VOLUME 8, NUMBER 12, DECEMBER 2008 Copyright 2008 by the American Chemical Society
Electromechanical Switch Based on Mo6S6 Nanowires Igor Popov,*,† Sibylle Gemming,‡ Shinya Okano,† Nitesh Ranjan,§ and Gotthard Seifert† Institut fu¨r Physikalische Chemie, Technische UniVersita¨t Dresden, D-01062 Dresden, Germany, Institute of Ion-Beam Physics and Materials Research, Forschungszentrum Dresden-Rossendorf, PF 51 01 19, D-01314 Dresden, Germany, and Institute for Materials Science and Max Bergmann Center for Biomaterials, Technische UniVersita¨t Dresden, Germany Received May 21, 2008; Revised Manuscript Received September 8, 2008
ABSTRACT We investigate the structural, electronic, and transport properties of mechanically deformed Mo6S6 nanowires using a density-functional based tight binding method extended with a Green’s functions formalism. We present two interesting results: first, the properties of the wire are not affected by bending, and second, a metal-insulator transition occurs when the wire is twisted. This indicates that molybdenum sulfide nanowires can be used as a nanocable to flexibly transfer information between electromechanical switches, which can be also constructed from the same wires. Hence, our results suggest the Mo6S6 nanowires as unique building blocks for future nanodevices.
The structural, electronic, and optical properties of ideal molybdenum-sulfide Mo6S6 nanowires (NWs) and related structures such as Mo6S6-xIx have been investigated in detail, both by experiment and theory.1-9 Molybdenum sulfide NWs form weakly bound bundles of parallel wires that exhibit high mechanical stability, metallic conductivity, and a strictly determined atomistic structure built from alternating Mo3S3 triangles. These properties make molybdenum sulfide NWs quite favorable building blocks for nanoscale electronic devices compared with carbon nanotubes (CNTs), for which a wealth of structural variants introduces a wide spread of * Corresponding author. E-mail:
[email protected]. † Institut fu ¨ r Physikalische Chemie, TU Dresden. ‡ Institute of Ion-Beam Physics and Materials Research, Forschungszentrum Dresden-Rossendorf. § Institute for Materials Science and Max Bergmann Center for Biomaterials, TU Dresden. 10.1021/nl801456f CCC: $40.75 Published on Web 10/29/2008
2008 American Chemical Society
electronic properties, and the separation of single tubes from bundles is impeded by strong intertubular interactions.1 In detail, the specific electronic and transport properties of Mo6S6-xIx NWs resemble values obtained for metallic CNTs.1,2,10 Additionally, the NWs form ideal Ohmic contacts with gold electrodes,11 quite in contrast to CNT-Au contacts, where the electronic transport is significantly affected by relatively high potential barriers at the CNT-Au interface. For these reasons, a series of studies on MoxSyIz NWs12,13 and on the isoelectronic Mo6Se6 NWs14 has been carried out recently. The NWs tend to self-assemble into networks, which may be a breakthrough toward a bottom-up integration of the NWs into electronic devices.12,13 However, to reach such a goal, the NWs must be sufficiently flexible to adjust to fine structures within a device. While the effects of bending and twisting on the electronic transport properties
Figure 1. Geometry of structure models for bent (a) and twisted (b) Mo6S6 nanowires prior to structural relaxation. Bent and twisted regions consist of 20 unit cells. In the bent part of the NW in panel a, the axis is aligned to a circle of radius R, whereas the twisted part in panel b is considered as straight fragment. The electrodes are semi-infinite, ideal, straight nanowires.
