Tunable SnO 2 Nanoribbon by Electric Fields and Hydrogen Passivation

Under external transverse electronic fields and hydrogen passivation, the electronic structure and band gap of tin dioxide nanoribbons (SnO2NRs) with both zigzag and armchair shaped edges are studied by using the first-principles projector augmented wave (PAW) potential with the density function theory (DFT) framework.The results showed that the electronic structures of zigzag and armchair edge SnO2NRs exhibit an indirect semiconducting nature and the band gaps demonstrate a remarkable reductionwith the increase of external transverse electronic field intensity, which demonstrate a giant Stark effect. The value of the critical electric field for bare Z-SnO2NRs is smaller than A-SnO2NRs. In addition, the different hydrogen passivation nanoribbons (Z-SnO2NRs2H and A-SnO2NRs-OH) show different band gaps and a slightly weaker Stark effect. The band gap of A-SnO2NRs-OH obviously is enhanced while the Z-SnO2NRs-2H reduce. Interestingly, the Z-SnO2NRs-OH presented the convert of metal-semiconductormetal under external transverse electronic fields. In the end, the electronic transport properties of the different edges SnO2NRs are studied. These findings provide useful ways in nanomaterial design and band engineering for spintronics.


Introduction
The low-dimensional materials have attracted extensive attentions due to their excellent physical properties and novel electronic properties in the past decade.The graphene is especially discovered in 2004 [1]; it provides the new foundation for the research of low-dimensional systems [2][3][4][5][6].However, graphene still faces many challenges, such as toxicity, lacking an intrinsic band gap, and incompatibility with current silicon-based electronic technology, which are in the way of the applications of graphene in electric devices [7].Since the discovery of graphene, various 2D materials have been predicted and synthesized [8,9], particularly, the group IV (Si, Ge, and Sn) analogs of graphene.The stanene may be a competitive candidate of graphene, because of the high conductivity of stanene [10], and its electric structure can be easily tuned [11].The existing works have studied the effect of stain, substrate, external electric field, modification by functional groups, and so on [12,13].As in Modarresi et al. [14] tuning the band gap by the strain effect and external electric field (E-field) tends to open an energy gap predicated by Ren et al. [15].In addition, Li and Zhang [16] studied tunable electronic structures and magnetic properties in twodimensional stanene.Recently, the experiment and theory of one-dimensional (1D) graphene nanoribbons (GNRs) have been widely reported.In theoretical research, the zigzag GNRs can display the properties of half-metallicity by applying transverse electric field, promising candidate materials for spintronic devices [2,4].The electronic and optical properties of GNRs can be also modulated by changing edge termination [17].Experimental results prove that the GNRs with various widths and crystallographic orientations are more facilitative and flexible than carbon nanotubes (CNTs), through standard lithographic procedures or chemical methods [3,5].Inspired by the fruitful results based on GNRs, recently a lot of interest has been drawn to nanoribbons of wide bandgap semiconductor, such as boron nitride (BNNRs) [18], molybdenum disulfide (MoS 2 NRs) [19,20], and zinc oxide (ZnONRs) [21].In the calculation of zinc oxide (ZnONRs), the polarized spin density of states is a function of the nanoribbons width.Kou et al. demonstrate that the band gap of ZnO nanoribbon can be reduced monotonically with increasing transverse field strength, demonstrating a giant Stark effect [22].The titania nanoribbons (TiO 2 NRs) also predicate that the edge states and band gaps are sensitive to edge termination and ribbon width [23].Tin dioxide (SnO 2 ) is also a typical wide-gap semiconductor with band gap   = 3.6 eV, because of the fascinating electronic properties and optical transparency they have been widely used in photovoltaic devices, transparent conducting electrodes, solar cells, chemical gas sensors, and panel displays [24][25][26][27][28][29][30].Recently, many theoretical researches have reported the electronic structures and geometric properties of SnO 2 nanomaterials using first-principles [31,32].More fortunately, the ultrathin SnO 2 nanofilm and one-dimensional (1D) SnO 2 nanoribbon have been synthesized by thermal evaporation and postprocessing in experiments [33].Motivated by the outstanding properties of GNRs and wide band gap semiconductor, we put our emphasis on the SnO 2 nanoribbons, which may obtain more excellent achievement.In previous work, Huang et al. study the electronic structure bandgap modulations of SnO 2 nanoribbon by ribbon width [34].
In this paper, we perform first-principles calculations to study the bandgap modulations, electronic structures, and hydrogen passivation of SnO 2 NRs under transverse electric fields.We found that both armchair and zigzag SnO 2 NRs without hydrogen passivation are semiconductor with indirect gap and the semiconductor-metal transition occurs at a certain critical electric field.More interesting, partially passivating all the edge O atoms and passivating all the O and Sn atoms of SnO 2 NRs could present the distinct properties.Our work offers a promising route toward modulating lowdimensional SnO 2 nanomaterials bandgap which have potential applications in nanoscale optical devices.

