J. Cent. South Univ. (2012) 19: 299-303

DOI: 10.1007/s11771-012-1004-7

Negative differential resistance behavior in doped C₈₂ molecular devices

XU Hui(徐慧)¹, JIA Shu-ting(贾姝婷)¹, CHEN Ling-na(陈灵娜)^{1, 2}

1. School of Physics Science and Technology, Central South University, Changsha 410083, China;

2. School of Computer Science and Technology, University of South China, Hengyang 421001, China

? Central South University Press and Springer-Verlag Berlin Heidelberg 2012

Abstract: By using the first-principle calculations and nonequilibrium Green functions method, the electronic transport properties of molecular devices constructed by C₈₂, C₈₀BN and C₈₀N₂ were studied. The results show that the electronic transport properties of molecular devices are affected by doped atoms. Negative differential resistance (NDR) behavior can be observed in certain bias regions for C₈₂ and C₈₀BN molecular devices but cannot be observed for C₈₀N₂ molecular device. A mechanism for the negative differential resistance behavior was suggested.

Key words: electronic transport properties; negative differential resistance; first-principle; molecular device

1 Introduction

In recent years, the fullerene has attracted intensive interests due to its fundamental properties and potential applications in future electronic devices [1-5]. Doping of the fullerenes is a central issue [6-9]. WANG et al [10] reported the orbital hybridization and charge transfer for the interaction between the cage and the metal atom in Dy@C₈₂ metallfullerenes. LU et al [11] found that La@C₈₂, La₂@C₈₀ and Sc₃N@C₈₀ are endothermically encapsulated inside the (17,0) nanotube and electron transfer takes place from the nanotubes to strongly electrophilic La@C₈₂ and La₂@C₈₀. Previous studies mainly focus on the effect on the electronic structure of single fullerene molecules by endothermal doping, but rarely focus on the effect on electronic properties of single fullerene molecules by substitutional doping. Recently, transport properties of fullerenes molecular devices have been receiving great attentions, because they are the most prospective candidates in the nanoelectronic devices [12]. FAN et al [13], ZHANG  et al [14], LI et al [15] observed the negative differential resistance (NDR) in fullerenes molecular devices. NDR effect, which is characterized by the phenomenon of decreasing current with the increase of bias, has gained a wide range of applications including logic circuits [16], memory [17], 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 suppressed at a certain bias [22] and the bias-induced alignment of molecular orbit [23] have been proposed to explain the NDR behavior in molecule devices.

In this work, the electronic transport properties for molecular devices constructed by C₈₂, C₈₀BN and C₈₀N₂ coupled with carbon nanotubes (CNTs) electrodes were investigated by applying nonequilibrium Green functions in combination with the first-principle theory. Here, C₈₀BN is formed by replacing a pair of carbon atoms of the C₈₂ with a pair of B/N atoms, and C₈₀N₂ is formed by replacing a pair of carbon atoms of the C₈₂ with a pair of N atoms. The present work focuses on the effect of doped atoms on the electronic transport properties    for molecular devices constructed by C₈₂, C₈₀BN and C₈₀N₂.

2 Method and model

The model structures are shown in Fig. 1(a). These devices are divided into three parts including left lead, scattering region and right lead. Both leads are semi-infinite CNTs and scattering region is composed of different molecular configurations (Fig. 1(b)). The structures are optimized and the quantum transport calculations are carried out by using an ab initio code package, ATK. ATK is based on the real space, nonequilibrium Green functions (NEGF) formalism and the density-functional theory (DFT) [24]. After relaxing the structures, the distance between the surface of CNTs of CNTs and the central of C₈₂ is about 5.0 ?. The generalized gradient approximation (GGA) and the Perdew-Wang 91 (PW91) exchange-correlation function are chosen. The electrode calculations are performed under periodical boundary conditions, and Brillouin-zone integration is performed using a 1×1×500 Monkhorst- Pach (MP) grid. Single-ζ basis set is used and a mesh cutoff is set to be 150 Ry to save computational time. Test calculations with larger basis set and cutoff energy are also performed, which give almost the same results. The conductance is given within Landauer-Büttiker formalism [25-26].

Fig. 1 Schematic views of molecular device and molecules: (a) Molecular device; (b) Molecules

3 Results and discussion

Figure 2 shows the current as a function of the bias voltage for three molecular devices. From Fig. 2, it can be found that all the molecular devices display metallic transport behavior. It can be seen clearly that when the bias is lower than 0.7 V, at the low bias range, the current of C₈₀N₂ is the maximum. When the bias 0.8 V≤ |V_b|≤0.9 V, the sequence of currents is C₈₀BN>C₈₂>C₈₀N₂. This means that at very low bias, the introduction of impurity enhances the electron transport. In addition, it is found that when the bias takes a value between -0.9 V and -1.5 V for C₈₂ and when the bias takes a value between -0.9 V and -1.2 V for C₈₀BN, the current decreases with the increases of the bias, which shows that the NDR behavior is in the negative bias range. The peak-to-valley ratios are 1.63 and 1.43 corresponding to C₈₂ and C₈₂BN, respectively. However, the NDR behavior for C₈₂N₂ system is not found.

