in the calculation. Structural geometry optimization is defined in terms of the forces which are smaller than 0.01 eV Å1. On the basis of optimized structures of the graphyne and its family, the I–V characteristics are calculated using the quantum transport code SMEAGOL [30,31] in which the SIESTA is applied as a platform. The code SMEAGOL is a practical implementation of the non-equilibrium Green’s functions (NEGF) and the DFT method. The NEGF provides a sound conceptual basis for the development of atomic-level quantum mechanical simulators and can lead to physically sensible results for a simple short resistor [32], which should be able to capture the essential physics of most nanoscale devices. Recently, the NEGF method has been employed extensively to study the transport characteristics of nanostructures such as molecular wire [33], graphene nanoribbon [34], and molecular device [35]. For the NEGF formalism, the three parts: the left electrode, the right electrode, and the central scattering region, are required. By the Landauer–Büttiker formula [36], the current is calculated from the corresponding Green’s function and the self-energies:
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CRðLÞ
" #, y X X 2 ¼i ðEÞ ðEÞ R;L
ð3Þ
R;L
P where R,L(E) is the self-energy describing the coupling of the left and right electrode to the semi-infinite electrode. 3. Results and discussion 3.1. Geometrical properties Fig. 1 shows the configurations of graphyne family and graphdiyne nanoribbon discussed in our article. Fig. 1a gives the structure of graphdiyne to describe the configuration of graphyne family, and Fig. 1b shows the acetylene links in different graphyne structures. The graphyne-n denotes the structure that contains nacetylenic linkages between the nearest-neighboring carbon hexagons. Fig. 1c and d shows the structures of zigzag and armchair graphdiyne nanoribbons respectively. The optimized bond lengths of graphyne and its family are given in Table 1. Our results are consistent with the previous results [20]. The C–C bond lengths of the graphyne family display different values which imply that the different C–C hybridization in C links of graphyne family. To construct logic circuits based on GNRs or graphyne nanostructures as building block units, it is necessary to joint them and discuss the electronic properties of heterojunctions constructed by the GNR and graphyne nanostructure. Therefore, we construct and relax the heterojunctions of zigzag GNR-graphdiyne nanoribbon (Fig. 2a) and armchair GNR-graphdiyne nanoribbon (Fig. 2b). 3.2. Electron transport properties of graphyne and its family
Fig. 3. The I–V curves of graphene and graphyne family structures. (a) Graphene. (b) Graphyne, graphyne-3, and graphyne-5. (c) Graphdiyne, graphyne-4, and graphyne6.
IðVÞ ¼ 2e=h
Z
þ1
1
dE fl ðE ll Þ fr ðE lr Þ TðE; VÞ
ð1Þ
where e is the electronic charge, h is the Planck constant, ll and lr are the electrochemical potentials of the left and right electrodes, respectively, and fr and fl are the corresponding Fermi distributions of the two electrodes. T(E, V) is the transmission coefficient at energy E and bias voltage V, which can be expressed as:
h i TðE; VÞ ¼ Tr CR GR ðEÞCL GA ðEÞ
ð2Þ
where GR(E) and GA(E) are the retarded and advanced Green’s function of the conductor, respectively, and CR(L) is the coupling matrices from the conductor to the right (left) lead; they are given by:
Fig. 3 gives the calculated I–V characteristics of the structures including graphene and different graphyne family structures. It can be seen that graphene and different graphyne family structures display different I–V curves in the different current transport directions. For a single layer graphene structure, it shows the superior metallic characteristic along the zigzag direction. However, along the armchair direction the graphene shows semi-conductive properties obviously (Fig. 3a). The zigzag graphene shows the negative differential resistance (NDR) characteristic around 1.6 V. The truncation voltage of the armchair semi-conductive graphene is about 2.0 V and the current is about 0.03 lA. The current rises sharply when the bias voltage exceeds the truncation voltage. For the graphyne family structures, the I–V curve characteristics also display the different transport properties along the different directions (Fig. 3b and c). We define the style of the graphyne family according to the shape of the C hexagon structure. The graphyne family structure is zigzag configuration when the C hexagon structure is along the zigzag direction as in the graphene. Otherwise, the graphyne family structure is considered as armchair configuration. Interestingly, the graphyne family structures show the opposite transport properties compared with graphene in the same transport directions. Graphyne family structures show metallic properties along armchair direction and show semi-conductive characteristic along zigzag direction. Compared with the I–V curve of the graphene, the metallic graphyne family structures show a current suppression region with the width around 0.6 V and the semi-conductive graphyne family structures display the different truncation voltages, which are related with the unique configurations of the graphyne family. The conductivities of the metallic graphyne family structures are smaller than that of the metallic graphene. The C atomic links in the graphyne family structures may be responsible for significant reduction in the superior
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Fig. 4. The PDOS spectrums of C atoms at different positions in graphyne family, graphene, and 8-C atomic link structures. (a) Graphene. (b) 8-C atomic link. (c) Graphyne-3.
