Engineering the Electronic Structure of Tin Sulfide Nanoribbons: A

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Engineering the Electronic Structure of Tin Sulphide Nanoribbons: A Computaional Study Moumita Kar, Biplab Rajbanshi, Sougata Pal, and Pranab Sarkar J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11453 • Publication Date (Web): 28 Feb 2018 Downloaded from http://pubs.acs.org on March 2, 2018

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The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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The Journal of Physical Chemistry

Engineering the Electronic Structure of Tin Sulphide Nanoribbons: A Computaional Study Moumita Kar,† Biplab Rajbanshi,† Sougata Pal,‡ and Pranab Sarkar∗,† Department of Chemistry, Visva-Bharati University, Santiniketan- 731235, India, and Department of Chemistry, University of Gour Banga, Malda- 732103, India E-mail: [email protected]

Abstract We have investigated the structure, stability and the electronic properties of bare and edge hydrogenated tin sulphide nanoribbons (SnSNRs) using first-principles density functional theory calculation. In contrast to the 2D sheet of SnS, which is an indirect band gap semiconductor, bare 1D SnSNRs are either metallic (in case of zigzag (zz) edge termination) or direct/indirect band gap semiconductor (in case of armchair (ac) edge termination) in nature. The edge hydrogenated zigzag nanoribbons are direct band gap semiconductors and the edge hydrogenated armchair nanoribbons are direct/indirect band gap semiconductor depending on width. The edge hydrogenated nanoribbons have low edge energies and quite high mechanical strength, indicating their energetic as well as mechanical stabilities. Moreover, armchair SnSNRs can tolerate very high expansive strain (∼ 65%) due to their morphological transformation from puckered to buckled ones. On the application of uniaxial strain (both expansive and compressive), the edge hydrogenated SnSNRs provide interesting strain induced band gap variation. In addition, an in-plane semiconductor-metal schottky junction has been made by ∗ To

whom correspondence should be addressed University ‡ Gour Banga University † Visva-Bharati

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conjunction of edge hydrogenated and bare zz-SnSNRs which shows good rectifying currentvoltage characteristics.

1. INTRODUCTION On the recent past, two dimensional (2D) materials having extraordinary electronic properties have attracted great research interest as potential candidate for future generation optoelectronic devices. Various type of 2D materials such as graphene, 1,2 graphane, 3,4 boron-nitride, 5,6 hexagonal aluminum nitride, 7,8 silicene, 9,10 transition metal dichalcogenides (MoS2 and WS2 ), 11–18 pentagraphene, 19,20 phosphorene, 21–28 phosphorus carbide 29,30 have been studied extensively due to their unique electronic and mechanical properties. The era of 2D material starts with the invention of graphene in 2004. 1 Graphene possess extremely high electron mobility, but its zero band gap limits its application in photovoltaics. On the other hand, inorganic analogous of graphene, the transition metal dichalcogenides possess wide direct band gap of ∼2 eV, 31–33 but their low carrier mobilities restrict them in the applications of electronic devices. 34,35 Recently, phosphorus analogue of graphene (phosphorene) having direct band gap of 1.51 eV has also drawn great attention due to its high mobility about 1000 cm2 /Vs. 24,36–39 But unfortunately it suffers from aerial instability. 23,40 So, searching for new potential 2D materials is still highly desirable. In this context, group-IV monochalcogenides having layered structure with interlayer weak van der Waals interaction between the layers has great promise to be synthesized in 2D forms. Among all group-IV monochalcogenides, tin sulphide (SnS) is very much important material because of its nontoxic nature and both the constituents Sn and S are naturally abundant and hence cheap. In addition to this, SnS has very high absorption coeffecient (104 cm−1 ) in the UV and near IR range indicating great potential in photovoltaics usage. 33 Very recently, the SnS monolayer has successfully been synthesized with greater carrier mobility (104 cm2 /Vs) as compared to phosphorene. 41,42 Recent theoritical sudies reveal that SnS monolayer has an indirect band gap 43,44 and the elctronic properties of 2D sheet can be tuned by the applying strain. 44

