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Effects of partial hydrogenation on electronic transport properties in C60 molecular devices
Solid State Communications 152 (2012) 2123–2127
Contents lists available at SciVerse ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Effects of partial hydrogenation on electronic transport properties in C60 molecular devices L.N. Chen a,b, C. Cao b, X.Z. Wu b, S.S. Ma b, W.R. Huang b,c, H. Xu b,n a
School of Computer Science and Technology, University of South China, Hengyang 421001, People’s Republic of China School of Physics Science and Technology, Central South University, Changsha 410083, People’s Republic of China c School of Physics and Electronic Science, Changsha University of Science and Technology, Changsha 410004, People’s Republic of China b
a r t i c l e i n f o
abstract
Article history: Received 5 May 2012 Received in revised form 22 August 2012 Accepted 16 September 2012 by F. Peeters Available online 25 September 2012
By using nonequilibrium Green’s functions in combination with the density–function theory, we investigate electronic transport properties of molecular devices with pristine and partial hydrogenation. The calculated results show that the electronic transport properties of molecular devices can be modulated by partial hydrogenation. Interestingly, our results exhibit negative differential resistance behavior in the case of the imbalance H-adsorption in C60 molecular devices under low bias. However, negative differential resistance behavior cannot be observed in the case of the balance H-adsorption. A mechanism is proposed for the hydrogenation and negative differential resistance behavior. & 2012 Elsevier Ltd. All rights reserved.
Keywords: A. Molecular device D. Transport property D. Hydrogenation E. First-principles
1. Introduction In recent years, the molecular devices have attracted intensive interests for the fundamental properties and its potential applications in future electronic devices [1–5]. A lot of interesting behaviors, such as negative differential resistance (NDR) [6–9], molecular switch [10], and current rectification [11,12], are found in molecular devices. Recently, transport properties of molecular devices have been receiving great attention, because it is one of the most prospective candidates in the nanoelectronic devices. Several groups observed the negative differential resistance (NDR) in C60 molecular device [13–15]. NDR effect, which is characterized by the phenomenon of decreasing current with increasing bias voltages, has gained a wide range of applications including logic circuits [16], memory effects [17], current switching [18] and amplification [19]. Different mechanisms such as chemical changes [20], local orbital symmetry matching between electrodes and scatting region [21], the channel conduction being suppressed at a certain bias [22], and the bias-induced alignment of molecular orbital [23] have been proposed to explain the NDR behavior in molecule devices. The fullerence C60 is a semiconducting molecule that finds application in many aspects of physical and biological sciences. Doping the C60 molecular devices with different impurities is a
n
Corresponding author. Tel.: þ86 731 88836762; fax: þ 86 731 88830802. E-mail address: [email protected] (H. Xu).
0038-1098/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ssc.2012.09.011
central issue [24,25]. Doping can dramatically change the electronic structure of the pristine fullerence, and thus give new inroads in the fine tuning of its transport properties. Very recently, transport properties of C60 molecular devices connected with Au as the electrodes are actively studied for numerous applications. Zheng et al. [26] found that devices in which a single C60 molecule is connected with different electrodes show completely different transport behavior. Chen et al. [27] found that the negative differential resistance behavior can be observed in the C60 molecular junction, but cannot be observed in the C59N and C59B molecular junction. In the present work, we investigate the electronic transport properties of C60 molecular device with partial hydrogenation. It has been observed that, the H-adsorption site has significant impact on the electronic transport properties of C60 molecular device. We systematically change the number of H atom and H-adsorption site in order to investigate the effect of the partial hydrogenation on the electronic transport properties of C60 molecular device. 2. Methods and model In this paper, we investigate the transport properties of C60 molecular devices coupled to Au chain electrodes by applying nonequilibrium Green’s functions as implemented in ATK (Atomistix ToolKit) [28,29], which is based on real-space, nonequilibrium Green’s function (NEGF) formalism and the density-functional theory (DFT). The approximation for the exchange–correlation
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Fig. 1. (Color online) Schematic plot of the molecular devices: the molecule is coupled to two semi-infinite Au electrodes, and the extended molecule consists of three layers of Au chain with three atoms in both Au electrodes. M0, M1, M2, M3, M4, and M5 correspond to C60 molecular device without H-absorption, C60 molecular device with H-absorption at site 1, sites 1, 2, and 3, sites 1 and 2, and sites 1 and 3, near the Au electrodes, respectively.
