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Humidity effects on the electronic transport properties in carbon based nanoscale device
Physics Letters A 376 (2012) 869–874
Contents lists available at SciVerse ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Humidity effects on the electronic transport properties in carbon based nanoscale device Jun He, Ke-Qiu Chen ∗ Department of Applied Physics and Key Laboratory for Micro-Nano Optoelectronic Devices of Ministry of Education, Hunan University, Changsha 410082, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 8 October 2011 Received in revised form 24 December 2011 Accepted 17 January 2012 Available online 20 January 2012 Communicated by R. Wu
a b s t r a c t By applying nonequilibrium Green’s functions in combination with the density functional theory, we investigate the effect of humidity on the electronic transport properties in carbon based nanoscale device. The results show that different humidity may form varied localized potential barrier, which is a very important factor to affect the stability of electronic transport in the nanoscale system. A mechanism for the humidity effect is suggested. © 2012 Elsevier B.V. All rights reserved.
Keywords: Humidity effect Fullerenes and related materials Electronic transport First-principles
1. Introduction Molecular electronics have received increasing attention owing to realization of next generational electronic components based on single molecular devices. Recently, functional molecular devices have been designed and interesting physical phenomena including switching [1], molecular rectification [2], field-effect characteristics [3,4], negative differential resistance (NDR) [5–7], and nonoscale spin effects [8,9], etc., have been observed in these molecular devices. The most prominent nanostructures to construct molecular devices are carbon based materials, such as fullerenes, single wall carbon nanotubes (SWCNTs), and graphene. Particularly, as a result of the remarkable spherical symmetry, mechanical stability and electronic properties, the fullerene C 60 has been extensively studied experimentally [10–12] and theoretically [13–15]. It is well known that single C 60 molecule has poor electronic conductance due to its large HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) gap [7]. However, the metal–C 60 –metal junction exhibits metallic properties due to charge transfer from electrodes to molecule [13]. Several physical and chemical methods such as deformation [14], doping [12, 15], gate voltage [13] have been applied in this C 60 based devices to tune their electronic transport properties. NDR behavior was also found in the C 60 based molecular devices experimentally and theoretically [7,11]. In a parallel development, the use of SWCNT
*
Corresponding author. Tel./fax: +86 0731 88822332. E-mail addresses: [email protected], [email protected] (K.-Q. Chen).
0375-9601/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2012.01.026
as electrode materials was reported [16–24]. In fact, the SWCNTs are a real quasi-one-dimensional materials and the use of SWCNTs as electrodes in molecular junctions is of many advantages on constructing stable molecular device by forming strong covalent bonds with organic molecules [25,26]. Gutierrez and coworkers have investigated the molecular junction constructed by a single C 60 molecule sandwiched in two metallic SWCNTs. They suggested that the transmission spectra can be controlled by the rotation of the C 60 molecule [20]. Very recently, Shokri and coworkers investigated the same structure in the framework of a nearest neighbor tight-binding approximation, and found that the number of contact points between the electrodes and the molecule plays an important role in the electronic transport [27]. However, most of the previous works have been paid to understand how the intrinsic factors, such as intermolecular interaction [28], side groups [29], doping atoms [30], affect the electronic transport properties in molecular devices. The environment factors including humidity and atmosphere are generally neglected in theoretical calculations [31,32]. For the purpose of practical applications, it is very important to examine the stability and reliability of electronic transport properties for nanoscale electronic device under various possible conditions [33]. In the present work, we choose carbon based nanoscale device which is constructed by a C 60 molecule sandwiched between two SWCNT leads as a representative prototype. By applying nonequilibrium Green’s function in combination with the density functional theory, we investigate the humidity effect on the electronic transport properties in carbon based nanoscale device. The results show that the humidity is a very import factor in the stability of electronic transport in nanoscale electronic system.
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J. He, K.-Q. Chen / Physics Letters A 376 (2012) 869–874
Fig. 1. (a) Schematic description of a carbon based molecular junction consisting of a C 60 molecule sandwiched in two semi-infinite metallic open-end (5, 5) SWCNT leads and the SWCNT ends are saturated by H atoms to eliminate the dangling bonds. The molecules adsorbed on the SWCNTs are water molecule. (b) is in the top view for an electrode unit which contains three unit cells of (5, 5) SWCNT and an adsorbed water molecule, and (c) is in the side view for it. (d) is in the side view for five water molecules adsorbed on the electrode unit.
