Article pubs.acs.org/JPCC
Large Low Bias Negative Differential Resistance in an Endohedral Li@C60 Dimer Junction P. Zhao,*,† D. S. Liu,‡,§ Y. Zhang,† Y. Su,† H. Y. Liu,† S. J. Li,† and G. Chen*,† †
School of Physics and Technology, University of Jinan, Jinan 250022, China School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China § Department of Physics, Jining University, Qufu 273155, China ‡
ABSTRACT: By applying the nonequilibrium Green function formalism combined with density functional theory, we have investigated the electronic transport properties of the C60 dimer and its endohedral complex Li@C60 dimer. Our results show that the doping of Li atoms significantly changes the transport properties of the C60 dimer. Negative differential resistance is found in such systems. Especially, the doping of Li atoms can lead to a much larger negative differential resistance at much lower bias, and it is quite evident from the plot of differential conductance versus bias. The negative differential resistance behavior is understood in terms of the evolution of the transmission spectrum and projected density of states spectrum with applied bias combined with molecular projected self-consistent Hamiltonian states analyses.
I. INTRODUCTION One of the fascinating aspects of the modern quantum transport phenomena is the negative differential resistance (NDR) behavior, which is described by an increase followed by a decease in current with the steady increase in applied bias. It is essential for many device applications including highfrequency oscillators,1 analog-to-digital converters,2 and logic.3 Chen et al. discovered NDR behavior in oligo(phenylene ethynylene) (OPE) molecular junctions with nitro and/or amino groups on the central phenyl ring,4 triggering a gamut of experimental and theoretical studies to understand the phenomenon. Different mechanisms have been proposed to explain the observed NDR, such as a two-step reduction process,4,5 an intramolecular phenomenon,6 and the change in the molecular conformation due to the change in the electronic charge state of the molecule under increasing bias (in this mechanism, controversy still remains concerning whether the conformational change arises from the rotation of the molecular group within the molecular backbone7−9 or from the rotation of the side group10). However, Khondaker et al. observed NDR behavior in the OPE molecular junction irrespective of whether the system contains a nitro side group or not,11 while Yin et al.12 and Bauschilicher et al.13 did not observed NDR in the same molecular junctions. NDR behavior has also been found in other molecular devices such as porphyrin junction with side groups,14 squashed C60 junction,15 anthracene junction,16,17 phenalenyl junction with different contact geometries,18 Nterminated single-wall carbon nanotube (SWCNT) junction,19 unsymmetrical C121 junction,20 etc. © 2012 American Chemical Society
Though NDR behavior has been found in a variety of molecular devices, the origin for NDR in molecular devices is still under intense debate due to their structural complexity, it is even still controversial whether NDR is intrinsic to the molecule or junction dependent.4,7−10 Moreover, these NDR behaviors can typically only be observed at a relatively high bias. Ideally, NDR-based devices should be developed for operation at much lower bias to reduce power consumption. This would enable low bias nanoelectronic components. Therefore, the quest for low bias NDR in molecular junctions has attracted more and more attention. Due to their outstanding physical and chemical properties, fullerene dimers have proven to be attractive nanoscale organic compounds in various fields such as nonlinear optics, organic materials, biology, and medicine.21 C120 is the simplest synthesized fullerene dimer, in which two C60's are linked by a cyclic C4 unit in a [2 + 2] cycloaddition.22,23 The C60 cage, with an internal diameter of approximately 7.1 Å,24 is therefore sufficiently large to be capable of enclosing small quest species. However, though endohedral fullerenes that encapsulate atoms, molecules, or clusters inside the carbon cages have attracted increasing attention during recent decades,25−29 endohedral fullerene dimers have scarcely been studied in both theory and experiment.30 To completely understand the properties of the C60 dimer and its endohedral complex Li@C60 dimer, in this work, we Received: November 11, 2011 Revised: February 6, 2012 Published: March 5, 2012 7968
dx.doi.org/10.1021/jp210880j | J. Phys. Chem. C 2012, 116, 7968−7974
The Journal of Physical Chemistry C
Article
Figure 1. Schematic description of the (a) C60 dimer and (b) Li@ C60 dimer junctions. The region in the box indicates the electrode, and the one between two boxes is the central scattering region. The gray, purple, and yellow spheres represent C, Li, and Au atoms, respectively.