electronic transport properties of graphene. In addition, the conductivities of metallic graphyne family structures decrease with the increasing of the length of the C atomic link. From Fig. 3b and c, we can find the I–V curves present regular changes with the increase of the C amounts of the C atomic links in graphyne family structures. Graphyne with 2 C atoms link, graphyne-3 with 6 C atoms link, and grahpyne-5 with 10 C atoms link display the similar transport properties (Fig. 3b). Graphdiyne with 4 C atoms link, graphyne-4 with 8 C atoms link, and graphyne-6 with 12 C atoms link show the similar transport properties (Fig. 3c). The armchair graphyne, graphyne-3, and graphyne-5 structures show the similar metallic characteristics though the current is lower than that of the zigzag graphene. The zigzag graphyne, graphyne-3, and graphyne-5 display the similar semiconductive properties like the armchair graphene I–V curve. They can be considered as good semi-conductive materials and the truncation voltages for the three structures are around 2.0, 1.4, and 1.2 V, respectively. The armchair graphdiyne and graphyne-4 structures show the similar metallic characteristics, and the NDR phenomenon appears under 2.0 V like graphene. The zigzag graphdiyne and graphyne-4 display the similar transport properties which show narrow current suppression region around 0.6 V. The zigzag graphyne-6 structure shows little increasing of the current around 1.0 V, which is similar with graphyne-4. The armchair graphyne-6 structure makes a lower conductivity than graphyne4 and the NDR phenomenon appears obviously. When the bias voltage surpasses the truncation voltage, the current does not rise sharply as the zigzag graphene. The conductivities are below 20, 10, and 10 lA for the zigzag graphdiyne, graphyne-4, and graphyne-6 structures respectively when the voltage is below 2.4 V.
The graphyne-6 shows smallest conductivity among the graphyne family structures due to the increasing of the C atom amounts in the C links. In order to gain a deep insight into the unique transport properties of the graphyne family, the partial density of states (PDOS) of the graphyne family structures are shown in Fig. 4. Because graphyne family structures are constructed with benzene rings and C atomic links, we show the PDOS of graphene and 8-C atomic link structures in Fig. 4a and b respectively in order to understand the electronic structures of graphyne family structures. Graphene shows the sp2 hybridization configuration which can be seen from the PDOS spectrum (Fig. 4a). The wave around Fermi energy is supplied by the 2p-y orbital which is seen as p orbital. The 2s and other 2p orbitals showing the similar flat zero wave shapes around Fermi energy are supposed to be r orbital. The unique transport property of graphene is due to the electronic transport through p orbital and the r orbital constructs the r bonds which make the graphene behave the strongest mechanic characteristic. For the 8-C atomic link structure, 2s and 2p-z orbitals display the similar wave shape with the value of 0 around Fermi energy, and 2p-x and 2p-y orbital show the same spectrum around Fermi energy (Fig. 4b). From the PDOS spectrum of the 8-C link structure, it can be seen that its transport property is weaker than that of the graphene. However, when the link structure is connected to the benzene ring to construct the graphyne family structure, the electronic structures of C atoms are changed and the brand new transport properties of graphyne family are obtained. We define the C atom at the position of the benzene in the graphyne family structures as C-0 atom, and the C atoms in the atomic link from the near to the distant as C-1, C-2, C-3, and C-4
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Fig. 6. The (a) I–V curves and (b) average DOS for per C atom of the graphdiyne nanoribbons and graphdiyne.