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Although, a 2D monolayer show unique electronic and physical properties, the nanoribbons, the 1D stripes of mother monolayer can also exibit interesting edge dependent intriguing electronic properties for electronic and spintronic applications. For example, although graphene 2D sheet is semimetallic in nature, however, the graphene nanoribbons are either metal or semiconductor depending on the edge termination. 45,46 On the other hand, 2D sheet of inorganic graphene analogous like molybdenum disulphide (MoS2 ) and phosphorene are semiconductor but their nanoribbons show metallic or semiconducting behaviour depending on edges. 32,47–50 Nevertheless, extensive studies addressing the electronic and physical properties of nanoribbons made up of abundant materials are very much essential for generating potential future generation optoelectronic devices. Very recently SnS nanoribbons (SnSNRs) have been successfully synthesized with exciting optoelectronic properties. 51 The photocurrent density of SnSNRs is about 87 µAcm−2 , which is the highest one among all the reported SnS photoelectrodes. 52 Although SnSNRs have been experimentally synthesized but theoritical studies addressing detail structure, stability, electronic properties and tuning of electronic properties of these nanoribbons are still missing. In a very recent study, Li et al. have reported a priliminary results on bare SnSNRs. 53 However, we believe that to further explore the tin sulphide nanoribbons for different optoelectronic applications the detailed understanding of the electronic structure and its tuning is utmost important. In this article, using first-principles density functional theory based calculations we have explored the stability and electronic properties of SnSNRs with and without edge hydrogenation. The tunability of the electronic properties has been explored by employing two different approaches; i) varying the width of the nanoribbons, and ii) applying uniaxial strain (both expansive and compressive) along the axis of the nanoribbons. In addition, an in-plane semiconductor-metal schottky junction between edge hydrogenated and bare zz-SnSNRs is also explored with the aim to achieve rectifying current-voltage characteristics.

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2. DETAILS OF COMPUTATION We performed all the calculations using projector augmented wave (PAW) 54 and generalized gradient approximation (GGA) 55 with the Perdew, Burke and Ernzerhof (PBE) exchange correlation functional, as implemented in Vienna ab initio simulation package (VASP). 56,57 The plane-wave cutoff energy for the wave function is 500 eV. For the geometry optimization of zigzag and armchair nanoribbons and monolayer (1 × 1 × 5) and (5 × 1 × 1) and (5 × 1 × 5) Monkhorst-Pack kgrid 58 are used, respectively. The whole system has been relaxed untill the maximum forces per atom is lower than 0.001 eV/Å and the tolerance criterion for energy minimization is 0.0001 eV. Along the perpendicular to the ribbon axis a vacuum distance of 15 Å was kept to avoid interaction between the replicas. To see whether the spin-orbit coupling has any effect on the electronic properties of SnS system, we have done the calculation on SnS monolayer and one representative SnSNRs with the inclusion of spin-orbit coupling. The phonon calculations are done using finite displacement method implemented in the Vibra utility of the SIESTA package. 59 The transport properties are calculated using TranSIESTA module within the SIESTA package, which is based on the combination of density functional theory and nonequilibrium Green’s functions (NEGF). 60,61 We have used GGA-PBE exchange correlation functional and double zeta polarisation function (DZP) basis set and a real space mesh cutoff of 300 Ry and 1 × 1 × 8 Mohnkhorst-Pack k-grid. The current is calculated using Landauer-Buttiker formula: 62,63

I(Vb ) =

Z µR 2e µL

h

T (E,Vb )[ fL (E − µL ) − fR (E − µR )]dE.

(1)

where, Vb is the bias voltage, T(E, Vb ) is the transmission coeffecient, µ L and µ R are the electrochemical potential of the left and right electrodes and fL (E − µ L ) and fR (E − µ R ) are the FermiDirac distribution functions of the left and right electrodes.

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3. RESULTS AND DISCUSSION Before discussing the electronic structure of SnSNRs, let us first reproduce the structural parameters and electronic properties of 2D SnS sheet. The optimized structure of 2D-SnS sheet is shown in Figure 1a and the optimized structural parameters are enlisted in Table 1. The results agree well with the experiment and other theoritical studies. 33,43,44,64 The calculated electronic structure (Figure 1b) with a band gap of 1.46 eV is consistent with the previous theoretical works. 44,65 In order to understand the effect of spin-orbit coupling (SOC) on the electronic properties, the band structure of SnS monolayer with inclusion of SOC is plotted in Figure 1b. We have found that the indirect bandgap character and also the position of valance band maximum (VBM) and conduction band minimum (CBM) are not changed but the degenerate bands at the CBM splits into non-degenerate ones, as a result there is a slight decrease in bandgap value (1.39 eV). However, the main electronic properties of SnS momolayer remain same. Being satisfied with the parameters of mother sheet, we now proceed to explore the stability and electronic structure of SnSNRs.

