Electronic transport properties of doped [C.sub.28] fullerene.
The last few decades of the twentieth century witnessed an upsurge in development of electronics based on molecular devices . Electrical measurements on single molecules embedded between electrodes have attracted special attention [2-5]. Electron transport across such molecular junctions gives rise to interesting phenomena like negative differential resistance, rectification, single electron characteristics [5-7], and so forth. This has resulted in their application as field effect transistors , logic gates , switches , and sensors . Numerous attempts have been made to investigate transport properties of a fullerene molecule [12-14]. A fullerene molecule possesses unique structural and electronic properties, and its role as a functional electronic device [15, 16] has been widely analyzed. The transport properties of a fullerene molecule are influenced by its orientation between the electrodes , the nature of contact with the electrodes , and also on the type of doping and nature of dopant [19, 20]. An et al. found that insertion of Li into [C.sub.20] cage improves its transmission capacity and increases the equilibrium conductance by about 66.67% . Zhang et al. revealed that the conductivity for the doped [C.sub.60] fullerene is higher than that of the pristine fullerene .
The spin-resolved transport properties of [C.sub.28] molecule sandwiched between Au electrodes with different contact configurations have been examined theoretically . [C.sub.28] is the smallest fullerene that has been found to be experimentally significant [23, 24]. Since [C.sub.28] molecule is very active, it can form particularly stable endohedral complexes [25-27]. Guo et al. found that empty [C.sub.28] fullerene behaves as a hollow tetravalent superatom with tetrahedral symmetry . It was proposed that metals with electronegativities smaller than 1.54 should form endohedral fullerenes larger than a minimum size, which depends on the radius of the trapped atom. Based on the above size and electronegativity considerations, it should be possible to encapsulate Li atom in [C.sub.28] cage. Insertion of Li atom in a smaller fullerene molecule has been found to increase its conductivity , and also endohedral derivatives of fullerene molecules based on Li have been investigated [29, 30]. In this work we undertake the study of transport properties of endohedral fullerene Li@[C.sub.28] sandwiched between Au (111) electrodes using a first-principles computational method based on density functional theory in combination with nonequilibrium Green's function theory. Doping can effectively change the electronic properties of fullerenes and hence provides an opportunity to modify transport properties as well. Thus we attempt to understand the effect of single-atom change on transport properties of [C.sub.28] fullerene. The transmission spectra at different bias voltage and IV characteristics are plotted and compared for both pure and doped [C.sub.28] molecules.
2. Computational Details
The geometry relaxations and electronic structure calculations for both Li@[C.sub.28] and [C.sub.28] molecules are performed based on DFT formulism using SIESTA  package with LDA functional in Ceperley and Alder form . A SZP basis set is employed to describe the localized atomic orbitals. The core electrons are modeled with Troullier and Martins  nonlocal pseudopotential. An energy cutoff for real-space mesh size is set to be 400 Ry. All atomic positions are fully relaxed with a force tolerance of 0.04 eV/[Angstrom]. For the analysis of electron transport through the molecular contact we used the TRANSIESTA  code, which implements the NEGF formalism for the single-particle Kohn-Sham Hamiltonian obtained from DFT calculations performed with SIESTA.
The current through the atomic scale system is calculated from Landauer-Buttiker  formula:
I = [e/h]([[integral].sup.[infinity].sub.-[infinity]])T(E,V)[f(E-[[mu].sub.1]) - f(E-[[mu].sub.2])]dE, (1)
where [[mu].sub.1] and [[mu].sub.2] are the electrochemical potentials of the left and right electrodes, V is the external bias, and f(E) is the Fermi-Dirac distribution function. T(E, V) is the transmission coefficient at energy E and bias voltage V and represents the quantum mechanical transmission probability for electrons. Consider
[[mu].sub.1,2] = [E.sub.f] [+ or -] [eV/2]. (2)
The energy region between [[mu].sub.1] and [[mu].sub.2], which contributes to the current integral above, is referred to as the bias window. A sample of 3 x 3 x 30 k-points for computing transport properties was employed by the method of Monkhorst-Pack  to describe the Brillouin zone.