2. Model and computational method
The typical molecular device we study are shown in Fig. 1. A single C 60 molecule is sandwiched between two open-ended (5, 5) SWCNT leads. The H2 O molecules is allowed to be adsorbed on the (5, 5) SWCNT electrodes. In the present work, we choose three (5, 5) SWCNT unit cells as an electrode unit and each electrode unit adsorbs different number of water molecules to stand for different humidity conditions. Here, we consider two different states: SWCNT@H2 O corresponds to each electrode unit adsorbing one water molecule, and SWCNT@5H2 O corresponds to each electrode unit adsorbing five water molecules. The structures shown in Figs. 1(c)–(d) correspond to SWCNT@H2 O and SWCNT@5H2 O, respectively. The positions of all atoms in the electrode units were fully relaxed during geometry optimizations, which were performed by an ab initio code package, ATOMISTIX TOOLKIT (ATK). All the configurations were relaxed until their force tolerance being less than 0.05 eV/Å. In the relaxed bulk systems, the H2 O molecules are weakly physical adsorbed on (5, 5) SWCNTs, which is the best adsorption position where the H2 O molecule with OH bond points towards the SWCNT surface and the oxygen atom just lies over the center of a hexatomic ring (as seen in Fig. 1(b)). During the geometry optimizations, we fully relax the carbon nanotube and water molecule, which is relaxed as a bulk system. The chief purpose to do that is to consider the interaction of carbon nanotube and water molecule. For the relaxed CNT@H2 O system, the mulliken population shows that there is 0.0319e transferred from water molecule to carbon nanotube. The change of the bond angle of the water molecule is 0.056◦ caused by the charge transfer. For the relaxed CNT@5H2 O system, the mulliken population shows that there is 0.1786e transferred from water molecules to carbon nanotube. The change of the bond angle of the water molecules is 0.072◦ due to the charge transfer. However, for all the systems, the bond length of the water molecules is almost not changed. For the nanoscale device, the electronic transport properties are also calculated by using ATK, which is based on
the real-space, fully self-consistent nonequilibrium Green’s functions formalism combining with first-principles density functional theory (DFT) [34,35]. In the calculations, the nanoscale device is divide into three parts: left electrode, central scattering region, and right electrode. The core electrons are modeled by normconserving pseudopotentials, while the valance electrons wave function were expanded by a SIESTA basis set. The single ξ + polarization basis set was used for the geometrical optimization and the electronic transport calculation. The cutoff energy is set to be 150 Ry and the Brillouin zone is sampled by a 1 × 1 × 100 k-point grid. The nonlinear current through the scattering region is calculated by the Landauer formula [36]
I (V b ) =
2e
μr ( V b )
T ( E , V b ) f ( E − μl ) − f ( E − μr ) dE ,
h
(1)
μl ( V b )
where μl ( V b ) and μr ( V b ) are electrochemical potentials of the left and right electrodes and f is the Fermi distribution function. With the applied bias potential V b , the electrochemical potentials will shift up and down, respectively. As a result, the electrochemical potentials correspond to μl ( V b ) = μl (0) − eV b /2 and μr ( V b ) = μr (0) + eV b /2 when the external bias is V b . Consider the fact that the Fermi level is set to be zero, the region of the energy integral window [μl ( V b ), μr ( V b )] can be written as [− V b /2, V b /2]. The electron transmission coefficient T ( E , V b ) can be written as
T ( E , V b ) = Tr Γl G R Γr G A ,
(2)
where G R ( A ) are the retarded and advanced Green’s function of the scattering region. 3. Results and discussion The humidity effects on the band structure of the (5, 5) SWCNT are shown in Fig. 2. From Fig. 2(a), it is clearly seen that the conductance and valence bands cross the Fermi level. This indicates
J. He, K.-Q. Chen / Physics Letters A 376 (2012) 869–874
871
Fig. 2. Band structures of the leads. The left panel (a) is the band structure for a pure (5, 5) SWCNT. (b) and (c) correspond to the band structures of (5, 5) SWCNT adsorbed by one and five water molecules, respectively. The inset figure in (c) is the magnified band structure near the Fermi level. The dashed lines stand for Fermi level, and it is set to be zero.