functional is the spin-polarized generalized gradient approximation ¨ (GGA). The conductance can be calculated by the Landauer–Buttiker formula [30,31], which separates the entire system into three parts: the central region and two leads. The electrode calculations are performed under periodical boundary conditions with the k-point grid being 1 1 500. The basis set of double-z plus one polarization function (DZP) quality is used and the mesh cutoff is 150 Ry to achieve a balance between calculation efficiency and accuracy. We consider the molecular device shown in Fig. 1, where a C60 molecule is coupled to two semi-infinite Au electrodes, and the extended molecule consists of three layers of Au chain with three atoms in both electrodes. The distance between the C60 center ˚ which is a typical distance and the gold surface is about 6.28 A, employed in most of the reference [27,32]. The pristine C60 molecule is made up of two sublattices of carbon atoms, which are marked as a and b atomic sublattices in model M0. By varying the number of H atom and the H-adsorption site, we consider models M1, M2, M3, M4, and M5. Models M1 and M2 adsorb one and three H atoms, respectively. According to Lieb’s theorem [33,34], site 1 is equivalent to site 3, and site 2 is equivalent to site 4. When H-adsorption site is site 1 (a sublattice) and site 2 (b sublattice) in M3, and the number of a sublattices is equal to the number of b sublattices. Because the a and the b sublattices have the same number of p-bond carbon atoms, so M3 is in the case of balance H-absorption with H atoms away from the Au electrodes. When H-adsorption site is main site 1(a sublattice) or site 3(a sublattice) in M1, M2, and M4, and the number of a sublattices is not equal to the number of b sublattices. Because the number of p-bond carbon atoms of the a sublattices are not equal to the number of p-bond carbon atoms of the b sublattices, thus the models M1, M2, and M4 are in the case of the imbalance H-adsorption and have a spin-polarized ground state with the magnetic moment. Model M5 is also in the case of balance H-absorption, similar to the structure of M3, but two H atoms are near the Au electrodes. The present work focuses on the effect of partial hydrogenation on electronic transport properties for C60 molecular devices.
3. Results and discussion Fig. 2(a) shows the current as a function of the bias for all the molecular devices. From Fig. 2(a), we find that the molecular devices display different transport behavior. Under the low bias (Vb o0.6 V), models M1, M2, and M4 show the liner I–V characteristic while models M3 and M5 show the nonlinear I–V
behavior. Meanwhile, the current of M4 for the imbalance H-adsorption is higher than that of M3 and M5 for the balance H-adsorption, and the current of M3 for two H atoms away from the Au electrodes is slightly higher than that of M5 for two H atom near the Au electrodes. We can also see clearly that when the bias is lower than Vb ¼1.0 V, the current of M0 is less than that of M1, M2, M3, M4, and M5. This means that at low bias, the H-adsorption enhances the electron transport due to the introduction of more electrons. But, when the bias is further increased and higher than 1.2 V, the H-adsorption with two H atoms away from the Au electrodes suppresses the electron transport. Moreover, we find that when the bias takes a value between Vb ¼0.6 V and Vb ¼0.8 V for M1 and M2 and when the bias takes a value between Vb ¼ 0.7 V and Vb ¼ 0.9 V for M4, the current decreases with the increases of the bias, which shows NDR behavior under the imbalance H-adsorption. Fig. 2(b) shows the transmission spectrum T(E,Vb) and the projected density of states (PDOS) of molecular devices at zero bias (Vb ¼0) for M0, M1, M2, M3, M4, and M5, respectively. For M0 one high transmission peak is away from the Fermi level and originates from HOMO. For M1, M2, and M4, we find that near Fermi level there are one high and broad transmission peak which originates