Fig. 5. The total transmission spectrums of graphene and graphyne family structures. (a) Graphene. (b) Graphyne and graphyne-3. (c) Graphdiyne and graphyne-4.
atoms (Fig. 1b). Because the electronic structures for graphyne family show the similar effect from C atomic link structure, only the different PDOS spectrums of the C atoms at different positions in graphyne-3 structure are shown in Fig. 4c for brevity. For the PDOS spectrum of each graphyne family structure, the 2p-y orbital shows the similar wave shape no matter what position the C atom is, however, the 2p-x orbital displays the different PDOS spectrum. For C-0 atoms in graphyne family structures, the 2p-y orbital shows the small wave shape around Fermi energy which is just like the p orbital in graphene and other orbitals show flat zero wave
shape just like r orbital. Therefore, the benzene rings in graphyne family structures have sp2 hybridization configuration. The C atoms at the positions of the C atomic link in graphyne family structures show different PDOS spectrum for the 2p-x orbital though the 2p-y orbitals display the similar spectrum as the C-0 atoms. Since all the C atoms show the similar p orbital like spectrum, the graphyne family structures may have the similar transport properties as graphene in which the 2p-y orbital is in charge of electronic transporting. The spectrums of the C atoms in C atomic links show high peaks of wave in a long distance more than 1.5 eV around Fermi energy. Thus, the transport properties have little relationship with the 2p-x orbital. Because the PDOS spectrum of the C atoms in the atomic links in graphyne family structures are different from the 8-C atomic link structure, the electronic structures of the C atoms can be affected by the benzene ring and have the brand new hybridization configuration which is different from the ethylenic or acetylenic configuration. The PDOS spectrum results show that the p orbitals still exist in graphyne family structures to supply the electronic transport paths and make graphyne family structures have unique transport properties just like graphene. Fig. 5 shows the total transmission curves at zero voltage (T(E, V = 0)) of the graphene and graphyne family structures corresponding to the I–V curves (Fig. 3). It can be seen from Fig. 5a that the zigzag graphene displays great metallic characteristic due to the broad peak of wave around Fermi energy. The armchair graphene displays good semi-conductive characteristic because of the 0 energy band with the width about 2 eV around Fermi energy. They are consistent with the I–V curves of the graphene (Fig. 3a). The
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DOS for per C atom of the zigzag graphdiyne nanoribbon, armchair graphdiyne nanoribbon, and graphdiyne. The wave shapes of the DOS are similar for these three different structures and the DOS spectrum of armchair graphdiyne nanoribbon and graphdiyne are almost same. Because of the similar electronic structures for graphdiyne nanoribbons and graphydiyne, the graphdiyne nanoribbons should have the similar transport properties with the graphdiyne. The reduction of the width of the nanoribbons makes the conductivity of the graphdiyne reduce. The different transport properties of zigzag and armchair graphdiyne nanoribbons should be associated with the transport directions and have less relationship with the H atoms. The electronic structures of the graphdiyne nanoribbons are less affected by the H atoms at the edge, which is quite different from the properties of GNRs. Since the transport properties of graphyne family structures are not sensitive to the H atoms at the edges, it may be easier to design the future nanodevices with graphdiyne nanoribbons rather than the GNRs with complex transport properties depending on the chirality and width. 3.4. Electron transport properties of the heterojunctions
Fig. 7. The I–V curves of the heterojunctions of (a) armchair GNR-graphdiyne nanoribbon and (b) zigzag GNR-graphdiyne nanoribbon. The inset in Fig. 7a shows the I–V curve between the truncation voltages. The inset in Fig. 7b shows the rectification ratio changing with bias voltages.