Fig. 3. (a) is the calculated current–voltage curves for the molecular devices, and (b) is the relative variation of current (RI) as a function of voltage.
that the (5, 5) SWCNT is metallic electrode materials. Comparing Fig. 2(b) with Fig. 2(a), we can find that when one water molecule is adsorbed on SWCNT, there is an electronic level located near the Fermi level and the symmetry between the conductance band and valence band is broken. This is similar to the case that NO2 molecules are adsorbed on SWCNTs [37]. When we pay attention to SWCNT@5H2 O system, it can be clearly seen from the magnified band structure in Fig. 2(c) that there are five high level states near the Fermi level. From these results, we can conclude that the adsorbed water molecules mainly affect the electronic structures near the Fermi level of SWCNT electrode and each adsorbed water molecule will induce a localized state near the Fermi level. As we know, the electronic states near the Fermi level play an important role in electronic transport properties. Therefore, it is predicted that the water molecules will obviously affect the electronic transport properties in this carbon based nanoscale device. In Fig. 3(a), we give the current–voltage curves for all systems considered here under bias ranging from 0.0 V to 1.6 V. As seen from Fig. 3(a), the adsorbed water molecule has a great effect on the currents. Especially, in SWCNT@5H2 O system, the current is al-
most zero as the bias increases from 0.0 V to 0.9 V. For the systems with the adsorbed water molecules, the electronic transport becomes instability and the currents have a large oscillation at high bias (ranging from 1.0 V to 1.6 V). To evaluate the instability of the electronic transport, we calculated the relative variation in current with reference to the nonadsorbed case and it was defined as RI = ( I ads − I pure )/ I pure × 100%, where I ads and I pure are the currents under the same voltage values corresponding to the case with or without adsorbed water molecules, respectively. The calculated RI as a function of voltage is shown in Fig. 3(b). It indicates that the RI of the SWCNT@5H2 O system is very stable and large at low bias, and the values are closed to 100% at some special biases. However, the RI of the SWCNT@H2 O system is small at low bias and it gradually increases with the increase of bias, and approaches 100% at the bias of 0.9 V. As the bias increases from 0.9 V to 1.6 V, the RI has a large oscillation but the value trends to decrease. This indicates that the humidity effect trends to decrease at higher bias. In order to understand the interesting current–voltage characteristics, in Fig. 4, we calculated the transmission spectra T ( E , V b ) for all the systems at several different biases, 0.0 V, 0.2 V, 0.9 V,
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J. He, K.-Q. Chen / Physics Letters A 376 (2012) 869–874
Fig. 4. The calculated transmission spectra at different voltages. (a) is the case of pure molecular device. (b) and (c) correspond to the case of SWCNT@H2 O and SWCNT@5H2 O, respectively. The region between two solid lines is the bias window.
1.2 V, 1.4 V, and 1.6 V. It is well known that the transmission spectra is related to the wave function overlap between central scattering region and electrodes [38]. This is to say, the transmission spectra reflect the coupling degree between the molecular orbitals of the scattering region and the incident electronic states from the electrodes. When the water molecules are adsorbed on the (5, 5) SWCNT leads, the electronic states of the electrodes will change (see Fig. 2). It results in the variation of coupling degree between the molecular orbitals of C 60 molecule and the incident electronic states from the (5, 5) SWCNT leads. Therefore, the transmission spectra of the systems are obviously affected by the adsorbed water molecules, which can be clearly seen from Fig. 4. Note that the currents are calculated by formula (1). Thus, the current is determined by T ( E , V b ) in the bias window, which is dependent on the transport spectra and the magnitude of the bias window. For convenience, the bias window for each voltage is marked by the region between two solid lines. Comparing Fig. 4(b) with Fig. 4(a), we can find that the transmission peak near the Fermi level at equilibrium state is almost not affected when each electrode unit is adsorbed by one water molecule. However, the magnitude of the transmission peak inside the bias window gradually decreases as the bias increases. Thus, it results in the RI of SWCNT@H2 O system is small at very low bias and then gradually increases with the increasing of the bias. As we put eyes on Fig. 4(c), it is seen clearly that there is a great effect on the transmission peak near the Fermi level at equilibrium state when each electrode unit is adsorbed by five water molecules. However, there is nearly no transmission spectrum inside the bias window when the bias increase to 0.9 V. Therefore, the current is almost zero as the bias increases from 0.0 V to 0.9 V in SWCNT@5H2 O system. Similarly, we can also understand the oscillating behavior of the currents by comparing the transmission spectra inside bias window at different biases. In order to further explore the influence of humidity on electronic transport properties, we calculated the transmission eigenstates in the real space at zero bias for all the systems, which is plotted in Fig. 5. The transmission eigenstates ψ( E , k) is the self-consistent eigenstate of the scattering region and it contains the molecule–electrode coupling effects. Firstly, we calculated the
