Metallic and semi-metallic<100>silicon nanowires

Silicon nanowires grown along the<100>-direction with a bulk Si core are studied with density functional calculations. Two surface reconstructions prevail after exploration of a large fraction of the phase space of nanowire reconstructions. Despite their energetical equivalence, one of the reconstructions is found to be strongly metallic while the other one is semi-metallic. This electronic-structure behavior is dictated by the particular surface states of each reconstruction. These results imply that doping is not required in order to obtain good conducting Si nanowires.

reported extremely thin SiNWs grown along the 110 lattice direction, whose diameters range from 1.3 to 7 nm. Previously, Holmes et al. [8] obtained 100 and 110 SiNWs of 4 to 5 nm and discussed the influence of lattice orientation. Wu et al. [9] have grown 110 , 111 and 112 SiNWs down to 3 nm. Colemann et al. [10] have reported SiNWs of 3 to 5 nm diameter.
Thus, a detailed understanding of thin SiNWs structure and of their mechanical and electrical properties as a result of the different growth conditions is required. While it has been extensively demonstrated that in H-terminated SiNWs quantum confinement induces a gap-broadening effect [11,12,13], little is known about surface reconstruction of nonpassivated wires and about their electronic structure. Theoretical studies of the structure of the thinnest possible SiNW [14,15] have been previously published. However, recent experiments have provided convincing evidence that some SiNWs grow around a monocrystalline bulk Si core [7,16]. Systems fulfilling such a requirement have been studied by Ismail-Beigi and Arias [17] ( 100 SiNWs) and by Zhao and Yakobson [18] ( 100 and 110 wires). Both studies show the paramount importance of facet edges in wires with diameters in the nanometer range.
Thin nanowires pose fundamental problems with respect to their conduction properties.
Recently, it has been discussed that doping may not be the advisable technique for tailoring nanodevice electrical properties, because of the expected statistical deviation of impurity concentration from one system to another [13,20]. Indeed, typical concentrations for attaining the measured SiNWs conductance [21,22] may well mean that no donor/acceptor is actually present in nm-wide SiNWs. Some of these measurements show that conductance is larger than expected for doped SiNW [21] and the authors suggest that surface states may 2 be responsible for the measured conduction.
In this Letter, we present a theoretical study of realistic 100 SiNWs, with a bulk Si core and a diameter of ∼ 1.5 nm [17,18], thoroughly exploring the phase space of SiNW reconstructions. We study different periodic cells, ranging from 57 to 912 atoms, so that periodicity does not prevent us from finding the lowest-energy reconstruction. The mechanical properties of the SiNWs are studied by computing their Young modulus and Poisson ratio.
Particularly, we focus our attention on the electronic properties of the wire as determined by the different possible lateral facet reconstructions. We give the first description of nanowire surface states as they evolve from the particular surface reconstruction of the studied SiNW.
Depending on the reconstruction, the surface state can cross the Fermi level affecting the electrical characteristics of the nanowire. Hence, there is an intrinsic relation between the reconstruction of nanowire facets and its transport properties. This is a remarkable finding that shows that doping is not needed for obtaining conducting SiNWs.
We have performed density-functional theory (DFT) calculations with both a numerical atomic orbital [23] and a plane-wave [24] basis set. We have used a double-ζ polarized basis set [23] and a plane-wave energy cutoff of 20 Ry [24], with the Generalized Gradient Approximation [25] for the exchange-correlation functional. We have studied wires in supercell geometry with a diameter of ∼ 1.5 nm. The axis periodicity will restrain the number of possible reconstructions and for this reason we have considered different supercell sizes, analyzing SiNWs of 57, 114 and 171 atoms. The reciprocal space has been sampled with a converged grid of 12, 6 and 4 k-points respectively. The atomic positions have been relaxed until the maximum force was smaller than 0.04 eV/Å. The faceting geometry adopted by the wire is given by thermodynamical considerations [17,18,19]. On the one hand, the formation of {100} facets is favored over {110} facets, due the lower corresponding surface energy; on the other hand, facets with an even number of atoms can dimerize, lowering their energy, and are thus favored over facets with an odd number of atoms [26].
We have obtained two competing geometries for the {100} facets: a 1c reconstruction [see reconstruction, while on the other side one every two dimers is flipped. In contrast to what has been proposed for the Si(100) surface [32], none of the two cases shows spin polarization.
