Tin monochalcogenide heterostructures as mechanically rigid infrared bandgap semiconductors
V. Ongun Özçelik, Mohammad Fathi, Javad G. Azadani, Tony Low
TTin monochalcogenide heterostructures as mechanically rigid infrared bandgapsemiconductors
V. Ongun ¨Oz¸celik, ∗ Mohammad Fathi, Javad G. Azadani, and Tony Low † Andlinger Center for Energy and the Environment,Princeton University, Princeton, NJ 08544, USA Department of Electrical Engineering, University of Texas at Dallas, Richardson, TX 75080, USA Department of Electrical and Computer Engineering,University of Minnesota, Minneapolis, MN 55455, USA
Based on first-principles density functional calculations, we show that SnS and SnSe layers canform mechanically rigid heterostructures with the constituent puckered or buckled monolayers. Dueto the strong interlayer coupling, the electronic wavefunctions of the conduction and valence bandedges are delocalized across the heterostructure. The resultant bandgap of the heterostructuresreside in the infrared region. With strain engineering, the heterostructure bandgap undergoes tran-sition from indirect to direct in the puckered phase. Our results show that there is a direct correlationbetween the electronic wavefunction and the mechanical rigidity of the layered heterostructure.
PACS numbers:
In the last decade, there has been substantial amountof research on two-dimensional (2D) materials which ex-hibit unique chemical, mechanical, electronic and opticalproperties. [1–5] Recently, tin monochalcogenides havegained attention due to their potential for applicationsin the fields of catalysis, opto-electronics, photovoltaicsand lithium ion batteries.[6–8] In particular, SnS andSnSe have excellent electronic properties for photovoltaicapplications with a higher optical adsorption coefficientthan CdTe.[9, 10] These materials are nontoxic, presentin high abundance on earth in bulk form and have in-direct band gaps similar in energy to silicon. [11] Theyare also attractive for large-scale thermoelectric appli-cations due to their high thermoelectric figure-of-meritvalues.[12] In addition, tin monochalcogenide nanosheetscan be easily produced by bottom-up methods, [13–16]conventional CVD,[17, 18] atomic layer deposition[19] orby liquid phase exfoliation process.[11]Despite notable studies on tin monochalcogenides,studies on its heterostructures have been few.[20–24] Ver-tical heterostructures with 2D materials provide promis-ing routes towards building materials on-demand [1]where the nature of the interlayer interactions plays adecisive role on the properties of the heterostructure.The interlayer interaction is of particular importance forunderstanding the nanoscale tribological behavior of 2Dmaterials and designing structures with desired electro-mechanical properties. Previous studies have shown thatinterlayer potentials are mainly determined by electro-static interactions and van der Waals (vdW) forces wherethe electronic and mechanical properties of the final het-erostructure will be affected by the stacking order, latticemismatch between individual layers, long range Coulombinteraction between the layers, and any reconstructionsthat might occur during stacking.[25–30] However, theunderlying friction at nanoscale and the interplay be-tween the electronic structure and the sliding barriers of stacked 2D materials is not well understood. For prac-tical device applications, it is also desirable for the newheterostructures to be mechanically rigid against sliding.In this letter, we show that SnS and SnSe mono-layers can be used to construct mechanically rigidsemiconducting heterostructures with narrow bandgaps.Using first-principles density functional theory (DFT)calculations,[31] we identify the optimized geometriesof various possible SnS/SnSe heterostructures and re-veal their geometry dependent mechanical and electronicproperties. In particular, we show that this class of het-erostructures presents conduction and valence band edgeswhere the electronic wavefunctions are strongly delocal-ized across the two constituent monolayers. The strongelectronic