transmission eigenvalues at the given energy, and the results show that there are only two eigenchannels contributing to the transmission coefficient. Considering the fact that the second one is almost zero, we only give the transmission eigenstates of the first eigenchannel to analyse the humidity effects. Moreover, the given energy E in our calculation is the energy site of the LUMO, which is the exclusive molecular orbital near the Fermi level for all the systems. It is well known that the frontier molecular orbitals near the Fermi level play an important role in electronic transport. From Fig. 5(a), it clearly shows that the transmission eigenstate is delocalized. This means that the transmission eigenchannel is opened and the electrons can transport from left electrode to the other, which results in a high transmission peak near the Fermi level at zero bias (as shown in Fig. 4(a)). Comparing Fig. 5(b) with Fig. 5(a), we can find that a part of electrons localized at the adsorbed water molecules in left electrode, but the transmission eigenstate is the same as pure case. Therefore, there is nearly no effect on the transmission spectra at the zero bias. However, the localized state on the left electrode will form a potential barrier, which will induce electronic transport instability under applied biases. As we pay attention to Fig. 5(c), it clearly shows that more electronic states localize at the adsorbed water molecules on the surface of left electrode. It obviously shows that there is a more stronger potential barrier at the left electrode and the transmission eigenstate becomes weakened. In other words, the electronic transport become difficult and less electrons can transport from left electrode to right electrode due to the stronger potential barrier in left lead. Thus, we can see that the transmission peak have a great decrease near the Fermi level at zero bias (as shown in Fig. 4(c)). From these results, we can conclude that the electronic transport instability may steam from the localized potential barrier formed by the adsorbed water molecules on the SWCNT leads. 4. Conclusion In summary, by applying first-principles quantum transport calculations, we have investigated the electronic transport properties of the carbon based molecular device constructed by a
J. He, K.-Q. Chen / Physics Letters A 376 (2012) 869–874
873
Fig. 5. Isosurfaces of the transmission eigenstates in the real space at zero bias. (a)–(c) correspond to pure molecular devices at energy point E = 0.06 eV, SWCNT@H2 O system at energy point E = 0.08 eV, and SWCNT@5H2 O system at energy point E = 0.11 eV, respectively. The isovalue is 0.04 a.u. In order to translate the colors to values, we insert a color bar in the bottom. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)
C 60 molecule sandwiched in two semi-infinite SWCNT electrodes. Three systems including pure device, SWCNT@H2 O system and SWCNT@H2 O system have been considered in the present work. The results suggest that the humidity has a great effect on electronic transport properties and its instability. The electronic transport instability steams from the localized potential barrier formed by the adsorbed water molecules. It is suggested that humidity is a very import factor influencing the stability of electronic transport in nanoscale electronic system and it should not be neglected. Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 60871065), by the National Basic Research Program of China (No. 2011CB606405), by the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 200805320011), by Hunan Provincial Innovation Foundation For Postgraduate (No. CX2011B151) and by Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province. References [1] S.Y. Quek, M. Kamenetska, M.L. Steigerwald, H.J. Choi, S.G. Louie, M.S. Hybertsen, J.B. Neaton, L. Venkataraman, Nat. Nanotechnol. 4 (2009) 230. [2] R.M. Metzger, Chem. Rev. 103 (2003) 3803. [3] Y.S. Fu, S.H. Ji, X. Chen, X.C. Ma, R. Wu, C.C. Wang, W.H. Duan, X.H. Qiu, B. Sun, P. Zhang, J.F. Jia, Q.K. Xue, Phys. Rev. Lett. 99 (2007) 256601. [4] Q.M. Yan, B. Huang, J. Yu, F.W. Zheng, J. Zang, J. Wu, B.L. Gu, F. Liu, W.H. Duan, Nano Lett. 7 (2007) 1469. [5] J. Chen, M.A. Reed, A.M. Rawlett, J.M. Tour, Science 286 (1999) 1550; J. Chen, W. Wang, M.A. Reed, A.M. Rawlett, D.W. Price, J.M. Tour, Appl. Phys. Lett. 77 (2000) 1224. [6] Y. Ren, K.Q. Chen, Q. Wan, A.l. Pan, W.P. Hu, Phys. Lett. A 374 (2010) 3857.
