Orientation dependence of electronic properties of antimony selenide nanowires

We present a comprehensive DFT study of size-dependent atomic and electronic properties of antimony selenide (Sb 2 Se 3) nanowires in three main crystallographic directions. Our calculations show a significant enhancement in the band gap of wires oriented in [100] and [010] directions due to confinement effects, however the band gap of [001] oriented wires is reduced with respect to bulk. We attribute this anomaly in band gap reduction to the surface reconstructions in these nanostructures. These surface reconstructions are similar to the polyhedral distortions observed in bulk Sb 2 Se 3 under high pressure leading to the insulator-metal transition related to the topological insulating states and then at lower temperature (8K) to superconductivity.

Nanostructures of Sb 2 Se 3 have been synthesized using various growth methods. Of these nanostructures reported so far, the smallest sizes are 4 nm nanorods [22] & 20 nm nanowires [23] by chemical & physical methods respectively. According to the effective mass approximation (EMA) ( [24]), at these sizes, the band gap is expected to be near the bulk value with no significant change. However, a wide range of band gaps from 1.13 eV to 1.49 eV have been reported for these nanostructures [25] with a theoretical study reporting 1.66 eV for a stand alone single ribbon [26].
Most of the nanostructures of Sb 2 Se 3 have been grown by chemical methods and yields [001] oriented structures. Controlling the thermodynamical conditions we were able to grow [010] oriented Sb 2 Se 3 nanostructures employing the VLS growth method [23]. Considering the crystallographic orientations of synthesized nanostructures and anisotropic nature of the crystal structure of bulk Sb 2 Se 3 , we have studied the influence of orientation and size on the electronic behaviour of these nanostructures. Here, we explore Sb 2 Se 3 nanowires oriented in the three main crystallographic orientations of the bulk crystal ( Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Methods
Calculations were performed using the Vienna ab initio simulation package (VASP) [27,28] with generalized gradient approximation [29] and projector augmented wave potentials ( [30,31]). We used a kinetic energy cutoff of 300 eV and a gamma centered k-point grid of 1 × 1 × 18. Geometry optimizations were carried out until the force acting on each atom falls below 0.01 eV/Å. Since the surfaces of these nanostructures have dangling bonds, we also studied the structures with hydrogen saturation We would like to point out that DFT calculations with GW corrections would lead to more accurate bandgap results. However, in this report, we are interested in the relative variations of the band gap of different size nanowires in different orientations rather than the actual band gap values. Therefore, we will resort to conventional DFT calculations within GGA approximation to circumvent the computational cost involved in study of these large structures.