electrons are modeled with the Troullier−Martins nonlocal pseudopotential.36 The electrode calculations are performed under periodical boundary conditions, and the Brillouin zone has been sampled with 1 × 1 × 100 points within the Monkhorst−Pack k-point sampling scheme. In addition, to avoid the interaction between the molecule and its periodic images, a large supercell dimension (20 Å) in the plane perpendicular to the transport direction is adopted. The nonlinear current through the device is calculated using the Landauer−Bütiker formula I(V) = (2e/h)∫ μμLRT(E,V) dE,37 where h is the Planck’s constant, e the electron charge, f the Fermi function, μL/R(V) = EF ± eV/2 the electrochemical potential of the left and right electrodes, EF the Fermi level of the system which is set to be zero in our calculations, and T(E,V) the transmission function. The energy region [μL(V),μR(V)] contributing to the total current integral is called the bias window. In the approach, the molecular vibration effects have not been considered. Some deep discussions on these aspects in quantum transport can be found in ref 38.
employ the nonequilibrium Green function method combined with the density functional theory (NEGF+DFT) to investigate the electronic transport characteristics of both dimers under finite biases. Interestingly, NDR behavior is found in these two junctions. Especially, NDR with larger peak-to-valley ratio (PVR) at much lower bias is found in the Li@C60 dimer.
II. CALCULATION METHOD AND SIMULATION MODEL The molecular devices we study are illustrated in Figure 1. The C60/Li@C60 dimers are sandwiched between two gold electrodes which are extracted from the bulk gold along the (100) direction and have a finite cross section. The number of atoms in each atomic layer in the Au(100) electrode is periodically arranged as 5, 4, 5, 4, ..., as done by many authors.9,31,32 In NEGF theory, such a two-probe system is divided into three regions: a left electrode, a central scattering region, and a right electrode. The semi-infinite electrodes are calculated separately to obtain the bulk self-energy. The scattering region includes the C60/Li@C60 dimers and a portion of the semi-infinite electrodes to screen the perturbation effect from the central region. The geometrical optimizations and the electronic transport properties are all calculated by the ATK package,33,34 which is based on the NEGF+DFT technique. In our calculations, the exchange-correlation potential is described by the generalized gradient approximation (GGA) in Perdew, Burke, and Ernzerhof form.35 Valence electrons are expanded in a singleζ plus polarization basis set (SZP) for Au atoms and a double-ζ plus polarization basis set (DZP) for C and Li atoms. Core
III. RESULTS AND DISCUSSION From Figure 1, the encapsulated Li atoms obviously depart from the center of the cages. The off-center distance is 1.498 Å, which is very close to that in the endohedral fullerene Li@C60 monomer (about 1.5 Å).39,40 The distance between two Li atoms is 10.962 Å. Figure 2 describes the currents as a function of the applied bias for C60 and Li@C60 dimer junctions. From the figure, we can see that the I−V curve of the C60 dimer reveals semiconducting behavior, while the Li@C60 dimer is a 7969
dx.doi.org/10.1021/jp210880j | J. Phys. Chem. C 2012, 116, 7968−7974
The Journal of Physical Chemistry C
Article
Figure 2. Calculated current as a function of the applied bias for C60 (black line with squares) and Li@ C60 (red line with circles) dimer junctions.
good conductor, which agrees with the result obtained by Ono and Hirose.41 It is clear that the current through the Li@C60 dimer is significantly larger than the one through the C60 dimer at low biases (