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Contents lists available at SciVerse ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Humidity effects on the electronic transport properties in carbon based nanoscale device Jun He, Ke-Qiu Chen ∗ Department of Applied Physics and Key Laboratory for Micro-Nano Optoelectronic Devices of Ministry of Education, Hunan University, Changsha 410082, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 8 October 2011 Received in revised form 24 December 2011 Accepted 17 January 2012 Available online 20 January 2012 Communicated by R. Wu
a b s t r a c t By applying nonequilibrium Green’s functions in combination with the density functional theory, we investigate the effect of humidity on the electronic transport properties in carbon based nanoscale device. The results show that different humidity may form varied localized potential barrier, which is a very important factor to affect the stability of electronic transport in the nanoscale system. A mechanism for the humidity effect is suggested. © 2012 Elsevier B.V. All rights reserved.
Keywords: Humidity effect Fullerenes and related materials Electronic transport First-principles
1. Introduction Molecular electronics have received increasing attention owing to realization of next generational electronic components based on single molecular devices. Recently, functional molecular devices have been designed and interesting physical phenomena including switching [1], molecular rectification [2], field-effect characteristics [3,4], negative differential resistance (NDR) [5–7], and nonoscale spin effects [8,9], etc., have been observed in these molecular devices. The most prominent nanostructures to construct molecular devices are carbon based materials, such as fullerenes, single wall carbon nanotubes (SWCNTs), and graphene. Particularly, as a result of the remarkable spherical symmetry, mechanical stability and electronic properties, the fullerene C 60 has been extensively studied experimentally [10–12] and theoretically [13–15]. It is well known that single C 60 molecule has poor electronic conductance due to its large HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) gap [7]. However, the metal–C 60 –metal junction exhibits metallic properties due to charge transfer from electrodes to molecule [13]. Several physical and chemical methods such as deformation [14], doping [12, 15], gate voltage [13] have been applied in this C 60 based devices to tune their electronic transport properties. NDR behavior was also found in the C 60 based molecular devices experimentally and theoretically [7,11]. In a parallel development, the use of SWCNT
*
Corresponding author. Tel./fax: +86 0731 88822332. E-mail addresses: [email protected], [email protected] (K.-Q. Chen).
0375-9601/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2012.01.026
as electrode materials was reported [16–24]. In fact, the SWCNTs are a real quasi-one-dimensional materials and the use of SWCNTs as electrodes in molecular junctions is of many advantages on constructing stable molecular device by forming strong covalent bonds with organic molecules [25,26]. Gutierrez and coworkers have investigated the molecular junction constructed by a single C 60 molecule sandwiched in two metallic SWCNTs. They suggested that the transmission spectra can be controlled by the rotation of the C 60 molecule [20]. Very recently, Shokri and coworkers investigated the same structure in the framework of a nearest neighbor tight-binding approximation, and found that the number of contact points between the electrodes and the molecule plays an important role in the electronic transport [27]. However, most of the previous works have been paid to understand how the intrinsic factors, such as intermolecular interaction [28], side groups [29], doping atoms [30], affect the electronic transport properties in molecular devices. The environment factors including humidity and atmosphere are generally neglected in theoretical calculations [31,32]. For the purpose of practical applications, it is very important to examine the stability and reliability of electronic transport properties for nanoscale electronic device under various possible conditions [33]. In the present work, we choose carbon based nanoscale device which is constructed by a C 60 molecule sandwiched between two SWCNT leads as a representative prototype. By applying nonequilibrium Green’s function in combination with the density functional theory, we investigate the humidity effect on the electronic transport properties in carbon based nanoscale device. The results show that the humidity is a very import factor in the stability of electronic transport in nanoscale electronic system.
870
J. He, K.-Q. Chen / Physics Letters A 376 (2012) 869–874
Fig. 1. (a) Schematic description of a carbon based molecular junction consisting of a C 60 molecule sandwiched in two semi-infinite metallic open-end (5, 5) SWCNT leads and the SWCNT ends are saturated by H atoms to eliminate the dangling bonds. The molecules adsorbed on the SWCNTs are water molecule. (b) is in the top view for an electrode unit which contains three unit cells of (5, 5) SWCNT and an adsorbed water molecule, and (c) is in the side view for it. (d) is in the side view for five water molecules adsorbed on the electrode unit.