have been studied in CNTs,15-18 the response of molybdenumchalcogenide NWs to mechanical deformation has not been studied in detail, so far.2,10 Here, we present results on the electronic transport of bent and twisted NWs. Similar to CNTs, Mo6S6 NWs resist uniform bending. Up to a curvature of about 0.18 nm-1, which corresponds to a tilt of 4.5° between adjacent Mo6S6 units, the structural integrity of the NW is intact, and the electron transmission properties are nearly unchanged. Thus, this type of NW remains metallic even under a curvature, which is considerably larger than the one observed experimentally for Li-separated wires of the selenium analogue.14 On the other hand, twisting of the NWs already by small angles causes significant changes of the electronic properties and initiates a metal-insulator transition, which will be discussed in more detail below. Hence molybdenum-sulfide NWs may be employed as electromechanical switch similar to CNTs in the seminal experiment by Cohen-Karni et al.,18 but NWs exhibit further advantages which will be elaborated in the present letter. The density-functional-based tight-binding (DFTB) method19,20 is employed for the calculations of the energies, and a DFTB variant extended by a Green’s function formalism21,22 is used to determine the conductance properties (electron transmission T(E)). The Ceperly-Alder parametrization of the exchange-correlation functional in the local density approximation (LDA) is employed, and scalar relativistic corrections are included. The DFTB method utilizes a valence-only local atomic orbitals basis set (including Mo(5p) orbitals), and yields structural and electronic properties of molybdenum chalcohalides in very good agreement with recent results obtained using full densityfunctional theory (DFT) both with a local, orbital-based1 and with a nonlocal, plane-wave basis set.3 For the ideal Mo6S6 NW, the present approach yields an optimized repeat unit of 4.35 Å, which agrees excellently with the value of 4.34 Å calculated by the other DFT approaches.1,3 The DFTB method has also been used successfully for the description of various complex molybdenum-chalcohalide structures.23-26 4094
The investigated geometries of the mechanically deformed NWs are depicted in Figure 1. The deformed region contains twenty unit cells, corresponding to a length of about 9 nm. The initial geometry of the bent NWs (Figure 1a) is designed with the constraints that alternating triangles of the NWs are positioned perpendicularly to the tangent of the bending path and that the wire axis of the bent fragment is aligned along a circle of radius R and the triangles are tilted with respect to each other by the bending angle. In addition, the length of the deformed fragment measured along the axis is initially chosen as identical to the corresponding segment of the ideal wire. In the twisted wire sketched in Figure 1b, the axis is initially chosen as linear and the Mo3S3 triangles are homogeneously rotated around the axis by the twisting angle. The structural relaxation was carried out for finite nanowire geometries, i.e. for clusters, which contain the deformed region in the center and which are saturated at the ends by straight wire segments of four unit cells in length terminated by a capping sulfur atom. The atom positions of the straight parts were fixed during the structural relaxation. The straight segments are substituted by two straight semi-infinite Mo6S6 NWs in the calculations of the transmission function, in which the semi-infinite parts serve as electrodes. For the twisted NWs, this model structure corresponds closely to the experimental setup in the measurements of Cohen-Karni et al.18 with CNTs. First we investigated the influence of the deformations on the stability and structure of the NWs. The potential energy of the deformations, defined as difference between the total energies of straight and deformed NWs, are shown in Figure 2 as function of the deformation angles. A parabolic fit (see Figure 2) matches the calculated data very well up to a bending angle of about 10° nm-1, which corresponds to a curvature of 0.18 nm-1. This is an indication that the bending does not introduce plastic deformations in the NW. Careful investigation of the relaxed geometries supports this conclusion; there are no significant reconfigurations of the atomic structure of the bent wire. For the wire with the largest investigated curvature, the Mo-Mo bond lengths within the Mo3S3 triangles remain close to their ideal value, 2.78 Å. Nano Lett., Vol. 8, No. 12, 2008
Figure 2. Potential energy of the deformation in bent (a) and twisted (b) geometry with respect to straight NWs. The bending and twisting angles are indicated in Figure 1. Red diamonds represent data obtained after a full structural relaxation. Blue lines are parabolic fits to the weakly deformed part of the curves, i.e. for bending angles below 3° nm-1 and twisting angles below 10° nm-1.