coupling also leads to an interesting interplaybetween electronic and mechanical properties, an issuethat has not been systematically studied in the contextof 2D materials’ heterostructures. The SnS/SnSe mate-rial formed has a much smaller bandgap in the infraredcompared to individual monolayers. We also discuss theband alignments, sliding barriers and band gap variationas we apply external strain and note that the heterostruc-ture which forms from the puckered phases of SnS andSnSe monolayers undergoes a direct-indirect gap transi-tion with external strain.Tin monochalcogenides can possess two geometries.The first one is the buckled(B) structure where the ad-jacent atoms of the monolayer are in two parallel planesthat are separated by a buckling distance in the verticaldirection. The hexagonal unit cell of the buckled struc-ture is reminiscent of silicene [32, 33] and blue phospho-rene [34] where the structure maintains planar stabilitydespite buckling. The second phases is the puckered(P)structure where the hexagonal symmetry is lost and theunit cell becomes rectangular. This phase is reminiscentof black phosphorene [35, 36] and it is energetically morefavorable than the buckled phase as far as SnS and SnSe a r X i v : . [ c ond - m a t . m t r l - s c i ] M a r FIG. 1: (a) SnS/SnSe heterostructures created from buckled (B) and puckered (P) monolayers. Sn, S and Se atoms arerepresented by purple, yellow and green spheres in the ball-and-stick model. Detailed geometrical parameters of the optimizedstructures are presented in the Supplementary Material. (b) Top views of the heterostructures where the upper and lowermonolayers are shown by blue and red spheres. The unit cell of each heterostructure is indicated. (c) Change in the totalenergy of the heterostructures as SnS and SnSe monolayers are slid on top of each other along armchair and zigzag directions.In each heterostructure, the minimum energy corresponding to the optimum stacking is set to zero. In the color map, darkerregions correspond to energetically more favorable configurations whereas brighter regions indicate sliding barriers.FIG. 2: Effect of strain direction on the sliding barrier ofthe SnS-P / SnSe-P heterostructure. The barrier increaseswhen the heterostructure is subjected to strain in armchairand zigzag directions. Energy landscapes plotted for differentstrain values indicate that the sliding path with minimumbarrier is along the diagonal of the unit cell. are concerned.Using the buckled and puckered phases, one can ob-tain four different types of SnS/SnSe heterostructures asshown in Fig. Figure 1(a-b) (We denote these phases asBB, BP, PB, and PP, where the first letter indicates thegeometry of SnS and the second letter indicates the ge-ometry of SnSe). The interlayer distances and the atomicpositions of each heterostructure were optimized by slid-ing the layers on top of each other until the minimumenergy configurations are obtained. For each optimized heterostructure, the interlayer binding energy was cal-culated by subtracting the minimum energy of the het-erostructure from the sum of energies of separated in-dividual layers. Applying this method we calculate thebinding energies of BB, BP, PB and PP structures as0.88eV, 0.76eV, 0.71eV and 0.69eV, respectively. Thechange in the interlayer binding energies suggest thatas the puckering of the heterostructure increases, thereis strong departure from weak vdW interaction betweenconstituent layers. To evaluate the possibility of slidingthe layers on top of each other, we calculate the staticfriction force needed to overcome the energy barrier alonga certain path. The friction value can be obtained byfinding the maximum value of the derivate of the po-tential energy with respect to displacement ( r ), namely F f = max(dE/dr). [37] We focus on the PP heterostruc-ture since it has the lowest sliding barrier among otherSnS/SnSe variants. The sliding barriers of the PP struc-ture along the armchair(AC) and zigzag(ZZ) directionsare 0.56 eV and 0.29 eV whereas this barrier drops to 0.18eV along the diagonal of the unit cell. These correspondto friction values of 51.77, 26.81 and 16.64 pN/atomin AC, ZZ and diagonal directions, respectively. Thesesliding barriers are much larger than those reportedwith other 2D heterostructures. For instance, the slid-ing barriers for isolated graphene and hexagonal boron-nitride was calculated to be between 1-20meV along dif-ferent directions.