2. Model and computational method
The typical molecular device we study are shown in Fig. 1. A single C 60 molecule is sandwiched between two open-ended (5, 5) SWCNT leads. The H2 O molecules is allowed to be adsorbed on the (5, 5) SWCNT electrodes. In the present work, we choose three (5, 5) SWCNT unit cells as an electrode unit and each electrode unit adsorbs different number of water molecules to stand for different humidity conditions. Here, we consider two different states: SWCNT@H2 O corresponds to each electrode unit adsorbing one water molecule, and SWCNT@5H2 O corresponds to each electrode unit adsorbing five water molecules. The structures shown in Figs. 1(c)–(d) correspond to SWCNT@H2 O and SWCNT@5H2 O, respectively. The positions of all atoms in the electrode units were fully relaxed during geometry optimizations, which were performed by an ab initio code package, ATOMISTIX TOOLKIT (ATK). All the configurations were relaxed until their force tolerance being less than 0.05 eV/Å. In the relaxed bulk systems, the H2 O molecules are weakly physical adsorbed on (5, 5) SWCNTs, which is the best adsorption position where the H2 O molecule with OH bond points towards the SWCNT surface and the oxygen atom just lies over the center of a hexatomic ring (as seen in Fig. 1(b)). During the geometry optimizations, we fully relax the carbon nanotube and water molecule, which is relaxed as a bulk system. The chief purpose to do that is to consider the interaction of carbon nanotube and water molecule. For the relaxed CNT@H2 O system, the mulliken population shows that there is 0.0319e transferred from water molecule to carbon nanotube. The change of the bond angle of the water molecule is 0.056◦ caused by the charge transfer. For the relaxed CNT@5H2 O system, the mulliken population shows that there is 0.1786e transferred from water molecules to carbon nanotube. The change of the bond angle of the water molecules is 0.072◦ due to the charge transfer. However, for all the systems, the bond length of the water molecules is almost not changed. For the nanoscale device, the electronic transport properties are also calculated by using ATK, which is based on
the real-space, fully self-consistent nonequilibrium Green’s functions formalism combining with first-principles density functional theory (DFT) [34,35]. In the calculations, the nanoscale device is divide into three parts: left electrode, central scattering region, and right electrode. The core electrons are modeled by normconserving pseudopotentials, while the valance electrons wave function were expanded by a SIESTA basis set. The single ξ + polarization basis set was used for the geometrical optimization and the electronic transport calculation. The cutoff energy is set to be 150 Ry and the Brillouin zone is sampled by a 1 × 1 × 100 k-point grid. The nonlinear current through the scattering region is calculated by the Landauer formula [36]
I (V b ) =
2e
μr ( V b )
T ( E , V b ) f ( E − μl ) − f ( E − μr ) dE ,
h
(1)
μl ( V b )
where μl ( V b ) and μr ( V b ) are electrochemical potentials of the left and right electrodes and f is the Fermi distribution function. With the applied bias potential V b , the electrochemical potentials will shift up and down, respectively. As a result, the electrochemical potentials correspond to μl ( V b ) = μl (0) − eV b /2 and μr ( V b ) = μr (0) + eV b /2 when the external bias is V b . Consider the fact that the Fermi level is set to be zero, the region of the energy integral window [μl ( V b ), μr ( V b )] can be written as [− V b /2, V b /2]. The electron transmission coefficient T ( E , V b ) can be written as
T ( E , V b ) = Tr Γl G R Γr G A ,
(2)
where G R ( A ) are the retarded and advanced Green’s function of the scattering region. 3. Results and discussion The humidity effects on the band structure of the (5, 5) SWCNT are shown in Fig. 2. From Fig. 2(a), it is clearly seen that the conductance and valence bands cross the Fermi level. This indicates
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Fig. 2. Band structures of the leads. The left panel (a) is the band structure for a pure (5, 5) SWCNT. (b) and (c) correspond to the band structures of (5, 5) SWCNT adsorbed by one and five water molecules, respectively. The inset figure in (c) is the magnified band structure near the Fermi level. The dashed lines stand for Fermi level, and it is set to be zero.