from LUMO. The strong and broad transmission peak corresponds to a strong transmission channel being opened. Such results mean that under the imbalance H-adsorption there is a strong coupling between electrode and molecule orbits at the low bias. However, it is clearly observed that one transmission peak corresponding to HOMO appears in M3 and one transmission peak corresponding to LUMO is away from the Fermi level in M5. Therefore, the symmetry of H-adsorption can modulate the transport properties of C60 molecular devices. To understand the transport properties of molecular devices, the transmission spectrum as a function of the electron energy and bias are plotted in Fig. 3. At low bias, a wide transmission gap (TG) can be observed near the Fermi level and is broaden with the increase of bias for M0. However, the transmission spectrum begins to enter into the bias window and contributes to the current for M1, M2, and M4, leading to the rapid increase of the current. This result means that under the imbalance H-adsorption, the transport behavior result from the strong coupled electronic states due to the imbalance of a and b atomic sublattices in the C60 molecule. Moreover, we can find that when the bias is less than 0.3 V, the TG has almost similar characteristics for M3 and M5 at the low bias, showing the semiconductor behavior. Thus, when the bias is less than 0.7 V, models M3 and M5 have the similar I–V curve due to the balance
L.N. Chen et al. / Solid State Communications 152 (2012) 2123–2127
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Fig. 2. (Color online) (a) Currents as a function of bias for M0, M1, M2, M3, M4, and M5. (b) Refer to the transmission coefficient (black solid lines) and the corresponding PDOS (blue solid lines) on the electron energy at zero bias for M0, M1, M2, M3, M4, and M5. The vertical red dashed stand for the Fermi level. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. (Color online) Calculated transmission spectrum as a function of the electron energy E and bias Vb for M0, M1, M2, M3, M4, and M5. The region between the red solid lines is referred to bias window. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
of a and b atomic sublattices in the C60 molecule under the balance H-adsorption. To understand the NDR behavior clearly, in Fig. 4, we present the transmission spectrum and the corresponding PDOS of M1
under different bias. The current through a molecular devices is calculated by integrating the transmission coefficient over the Rm bias window: I ¼ ð2e=hÞ m RðVbÞ TðE,V b ÞdE. The transmission coeffiLðVbÞ cient T(E,Vb) is the function of energy level E at a certain bias Vb,
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strong coupling between the HOMO and the electrode states appears. But the MPSH state partly distribute on the Au chain of M5 system, resulting in the weak coupling between the HOMO and the electrode states. When the bias increases to 1.0 V, the MPSH states of M3 and M4 is delocalized throughout the scattering region and the terminating atoms, which means that the strong coupling between the frontier molecular orbits and the electrode states can make larger contribution to the current. Although, the MPSH state of HOMO is localized for M5, the additional channel LUMOþ 1 starts to contribute due to the increase of chemical potential window, giving rise to the increase of current. Therefore, the different I–V characteristics in the M3, M4, and M5 are due to the different coupling dependence of the frontier molecular orbits states to the electrodes as a function of bias.
4. Conclusions Fig. 4. (Color online) The transmission coefficient and the corresponding PDOS for M1 under biases Vb ¼0.6, 0.8, and 1.0 V, respectively. The region between the solid lines is the bias window and the shaded area denotes the integration area in the bias window.
Fig. 5. (Color online) Frontier molecular orbits of the MPSH: M3, M4, and M5 under biases Vb ¼ 0.0 and 1.0, respectively.