Results and discussion
The cross sectional view of [100] oriented optimized hydrogen saturated Sb 2 Se 3 nanowire (1.8 nm size) is shown in figure 1(a). In this orientation, the 1-D ribbons along [001] are confined by the size of the wire by breaking the strong covalent interactions within the ribbons. The cross sectional sizes (1.2 nm, 1.8 nm & 2.4 nm) of these nanowires were carefully chosen to avoid splitting the ribbons in the [010] direction. These nanostructures could be considered as clusters of molecules (terminated ribbons) infinitely stacked layer by layer (with Van der Waals interaction) along the [100] direction. Due to the inherent nature of the [010] oriented nanostructures, the very small cross sectional wires with cleaved half ribbons were found to be unstable and therefore, we selected a zigzag edged surface along the growth direction for our study (figures 1 (b) & (d)). Also, due to the hefty computational cost, we kept the size along the  such that they only have a single molecular unit of Sb 2 Se 3 along their cross section. We chose the structures of sizes 1.2 nm, 2.4 nm & 3.6 nm for our studies in this orientation.
The optimized structures show surface reconstruction due to the dangling bonds from the termination of ribbons. We also observed the bond formation between the neighboring ribbons in place of Van der Waals interactions. These structures were terminated with hydrogen to compensate the dangling bonds at the surface. Here, we report only the results of hydrogen saturated structures. The overall size changes due to optimization are shown in The electronic structure of the nanowires were studied with and without hydrogen saturation. Hydrogen saturation removes the bands introduced by the surface dangling bonds between valence and conduction bands and pushes the conduction bands towards a higher energy region in all cases. In the case of [100] oriented wires, the smallest nanowire shows a direct band gap, which changes to a indirect gap with further increase in sizes. These structures exhibit bands of more atomistic nature and it could be explained by the fact that the covalently bonded ribbons along [001] direction have been terminated. Also, in case of [010] oriented structures the band structure looks more atomistic owing to the termination of the strongly bound ribbons in these structures. All the [001] oriented nanowires display indirect band gaps (figure 2). Since the valance band maximum(VBM) near Gamma region has a nearly flat contour, at room temperature these nanowires will exhibit both direct and indirect transitions in a narrow energy range. Interestingly, the band gap of these wires is smaller than that of the bulk, contrary to the simple effective mass approximation (EMA).
The size dependence of the band gaps for all three orientations is presented in figure 3. The variation in band gap is fitted to the following equation for [100] & [010] orientations to explore the confinement effects: where, E g & E g,bulk are the DFT band gap of the nanostructure and the corresponding bulk structure respectively. d is the size of the structures and α is the scaling index. The value of constant A and α were found to be 0.61 and 1.19 respectively for the [100] oriented nanowires, and 0.47 and 1.03 respectively for [010] oriented ones. It should be noted that in simple EMA models the value of α is predicted to be 2, however this   3). In order to understand the reason behind the reduction in the band gap of [001] oriented wires, we investigate the atom resolved partial density of states (p-DOS) of different atoms in these structures. Although all atoms contribute to the bands at the conduction band minimum (CBM), the contribution is much higher for the non-fuctionalized Sb atoms (Sb nf ) of cleaved 5-atom ribbons located at the surfaces ( figure 4). Also, it's interesting to note that the cleaved surface atoms have little contribution to the valence band maximum (VBM). This suggests that the reduction in band gap in these nanostructures is mainly due to restructuring of the lattice with major contributions coming from the surface cleaved atoms.
Further to explore the rationale behind this anomalous band gap reduction in [001] oriented nanostructures, we take a closer look at the bondangle variations. We studied the variation of the polyhedral angles, ∠Se1 − Sb2 − Se3 & ∠Se3 − Sb2 − Se3 in these nanostructures ( figure 5 (b) & (c)). Variations of these angles with respect to the nanowire size are presented in ( figure 5 (d) & (e)) for the ribbons located at different spatial positions in the nanowires. We observe large deviation in the polyhedral angles of these nanowires compared to their bulk counterpart. Moreover, the deviations are lower in 10-atom ribbons at the centre (Centre10) but higher in 5-atom cleaved ribbons (Surface5) at the surface, created by the spatial restriction at  Energetically, the [001] oriented nanowires with 5-atom ribbons at the surface could be considered as a metastable structure and potentially realized by adopting appropriate physical methods. Nonetheless, this work intends to show that the drastic variations in the polyhedral angles of the 5-atom cleaved ribbons at the surface of [001] wires and the resultant peculiar electronic properties closely resemble the recent experimental study of structural and electronic properties of bulk Sb 2 Se 3 under high pressure [20]. This similarity is interesting because the above experimental study has shown that Sb 2 Se 3 goes through semiconductor-metal transition around 3 GPa and then becomes superconductive for pressures above 10 GPa. Our results here provide important clue in understanding of the above observation and thus, the anomaly of reduction in band gap of our [001] oriented nanostructure could be attributed to this insulator-metal transition related to the topological insulating transition.

Conclusion
We have studied nanowires of Sb 2 Se 3 with three different orientations and sizes for their stability and dependency on electronic structure. We found that the [010] oriented nanowires were stable only for the zigzag edged surface along the growth direction. All of the studied nanowires show confinement effect with inverse dependence on size. The [001] oriented structures show reduction in band gap compared to the bulk. This anomalous band gap reduction could be attributed to the insulator-metal transition related to the topological insulating transition observed in bulk Sb 2 Se 3 at high pressure ∼3 GPa.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.