Fig. 3. (a) is the calculated current–voltage curves for the molecular devices, and (b) is the relative variation of current (RI) as a function of voltage.
that the (5, 5) SWCNT is metallic electrode materials. Comparing Fig. 2(b) with Fig. 2(a), we can find that when one water molecule is adsorbed on SWCNT, there is an electronic level located near the Fermi level and the symmetry between the conductance band and valence band is broken. This is similar to the case that NO2 molecules are adsorbed on SWCNTs [37]. When we pay attention to SWCNT@5H2 O system, it can be clearly seen from the magnified band structure in Fig. 2(c) that there are five high level states near the Fermi level. From these results, we can conclude that the adsorbed water molecules mainly affect the electronic structures near the Fermi level of SWCNT electrode and each adsorbed water molecule will induce a localized state near the Fermi level. As we know, the electronic states near the Fermi level play an important role in electronic transport properties. Therefore, it is predicted that the water molecules will obviously affect the electronic transport properties in this carbon based nanoscale device. In Fig. 3(a), we give the current–voltage curves for all systems considered here under bias ranging from 0.0 V to 1.6 V. As seen from Fig. 3(a), the adsorbed water molecule has a great effect on the currents. Especially, in SWCNT@5H2 O system, the current is al-
most zero as the bias increases from 0.0 V to 0.9 V. For the systems with the adsorbed water molecules, the electronic transport becomes instability and the currents have a large oscillation at high bias (ranging from 1.0 V to 1.6 V). To evaluate the instability of the electronic transport, we calculated the relative variation in current with reference to the nonadsorbed case and it was defined as RI = ( I ads − I pure )/ I pure × 100%, where I ads and I pure are the currents under the same voltage values corresponding to the case with or without adsorbed water molecules, respectively. The calculated RI as a function of voltage is shown in Fig. 3(b). It indicates that the RI of the SWCNT@5H2 O system is very stable and large at low bias, and the values are closed to 100% at some special biases. However, the RI of the SWCNT@H2 O system is small at low bias and it gradually increases with the increase of bias, and approaches 100% at the bias of 0.9 V. As the bias increases from 0.9 V to 1.6 V, the RI has a large oscillation but the value trends to decrease. This indicates that the humidity effect trends to decrease at higher bias. In order to understand the interesting current–voltage characteristics, in Fig. 4, we calculated the transmission spectra T ( E , V b ) for all the systems at several different biases, 0.0 V, 0.2 V, 0.9 V,
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Fig. 4. The calculated transmission spectra at different voltages. (a) is the case of pure molecular device. (b) and (c) correspond to the case of SWCNT@H2 O and SWCNT@5H2 O, respectively. The region between two solid lines is the bias window.
1.2 V, 1.4 V, and 1.6 V. It is well known that the transmission spectra is related to the wave function overlap between central scattering region and electrodes [38]. This is to say, the transmission spectra reflect the coupling degree between the molecular orbitals of the scattering region and the incident electronic states from the electrodes. When the water molecules are adsorbed on the (5, 5) SWCNT leads, the electronic states of the electrodes will change (see Fig. 2). It results in the variation of coupling degree between the molecular orbitals of C 60 molecule and the incident electronic states from the (5, 5) SWCNT leads. Therefore, the transmission spectra of the systems are obviously affected by the adsorbed water molecules, which can be clearly seen from Fig. 4. Note that the currents are calculated by formula (1). Thus, the current is determined by T ( E , V b ) in the bias window, which is dependent on the transport spectra and the magnitude of the bias window. For convenience, the bias window for each voltage is marked by the region between two solid lines. Comparing Fig. 4(b) with Fig. 4(a), we can find that the transmission peak near the Fermi level at equilibrium state is almost not affected when each electrode unit is adsorbed by one water molecule. However, the magnitude of the transmission peak inside the bias window gradually decreases as the bias increases. Thus, it results in the RI of SWCNT@H2 O system is small at very low bias and then gradually increases with the increasing of the bias. As we put eyes on Fig. 4(c), it is seen clearly that there is a great effect on the transmission peak near the Fermi level at equilibrium state when each electrode unit is adsorbed by five water molecules. However, there is nearly no transmission spectrum inside the bias window when the bias increase to 0.9 V. Therefore, the current is almost zero as the bias increases from 0.0 V to 0.9 V in SWCNT@5H2 O system. Similarly, we can also understand the oscillating behavior of the currents by comparing the transmission spectra inside bias window at different biases. In order to further explore the influence of humidity on electronic transport properties, we calculated the transmission eigenstates in the real space at zero bias for all the systems, which is plotted in Fig. 5. The transmission eigenstates ψ( E , k) is the self-consistent eigenstate of the scattering region and it contains the molecule–electrode coupling effects. Firstly, we calculated the