3.1. Bare Zigzag and Armchair Nanoribbons The SnSNRs were modelled by cutting an infinite 2D SnS sheet along zigzag (armchair) direction with different widths. After optimization both the edges of bare SnSNRs show slight edge deformation (see Figure S1 of Supporting Information). The unit cell of the representative zigzag and armchair nanoribbon are shown by blue dashed line in the same figure and following the conventional notation the number Nz (or Na ) are used to denote the width of the zigzag (or armchair) nanoribbons. The band structure of bare zigzag SnSNR (zz-SnSNR) Nz = 20 (Figure 2a) clearly shows that two bands cross the fermi energy level, indicating its metallic character. From the charge density plots (Figure 2b) corresponding to those bands, it is clear that the metallic character stems from the one dimensional metallic edge states. So, one can achieve a metallic nanoribbon from semiconductor SnS sheet by cutting it along zigzag direction. On the other hand, the bare armchair SnSNRs (ac-SnSNRs) show direct band gap semiconductor behaviour upto Na < 26 and thereafter

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they become indirect band gap semiconductor (Figure 3a-d) like the mother sheet. Hence, the transition from indirect band-gap semiconductor to direct band-gap semiconductor can be achieved by cutting a SnS monolayer into narrow width armchair nanoribbons. The inclusion of spin-orbit coupling (SOC) in electronic structure calculation shows that the main electronic properties remain same with slight decrease of band gap, as for example, the bandgap values of bare 20-ac-SnSNR without and with inclusion of SOC are 1.45 eV and 1.42 eV, respectively. Therefore, we conclude that spin-orbit coupling has only little influence on the electronic structure of SnSNRs. We have therefore present the results of electronic structure calculations without spin-orbit coupling. The band gap variation of ac-SnSNRs with ribbon width is plotted in Figure 3e, where one can clearly find that the theoreticaly calculated band gap around 1.4 eV is in good line with the experimentally reported band gap value (1.2 eV) of SnS nanoribbons. 51,52 We have also calculated the magnetic properties of both zigzag and armchair bare nanoribbons and found that they are nonmagnetic in nature.

3.2. Edge Hydrogenated Zigzag and Armchair Nanoribbons With chirality dependent metallic and semiconducting behaviour, bare zigzag and armchair SnSNRs offer new challenges for application in opto-electronic devices. However, in search of uniform electronic property and to avoid edge reconstruction, one can think of passivated nanoribbons. Here, we discuss the structure, stability and electronic properties of edge hydrogenated SnSNRs.

3.2.1. Structural Properties and Energetic Stability The optimized geometries of edge passivated zigzag and armchair nanoribbons are shown in Figure S2 of Supporting Information. The unit cell of the representative zigzag and armchair nanoribbon are shown by blue dashed line in the same figure and the number Nz (or Na ) are used to denote the width of the zigzag (or armchair) nanoribbons. After edge passivation the edge reconstruction is not seen. However, due to the edge confinement effect, the bond lengths of the ribbons may vary from their respective bond lengths in monolayer. The bond lengths along armchair dirction of 4-ac6


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SnSNR and the bond lengths along zigzag direction of of 4-zz-SnSNR are labeled 1-4 in Figure 4a and b, respectively and the bond-lengths values are enlisted in Table 2. As compared to monolayer, the lengths of bonds 2 and 3 in 4-ac-SnSNR decrease but the lengths of edge bonds 1 and 4 significantly increase. Therefore, the bonds at the edges show elongative behaviour. Elongative edge stress increases the lattice constant of the ac-SnSNRs. In the case of 4-zz-SnSNR, all the bond lengths decrease and the length of edge bond 1 decreases significantly. Therefore bonds at the edge exibit contractive behaviour. Contractive edge stress decreases the lattice constants of the zz-SnSNRs. Kang et al have reported similar type of phenomenon for TiS3 nanoribbons. 66 However, with increasing ribbon width the lattice constants of the nanoribbons approach to that of monolayer (Figure 4c). It is worth to mention here that the edge confinement of 2D material may lead to instability of the system. That’s why, it is important to examine the relative energetic stabilities of the edge hydrogenated SnSNRs from different aspects. First, we have calculated the cohesive energy per atom for both armchair and zigzag SnSNRs. The cohesive energy is defined by

Ec =

ESnSNR − [n(Es + ESn ) + m2 EH2 ] n+m

(2)

where ESnSNR is the total energy for SnSNRs and ES , ESn and EH2 are the total energies of single S, Sn atoms and H2 , respectively; n and m are the number of Sn (S) and H atoms, respectively. From equation (2) we can find that the SnSNRs with greater negative cohesive energy are themodynamically more feasible. The cohesive energy of SnSNRs are shown as a function of the width of the nanoribbons in Figure 4d. From the figure it is seen that the stability of SnSNRs increases with increasing ribbon width and the zigzag nanoribbons are slightly more stable than the armchair analogue which is quite similar to that of phosphorene nanoribbons. 31 Secondly, we have also examined the edge stability by calculating edge energy, which describes the energy cost to create a

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new edge from the 2D sheet. The edge energy is defined by

Eedge =

ESnSNR − [ n2 E2D + m2 EH2 ] 2LO

(3)

where LO is the equlibrium lattice constant of the optimized nanoribbons and E2D is the energy of four atom primitive unit cell of tin sulphide monolayer and EH2 is the energy of hydrogen molecule and n, m are the total number of tin-sulfur pairs, hydrogen atoms, respectively, in the unit cell of the nanoribbon. Figure 4e shows that the edge energy variation with ribbon width is very small and zigzag nanoribbons have comparatively less edge energies as compared to armchair nanoribbons. So, cutting into zigzag nanoribbon is energetically more favourable than armchair one, which is in contrast to phosphorene nanoribbons. 32 The edge enegy values of SnSNRs are slightly higher than phosphorene nanoribbons (in the order of 0.1 eV/Å) 32 but significantly lower than graphene and transition metal dichalcogenide nanoribbons (in the order of 1.0 eV/Å). 20,67,68 The low edge energy values indicate the edge hydrogenated SnSNRs are energetically feasible.