Model and Computational Methods
The electronic and optical properties of 1D SnO 2 nanostructures are performed with the spin-polarized first-principles methods as implemented in the Vienna ab initio simulation package (VASP) [35] and the subsequent electronic transport properties calculations are performed by the Atomistix Toolkit Package (ATK).Projector augmented wave (PAW) potentials and the Perdew et al. [36] function under the spin-polarized generalized gradient correlation are used to describe the exchange and correlation interaction.The supercells are large enough to ensure that the vacuum space is at least 15 Å, so that the interaction between nanostructures and their periodic images can be safely avoided.Following the Monkhorst-Pack scheme [37], 12 k points were used to sample the 1D Brillouin zone, and the convergence threshold was set as 10 −4 eV in energy and 0.02 eV/ Å in force.The valence electrons for the Sn, O, and Ag are 14 (Sn: 4d 10 5s 2 5p 2 ), 6 (O: 2s 2 2p 4 ), and 11 (4d 10 5s 1 ).The positions of all the atoms in the supercell were fully relaxed during the geometry optimizations.
The model structures of SnO 2 NRs were generated by cutting an SnO 2 NS (tin dioxide nanosheets) along armchair and zigzag orientations, which are referred to as zigzag SnO 2 nanoribbons (Z-SnO 2 NRs) and armchair SnO 2 nanoribbons (A-SnO 2 NRs), as shown in Figure 1.The external electric field is modelled by transversely adding a sawtooth-like potential to the nanoribbon.We should explain that the DFT functional always underestimates the band gap of semiconductors, but it is powerful to predict a correct trend toward the band gap change and efficiently unveil the physical mechanism [38,39].