The system under study can be divided into three parts: left electrode, right electrode, and the scattering region, which includes the fullerene molecule and a few atomic layers of the electrodes. [C.sub.28] molecule is rigidly attached to Au (111) surface by first positioning it between the two surfaces such that it has a desirable Au-C bonding distance 0.225 nm and then relaxing the whole system until the forces on all atoms are less than 0.04 eV/[Angstrom]. Two Au adatoms in the right and left electrodes are adopted for effective coupling with electrodes due to the small [C.sub.28] molecular radius. After structural relaxation, the equilibrium Au-C distances become 2.285 [Angstrom] and 2.289 [Angstrom], respectively, for the left and right electrodes. The distance between Au adatom and the nearest neighboring Au atom of Au (111) surface is about 2.64 [Angstrom] (Figure 1).
3. Results and Discussion
3.1. Structures of Pristine and Doped [C.sub.28] Molecules. The ground-state structure of [C.sub.28] molecule has [T.sub.d] symmetry with three unique carbon atoms. The three C-C bond lengths [R.sub.1], [R.sub.2], and [R.sub.3] in the relaxed structure are 1.477, 1.575, and 1.457 [Angstrom], respectively (as shown in Figure 2). The binding energy is calculated to be 8.42 eV. These values agree well with the previous reports . The endohedral atom was placed at the centrosymmetric position inside the cage and the structure was allowed to relax. It was observed that the dopant occupies the central position, maintaining the overall tetrahedral symmetry of the cage. An elongation in bond lengths as a result of the expansion of the cage is observed.
[C.sub.28] molecule is known to have a small band gap. However, it is found that, as a result of insertion of Li, its HOMO-LUMO gap reduces further from 0.326 to 0.143 eV, and therefore it is expected that it should have a higher equilibrium conductance (i.e., transmission coefficient at the Fermi energy of the system). The electronic energy levels of [C.sub.28] and Li@[C.sub.28] molecules near Fermi level are illustrated in Figure 3. Both HOMO and LUMO levels move closer to the Fermi level as a result of doping with Li, thus decreasing the energy difference between these levels.
3.2. Transport Properties under Zero Bias. Transmission function is the most important physical quantity for determining electron transport through single molecular junctions. The zero bias transmission functions for pure [C.sub.28] molecule and Li@[C.sub.28] systems in the energy range of -1 to 1 eV have been shown in Figures 4(a) and 4(d), respectively; the Fermi level has been shifted to zero for clarity. The equilibrium conductance of the system can be computed as G = [G.sub.0]T([E.sub.f]), where [G.sub.0] = [2e.sup.2]/h. It is found that zero bias conductance for the junction formed by [C.sub.28] is 0.935[G.sub.0] and that of Li@[C.sub.28] is 0.311[G.sub.0], respectively.
For the molecular junction formed by [C.sub.28], there are two transmission peaks near the Fermi level, which contribute to transport of electrons across the junction. However, in Figure 4(d), it is found that, as a result of Li doping, there is a shift in molecular orbitals as a transmission valley is developed near the Fermi level. Hence the zero bias conductance for Li@[C.sub.28] is less as compared to the undoped molecule even though the band gap of the isolated [C.sub.28] molecule is found to decrease upon endohedral doping with Li. This is mainly because the electronic transport depends on several factors, such as the broadening of the energy levels of the central cluster, the alignment of the Fermi level of the electrodes within the HOMO-LUMO gap, charge transfer between the electrodes and the central cluster, and so forth.
The molecular projected self-consistent Hamiltonian (MPSH) eigenstates near Fermi level for both devices are shown in Figure 5, which are the perturbed molecular orbitals due to coupling between molecule and the electrodes. The calculated results show that, under zero bias voltage, the HOMO of [C.sub.28] is very close to the Fermi level, so the HOMO mostly contributes to the equilibrium conductance.