and [mL(Vb),mR(Vb)] is the energy region which contributes to the current integration. This is called the bias window or integral window. Consider the fact that Fermi level is set to be zero, and the region of the bias window is [ Vb/2, þVb/2]. Thus, the current is determined by T(E,Vb) in the bias window, and it is further determined only by the integral area (namely, a shaded area in the bias window). We find that at the bias Vb ¼0.6 V a high and broad transmission peak enters into the bias window. This is the bias corresponding to the current maximum and it denotes the beginning of the NDR. When the bias increases to 0.8 V, the total magnitude of transmission coefficient in the bias window becomes smaller, so the weak coupling between the molecule and Au electrode and the NDR behavior appear in M1. This bias (Vb ¼0.8 V) is that of the current minimum and corresponds to the end of the NDR. But with the further increase of bias the new transmission coefficients enter bias windows, leading to the disappearance of the NDR. Such results suggest that the H-absorption induces the imbalance of a and b sublattices of carbon atoms, leading to a nonlinear change in coupling between the molecule and electrode, which triggers the NDR behavior. In order to further understand the transport behavior of M3, M4, and M5 for the equal number of H atoms, we give the molecular projected self-consistent Hamiltonian (MPSH). Fig. 5 shows frontier molecular orbits for the M3, M4, and M5 under different bias. From Fig. 5, we find that when a bias is equal to 0.0 V, the MPSH state is delocalized throughout the scattering region and the terminating atoms in M3 and M4, indicating a
In conclusion, the first-principle calculations of the electronic transport properties of C60 molecular device. We find that C60 molecular device with partial hydrogenation display different transport behavior. At low biases, the H-adsorption enhances the electron transport due to the introduction of more electrons. Meanwhile, the liner I–V characteristic appears under the imbalance H-adsorption while the nonlinear I–V behavior shows for the balance H-adsorption. Our calculation in C60 molecular devices reveals the NDR features in the I V curves. These results show that the electronic transport properties of C60 molecular device can be modulated by partial hydrogenation. The electronic transport properties depend on absorption sites and the number of H atom. We suggest that the absorption induces the imbalance of a and b sublattices of carbon atoms, leading to a nonlinear change in coupling between the molecule and electrode, which triggers the NDR behavior.
Acknowledgments This work was supported by National Natural Science Foundation of China (Grant no. 50721003), the Natural Science Foundation of Hunan Province (Grant no. 11JJ3073), the Scientific Research Fund of Hunan Provincial Education Department (Grant no. 10C1171), and High Performance Computing Center of CSU. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
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Contents lists available at SciVerse ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Effects of partial hydrogenation on electronic transport properties in C60 molecular devices L.N. Chen a,b, C. Cao b, X.Z. Wu b, S.S. Ma b, W.R. Huang b,c, H. Xu b,n a
School of Computer Science and Technology, University of South China, Hengyang 421001, People’s Republic of China School of Physics Science and Technology, Central South University, Changsha 410083, People’s Republic of China c School of Physics and Electronic Science, Changsha University of Science and Technology, Changsha 410004, People’s Republic of China b
a r t i c l e i n f o
abstract
Article history: Received 5 May 2012 Received in revised form 22 August 2012 Accepted 16 September 2012 by F. Peeters Available online 25 September 2012
By using nonequilibrium Green’s functions in combination with the density–function theory, we investigate electronic transport properties of molecular devices with pristine and partial hydrogenation. The calculated results show that the electronic transport properties of molecular devices can be modulated by partial hydrogenation. Interestingly, our results exhibit negative differential resistance behavior in the case of the imbalance H-adsorption in C60 molecular devices under low bias. However, negative differential resistance behavior cannot be observed in the case of the balance H-adsorption. A mechanism is proposed for the hydrogenation and negative differential resistance behavior. & 2012 Elsevier Ltd. All rights reserved.