The two arrangements do not correspond to any infinite surface reconstruction, even though they loosely resemble the Si(100) c(4 × 2) and p(4 × 2) (but not the p(2 × 2), for the Si(100) surface reconstructions see for example Ref. [29]). The difference between surface and SiNW reconstructions stems from the lower coordination of the facet atoms. Between two adjacent dimers on the facet there is one single atom in the underneath layer, while between the corresponding dimers on the (100) surface there are two. This reduced coordination leads to a lateral shift of the dimers, increasing their packaging.
In order to extensively explore other possible reconstructions, we have also performed non-orthogonal tight-binding (TB) [33,34] calculations, considering supercells with a lattice parameter along the wire axis up to 16c (912 atoms). The TB structural relaxations are in very good agreement with the DFT results and no new reconstruction was found. We have also taken into account other faceting arrangements prior to relaxations, but we confirm that the minimum energy configurations are obtained when {100} facets prevail [17,18,19].
Second-neighbor empirical potentials [35,36] have also been tested, but they have proven to be unsuitable to reproduce the complexity of these reconstructions.
Given the small energy difference between the two reconstructions, we have checked if at finite temperatures one of the two phases prevailed more clearly. We have calculated the Helmholtz free energy F following a quasi-harmonic approach up to 300 K [37]. We have found that the difference between the two structure remains practically unchanged all over the temperature range analyzed. This is due to the fact that the vibrational contribution to F is determined by the integrated phonon density of states which hardly changes from one case to the other.
If SiNWs are to be used as nanoswitches or for manipulation purposes, it is important that they have a certain stiffness that prevents them from collapsing as a result of mechanical tensions. We have studied the response to axial stress in 100 SiNWs within non-orthogonal TB, finding a Young's modulus of ∼ 137 GPa (∼ 195 GPa for bulk Si) and a Poisson ratio of ∼ 0. 35 [38]. These values confirm the intuition that their bulk core make SiNWs mechanically stable.
We have calculated the band structure diagrams corresponding to the two different reconstructions. Surprisingly, the electronic structures turn out to be utterly different, especially if compared to their rather similar geometries. The 1c-reconstruction has four clearly metallic states [see Fig. (2a)], while the 2c wire shows a semi-metallic behavior with a single  Fig. (2). This shift is due to the reduction of symmetry by the flipped dimer. The flipped dimer interrupts the surface Bloch states, hence the overlap between dangling bonds is reduced in the 2c-reconstruction and the energy of the surface states increases. Electronic localization induces an increase of energy by breaking the one-dimensional Bloch state, but on the other hand makes the system lower its energy locally by increasing the bonding of one of the dimers.
The bands of the 1c-reconstruction can be identified with the 2c-reconstruction ones, Fig. (2). The (ii) band of Fig. (2a) shows similar symmetry as the (2) of Fig. (2b) (see Fig. 3 below). An adiabatic calculation, slowly flipping the dimer yields this one-to-one correspondence. In the same manner, bands (iii) and (iv) of Fig. (2a) can be identified with (4) and (3) of Fig. (2b) respectively. The effect on the electronic structure of flipping one dimer is to localize, leading to higher-energy and flatter bands, Fig. (2b).
The electronic structure about the Fermi energy is given by the surface states originating in the dimer dangling bonds. This is shown in Fig. (3). Iso-surfaces of wave-function amplitude have been plotted on the SiNW atomic structure, showing that Bloch states originate on the facet dangling bonds. Figure (3 Conductance through thin SiNWs remains a difficult issue [21]. The way SiNWs bind to metal electrodes is complex and crucial for determining the actual conductance of SiNWbased devices. In the absence of defects and in the case of excellent electrode contacts, the strongly metallic SiNW (1c-reconstructed) will present a maximal conductance of four quanta, equivalent to a resistance of only ∼ 3kΩ per SiNW. In the same conditions the semi-metallic SiNW (2c-reconstructed) exhibits a minimum resistance of ∼ 13kΩ per SiNW.
These results show that SiNWs can be good conductors, and their actual electrical properties will be strongly dependent on the growth conditions. Experimental studies [21] show that despite diffusion from the metallic contacts and/or surface contamination the measured conductance of thin SiNWs after annealing is much higher than the one expected from doping the SiNWs. This finding is in qualitative agreement with the above surface-state driven conduction.
Any perturbation on the surface states will drastically affect the conduction properties of the wires. These wires will be extremely sensitive to the chemical environment and therefore are good candidates for molecular detection [4,5,6]. [38] The Young's modulus is the ratio between stress and the axial strain ǫ and is conventionally where V 0 and E are the equilibrium volume and the total energy respectively; the Poisson ratio is defined as σ = − 1 ǫ R−R 0 R 0 , where R 0 is the equilibrium radius of the SiNW and R is the radius at strain ǫ.