The Band Gap Modulation under External Electric Field
in Bare SnO 2 Nanoribbon.In both zigzag nanoribbon and armchair nanoribbon, the original package contains 8 tin atoms and 16 oxygen atoms.So, in our calculations we choose zigzag and armchair SnO 2 nanoribbons with width  = 8.The results show that the electronic structures of zigzag and armchair edge SnO 2 nanoribbon exhibit an indirect semiconducting nature with the band gap of about 2.19 eV and 2.08 eV, respectively, which are well consistent with our previous results [34].Firstly, we modulate band gaps of the bare SnO 2 nanoribbon by applying the transverse electronic fields.Considering the symmetrical structure of the Z-SnO 2 NRs and A-SnO 2 NRs, the external electric fields are added to the  direction in Figure 1.The evolution of the band gaps for Z-SnO 2 NRs and A-SnO 2 NRs under different external electric field intensity is shown in Figure 2. From Figure 2, the band gaps of bare Z-SnO 2 NRs and A-SnO 2 NRs demonstrate a remarkable reduction when an external electric field is applied.The band gaps eventually closed when the electric field reached a critical value for each specified SnO 2 nanoribbon; this phenomenon is similar to the armchair ZnO nanoribbon [22].The values of the critical electric field for bare Z-SnO 2 NRs and A-SnO 2 NRs are 0.124 V/ Å and 0.210 V/ Å, respectively.This suggests that the semiconductormetal transition occurs at a certain value of critical electric field for Z-SnO 2 NRs compared to A-SnO 2 NRs.
To further investigate the underlying physical mechanism, the charge redistribution of Z-SnO 2 NRs and A-SnO 2 NRs is studied with and without an external electronic field, respectively.Figures 3(a  0 V/>.While the band gap of the Z-SnO 2 NRs obviously becomes narrow and the DOS near the Fermi level are mainly ascribed to O 2p states and Sn 5d states under the electric field of 0.13 V/>.In addition, from Figure 3 (charge densities for CBM and VBM of Z-SnO 2 NRs), we can find that when we applied an external electric field (0.13 V/>), the charge is evenly distributed, whereas VBM is a different localized state in which the wave function mainly focused on both sides of the O atoms for the whole nanoribbon.
In Figures 4(a)-4(b), band structure, DOS, and the corresponding charge densities for the CBM and VBM of the A-SnO 2 NRs are illustrated at 0 V/> and 0.2 V/>.From Figure 4 we can find that the band gap of A-SnO 2 NRs is 2.08 eV without electric field; the charge density of the CBM and VBM is different from the Z-SnO 2 NRs and is edge state with wave function localized at the edge of the O atoms.The band gap becomes narrower and the DOS near the Fermi level is mainly caused by O 2p states with the external electric field of 0.2 V/>.Meanwhile, it is found that the charges are redistributed and the phenomenon of giant Stark effects appears, which is similar to ZnO nanoribbons [22,40].For the Z-SnO 2 NRs, with the external electric field, the band gap is similar to the A-SnO 2 NRs.In addition, the distribution of the wave function for CBM has no obvious change, while the wave functions of VBM gather to the edge O atoms and hardly have any wave function at the ribbon center, as shown in Figure 3(b).All in all, when we apply external electric field, due to the splitting of subbands levels caused by the charge redistribution, this makes the band gaps of SnO 2 nanoribbons decrease.Compared to the bare SnO 2 NRs, the behavior of the H passivation nanoribbons changed significantly.The A-SnO 2 NRs-OH and Z-SnO 2 NRs-2H remain semiconducting properties (the band gaps are 2.64 eV and 2.41 eV, resp.), but the band gap of A-SnO 2 NRs-OH is obviously enhanced while the Z-SnO 2 NRs-2H reduce.Similarly, we take the A 8 -SnO 2 NR-OH (width  = 8) as an example; the calculated band gap is 2.42 eV, slightly larger than 2.08 eV of the bare armchair ribbon.For Z 8 -SnO 2 NR-2H, the calculated band gap is 1.71 eV, obviously smaller than 2.19 eV of the bare zigzag nanoribbon.The A 8 -SnO 2 NR-2H and Z 8 -SnO 2 NR-OH present the metallic property which supplied by the 2p state of edge O atoms and the 5s state of the edge Sn atoms.

The Band Gap Modulation under
To further study the effect of external electronic field for H passivation SnO 2 NRs, we calculate the evolutions of the band gap for H passivation with different external electric field in Figure 5. From Figure 5 we can find that because no pronounced differences are found when the field direction is reversed, owing to the symmetrical structure, A-SnO 2 NRs-OH has a slower decreasing rate of the band gap with the increase of electric field and requires a larger critical electric field to close its band gap, which is similar to Kou et al. [22].A vital reason is that the A-SnO 2 NRs-OH has larger band gaps than the bare ones and the unpaired electrons reduce when H atoms are introduced.For the Z-SnO 2 NRs-2H, the decreasing rate of the band gap is faster than A-SnO 2 NRs-OH and it has a lower critical electric field of 0.13 eV to close its band gap.This phenomenon well corresponds to the bare SnO 2 nanoribbons.It illustrates that the Z-SnO 2 NRs-2H are more sensitive to external electric field than A-SnO 2 NRs-OH.There is special phenomenon that presents metallic property for Z-SnO 2 NRs-OH (the band gap is 0 eV) when it is without external electric field.Interestingly, it realizes a transformation from metal to semiconductor when the electric field reaches 0.07 eV/ Å.The band gap has the maximum value of 1.3 eV when the external electric field increases to 0.15 eV/ Å and subsequently the band gap decreases with the increase of the external electric field which is similar to Zheng et al. [41].
To reveal the underlying physical mechanism for the different H passivation models, band structure and the charge redistribution of the CBM and VBM are examined.Figures 6(a the whole ribbon except for the ribbon edges, while the charge distribution of the VBM is totally concentrated at the Sn atoms and O atoms of the ribbon edges which is similar to the VBM of A-SnO 2 NRs.Once an external electric field is applied, the charge distributions of the CBM and VBM are driven to localize at opposite edges owing to the different electrostatic potential, as analyzed above, as shown in Figure 6(b).This can shift down the CBM because the charge easily redistributes in external electric fields, while the VBM also obviously upshifts in energy band toward the Fermi level, thereby further narrowing the energy gap.Band structure and the charge redistribution of H passivation Z-SnO 2 NRs were presented in Figures 7 and 8. From Figure 7, we can conclude that it is an indirect gap semiconductor regardless of whether or not the electric field is applied.The charges of CBM and VBM mainly concentrate at the O atoms and Sn atoms of the ribbon edges as shown in Figure 7(a).That is different from the bare Z-SnO 2 NRs in which the charge mainly concentrates at the O atoms in whole nanoribbon.From Figure 7(b), under the electronic field of 0.2 v/>, the charge distributions of the CBM and VBM are driven to localize at opposite edges; this situation is similar to the A-SnO 2 NRs-OH.In Figure 8, the wave function of the CBM primarily localize at O atoms and Sn atoms of the nanoribbon center, whereas the wave function of VBM mainly concentrates at the O atoms of the whole nanoribbon and the Sn atoms of the right nanoribbon edge.The hydrogenation of Z-SnO 2 NRs destructed the symmetry

