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Strain engineering the work function in monolayer metal dichalcogenides
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 J. Phys.: Condens. Matter 27 175501 (http://iopscience.iop.org/0953-8984/27/17/175501) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 128.226.136.66 This content was downloaded on 07/05/2017 at 02:02 Please note that terms and conditions apply.
You may also be interested in: Semiconductor to metal transition in bilayer transition metals dichalcogenides MX2 (M=Mo, W; X=S, Se, Te) Ashok Kumar and P K Ahluwalia Strain engineering in semiconducting two-dimensional crystals Rafael Roldán, Andrés Castellanos-Gomez, Emmanuele Cappelluti et al. Equibiaxial strain: tunable electronic structure and optical properties of bulk and monolayer MoSe2 C K Ghosh, D Sarkar, M K Mitra et al. Effect of strain on electronic and thermoelectric properties of few layers to bulk MoS2 Swastibrata Bhattacharyya, Tribhuwan Pandey and Abhishek K Singh Substrate dependent electronic structure variations of van der Waals heterostructures of MoSe2 or MoSe2(1x)Te2x grown by van der Waals epitaxy Horacio Coy Diaz, Yujing Ma, Sadhu Kolekar et al. Band engineering of the MoS2/stanene heterostructure: strain and electrostatic gating Wenqi Xiong, Congxin Xia, Juan Du et al. The strain effect on superconductivity in phosphorene: a first-principles prediction Yanfeng Ge, Wenhui Wan, Fan Yang et al. Control of biaxial strain in single-layer molybdenite using local thermal expansion of the substrate Gerd Plechinger, Andres Castellanos-Gomez, Michele Buscema et al.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 175501 (6pp)
doi:10.1088/0953-8984/27/17/175501
Strain engineering the work function in monolayer metal dichalcogenides Nicholas A Lanzillo1,2 , Adam J Simbeck1 and Saroj K Nayak1,3 1 Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180, USA 2 Division of Science, Mathematics and Computing, Bard College, 30 Campus Road, Annandale-on-Hudson, NY 12504, USA 3 School of Basic Sciences, Indian Institute of Technology, Bhubaneswar, Odisha 751007, India
E-mail: [email protected] Received 12 January 2015, revised 2 March 2015 Accepted for publication 5 March 2015 Published 2 April 2015 Abstract
We use first-principles density functional theory to investigate the effect of both tensile and compressive strain on the work functions of various metal dichalcogenide monolayers. We find that for all six species considered, including MoS2 , WS2 , SnS2 , VS2 , MoSe2 and MoTe2 , that compressive strain of up to 10% decreases the work function continuously by as much as 1.0 eV. Large enough tensile strain is also found to decrease the work function, although in some cases we observe an increase in the work function for intermediate values of tensile strain. This work function modulation is attributed to a weakening of the chalcogenide-metal bonds and an increase in total energy of each system as a function of strain. Values of strain which bring the metal atoms closer together lead to an increase in electrostatic potential energy, which in turn results in an increase in the vacuum potential level. The net effect on the work function can be explained in terms of the balance between the increases in the vacuum potential levels and Fermi energy. Keywords: work function, density functional theory, strain, monolayer, metal dichalcogenide (Some figures may appear in colour only in the online journal)
is a crucial quantity for opto-electronic device applications, the work function is another material-specific property that is important in field-emission based devices as well in layered heterostructures involving MDCs. There have been relatively few first-principles studies on the work function and strain-induced modulation in low-dimensional nanostructures systems [15, 16]. The effect of a backgate electric field was shown to decrease the value of the work function in bilayer MoS2 as the voltage increases from −5 V to 13 V [17]. The work function of graphene can be favorably tuned through the application of an electric field [18] and the work function of graphenebased contacts can be tuned through chemical doping [19]. Compressive strain is found to decrease the work function of armchair graphene nanoribbons, while tensile strain is found to increase the work function in both pure graphene and graphene nanoribbons [15, 16]. Changes in the work function in these materials correlates to changes in the Fermi energies and
1. Introduction
The discovery of graphene [1] has spurred enormous research interest in the field of two-dimensional materials for applications in nanoelectronics [2–5]. In particular, the metal dichalcogenide (MDC) family are attractive candidates for opto-electronic applications due to the presence of a direct band gap in monolayer samples [2, 6] and favorable structural properties [7]. Metal dichalcogenides consist of covalently bound layers of chalcogenides (for example: S, Se, Te) and metals (for example: Mo, W, V), with adjacent layers held together by the weak van der Waals interaction. Analogous to graphene, the weak interlayer interaction allows for singlelayer samples to be fabricated via mechanical exfoliation [8]. The electronic and vibrational properties of the monolayer MDCs have been studied both experimentally [2–4, 9] and theoretically [10–14, 33] while the work function has received considerably less attention. While the electronic band gap 0953-8984/15/175501+06$33.00
1
© 2015 IOP Publishing Ltd Printed in the UK
J. Phys.: Condens. Matter 27 (2015) 175501
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vacuum potential energies. The effect of both compressive and tensile strain on the work functions of monolayer MDC materials remains an open question and the ability to control the work function would have enormous implications on the engineering of field-emission based devices fabricated from MDC materials [20, 21]. In this work, we investigate the effect of strain on the work functions of MoS2 , WS2 , MoSe2 , MoTe2 , VS2 and SnS2 . These choices of metal dichalcogenides allow us to study any effects that may arise between different metals (i.e. Mo, W,V) and different chalcogenides (i.e. S, Se, Te). We also examine the effect of strain on a metallic MDC (VS2 ) as well as an MDC with a different crystal structure (SnS2 ) relative to the others. We find that for all systems considered, compressive strain decreases the work function while tensile strain may initially increase the work function but will ultimately lead to a decrease when the lattice is stretched more than a few percent. The changes in the work function can be traced back to the balance between electrostatic potential energy and Fermi level modulation as the lattice is strained.