Figure 3. Transmission of the bent (a) and twisted (b) nanowire. The Fermi level is set to zero. On the right side, the color scale of the electron transmission is given: white areas represent the maximum transmission of 12, and areas shaded in blue correspond to a minimum transmission of zero. The transmission is calculated in the steps of 1° nm-1, and the transmission data is a posteriori interpolated.
The Mo-Mo bond lengths between Mo atoms placed on neighboring Mo3S3 triangles change from 2.70 Å by (0.08 Å. Thus, the molybdenum sulfide NWs are considerably more flexible than carbon nanotubes,15 which tend to kink upon bending. In contrast, the homogeneous twisting a priori (prior to structural relaxation) introduces significant changes to the local atomic structure of the nanowire. Again, the twist initially does not affect the bond lengths within the Mo3S3 triangles that are rigidly rotated around the axis of the wire, but their relative rotation introduces a shrinkage or elongation of bond lengths between atoms belonging to neighboring triangles by up to 0.14 Å (for a twisting angle of 46° nm-1). The a posteriori structural relaxation of the twisted nanowire does not introduce a remarkable additional relocation of the atoms, when the twisting angle is less than 50° nm-1; Mo triangles remain almost intact and the bond lengths between neighboring triangles change by up to 0.02 Å, i.e. they vary between 2.54 and 2.86 Å. For the twisting angles larger than 50° nm-1, the wires have a tendency to bend as observed for CNTs.27 Upon twisting, the potential energy curve deviates more strongly from the parabolic fit than upon bending (Figure 2b). That finding already indicates a plastic process coupled to stronger changes of the electronic structure as the twisting angle increases. Although the twisting energy of the wire is higher than the energy of bending, both values are remarkably smaller than the twisting energy observed for CNTs.15 Hence, the molybdenum sulfide nanowires are relatively flexible and Nano Lett., Vol. 8, No. 12, 2008
may easily adapt also to very fine features of a nanostructured template. The calculated transmission functions T(E) with respect to bending and twisting angles are shown in Figure 3a and b, respectively. As shown previously the ideal, undistorted Mo6S6 nanowire1 exhibits the following regions of constant transmission: from -0.4 eV to the Fermi level three open channels exist, up to 0.8 eV there are two open channels, and one open channel is obtained up to 1.7 eV. Below -0.4 eV, the transmission is not constant, but fluctuates similar to the density of states (DOS) in this energy region. Bending does not have any significant impact on the transmission for bending angles up to 10° nm-1, i.e. for curvatures of up to 0.18 nm-1 ideal metallic transmission along the wire is obtained. In contrast, twisting causes significant changes in the transmission of the nanowires. The most remarkable one is the opening of an energy gap in the region of the Fermi level, which is observable already at a twisting angle of 5° nm-1. This gap widens linearly and monotonically with increasing twist angle, and leads to a semiconducting state with an energy gap of about 0.3 eV for a twisting angle of 46° nm-1. From the Fermi level up to 0.8 eV, oscillations in the transmission spectrum are present. One can note the absence of oscillations in the projected density of states (PDOS) (see Figure 4) in this region. This indicates that the oscillations are not intrinsic to the twisted wire alone, but rather reflect a resonance-type property of the whole device. 4095
Figure 4. Projected density of states on Mo atoms (upper graph) and S atoms (lower graph) of the twisted wire by 10° between the neighboring alternating triangles, (which corresponds to 45.87° nm-1).
