Abstract
Endohedral doping of small fullerenes like C28 affects their electronic structure and increases their stability. The transport properties of Li@C28 sandwiched between two gold surfaces have been calculated using first-principles density functional theory and nonequilibrium Green’s function formalism. The transmission curves, IV characteristics, and molecular projected self-consistent Hamiltonian eigenstates of both pristine and doped molecule are computed. The current across the junction is found to decrease upon Li encapsulation, which can be attributed to change in alignment of molecular energy levels with bias voltage.
1. Introduction
The last few decades of the twentieth century witnessed an upsurge in development of electronics based on molecular devices [1]. 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 [8], logic gates [9], switches [10], and sensors [11]. 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 [17], the nature of contact with the electrodes [18], and also on the type of doping and nature of dopant [19, 20]. An et al. found that insertion of Li into C20 cage improves its transmission capacity and increases the equilibrium conductance by about 66.67% [21]. Zhang et al. revealed that the conductivity for the doped C60 fullerene is higher than that of the pristine fullerene [22].
The spin-resolved transport properties of C28 molecule sandwiched between Au electrodes with different contact configurations have been examined theoretically [14]. C28 is the smallest fullerene that has been found to be experimentally significant [23, 24]. Since C28 molecule is very active, it can form particularly stable endohedral complexes [25–27]. Guo et al. found that empty C28 fullerene behaves as a hollow tetravalent superatom with tetrahedral symmetry [28]. 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 C28 cage. Insertion of Li atom in a smaller fullerene molecule has been found to increase its conductivity [21], 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@C28 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 C28 fullerene. The transmission spectra at different bias voltage and IV characteristics are plotted and compared for both pure and doped C28 molecules.
2. Computational Details
The geometry relaxations and electronic structure calculations for both Li@C28 and C28 molecules are performed based on DFT formulism using SIESTA [31] package with LDA functional in Ceperley and Alder form [32]. A SZP basis set is employed to describe the localized atomic orbitals. The core electrons are modeled with Troullier and Martins [33] 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/Å. For the analysis of electron transport through the molecular contact we used the TRANSIESTA [34] 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-Büttiker [35] formula: where and are the electrochemical potentials of the left and right electrodes, is the external bias, and is the Fermi-Dirac distribution function. is the transmission coefficient at energy and bias voltage and represents the quantum mechanical transmission probability for electrons. Consider The energy region between and , which contributes to the current integral above, is referred to as the bias window. A sample of k-points for computing transport properties was employed by the method of Monkhorst-Pack [36] 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. C28 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/Å. Two Au adatoms in the right and left electrodes are adopted for effective coupling with electrodes due to the small C28 molecular radius. After structural relaxation, the equilibrium Au–C distances become 2.285 Å and 2.289 Å, 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 Å (Figure 1).
3. Results and Discussion
3.1. Structures of Pristine and Doped C28 Molecules
The ground-state structure of C28 molecule has symmetry with three unique carbon atoms. The three C–C bond lengths R1, R2, and R3 in the relaxed structure are 1.477, 1.575, and 1.457 Å, respectively (as shown in Figure 2). The binding energy is calculated to be 8.42 eV. These values agree well with the previous reports [37]. 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.
C28 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 C28 and Li@C28 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.
(a)
(b)
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 C28 molecule and Li@C28 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 , where . It is found that zero bias conductance for the junction formed by C28 is 0.935 and that of Li@C28 is 0.311, respectively.
For the molecular junction formed by C28, 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@C28 is less as compared to the undoped molecule even though the band gap of the isolated C28 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 C28 is very close to the Fermi level, so the HOMO mostly contributes to the equilibrium conductance. For Li@C28 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 C28 and Li@C28 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 C28 are more delocalized in character, which indicates stronger molecule-electrode interaction. Additionally, the charge density for HOMO is more in case of C28 and is also aligned along the transmission axis (-axis).
(a)
(b)
(c)
(d)
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 C28, 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@C28, 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 C28 molecule, a transmission valley appearing in Figure 4(f) suggests weak effective coupling of the Li@C28 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 C28 cage and Li@C28 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 C28 is more as compared to Li@C28 molecule.
4. Conclusion
Endohedral doping of C28 with Li atom is found to affect its electronic structure and hence the transport properties. The electronic transport properties of doped fullerene Li@C28 and host C28 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 C28 cage weakens the electron transport, and can be attributed to modification in alignment of the molecular orbitals in presence of electrodes.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.