Keywords: A. Molecular device D. Transport property D. Hydrogenation E. First-principles
1. Introduction In recent years, the molecular devices have attracted intensive interests for the fundamental properties and its potential applications in future electronic devices [1–5]. A lot of interesting behaviors, such as negative differential resistance (NDR) [6–9], molecular switch [10], and current rectification [11,12], are found in molecular devices. Recently, transport properties of molecular devices have been receiving great attention, because it is one of the most prospective candidates in the nanoelectronic devices. Several groups observed the negative differential resistance (NDR) in C60 molecular device [13–15]. NDR effect, which is characterized by the phenomenon of decreasing current with increasing bias voltages, has gained a wide range of applications including logic circuits [16], memory effects [17], current switching [18] and amplification [19]. Different mechanisms such as chemical changes [20], local orbital symmetry matching between electrodes and scatting region [21], the channel conduction being suppressed at a certain bias [22], and the bias-induced alignment of molecular orbital [23] have been proposed to explain the NDR behavior in molecule devices. The fullerence C60 is a semiconducting molecule that finds application in many aspects of physical and biological sciences. Doping the C60 molecular devices with different impurities is a
n
Corresponding author. Tel.: þ86 731 88836762; fax: þ 86 731 88830802. E-mail address: [email protected] (H. Xu).
0038-1098/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ssc.2012.09.011
central issue [24,25]. Doping can dramatically change the electronic structure of the pristine fullerence, and thus give new inroads in the fine tuning of its transport properties. Very recently, transport properties of C60 molecular devices connected with Au as the electrodes are actively studied for numerous applications. Zheng et al. [26] found that devices in which a single C60 molecule is connected with different electrodes show completely different transport behavior. Chen et al. [27] found that the negative differential resistance behavior can be observed in the C60 molecular junction, but cannot be observed in the C59N and C59B molecular junction. In the present work, we investigate the electronic transport properties of C60 molecular device with partial hydrogenation. It has been observed that, the H-adsorption site has significant impact on the electronic transport properties of C60 molecular device. We systematically change the number of H atom and H-adsorption site in order to investigate the effect of the partial hydrogenation on the electronic transport properties of C60 molecular device. 2. Methods and model In this paper, we investigate the transport properties of C60 molecular devices coupled to Au chain electrodes by applying nonequilibrium Green’s functions as implemented in ATK (Atomistix ToolKit) [28,29], which is based on real-space, nonequilibrium Green’s function (NEGF) formalism and the density-functional theory (DFT). The approximation for the exchange–correlation
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Fig. 1. (Color online) Schematic plot of the molecular devices: the molecule is coupled to two semi-infinite Au electrodes, and the extended molecule consists of three layers of Au chain with three atoms in both Au electrodes. M0, M1, M2, M3, M4, and M5 correspond to C60 molecular device without H-absorption, C60 molecular device with H-absorption at site 1, sites 1, 2, and 3, sites 1 and 2, and sites 1 and 3, near the Au electrodes, respectively.
functional is the spin-polarized generalized gradient approximation ¨ (GGA). The conductance can be calculated by the Landauer–Buttiker formula [30,31], which separates the entire system into three parts: the central region and two leads. The electrode calculations are performed under periodical boundary conditions with the k-point grid being 1 1 500. The basis set of double-z plus one polarization function (DZP) quality is used and the mesh cutoff is 150 Ry to achieve a balance between calculation efficiency and accuracy. We consider the molecular device shown in Fig. 1, where a C60 molecule is coupled to two semi-infinite Au electrodes, and the extended molecule consists of three layers of Au chain with three atoms in both electrodes. The distance between the C60 center ˚ which is a typical distance and the gold surface is about 6.28 A, employed in most of the reference [27,32]. The pristine C60 molecule is made up of two sublattices of carbon atoms, which are marked as a and b atomic sublattices in model M0. By varying the number of H atom and the H-adsorption site, we consider models M1, M2, M3, M4, and M5. Models M1 and M2 adsorb one and three H atoms, respectively. According to Lieb’s theorem [33,34], site 1 is equivalent to site 3, and site 2 is equivalent to site 4. When H-adsorption site is site 1 (a sublattice) and site 2 (b sublattice) in M3, and the number of a sublattices is equal to the number of b sublattices. Because the a and the b sublattices have the same number of p-bond carbon atoms, so M3 is in the case of balance H-absorption with H atoms away from the Au electrodes. When H-adsorption site is main site 1(a sublattice) or site 3(a sublattice) in M1, M2, and M4, and the number of a sublattices is not equal to the number of b sublattices. Because the number of p-bond carbon atoms of the a sublattices are not equal to the number of p-bond carbon atoms of the b sublattices, thus the models M1, M2, and M4 are in the case of the imbalance H-adsorption and have a spin-polarized ground state with the magnetic moment. Model M5 is also in the case of balance H-absorption, similar to the structure of M3, but two H atoms are near the Au electrodes. The present work focuses on the effect of partial hydrogenation on electronic transport properties for C60 molecular devices.