3.2.2. Mechanical Stability We are now interested to check the mechanical stability of SnSNRs by applying uniaxial strain along the axis of the nanoribbons. To do so, we have calculated their in-plane stiffness from Es = 21 CAε 2 , where Es is strain energy, defined by the energy difference between a strained state and the relaxed state; C is the in-plane stiffness; and A is the equlilibrium area of unit cell of the nanoribbons; ε is uniaxial strain. 69 The calculated in-plane stiffness for zigzag and armchair nanoribbons as a function of ribbon width are plotted in Figure 5a. This figure shows that with increasing ribbon width, in-plane stiffness values approach to the 2D mother sheet (zigzag ∼ 39.88 N/m and armchair ∼ 16.71 N/m). In addition to in-plane stiffness, the ideal strength is also an important property to measure the mechanical stability of nanomaterials. To calculate the ideal strength we have computed the variation of stress with respest to the expansive and compressive strain for SnSNRs with two different width. For zz-SnSNRs the expansive strain with maximum

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stress is around 18%, while for compressive strain with the maximum stress is at 20% (Figure 5b-c) implying quite high ideal strength. For ac-SnSNRs, the maximum stress arises at 14% (12%) compressive strain for 8-ac-SnSNR (12-ac-SnSNR), indicating high ideal strength (Figure 5d). But the scenario becomes much interesting when an uniaxial expansive strain is applied along axis of the ac-SnSNRs as shown in Figure 5e. From the figure we can see that the stress versus strain curves form a plateau beyond 15% strain. At relaxed and low strain condition, in addition to strong covalent interaction there is also a relatively weak pucker-pucker interaction between two atoms situated at the adjacent pucker positions of ac-SnSNRs. The said plateau arises due to the breakdown of this pucker-pucker interaction after 15% expansive strain. Similar type of phenomenon for armchair phosphorene nanoribbons has already been reported by Sorkin et al. 70 However, the plateau ends up around 64% (66%) strain for 8-ac-SnSNR (12-ac-SnSNR) with a sudden increase of stress against strain. In search for the reason of this sudden jump we have plotted the strain energy versus strain for 8-, 12-ac-SnSNRs as shown in Figure 5f. The curve shows a sudden break at 64% (66%) strain for 8-ac-SnSNR (12-acSnSNR), indicating some morphological changes in the ribbon structure. The optimized structure of 12-ac-SnSNR at relaxed and 66% strain condition are shown in Figure S3 of Supporting Information. From the figure one can clearly finds that the black phosphorus like puckered structure of relaxed SnSNR trasforms into blue phosphorus like buckled structure after application of 66% expansive strain. Thus, the puckered to buckled morphological transformation is responsible for the sudden jump in stress and the sudden breakdown in strain energy as shown in Figure 5e and f, respectively. To ensure further, we have also calculated the variation of stress and strain energy as a function of expansive strain for 2D mother SnS sheet (Figure S4 of Supporting Information) along the armchair direction. For such sheet we have also found exactly similar observation, i.e, the puckered to buckled morphological transformation at 65% expansive strain. Now, the question is, can the SnS sheet along the armchair direction and the armchair nanoribbons really bear such high expansive strain? As we all know that the puckered structure (like black phosphorus) can bear high strain by changing its puckering angle, without breaking the structure. 40,71 The arm-