Electronic Transport.
The lower dimension semiconductors are usually used to fabricate electronic transport devices, such as graphene and silicone nanoribbon [42,43].The electronic transmission of SnO 2 nanoribbon can be explored in terms of transport property.The transmission of SnO 2 nanoribbon is determined with two probe methods.The two ends of SnO 2 nanoribbon are held within the electrodes.The width of left electrode and right electrode is 3.15 Å, respectively, as shown in Figure 1(h).The electrons near the Fermi level contribute to electronic transport property in SnO 2 nanoribbon.The orbital delocalization near the Fermi level results in high mobility of electrons which corresponds to certain peak amplitudes in the transmission spectrum [44,45].The current through the system is calculated using the Landauer-Büttiker formula:  = (2/ℎ) ∫ (, )[  ( −   ) −   ( −   )] [46,47], where  is the electron charge, ℎ is Planck's constant, (, ) is the transmission The electronic transmission is invoked with magnitude of transmission in a particular energy interval.Figure 9 represents the transmission spectrum of A-SnO 2 NRs and Z-SnO 2 NRs.The width of the center scattering region is 0.02 eV and 0.05 eV for A-SnO 2 NRs and Z-SnO 2 NRs, respectively.For A-SnO 2 NRs, the transmission peaks are observed for −2.8 V, −2.4 V, and −1.7 V in the valence band and 1.5 V and 2.8 V in the conduction band.Compared with A-SnO 2 NRs, more peaks of Z-SnO 2 NRs are observed in the valence band.The peaks locate at −2.8 V, −2.5 V, −1.7 V, and −1.1 V in valence band; the location of peaks is similar to A-SnO 2 NRs in conduction band.This is also in agreement with the electron density of Z-SnO 2 NRs, where the electron density is more intense than A-SnO 2 NRs.In addition, compared to Z-SnO 2 NRs, A-SnO 2 NRs has a larger cutting area near the Fermi surface, which is closely related to a larger band gap for A-SnO 2 NRs, which also shows that the transmission spectrum of materials has close correlation for electronic density of states.
The calculated I-V characteristics of SnO 2 NRs are illuminated in Figure 10.From Figure 10 we can find that the A-SnO 2 NR and Z-SnO 2 NR are in off state when the bias voltage is between −0.3 V and 0.3 V.When the bias voltage exceeds 0.3 V, the current presents a nonlinear increase and same change trend for A-SnO 2 NR and Z-SnO 2 NR, similar to the electrons conduction of the other semiconductors, such as ZnO and TiO 2 .Since 0.8 V, the change of the bias voltage not only produces the conduction current, which also makes the current have a nonlinear growth; this phase of the V-I characteristic curve is similar to general electronic conduction semiconductor devices.The difference of the I-V curve can be explained by the fact that the A-SnO 2 NR and Z-SnO 2 NR possess the different band gap and voltage sensitivity.The thickness of SnO 2 NR is similar to the thickness of three atoms and two-dimensional electron gas can be formed; in addition, similar to the graphene, SnO 2 can be self-assembled on the experimental generation.Based on these special electronic transport properties, the SnO 2 nanoribbons have enormous potential application in the switching, rectifying devices and the whole semiconductor industry.

Conclusions
In summary, the electronic structures and band gap modulations of the Z-SnO There is similar variation tendency of the I-V characteristics of both A-SnO 2 NR and Z-SnO 2 NR.Our results may be very useful theoretical reference to design nanoelectronic and spintronic devices.