3. Results and discussion Fig. 2(a) shows the current as a function of the bias for all the molecular devices. From Fig. 2(a), we find that the molecular devices display different transport behavior. Under the low bias (Vb o0.6 V), models M1, M2, and M4 show the liner I–V characteristic while models M3 and M5 show the nonlinear I–V
behavior. Meanwhile, the current of M4 for the imbalance H-adsorption is higher than that of M3 and M5 for the balance H-adsorption, and the current of M3 for two H atoms away from the Au electrodes is slightly higher than that of M5 for two H atom near the Au electrodes. We can also see clearly that when the bias is lower than Vb ¼1.0 V, the current of M0 is less than that of M1, M2, M3, M4, and M5. This means that at low bias, the H-adsorption enhances the electron transport due to the introduction of more electrons. But, when the bias is further increased and higher than 1.2 V, the H-adsorption with two H atoms away from the Au electrodes suppresses the electron transport. Moreover, we find that when the bias takes a value between Vb ¼0.6 V and Vb ¼0.8 V for M1 and M2 and when the bias takes a value between Vb ¼ 0.7 V and Vb ¼ 0.9 V for M4, the current decreases with the increases of the bias, which shows NDR behavior under the imbalance H-adsorption. Fig. 2(b) shows the transmission spectrum T(E,Vb) and the projected density of states (PDOS) of molecular devices at zero bias (Vb ¼0) for M0, M1, M2, M3, M4, and M5, respectively. For M0 one high transmission peak is away from the Fermi level and originates from HOMO. For M1, M2, and M4, we find that near Fermi level there are one high and broad transmission peak which originates from LUMO. The strong and broad transmission peak corresponds to a strong transmission channel being opened. Such results mean that under the imbalance H-adsorption there is a strong coupling between electrode and molecule orbits at the low bias. However, it is clearly observed that one transmission peak corresponding to HOMO appears in M3 and one transmission peak corresponding to LUMO is away from the Fermi level in M5. Therefore, the symmetry of H-adsorption can modulate the transport properties of C60 molecular devices. To understand the transport properties of molecular devices, the transmission spectrum as a function of the electron energy and bias are plotted in Fig. 3. At low bias, a wide transmission gap (TG) can be observed near the Fermi level and is broaden with the increase of bias for M0. However, the transmission spectrum begins to enter into the bias window and contributes to the current for M1, M2, and M4, leading to the rapid increase of the current. This result means that under the imbalance H-adsorption, the transport behavior result from the strong coupled electronic states due to the imbalance of a and b atomic sublattices in the C60 molecule. Moreover, we can find that when the bias is less than 0.3 V, the TG has almost similar characteristics for M3 and M5 at the low bias, showing the semiconductor behavior. Thus, when the bias is less than 0.7 V, models M3 and M5 have the similar I–V curve due to the balance
L.N. Chen et al. / Solid State Communications 152 (2012) 2123–2127
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Fig. 2. (Color online) (a) Currents as a function of bias for M0, M1, M2, M3, M4, and M5. (b) Refer to the transmission coefficient (black solid lines) and the corresponding PDOS (blue solid lines) on the electron energy at zero bias for M0, M1, M2, M3, M4, and M5. The vertical red dashed stand for the Fermi level. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 3. (Color online) Calculated transmission spectrum as a function of the electron energy E and bias Vb for M0, M1, M2, M3, M4, and M5. The region between the red solid lines is referred to bias window. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
of a and b atomic sublattices in the C60 molecule under the balance H-adsorption. To understand the NDR behavior clearly, in Fig. 4, we present the transmission spectrum and the corresponding PDOS of M1
under different bias. The current through a molecular devices is calculated by integrating the transmission coefficient over the Rm bias window: I ¼ ð2e=hÞ m RðVbÞ TðE,V b ÞdE. The transmission coeffiLðVbÞ cient T(E,Vb) is the function of energy level E at a certain bias Vb,
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strong coupling between the HOMO and the electrode states appears. But the MPSH state partly distribute on the Au chain of M5 system, resulting in the weak coupling between the HOMO and the electrode states. When the bias increases to 1.0 V, the MPSH states of M3 and M4 is delocalized throughout the scattering region and the terminating atoms, which means that the strong coupling between the frontier molecular orbits and the electrode states can make larger contribution to the current. Although, the MPSH state of HOMO is localized for M5, the additional channel LUMOþ 1 starts to contribute due to the increase of chemical potential window, giving rise to the increase of current. Therefore, the different I–V characteristics in the M3, M4, and M5 are due to the different coupling dependence of the frontier molecular orbits states to the electrodes as a function of bias.