Fig. 2 Curves for currents as function of bias for C₈₂, C₈₀BN and C₈₀N₂ molecular devices

To understand the origin of the transport properties of molecular devices, the transmission spectrum T(E, V_b) was presented and the projected densities of states (PDOS) of molecular devices at zero bias (V_b=0) are shown in Fig. 3. Figure 3 shows very distinct transmission spectra for three molecular devices. From Fig. 3(a), it can be found that near Fermi level there are two big transmission peaks which originate from HOMO and LUMO, respectively. Two strong and broad transmission peaks correspond to a strong transmission channel opened in C₈₂ system. When more electrons are introduced into the system, it is clearly observed that LUMO are split into more levels, and more transmission peaks appear in the system (Fig. 3(b)). This may lead to more opened transmission channels. From Fig. 3(c), it can also be found that transmission peaks of C₈₀N₂ near the Fermi energy are more than those of C₈₂ and C₈₀BN. Thus, it can be inferred that there is a strong coupling between electrode and molecular orbit, which dominates the electron transport in C₈₀N₂ at low bias. This may help explain why the current of the C₈₀N₂ system is larger than that of C₈₂ and C₈₀BN at low bias.

Fig. 3 Transmission coefficient and corresponding PDOS on electron energy at zero bias: (a) C₈₂; (b) C₈₀BN; (c) C₈₀N₂

To understand the NDR behavior clearly, the transmission spectrum and the corresponding PDOS of C₈₀, C₈₀BN and C₈₀N₂ under different biases are presented in Fig. 4. The region between the solid lines is the bias window and the shade area denotes the integral area in the bias window. As known, the current is determined by T(E, V_b) in the bias window and further determined by the integral area (namely, the shadow area in the bias window). From Fig. 4(a), it can be found that at the bias V_b=-0.9 V, high and broad transmission peaks enter into the bias window. This is the bias corresponding to the maximum current and it denotes the beginning of the NDR. Compared with Fig. 4(a), Fig. 4(b) shows that the total magnitude of transmission coefficient in the bias window becomes smaller, so the NDR behavior appears in C₈₂. This bias (V_b=-1.5 V) is at the minimum current and corresponds to the end of the NDR. From Fig. 4(c), it can be found that at the bias V_b=-1.6 V, new transmission peaks enter bias windows, so the NDR behavior disappears. Compared with C₈₂ system, C₈₀BN system can decrease the peak-to-valley ratio of NDR. From Fig. 5(a) and Fig. 5(b), it can be seen that when the bias takes a value between V_b=-0.9 V and V_b=-1.2 V, the bias window increases with the increase of the bias, but the total integral area gets smaller. As a result, the current decreases and NDR appears. From Fig. 5(c), it can be found that when the bias is further increased, the current increases again and NDR disappears. From Fig. 6, it can be seen that the total integral area increases with the increase of the bias, so there is no NDR in C₈₀N₂ molecular device.

Fig. 4 Transmission coefficient and corresponding PDOS for C₈₂ molecular device under different biases: (a) V_b=-0.9 V;     (b) V_b=-1.5 V; (c) V_b=-1.6 V

Fig. 5 Transmission coefficient and corresponding PDOS for C₈₀BN molecular device under different biases: (a) V_b=-0.9 V;     (b) V_b=-1.2 V; (c) V_b=-1.3 V

In order to further understand the NDR behavior, the molecular projected self-consistent Hamiltonian (MPSH) was presented. Note that MPSH contains the molecule-lead coupling effects, which decides the transport ability of molecular devices. Figures 7 and 8 show two frontier molecular orbits from HOMO to LUMO for C₈₂ and C₈₀BN molecular devices, respectively. From Fig. 7(a) and Fig. 7(b), the contribution of HOMO to transmission decreases with the increase of the bias from -0.9 V to -1.5 V, thus there is less current at -1.5 V compared with that at -0.9 V. Compared with Fig. 7(b), it can be seen from Fig. 7(c) that the contribution of HOMO and LOMO changes a little, but the contribution of additional channels LUMO+1 to transmission increases due to the increase of the chemical potential window, which leads to a higher current at -1.6 V compared with that at -1.5 V. From Fig. 8, it can be found that when bias increases from  -0.9 V to -1.3 V, the contribution of LUMO to transmission decreases. But at the bias V_b=-1.3 V, the contribution of additional channels LUMO+1 to transmission increases. According to the above results, it can be concluded that the nonlinear change in the coupling from a bias dependent transition in the broken symmetry phase of the molecular wave function is the origin of the NDR.

Fig. 6 Transmission coefficient and corresponding PDOS for C₈₂N₂ molecular device under different biases: (a) V_b=-0.9 V;     (b) V_b=-1.3 V; (c) V_b=-1.4 V

Fig. 7 Frontier orbits of MPSH from LOMO and HOMO for C₈₂ molecular device: (a) V_b=-0.9 V; (b) V_b=-1.5 V; (c) V_b= -1.6 V

Fig. 8 Frontier orbits of MPSH from LOMO and HOMO for C₈₀BN molecular device: (a) V_b=-0.9 V; (b) V_b=-1.2 V;     (c) V_b=-1.3 V

4 Conclusions

1) Using first-principle quantum transport calculations, all the molecular devices display metal transport behavior. At low bias, doping can enhance the electron transport.

2) The calculation in molecular devices reveals NDR features in the I-V curves and B/N pair dope of the C₈₂ molecule can decrease the peak-to-valley ratio.

3) The bias dependent transition in the broken symmetry phase of the molecular wave function leads to a nonlinear change in the coupling between the molecule and lead, triggering the NDR behavior.

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(Edited by HE Yun-bin)

Foundation item: Project(50721003) supported by the National Natural Science Foundation of China; Project(10C1171) supported by the Scientific Research Fund of Hunan Provincial Education Department, China; Project(11JJ3073) supported by the Natural Science Foundation of Hunan Province, China

Received date: 2011-03-04; Accepted date: 2011-09-20

Corresponding author: XU Hui, Professor; Tel: +86-731-88836762; E-mail: cmpxhg@csu.edu.cn