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chair phosphorene nanoribbons also can bear upto 50% expansive strain by changing its puckering angle. 40,70 Thus, due to puckered structure along armchair direction, ac-SnSNRs can bear high expansive strain. Moreover, we have already mentioned that the in-plane stiffness of SnS along armchair direction is much smaller than that of zigzag direction. That means the puckering angles of SnS is much more labile to the strain and thats why the SnS sheet along the armchair direction and ac-SnSNRs can bear such high expansive strain, before the morphological trasformation. Now, we have interested to see the dynamical stability of edge hydrogenated ac-SnSNRs within elastic limit. In case of expansive strain, the elastic range of ac-SnSNRs ends at that point in which strain energy drops suddenly (which dictate the morphological trasformation from puckered to buckled ones). Using finite displacement method, we have calculated phonon spectra of 8-ac-SnSNR at -12%, 0%, 40%, 60% strain (herein -ve strain indicate compressive strain and +ve strain indicate expansive strain) and are shown in Figure S5 of Supporting Information. The absence of negative frequencies indicate the dynamical stability of ac-SnSNRs in the elastic limit. The high frequencies phonons, such as, ∼ 1750 and ∼ 1250 cm−1 in the phonon spectra at 0% strain of 8-ac-SnSNR correspond to the S-H and Sn-H stretching frequencies, respectively and the lower frequencies correspond to Sn-S stretching modes. As S-H and Sn-H bond lengths decrease for expansive strain and increase for compressive strain, the frequencies corresponding this bonds increase (∼ 2570 and ∼ 1560 cm−1 , respectively) for expansive strain and decrease (∼ 1540 and ∼ 1120 cm−1 , respectively) for compressive strain. So, we conclude that edge hydrogenated tin sulphide nanoribbons are mechanically as well as dynamically highly stable within elastic limit.

3.2.3. Electronic Properties From the above discussion, it is convincing that SnSNRs are energetically feasible and mechanically highly stable. Now, we are interested to investigate the electronic properties of SnSNRs and their tunability. First to see whether the spin-orbit coupling has any influence on the electronic properties of SnSNRs, we have calculated the electronic structure of SnSNRs with and without spin-orbit coupling. As shown in Figure S6 of Supporting Information, the band structures with 10


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and without SOC of 4-zz-SnSNR and 4-ac-SnSNR looks very similar. The values of bandgap of 4-zz-SnSNR and 4-ac-SnSNR without (with) inclusion of spin-orbit coupling are 2.03 (2.01) eV and 2.49 (2.43) eV, respectively. As the SOC has only little influence on the electronic properties of SnSNRs, we present the results of electronic structures without including spin-orbit coupling. We have computed bandgap of the SnSNRs as a function of their widths (N = 4-30) and the values are plotted in Figure 6. The figure shows that, the band gap of ac-SnSNRs decreases rapidly upto Na =12, then decreases slowly and ultimately approaches to that of the monolayer (1.46 eV). The direct to indirect band gap semiconductor transition also exists for the edge hydrogenated ac-SnSNRs similar to bare ac-SnSNRs, but the transition occurs in much smaller ribbon width (Na =11) for edge hydrogenated SnSNRs. However, the band gap of the edge hydrogenated zigzag nanoribbons gradually decreases with increasing ribbon width and even it goes below to 0.27 eV for Nz =30, which is much lower than that of 2D sheet. Fan et al. 72 also recently calculated smaller band gap of the zigzag nanoribbons as compared to mother sheet for zigzag GeSe nanoribbons. Now, to find the reason behind such band gap tunability with respect to the width of SnSNRs we have computed the charge densities of VBM and CBM of both ac-SnSNRs and zz-SnSNRs in Figure 7. From the figure we find that the VBM and CBM charge densities for both the SnSNRs of very small width (4-ac and 4-zz) are delocalized throughout the ribbon width. But with the increase in width of ac-SnSNRs, both the VBM and CBM are localized over the central region of the ribbon. On the other hand for zz-SnSNRs, with increase in ribbon width, both the VBM and CBM are localized on the edge, VBM being situated at one edge and CBM on the other edge just like the bare zz-SnSNRs (Figure 2). Our results of localization of VBM and CBM at the edge is also consistent with that of zigzag GeSe nanoribbons. We have also computed the band structure of zz-SnSNRs of different widths (Figure S7 of Supporting Information) where we found that with increase in ribbon width both VBM and CBM shift towards the fermi energy level, leading to the band gap reduction but the shifting of CBM is much larger than that of VBM. This observation again reflects the delocalized edge CBM charge density along the ribbon axis. We have also calculated magnetic properties of edge hydrogenated SnSNRs and found that they are nonmagenetic in

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nature like bare ones. Tang et. al. have reported that carbon doped zigzag boron-nitride nanoribbons with H-passivated boron edge and bare carbon edge exibit spin polarized ground state which is very useful in spintronic devices. 73 In another recent work Tang et. al. have shown that when one edge of graphene zigzag nanoribbons are passivated by hydrogen and other edge by fluorine, they are spin polarized semiconductors for both spin channels. 74 Taking insipiration from this we have interested to see the electronic properties of zz-SnSNRs when one edge is passivated by hydrogen and other one is bare. As shown in Figure S8 of Supporting Information, whatever the edge (Sn or S) is passivated by hydrogen one band crosses the fermi energy level, indicating the zigzag nanoribbons show metallic character irrespective of the width of the nanoribbons and by calculating magnetic properties we have found that they are all nonmagnetic.