transmission spectrums shown in Fig. 5b and c display the similar wave shape respectively, which are also consistent with the results that graphyne and graphyne-3 have the similar transport properties (Fig. 3b), and graphdiyne and graphyne-4 have the similar transport properties (Fig. 3c). With the length of the C atomic links increasing, the height of the transmission spectrum around Fermi energy decreases resulting in the decrease of the conductivities of the graphyne family structures. The little 0 energy band about 0.5 eV explains the current suppression phenomenon in the graphyne family structures. 3.3. Electron transport properties of graphdiyne nanoribbons Fig. 6a shows the I–V curves of the graphdiyne nanoribbons in different directions (Fig. 1c and d), and the I–V curves of the graphdiyne for comparison. The zigzag and armchair graphdiyne nanoribbons display semi-conductive properties which are different from graphdiyne structure. The truncation voltages of zigzag and armchair graphdiyne nanoribbons are 1.2 eV. When the bias surpasses the truncation voltage, the current of both two nanoribbons increases sharply. However, the I–V curve of zigzag nanoribbon declines under 2.0 V. As shown in Fig. 6a, the graphdiyne structure and graphdiyne nanoribbons show the similar wave shape of the I–V curves, but the graphdiyne nanoribbons display the lower conductivity than the graphdiyne structure. Fig. 6b shows the average
Fig. 7 shows the I–V curves of the heterojunctions of armchair GNR-graphdiyne nanoribbon and zigzag GNR-graphdiyne nanoribbon (Fig. 2). It can be seen that the armchair and zigzag GNRgraphdiyne nanoribbon heterojunctions show different I–V curves. The armchair GNR-graphdiyne nanoribbon heterojunction shows the symmetrical wave shape and displays the semi-conductive characteristic. However, the zigzag GNR-graphdiyne nanoribbon heterojunction shows the asymmetric I–V curve and displays the metallic characteristic. The truncation voltages of the semi-conductive junction are 0.9 and 0.9 V (Fig. 7a (inset)). The current in this region is below 2.2 105 lA. The current increases sharply when the voltage surpasses the truncation voltage and the biggest value of the current can reach 99 lA. The current suppression region of the metallic junction is from 3.6 to 1.8 V and the current in the region is below 12 lA. The biggest conductivities under positive and negative bias voltage are 110 and 88 lA respectively. The NDR phenomenon appears under 3.5 V and the current increases again under 4.1 V. The transport properties of the heterojunctions are determined by the nanoelements constructing them. Because the armchair heterojunction is constructed by the semi-conductive GNR and graphdiyne nanoribbon, it shows the symmetrical semi-conductive characteristic. The zigzag heterojunction is constructed by metallic GNR and semi-conductive graphdiyne nanoribbon, and it displays the asymmetric metallic characteristic. Because of the asymmetry of the I–V curve for the zigzag heterojunction, it displays the superior rectification behavior. The biggest ratio of the current under the same absolute value of bias voltage can reach around 7.3 (Fig. 7b (inset)). Comparison with our previous study of zigzag and armchair GNR heterojunction [37], the junction constructed with the semi-conductive armchair GNR and metallic zigzag GNR also displays very superior rectification behavior. The similar rectification behavior also occurs for CNT heterojunction constructed with semi-conductive and metallic CNTs [38]. Therefore, it can be expected that the heterojunction constructed with metallic and semi-conductive nanoelements which behave distinct electronic structures can display the asymmetric rectification behavior, and it can open up opportunities for design of nanodevices. 4. Conclusions In this work, the electronic transport properties of graphyne family, graphdiyne nanoribbons and the heterojunctions constructed with the GNR-graphdiyne nanoribbon have been investi-
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gated systematically. It is found that the graphyne and its family display semi-conductive characteristic along zigzag direction and metallic characteristic along armchair direction, which is different from the graphene transport property. The transport properties of graphyne and its family are associated with the length of C links in the graphyne family structures. Graphyne, graphyne-3, and graphyne-5 show similar transport properties, and graphdiyne, graphyne-4, and graphyne-6 show similar transport properties. With the length of C links increasing, the conductivity of graphyne family decreases obviously. It is further found out that the C atoms in the C links behave p orbital PDOS spectrum. The C–C bonds in the C links display the brand new connection different from ethylene or acetylene bonds. In addition, both the zigzag and armchair graphdiyne nanoribbons display semi-conductive characteristic. From the results of the PDOS spectrum, the H atoms make little effect on the electronic structures of the graphdiyne nanoribbons. The armchair GNR-graphdiyne nanoribbon heterojunction displays symmetrical semi-conductive characteristic. However, the zigzag GNR-graphdiyne nanoribbon heterojunction shows asymmetrical metallic characteristics and displays the superior rectification behavior. The implication of this work is tremendously useful in understanding the electronic transport properties of graphyne and its family. The interesting electronic transport properties that differ from those of graphene in important aspects make graphyne and its family promising candidates for future applications in novel nanoelectronics and molecular devices. The rectification properties of heterojunctions constructed with metallic and semi-conductive nanoelements may open up opportunities for design of nanodevices.
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Acknowledgements The work is supported by NSFC (11072067), NCET (08-0151), China Postdoctoral Science Foundation, Fundamental Research Funds for the Central Universities under Grant No. HIT.NSRIF.2013031 and Science Funds for Distinguished Young Scholar of Heilongjiang Province, China. Thanks also to Prof. Stefano Sanvito for his kindly supply of SMEAGOL code.
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