[37] Sliding barrier of graphite on Ptand Au surfaces were reported as 1.6meV and 0.4meV,respectively.[38] For MoS /MoS , fluorographene/MoS and fluorographene/fluorographene, the sliding barrierswere calculated as 9, 0.12 and 1.4meV, respectively.[39], FIG. 3: (a) Electronic band structure of the SnS/SnSe het-erostructures. They re semiconductors with indirect bandgaps below 1eV. The Fermi level is set to zero and indicated bythe dash-dotted line. Bandgaps obtained from PBE and HSEcalculations are indicated. (b) Band alignment of SnS/SnSeheterostructure and their monolayers calculated with PBE.For the heterostructures, values obtained from HSE calcula-tions are indicated with line plot. whereas the MoS /MoS sliding barrier increases to150meV under an external pressure of 500MPa.[40]For practical purposes, we desire layered heterostruc-tures to be mechanically rigid against sliding. Here, aswe apply external strain to the PP heterostructure, thepuckered geometries of the monolayers get distorted. Thetotal energy landscapes are presented in Fig. Figure 2,where the change in layer-layer interaction as a functionof strain is shown. In Fig. Figure 2, bright and dark re-gions indicate strong and weak interactions between thelayers of the heterostructure. Thus, applied strain signif-icantly increases the layer-layer interaction and the slid-ing barriers of the layers on top of each other. Namely,as strain is increased from 0 to 8%, the sliding barriersalong the AC, ZZ and diagonal directions increase up to0.67, 0.51 and 0.31 eV, respectively, which correspond tofriction values of 61.94, 47.14 and 28.66 pN/atom. Notethat the diagonal direction has the lowest sliding barriervalue for each strain value.Having shown that it is possible to construct mechani-cally rigid heterostructures from SnS and SnSe monolay-ers, we turn our attention to the electonic structure ofthese materials as shown in Fig. Figure 3a. Accordingly,all of the heterostructures are indirect band-gap semi- conductors with gaps in the infrared region. The BBheterostructure has the lowest band gap with conduc-tion band minimum (CBM) and valence band maximum(VBM) along Γ and X points. Its CBM and VBM areclosest to each other, which is a direct result of its highinterlayer binding energy. Similarly in the PP structure,the CBM and VBM are furthest away from each other inthe momentum space where the VBM is between Γ and X and CBM is along Γ and Y . The diversity of bandstructures also leads to a variety of different band align-ments as shown in Fig. Figure 3b. For this purpose, wecalculate the energy values of VBM and CBM with refer-ence to the vacuum energies which are extracted from thelocal potential distribution within the unit cell.[41] Ac-cording to the band alignments of isolated monolayers,we would expect that the BB, BP and PB structures tobe type-2 whereas PP to be a type-1 heterostructure dueto its high VBM value. However, this behavior changeswhen the monolayers are stacked on top of each other.The interaction between the monolayers leads to bandmixing in the optimized heterostructures. The electronicwavefunctions of CBM and VBM bands are not isolatedon individual layers due to strong band hybridization asa result of interlayer coupling. The level of mixing can beevaluated by calculating the spatial profile of the electronand hole probability densities in the out-of-plane direc-tion for CBM and VBM edges as shown in Fig. Figure 4.In all four heterostructures, the valence and conductionbands show delocalized wavefunctions with substantialoverlaps. The electron/hole band profiles are totallyasymmetric and, except for the PP structure, all threeheterostructures have strong spin-orbit coupling both atCBM and VBM. The strong hybridization between thelayers account for the rigidity of the heterostructures withthe large sliding barriers. Note that in a recent study itwas shown that for transition metal dichalcogenide het-erostructures the wavefunction is totaly localized on in-dividual layers.