3.2.4. Strain Induced Electronic Properties As we have already mentioned that the edge hydrogenated SnSNRs are quite mechanically strong, we are curious to see the strain induced electronic properties of SnSNRs. To get a clear view one can tune the electronic properties of zigzag SnSNRs through application of strain. We have calculated strain induced electronic properties of edge hydrogenated zz-SnSNRs of two different widths (8-zz and 12-zz) within elastic limit. The variation of band gap with applied strain (Figure 8a-b) shows a decreasing nature of band gap with increasing expansive or compressive strain. The rate of decrease of band gap with compressive strain is greater than that of expansive strain and at 20% compressive strain both above two represantative zz-SnSNRs attain zero bandgap. The band structure of 8-zz-SnSNR under the applied strain in the range from -20% to 18% (herein -ve strain indicate compressive strain while +ve strain indicate expansive strain) is shown in Figure 8c. The figure shows that the direct band gap 8-zz-SnSNR retains its nature under expansive strain, whereas under compressive strain it becomes indirect band gap semiconductor with VBM at Γ point and CBM at Z point. The variation of bandgap with applied uniaxial strain is due to the change in bond length and bond angle of nanoribbons. As their variation differ depending on the positions relative to the edge of the nanoribbons, we have reported averaged result of them. We 12


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distinguish two different types of bond lengths i) along zigzag direction, i.e, zigzag bond length (d1 ) and ii) along armchair direction, i.e, armchair bond length (d2 ) (Figure 8d) and two different types of bond angles i) along zigzag direction, i.e, in-plane bond angle (α) and ii) along armchair direction, i.e, out-of-plane bond angle (β ) (Figure 8e). The figures show that with applied expansive strain along the axis of zigzag nanoribbons, the average zigzag bond lengths and in-plane bond angles which are along zigzag direction increase but the armchair bond lengths decrease and outof-plane bond angles which are along armchair direction increase slightly. On the other hand, for compressive strain along the axis of the nanoribbons, the zigzag bond lengths and in-plane bond angles which are along zigzag direction decrease continuously but the armchair bond lengths first increase slightly and then decrease followed by a maxima and out-of-plane bond angles increase slightly. This change of bond lengths and bond angles exert extensive influence on the interaction between Sn and S atom to decrease the band gap. The zero bandgap at high compressive strain perhaps due to the greater interaction as both armchair and zigzag bond lengths decrease at high compressive strain. From the calculated charge densities of VBM and CBM (Figure S9 of Supporting Information), we find that the VBM and CBM of 8-zz-SnSNR at both compressive and expansive strain become more edge centric than the free one. The edge switching of VBM and CBM charge densities for zz-SnSNRs at compressive strain compared to free one may arise due to the direct to indirect band gap transition. Similarly, we have calculated strain induced electronic properties of edge hydrogenated acSnSNRs of two different widths (8-ac and 12-ac) within elastic limit. So, in case of expansive strain, we have calculated strain induced electronic properties of ac-SnSNRs before the morphological transformation from puckered to buckled ones. We get band gap contraction with the application of expansive and compressive strain, where the contraction is again much larger for compressive strain (shown in Figure 9a and b, respectively). The band structures of 8-ac-SnSNR (Figure 9c) at different compressive and expansive strain remain direct as the free one. The change of bond length and bond angle of 8-ac-SnSNR with applied strain is plotted in Figure 9d and e, respectively. The armchair bondlengths and out-of-plane bond angles which are along the armchair

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direction increase with expansive strain along the axis of the armchair nanoribbons and at the same time zigzag bond lengths and in-plane bond angles which are along the zigzag direction decrease. On the other hand, for the compressive strain, opposite case is the true. Therefore, we see that when the armchair bond lengths and out-of-plane bond angles which are along armchair direction increase, zigzag bond lengths and in-plane bond angles which are along zigzag direction decrease and vice versa. This modulated bond lengths and bond angles may increase the interaction which results the decrease in band gap.

3.3. Transport properties of schottky barrier between edge hydrogenated and bare zz-SnSNRs From the results as discussed in the preceeding section, we found that the bare 4-zz-SnSNR is metallic, whereas edge hydrogenated 4-zz-SnSNR is a semiconductor with direct band gap of 2.00 eV. Thus, there is a great possibility to generate a schottky barrier through in-plane metalsemiconductor junction 72,75 between bare 4-zz-SnSNR and edge hydrogenated 4-zz-SnSNR. Herein, the junction is modelled in such a way that the left electrode contains one unit of edge hydrogenated 4-zz-SnSNR, the scattering region contains one unit (A=1) of edge hydrogenated 4-zz-SnSNR and one unit (B=1) of bare 4-zz-SnSNR and finally, the right electrode contains one unit of bare 4zz-SnSNR. We have named this junction as A1B1 and is shown in Figure 10a. The resulting I-V curve in the bias voltage ranging from -0.8 to 0.8 V (shown in Figure 10b) shows that the current in negative bias voltage is comparatively larger than positive bias voltage. Moreover, when the semiconductor portion of the scattering region is increased upto three units of edge hydrogenated 4-zz-SnSNR (A3B1) the current in negative bias voltage diminishes much than that of A1B1. Now, to understand the current-voltage (I-V) characteristics, we have plotted the transmission function and the corresponding projected density of states (PDOS) of left electrode (LE), scattering region (SR), and right electrode (RE) of A1B1 and A3B1 in Figure 10c at different applied bias. The