For Li@[C.sub.28] the projected HOMO-LUMO gap increases, which can be attributed to coupling with electrodes. This leads to a lower value of equilibrium conductance. In both cases it is the HOMO that contributes to conduction, more than the LUMO.
The HOMO and LUMO of [C.sub.28] and Li@[C.sub.28] are plotted in Figure 6. It is known that the charge density distribution of molecular orbitals affects the transport of electrons. The charge distribution of HOMO is clearly different for both cases. It can be observed that the molecular orbitals for [C.sub.28] are more delocalized in character, which indicates stronger molecule-electrode interaction. Additionally, the charge density for HOMO is more in case of [C.sub.28] and is also aligned along the transmission axis (z-axis).
3.3. Transport Properties under Finite Bias. The transport behavior of a molecular junction can be modulated by applying a bias voltage. Therefore we investigate the effect of applied bias in both directions. The electron transport across a junction and hence the current flow depend on the extent of coupling between molecule and electrodes. Strong coupling will aid transfer of electrons and hence a stronger peak will appear in transmission spectra. On the other hand, a vanishing transmission near the Fermi region indicates weakening of electronic transport.
For [C.sub.28], at a bias voltage of 0.5 V (Figure 4(b)), a diffusive transmission peak appears in the bias window just below the Fermi level, which contributes to current flow. In general, peaks in the bias window of transmission spectra represent hybridized molecular orbitals of the scattering region in presence of gold electrodes. Here, the transmission close to the Fermi energy appears to be dominated by HOMO of the molecule. For Li@[C.sub.28], a vanishing transmission near the Fermi region indicates a larger HOMO-LUMO gap. In the absence of any resonant peak, caused by a decrease in the degree of coupling between central cluster and electrodes, a lesser magnitude of current as compared to the pristine fullerene molecule is obtained.
Upon increasing the bias voltage to 1 V, there are more channels in the bias window contributing to the transmission, causing a further increase in current. While there are more and stronger conduction channels for undoped [C.sub.28] molecule, a transmission valley appearing in Figure 4(f) suggests weak effective coupling of the Li@[C.sub.28] molecule with electrodes, which is also apparent in the smaller width of the transmission peaks.
The current-voltage characteristics of the molecular device formed by sandwiching undoped [C.sub.28] cage and Li@[C.sub.28] cage, respectively, between two Au electrodes are shown in Figure 7. The current is found to increase with increase in bias voltage for all three molecular junctions. In general current increases nonlinearly with voltage. While a metal-like conduction is observed at small bias (-0.5 V to 0.5 V), a rapid increase in current occurs as the bias is further increased to 1 V. The increase in current for undoped [C.sub.28] is more as compared to Li@[C.sub.28] molecule.
Endohedral doping of [C.sub.28] with Li atom is found to affect its electronic structure and hence the transport properties. The electronic transport properties of doped fullerene Li@[C.sub.28] and host [C.sub.28] molecule sandwiched between two gold surfaces have been calculated using first-principles density functional theory and nonequilibrium Green's function formalism. The transmission curves and IV characteristics of both pristine and doped molecule are computed. The current across the junction is found to decrease upon Li encapsulation. The change in current is more pronounced at higher voltage, which indicates that introduction of the dopant atom in [C.sub.28] cage weakens the electron transport, and can be attributed to modification in alignment of the molecular orbitals in presence of electrodes.
Akshu Pahuja and Sunita Srivastava
Department of Physics, Panjab University, Chandigarh 160014, India
Correspondence should be addressed to Akshu Pahuja; email@example.com
Received 21 August 2014; Revised 19 October 2014; Accepted 11 November 2014; Published 26 November 2014
Academic Editor: Yuan Ping Feng
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
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|Title Annotation:||Research Article|
|Author:||Pahuja, Akshu; Srivastava, Sunita|
|Publication:||Physics Research International|
|Date:||Jan 1, 2014|
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