In order to gain insight into the mechanism of the transmission gap opening, we analyzed projected density of states (PDOS) curves and band structures in more detail. Figure 4 displays the PDOS curves for the ideal nontwisted NW (solid lines) and for a twisted wire with a twisting angle of 46° nm-1 (dashed lines), both calculated for a periodically repeated supercell containing six Mo6S6 units. Thus, in the twisted wire each Mo3S3 triangle is rotated by 10° with respect to the adjacent triangles. The Brillouin zone for the calculation of the PDOS is sampled by 40 k-points along the direction of the wire axis. The maximum of the Mo PDOS at -0.8 eV is considerably decreased upon twisting, which explains the rapid decrease of the transmission with
increasing the twisting angle. For both wires, the contribution from sulfur atoms is considerably smaller than the one from molybdenum atoms in the energy region around the Fermi level (see Figure 4), thus the Mo core dominates the conductance. However, for the twisted wire studied here, an energy gap between occupied and unoccupied states opens, which amounts to 0.2 eV and is flanked by van-Hove singularities. It should be noted that larger experimental gap values are expected, because the band gap is underestimated when employing the local-density approximation in the DFT. Since the gap is observed to open up linearly with the twist angle the semiconducting state may be experimentally detectable under even smaller angles than the ones investigated in the present study. To elucidate the origin of the energy gap and to rationalize the quantitative difference between the transmission energy gap and the band gap, the band structures were analyzed in more detail. Band structure plots of the two supercells are shown in Figure 5a and b along with the band structure calculated for the periodically repeated elementary Mo6S6 building block of the ideal wire (Figure 5c). The 6-fold folded band structure of the ideal NW in Figure 5a is more easily compared with the band structure of the twisted wire, and the unfolded band structure Figure 5c facilitates the band analysis. In the ideal wire, the states that contribute to the metallic conductivity in the vicinity of the Fermi level classify according to the C3V symmetry of the wire as a1-, a2-, and e-type, as indicated in Figure 5a and c. The e states touch the Fermi level close to the Γ point; the a1 and a2 states
Figure 5. (a) Band structure of the ideal wire obtained for a supercell consisting of 6 unit cells. (b) Band structure of the wire twisted with torsional angle of 45.87° nm-1. (c) Band structure of ideal nanowire obtained for a unit cell. Vertical dashed lines mark the k-vectors at which the band structure is folded into one shown in panel a. The gray area in panel c marks the energy region that are displayed in panels a and b. 4096
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intersect slightly below the Fermi level close to kz ) 0.6 in the large Brillouin zone obtained for the ideal wire. In a twisted NW, the symmetry is reduced to C3 and the states classify as e- or a-type (Figure 5b), i.e., the distinction between the a1 and a2 bands is lifted and both states are of a-type character. This leads to an avoided crossing of the two bands close to the intersection point in the ideal wire, which opens up a band gap, and two new van-Hove singularities appear at the edges of this band gap. However, the bands which constitute the singularities at these energies do not contribute to the electronic transport because of their small dispersion; therefore the gap in transmission (see Figure 3b) is somewhat larger than the gap obtained in the density of states. The doubly degenerate e band is shifted down to about -0.55 eV with respect to the Fermi level (at Γ point; out of the energy range in Figure 5b). From the comparison of the electronic band structures of ideal and twisted wire, it can be noted that the a-type bands of the twisted wire are misaligned with the corresponding a1 and a2 bands in the electrodes made of ideal wires. This may cause a partial backscattering of the propagating electron waves. In contrast to CNTs, the conductance of which oscillates with the increase of the twisting angle,18 the molybdenum sulfide NWs have the property of a unique unidirectional electromechanical switch, as a consequence of their simpler atomic structure. In conclusion, we have investigated the effects of mechanical deformations of Mo6S6 nanowires on their structural, electronic, and transport properties. We have found two remarkable features. First, a bending does not introduce any significant changes to the properties of the investigated system, hence the Mo6S6 nanowire can be exploited as a flexible nanocable in future electronic devices. On the other hand, the other type of deformation, twisting, opens a band gap, which indicates that the wires have the potential to be used as a nanoscale electromechanical switch. Thus, it is in principle possible to realize future nanodevices on the basis of all-Mo6S6 systems. Acknowledgment. We acknowledge financial support by the DFG and thank Dr. Andrey Enyashin for helpful discussions.
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