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transmission function is related with the PDOS as 76,77

T (E) = PDOS(LE) × PDOS(SR) × PDOS(RE) × λ (E)

(4)

where λ (E) is coupling strength between scattering region and electrodes. The resonance of the PDOS of electrodes with that of scattering region results in large transmission peak. Now, the b +Vb presence of more transmission peaks in the bias window region ( −V 2 , 2 ) at applied negative bias

(-0.5 V) than that of positive bias (0.5V) for A1B1, can clearly be explained by the resonance of PDOS of electrode and scattering region. From the PDOS figure we found that the PDOS of RE is resonating well with that of the scattering region for negative bias, while such resonance is poor in the positive bias. However, the resonance of PDOS of electrode and scattering region greatly diminishes when the junction becomes A3B1, which clearly explains the decreased current in negative bias for A3B1. Now, in order to see the rectification behaviour in such schottky contact, we have calculated the rectification ratio (RR) as a function of bias voltage for A1B1 and A3B1 and is shown in Figure 10d, where RR (V) =

I(+V ) 72 I(−V ) .

Although for A1B1, the RR value remains below

1, with increase in length of edge hydrogenated 4-zz-SnSNR to A3B1 it increases and reaches maximum value of 6.54 at an applied bias of 0.25 V. We hope that further increase in A unit of the scattering region will increase the rectification ratio.

4. CONCLUSION Using density functional theory based calculation we have systematically studied the stability and the electronic properties of bare and edge hydrogenated tin sulphide nanoribbons. Our study shows that the inclusion of spin-orbit coupling hardly affects the electronic properties of SnS nanoribbons. Bare ac-SnSNRs lead to direct-to-indirect bandgap transition and the bandgap decrease with increasing the ribbon width, only ranging from 1.45 eV (Na =20) to 1.41 eV (Na =30). On the other hand, bare zz-SnSNRs show metallic character regardless of the ribbon width, but show edge reconstruction. However, edge hydrogenation can fix the edge reconstruction of zz-SnSNRs. 15



Our calculations show that edge hydrogenated SnSNRs are energetically and mechanically highly stable. The energetic and mechanical stability increases with increasing ribbon width of edge hydrogenated SnSNRs. With increasing ribbon width of edge hydrogenated ac-SnSNRs, the band gap decreases and approaches to that of monolayer and also the direct to indirect band gap transition takes place like bare ac-SnSNRs. Importantly, in case of edge hydrogenated zz-SnSNRs, the band gap continuously decreases with ribbon width and even it goes much lower than that of monolayer. This tunable band gap may lead to potential applicability in the electronic devices. In addition, there is a clear charge separation of VBM and CBM charge densities in case of wider hydrogenated zz-SnSNRs, making it special in solar cell applications. On the application of uniaxial strain (both expansive and compressive), the band gap of edge hydrogenated SnSNRs decreases and compared to expansive strain, compressive strain is more effective to modulate the band gap. Very interestingly, ac-SnSNRs can tolerate huge uniaxial expansive strain (∼65%) through puckered to buckled morphological transition and provide very wide strain tunable band gap. Finally, we observed that the in-plane contact between the edge hydrogenated and bare zz-SnSNRs which generates a schottky barrier results in good rectifying current-voltage characteristics. With these novel mechanical and electronic properties, SnSNRs seem to be good potential candidate for future generation optoelectronic devices.

Supporting Information Available The optimized structures of bare ac-, zz-SnSNRs; optimized structures of edge hydrogenated ac-, zz-SnSNRs; optimized structures of edge-hydrogenated 12-ac-SnSNR at 0% and at 66%; the calculated stress and strain energy versus strain of SnS monolayer and the optimized structures of SnS monolayer at 0% and 65%; and phonon spectra of edge hydrogenated 8-ac-SnSNR at -12%, 0%, 40%, 60% strain (herein -ve strain indicate compressive strain and +ve strain indicate expansive strain); band structures of edge hydrogenated 4-ac-SnSNR and 4-zz-SnSNR with and without including spin-orbit coupling; band structures of edge hydrogenated zz-SnSNRs; optimized structures and band structures of 6-zz-SnSNR when one edge is passivated by hydrogen and other one 16


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is bare; charge densities of VBM and CBM of edge hydrogenated 8-zz-SnSNR at different strain. This material is available free of charge via the Internet at http://pubs.acs.org/.