4. Conclusions Fig. 4. (Color online) The transmission coefficient and the corresponding PDOS for M1 under biases Vb ¼0.6, 0.8, and 1.0 V, respectively. The region between the solid lines is the bias window and the shaded area denotes the integration area in the bias window.
Fig. 5. (Color online) Frontier molecular orbits of the MPSH: M3, M4, and M5 under biases Vb ¼ 0.0 and 1.0, respectively.
and [mL(Vb),mR(Vb)] is the energy region which contributes to the current integration. This is called the bias window or integral window. Consider the fact that Fermi level is set to be zero, and the region of the bias window is [ Vb/2, þVb/2]. Thus, the current is determined by T(E,Vb) in the bias window, and it is further determined only by the integral area (namely, a shaded area in the bias window). We find that at the bias Vb ¼0.6 V a high and broad transmission peak enters into the bias window. This is the bias corresponding to the current maximum and it denotes the beginning of the NDR. When the bias increases to 0.8 V, the total magnitude of transmission coefficient in the bias window becomes smaller, so the weak coupling between the molecule and Au electrode and the NDR behavior appear in M1. This bias (Vb ¼0.8 V) is that of the current minimum and corresponds to the end of the NDR. But with the further increase of bias the new transmission coefficients enter bias windows, leading to the disappearance of the NDR. Such results suggest that the H-absorption induces the imbalance of a and b sublattices of carbon atoms, leading to a nonlinear change in coupling between the molecule and electrode, which triggers the NDR behavior. In order to further understand the transport behavior of M3, M4, and M5 for the equal number of H atoms, we give the molecular projected self-consistent Hamiltonian (MPSH). Fig. 5 shows frontier molecular orbits for the M3, M4, and M5 under different bias. From Fig. 5, we find that when a bias is equal to 0.0 V, the MPSH state is delocalized throughout the scattering region and the terminating atoms in M3 and M4, indicating a
In conclusion, the first-principle calculations of the electronic transport properties of C60 molecular device. We find that C60 molecular device with partial hydrogenation display different transport behavior. At low biases, the H-adsorption enhances the electron transport due to the introduction of more electrons. Meanwhile, the liner I–V characteristic appears under the imbalance H-adsorption while the nonlinear I–V behavior shows for the balance H-adsorption. Our calculation in C60 molecular devices reveals the NDR features in the I V curves. These results show that the electronic transport properties of C60 molecular device can be modulated by partial hydrogenation. The electronic transport properties depend on absorption sites and the number of H atom. We suggest that the absorption induces the imbalance of a and b sublattices of carbon atoms, leading to a nonlinear change in coupling between the molecule and electrode, which triggers the NDR behavior.
Acknowledgments This work was supported by National Natural Science Foundation of China (Grant no. 50721003), the Natural Science Foundation of Hunan Province (Grant no. 11JJ3073), the Scientific Research Fund of Hunan Provincial Education Department (Grant no. 10C1171), and High Performance Computing Center of CSU. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
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