[42]Finally we show that the diverse band offsets ofSnS/SnSe heterostructures can be further modified un-der external strain. To model this, we apply strainto the unit-cells of the four heterostructures discussedabove in the AC and ZZ directions and re-optimize theiratomic configurations and electronic band diagrams foreach strain value. Strain applied in AC and ZZ direc-tions increases the band gaps of the heterostructuresmonotonously as shown in Fig. Figure 5(a-b). How-ever, PP heterostructure transforms into a direct band-gap semiconductor when strain in the ZZ direction is be-tween 3.5 % and 5.5 %. As the ZZ strain value increases,the conduction and valence bands shift toward higherenergies values as indicated with Pc and Pv in Fig. Fig-ure 5(c). Eventually, the location of the CBM changesand the heterostructure becomes a direct band-gap semi-conductor for strain values between 3 to 5.5 %. As thestrain value is further increased, the valence band at Pv FIG. 4: Real-space wavefunctions of the SnS/SnSe heterostructures computed at CBM and VBM for (a) BB, (b) BP, (c) PBand (d) PP stackings. In all cases, the bands show delocalized wavefunctions with substantial overlaps. shifts above the initial VBM energy, and the band-gaptransforms back to indirect.In conclusion, we propose novel stable phases ofSnS/SnSe heterostructures, which are narrow gap semi-conductors with bandgaps in the infrared region. Theseheterostructures exhibit strong hybridization and inter-layer coupling with highly delocalized electronic wave-functions. We showed that there is a direct correlationbetween the delocalization of the wavefunction and fric-tion at nanoscale where strong interlayer coupling leadsto stable heterostructures with high sliding barrier. Werevealed that it is possible to construct 4 different typesof SnS/SnSe heterostructure each with diverse electronicproperties due to their different stacking orders. Also, weshowed that external strain results in a direct to indirectband-gap transition in the PP heterostructure. Our com-putational predictions open an interesting avenue possi-bility of constructing tin monochalcogenide heterostruc-tures with stacking dependent electronic properties andshed light on the effect of electronic behavior on the me-chanical rigidity of layered heterostructures. ∗ Electronic address: [email protected] † Electronic address: [email protected][1] A. Geim and I. Grigorieva, Nature , 419 (2013).[2] S. Z. Butler, S. M. Hollen, L. Cao, Y. Cui, J. A. Gupta,H. R. Guti´errez, T. F. Heinz, S. S. Hong, J. Huang, A. F.Ismach, et al. , ACS Nano , 2898 (2013). [3] Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman,and M. S. Strano, Nat. Nanotechnol. , 699 (2012).[4] M. Xu, T. Liang, M. Shi, and H. Chen, Chem. Rev. ,3766 (2013).[5] P. Avouris, T. F. Heinz, and T. Low,
2D Materials (Cambridge University Press, 2017).[6] P. D. Antunez, J. J. Buckley, and R. L. Brutchey,Nanoscale , 2399 (2011).[7] G. A. Tritsaris, B. D. Malone, and E. Kaxiras, J. Appl.Phys. , 173702 (2014).[8] L. Li, Z. Chen, Y. Hu, X. Wang, T. Zhang, W. Chen,and Q. Wang, J. Am. Chem. Soc , 1213 (2013).[9] K. R. Reddy, N. K. Reddy, and R. Miles, Sol. EnergyMater Sol. Cells , 3041 (2006).[10] C. Ferekides, U. Balasubramanian, R. Mamazza,V. Viswanathan, H. Zhao, and D. Morel, Sol. Energy , 823 (2004).[11] J. R. Brent, D. J. Lewis, T. Lorenz, E. A. Lewis, N. Sav-jani, S. J. Haigh, G. Seifert, B. Derby, and P. OBrien,J. Am. Chem. Soc , 12689 (2015).[12] L.-D. Zhao, S.-H. Lo, Y. Zhang, H. Sun, G. Tan, C. Uher,C. Wolverton, V. P. Dravid, and M. G. Kanatzidis, Na-ture , 373 (2014).[13] Z. Deng, D. Han, and Y. Liu, Nanoscale , 4346 (2011).[14] J. Ning, K. Men, G. Xiao, L. Wang, Q. Dai, B. Zou,B. Liu, and G. Zou, Nanoscale , 1699 (2010).[15] Y. Zhang, J. Lu, S. Shen, H. Xu, and Q. Wang, Chem.Commun. , 5226 (2011).