transmission eigenvalues at the given energy, and the results show that there are only two eigenchannels contributing to the transmission coefficient. Considering the fact that the second one is almost zero, we only give the transmission eigenstates of the first eigenchannel to analyse the humidity effects. Moreover, the given energy E in our calculation is the energy site of the LUMO, which is the exclusive molecular orbital near the Fermi level for all the systems. It is well known that the frontier molecular orbitals near the Fermi level play an important role in electronic transport. From Fig. 5(a), it clearly shows that the transmission eigenstate is delocalized. This means that the transmission eigenchannel is opened and the electrons can transport from left electrode to the other, which results in a high transmission peak near the Fermi level at zero bias (as shown in Fig. 4(a)). Comparing Fig. 5(b) with Fig. 5(a), we can find that a part of electrons localized at the adsorbed water molecules in left electrode, but the transmission eigenstate is the same as pure case. Therefore, there is nearly no effect on the transmission spectra at the zero bias. However, the localized state on the left electrode will form a potential barrier, which will induce electronic transport instability under applied biases. As we pay attention to Fig. 5(c), it clearly shows that more electronic states localize at the adsorbed water molecules on the surface of left electrode. It obviously shows that there is a more stronger potential barrier at the left electrode and the transmission eigenstate becomes weakened. In other words, the electronic transport become difficult and less electrons can transport from left electrode to right electrode due to the stronger potential barrier in left lead. Thus, we can see that the transmission peak have a great decrease near the Fermi level at zero bias (as shown in Fig. 4(c)). From these results, we can conclude that the electronic transport instability may steam from the localized potential barrier formed by the adsorbed water molecules on the SWCNT leads. 4. Conclusion In summary, by applying first-principles quantum transport calculations, we have investigated the electronic transport properties of the carbon based molecular device constructed by a
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Fig. 5. Isosurfaces of the transmission eigenstates in the real space at zero bias. (a)–(c) correspond to pure molecular devices at energy point E = 0.06 eV, SWCNT@H2 O system at energy point E = 0.08 eV, and SWCNT@5H2 O system at energy point E = 0.11 eV, respectively. The isovalue is 0.04 a.u. In order to translate the colors to values, we insert a color bar in the bottom. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)
C 60 molecule sandwiched in two semi-infinite SWCNT electrodes. Three systems including pure device, SWCNT@H2 O system and SWCNT@H2 O system have been considered in the present work. The results suggest that the humidity has a great effect on electronic transport properties and its instability. The electronic transport instability steams from the localized potential barrier formed by the adsorbed water molecules. It is suggested that humidity is a very import factor influencing the stability of electronic transport in nanoscale electronic system and it should not be neglected. Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 60871065), by the National Basic Research Program of China (No. 2011CB606405), by the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 200805320011), by Hunan Provincial Innovation Foundation For Postgraduate (No. CX2011B151) and by Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province. References [1] S.Y. Quek, M. Kamenetska, M.L. Steigerwald, H.J. Choi, S.G. Louie, M.S. Hybertsen, J.B. Neaton, L. Venkataraman, Nat. Nanotechnol. 4 (2009) 230. [2] R.M. Metzger, Chem. Rev. 103 (2003) 3803. [3] Y.S. Fu, S.H. Ji, X. Chen, X.C. Ma, R. Wu, C.C. Wang, W.H. Duan, X.H. Qiu, B. Sun, P. Zhang, J.F. Jia, Q.K. Xue, Phys. Rev. Lett. 99 (2007) 256601. [4] Q.M. Yan, B. Huang, J. Yu, F.W. Zheng, J. Zang, J. Wu, B.L. Gu, F. Liu, W.H. Duan, Nano Lett. 7 (2007) 1469. [5] J. Chen, M.A. Reed, A.M. Rawlett, J.M. Tour, Science 286 (1999) 1550; J. Chen, W. Wang, M.A. Reed, A.M. Rawlett, D.W. Price, J.M. Tour, Appl. Phys. Lett. 77 (2000) 1224. [6] Y. Ren, K.Q. Chen, Q. Wan, A.l. Pan, W.P. Hu, Phys. Lett. A 374 (2010) 3857.
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