Figure 1 :
Figure 1: The structure model of (4 × 1 × 1) zigzag and (1 × 4 × 1) armchair SnO 2 nanoribbon for different hydrogen passivation (a-f) and the transport model (h) ( is the growth direction of nanoribbons and  is the direction of external electronic field).The big gray balls are Sn atoms, the small red balls are O atoms and the pink balls are H atom.In addition, the red-dotted lines would represent the unit cell.

Figure 2 :
Figure 2: Band gap evolution under various external electric fields in bare Z-SnO 2 NRs and A-SnO 2 NRs.
)-3(b) show the band structure, density of state (DOS), and the corresponding charge densities for the conduction band minimum (CBM) and the valence band maximum (VBM) of Z-SnO 2 NRs and A-SnO 2 NRs at 0 V/> (a) and 0.13 V/>, respectively.From Figure3, the band gap of the Z-SnO 2 NRs is 2.19 eV under the electric field of

Figure 3 :
Figure 3: Band structure and DOS (left) and the corresponding charge densities for CBM (right upper) and VBM (right lower) of Z-SnO 2 NRs at 0 V/> (a) and 0.13 V/> (b).The isosurface is 5.0 × 10 −3 e/> 3 .The Fermi level is shifted to zero.Different colors in curves represent different energy levels.

Figure 4 :
Figure 4: Band structure and DOS (left) and the corresponding charge densities for CBM (right upper) and VBM (right lower) of A-SnO 2 NRs at 0 V/> and 0.2 V/>.The isosurface is 5.0 × 10 −3 e/> 3 .The Fermi level is shifted to zero.Different colors in curves represent different energy levels.

2
NRs and A-SnO 2 NRs influenced by an external transverse electronic field and hydrogen passivation have been investigated by using the first-principle PAW potential within the DFT framework under GGA.As affected by a transverse electric field, the band gaps of bare Z-SnO 2 NRs and A-SnO 2 NRs demonstrate a remarkable reduction and the semiconductor-metal transition would appear at a lower value of critical electric field.The charge density near the Fermi can be redistributed.For the SnO 2 NRs with edge hydrogen termination through different way, the Z-SnO 2 NRs-2H and A-SnO 2 NRs-OH remain semiconducting properties, but the change of the band gap for the A-SnO 2 NRs-OH and Z-SnO 2 NRs-2H is obviously different.The Z-SnO 2 NRs-2H are more sensitive to external electric field than A-SnO 2 NRs-OH.For the Z-SnO 2 NRs-OH, it can realize transformation from metal to semiconductor when the electric field reaches 0.07 eV/ Å.Additionally, it indicates that more peaks of Z-SnO 2 NRs are observed in the valence band compared with A-SnO 2 NRs by electronic transport properties.

Table 1 :
External Electric Field in Hydrogen Passivation SnO 2 Nanoribbon.To explore the effect of edge hydrogen (H) termination on the electronic properties of the different SnO 2 nanoribbons, two different ways of nanoribbon edge hydrogen termination have been Figure 5: Band gap evolutions under various external electric fields in hydrogen passivation zigzag and armchair SnO 2 nanoribbon with width  = 8.Binding energy (per atom) and band gap of SnO 2 NRs for different configurations.andarethenumberand chemical potential for the corresponding element, respectively, and  tot is the total free energy of system.According to the laws of thermodynamics, the larger the binding energy is, the more stable the structure is.The values of   for different configurations of SnO 2 NRs are shown in Table1.From Table1, the SnO 2 NR-OH has a higher binding energy than bare SnO 2 NRs and SnO 2 NRs-2H.The binding energies of Z-SnO 2 NRs-2H are 2.41 eV, which are slightly lower than the A-SnO 2 NRs; this demonstrates that Z-SnO 2 NRs-2H is more active than the other SnO 2 nanoribbons.
studied: (i) the edge of Sn and O atoms are passivated with H atoms (denoted SnO 2 NR-2H) and (ii) the edge of O atoms are passivated (denoted SnO 2 NR-OH), as shown in Figures 1(b)-1(c) and 1(e)-1(f).It is important for evaluation of the stability of SnO 2 NRs because it can determine whether this nanostructure can be realized experimentally.The relative stability of bare and H passivated SnO 2 NRs is determined by the binding energy (  ).  is defined as   = (∑     −  tot )/ ∑   , where  represents different elements of Sn and O,