[16] H. Zhu, D. Yang, Y. Ji, H. Zhang, and X. Shen, J. Mater.Sci. , 591 (2005).[17] B. P. Bade, S. S. Garje, Y. S. Niwate, M. Afzaal, andP. O’Brien, Chem. Vap. Deposition , 292 (2008).[18] T. G. Hibbert, M. F. Mahon, K. C. Molloy, L. S. Price,and I. P. Parkin, J. Mater. Chem. , 469 (2001). FIG. 5: (a) Band gaps of the heterostructures under strain in the armchair direction. (b) Same for strain in the zigzagdirection. The PP heterostructure transforms into a direct band gap material between 3 - 5.5 % strain in the zigzag direction.(c) Transition of the band structure from indirect to direct under strain in zigzag direction.[19] J. Y. Kim and S. M. George, J. Phys. Chem. C ,17597 (2010).[20] B. Sa, Z. Sun, and B. Wu, Nanoscale , 1169 (2016).[21] W. Xiong, C. Xia, X. Zhao, T. Wang, and Y. Jia, Carbon , 737 (2016).[22] K. Cheng, Y. Guo, N. Han, Y. Su, J. Zhang, and J. Zhao,J. Mater. Chem. C , 3788 (2017).[23] A. Kandemir, F. ˙Iyikanat, and H. Sahin, J. Phys. Con-dens. Matter , 395504 (2017).[24] L. Peng, C. Wang, Q. Qian, C. Bi, S. Wang, andY. Huang, ACS Appl. Mater. Interfaces , 40969 (2017).[25] N. Marom, J. Bernstein, J. Garel, A. Tkatchenko,E. Joselevich, L. Kronik, and O. Hod, Phys. Rev. Lett. , 046801 (2010).[26] C. Lee, Q. Li, W. Kalb, X.-Z. Liu, H. Berger, R. W.Carpick, and J. Hone, Science , 76 (2010).[27] S. Cahangirov, C. Ataca, M. Topsakal, H. Sahin, andS. Ciraci, Phys. Rev. Lett. , 126103 (2012).[28] G. Constantinescu, A. Kuc, and T. Heine, Phys. Rev.Lett. , 036104 (2013).[29] S. Cahangirov, S. Ciraci, and V. O. ¨Oz¸celik, Phys. Rev.B , 205428 (2013).[30] K. Andersen, S. Latini, and K. S. Thygesen, Nano lett. , 4616 (2015).[31] We performed spin-polarized first principles calculationswithin generalized gradient approximation includingvdW corrections [43] and spin-orbit coupling. We usedprojector-augmented wave potentials[44] and approxi-mated the exchange-correlation potential with Perdew-Burke-Ernzerhof (PBE) functional.[45] We sampled theBrillouin zone (BZ) in the Monkhorst-Pack scheme wherethe k -point sampling of (21 × ×
1) was found to besuitable for the BZ corresponding to the primitive unitcell. The energy convergence value between two consec-utive steps was chosen as 10 − eV. Numerical calcula-tions were carried out using the VASP software.[46] Wealso calculated the band gaps using the HSE06 hybridfunctional[47], which is constructed by mixing 25% of the Fock exchange with 75% of the PBE exchange and100% of the PBE correlation energy. Electronic calcula-tions at the HSE06 level were performed using the struc-tures that were relaxed using PBE. Throughout this workwe present the band energies with reference to the vac-uum energy, which we extracted from the local potentialdistribution within the unit cell.[32] S. Cahangirov, M. Topsakal, E. Akt¨urk, H. S¸ahin, andS. Ciraci, Phys. Rev. Lett. , 236804 (2009).[33] V. O. ¨Oz¸celik, S. Cahangirov, and S. Ciraci, Phys. Rev.Lett. , 246803 (2014).[34] A. Jain and A. J. McGaughey, Sci. Rep. , 8501 (2015).[35] H. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tom´anek,and P. D. Ye, ACS nano , 4033 (2014).[36] T. Low, A. Rodin, A. Carvalho, Y. Jiang, H. Wang,F. Xia, and A. C. Neto, Phys. Rev. B , 075434 (2014).[37] W. Gao and A. Tkatchenko, Phys. Rev. Lett. , 096101(2015).[38] A. ¨Ozo˘gul, S. Ipek, E. Durgun, and M. Z. Baykara, Appl.Phys. Lett. , 211602 (2017).[39] L.-F. Wang, T.-B. Ma, Y.-Z. Hu, Q. Zheng, H. Wang,and J. Luo, Nanotechnology , 385701 (2014).[40] T. Liang, W. G. Sawyer, S. S. Perry, S. B. Sinnott, andS. R. Phillpot, Phys. Rev. B , 104105 (2008).[41] V. O. ¨Oz¸celik, J. G. Azadani, C. Yang, S. J. Koester,and T. Low, Phys. Rev. B , 035125 (2016).[42] A. Chaves, J. Azadani, V. O. ¨Oz¸celik, R. Grassi, andT. Low, arXiv preprint arXiv:1709.08315 (2017).[43] S. Grimme, J. Comput. Chem. , 1787 (2006).[44] P. E. Bl¨ochl, Phys. Rev. B , 17953 (1994).[45] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev.Lett. , 3865 (1996).[46] G. Kresse and J. Furthm¨uller, Phys. Rev. B , 11169(1996).[47] J. Paier, M. Marsman, K. Hummer, G. Kresse, I. C. Ger-ber, and J. G. ´Angy´an, J. Chem. Phys.124