17



ACKNOWLEDGMENTS The authors would like to thank the DST NanoMission, New Delhi, for financial support through research grant [Ref. No. SR/NM/NS-1005/2016]. Moumita Kar is grateful to CSIR, New Delhi for the award of Junior Research Fellowship (JRF) [CSIR Sanction No. 09/202(0056)/2016EMR-I].

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Figure 1: (a) Optimized tin sulphide monolayer (top and side view). The unit cell of the monolayer is denoted by red line. d1 and d2 are the in-plane and out-of-plane bond lengths, respectively. α is the in-plane bond angle and β is the out-of-plane bond angle. (b) Band structure. The Fermi level is set to zero.

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Figure 2: (a) Band structure of bare 20-zz-SnSNR. The Fermi level is set to zero. (b) Charge densities of 1 and 2 bands at Γ point.

Figure 3: Computed band structures of the bare (a) 22-, (b) 24-, (c) 26-, (d) 30-ac-SnSNRs. The Fermi level is set to zero. (e) The variation of band gap of bare ac-SnSNRs with ribbon width.

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Figure 4: The unit cell of the edge-hydrogenated 4-zz-SnSNR and 4-ac-SnSNR are denoted by red line in (a) and (b), respectively and the armchair bond lengths of 4-ac-SnSNR and the zigzag bond lengths of 4-zz-SnSNR are labeled 1-4. (c) The lattice constants of different Na -ac-SnSNRs and Nz -zz-SnSNRs. (d) and (e) are the variation of cohesive energy per atom and edge energy with different width of edge-hydrogenated SnSNRs, respectively.

Figure 5: (a) The variation of in-plane stiffness of edge-hydrogenated SnSNRs versus ribbon width. (b) and (c) are the calculated stress versus expansive and compressive strain of edge-hydrogenated zz-SnSNRs, respectively. (d) and (e) are the calculated stress versus compressive and expansive strain of edge-hydrogenated ac-SnSNRs, respectively. (f) The calculated strain energy versus expansive strain of ac-SnSNRs.

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Figure 6: The variation of the band gap of edge hydrogenated ac- and zz-SnSNRs with their width (N).

Figure 7: (a) and (b) are the charge densities of VBM and CBM of edge hydrogenated ac- and zz-SnSNRs, respectively.

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Figure 8: (a) and (b) are the variation of band gap of edge-hydrogenated zz-SnSNRs with expansive and compressive strain, respectively. (c) The band structure of 8-zz-SnSNR with -20%, -17%, 10%, 0%, 10%, 18% strain. (d) and (e) are the variation of bond lengths and bond angles of edge hydrogenated 8-zz-SnSNR with strain, respectively.

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Figure 9: (a) and (b) are the variation of band gap of edge-hydrogenated ac-SnSNRs with expansive and compressive strain, respectively. (c) The band structure of 8-ac-SnSNR with -12%, 0%, 20%, 40%, 60% strain. (d) and (e) are the variation of bond lengths and bond angles of edge hydrogenated 8-ac-SnSNR with strain, respectively.

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Figure 10: (a) The geometry of schottky contact between edge hydrogenated and bare 4-zz-SnSNR. A and B are the length of edge hydrogenated and bare 4-zz-SnSNR in the central region. (b) IV characteristics of A1B1 and A3B1 of 4-zz-SnSNR. (c) The transnission function and PDOS at different bias voltage of A1B1 and A3B1 of 4-zz-SnSNR. The dotted lines indicate the bias b +Vb window ( −V 2 , 2 ). (d) Rectification ratio of A1B1 and A3B1 of 4-zz-SnSNR.

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Table 1: Symmetry space group, Optimized lattice constant, d1 and d2 are the in-plane and outof-plane bond lengths and α and β are the in-plane and out-of-plane bond angles of optimized tin sulphide sheet. Symmetry Optimized lattice constants (Å) Pmn21 a = 4.39 b = 4.00

Bond length

Bond angle

(Å) d1 = 2.75 d2 = 2.63

α = 95.05◦ β = 87.5◦

Table 2: The armchair bond lengths of 4-ac-SnSNR and the zigzag bond lengths of 4-zz-SnSNR and the corresponding values of SnS monolayer. The labels of the bonds are shown in fig-4a,b. Bond index Bonds in 4-zz-SnSNR (Å) Bonds in monolayer (Å) Bonds in 4-ac-SnSNR (Å) Bonds in monolayer (Å)

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1 2.64 2.75 2.67 2.63

2 2.69 2.75 2.61 2.63


3 2.66 2.75 2.61 2.63

4 2.72 2.75 2.67 2.63


Graphical TOC Entry

Strain induced tuning of the electronic structures of edge hydrogenated SnSNRs.

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Engineering the Electronic Structure of Tin Sulfide Nanoribbons: A

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