(b)
(c)
(d)
Figure 1. The top views of metal dichalcogenide crystal structures with (a) P6 3/mmc and (b) P3m1 space groups, as well as the side views of (c) P6 3/mmc and (d) P3m1 space groups. Table 1. The values of the equilibrium lattice constants (in Å) and associated zero-strain work functions (in eV).
a0 MoS2 WS2 VS2 SnS2 MoSe2 MoTe2
2. Computational methods
Calculations were performed using the ABINIT [22–24] software package, which is a plane-wave pseudopotential implementation of density functional theory [25, 26]. Troullier–Martins [27] norm-conserving pseudopotentials were used with plane wave cut off energies of 40.0 Hartree for MoS2 , MoSe2 , MoTe2 and VS2 and a cutoff of 42.0 Hartree for SnS2 and WS2 . We used k-point sampling of 12 × 12 × 1 and simulated the effect of compressive/tensile strain by decreasing/increasing the lattice constants in increments of 1%. The geometry of each monolayer system was relaxed at each value of strain until the forces on the atoms were less than 10−2 eV Å−1 . This procedure was repeated for every value of strain considered. The values of strain are reported in the form 0 = a−a where a0 is the equilibrium lattice constant. Positive a0 values of correspond to tensile strain, while negative values correspond to compressive strain. The work function φ is calculated as the energy difference between the Fermi energy EF and the vacuum potential Evac . φ = Evac − EF
(a)
3.20 3.18 3.22 3.44 3.29 3.52
——
φ 6.11 5.89 5.45 6.86 5.49 5.15
3. Results and discussion
Before discussing the effects of strain on the work function, we present the optimized values of lattice constants and work functions for each monolayer MDC system considered. These results are summarized in table 1. The values of lattice constants considered here for MoS2 , WS2 , MoSe2 and MoTe2 are very close to ( within 0.08 Angstrom)—and in some cases identical to—the values presented in other works studying monolayer dichalcogenides [6, 13, 31]. Our lattice constant for VS2 is 3.22 Angstrom, which is slightly larger but comparable to the value of 3.174 Angstrom obtained in other work [32]. Both the crystal structure and the lattice constant of SnS2 agree well with earlier works [34–37]. It is worth noting that the work function of each MDC monolayer generally lies in the range of 5–7 eV, slightly larger than the reported value of 4.5 eV for graphene [28]. Upon applying biaxial compressive and/or tensile strain to each system, the total energy is expected to increase as the structure is moved away from equilibrium. We observe the general trend that as the lattice constant is reduced, the M–X bond becomes shorter while the X–M–X bond angle becomes larger. The corresponding total energies increase parabolically, as indicated in figure 2. The effect of strain on the work function will depend on how strain affects both the Fermi energy and the vacuum potential energy. We see that compressive strain decreases the work function for all species considered, while tensile strain may at first increase but eventually decreases the work function. These results are also shown in figure 2.
(1)
The Fermi energy is determined self-consistently in a ground state electronic structure calculation and the vacuum potential is calculated as the limiting value of the electrostatic potential in the direction perpendicular to the surface at a distance far away, generally 10 or more Å for the systems considered here. Note that the Fermi energy is taken to be the top of the valence band. While the most stable crystal structure of almost all MDC monolayers is a hexagonal lattice with space group P6 3/mmc, SnS2 crystallizes with a cadmium iodide structure (space group P3m1.) In both cases, however, the metallic atom remains sixfold coordinated to neighboring chalcogenide atoms atoms. In figure 1, we show the top and side views of both crystal structures. 2
J. Phys.: Condens. Matter 27 (2015) 175501
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1
1 E-E
0
E-E0
0
0
0
Energy (eV)
1 E-E0
φ-φ 0
WS 2
MoS2
-1 -0.1
φ-φ
0
0.1
1
-1 -0.1
φ-φ 0
0
-0.1
1
SnS2 0
1
0
0
φ-φ 0
0
0.1
-1 -0.1
φ-φ
φ-φ
0
0
0
MoSe2 0
0.1 E-E0
E-E0
E-E0
VS 2 -1 -0.1
-1 -0.1
0
0.1
-1 -0.1
MoTe2 0
0.1
Strain (ε) Figure 2. Calculated relative work functions (φ − φ0 ) and relative energies (E − E0 ) as functions of strain for six metal dichalcogenides monolayers.
The plots of total energy for each monolayer MDC system show the expected parabolic behavior as the structure is moved away from equilibrium. We also see that compressive strain universally decreases the work function by as much as 1.0 eV for all six monolayer MDC systems. The application of tensile strain, however, shows mixed results. In the cases of MoS2 , WS2 and VS2 , tensile strain reduces the work function although at a lesser rate than compressive strain. This is especially highighted for VS2 , in which the work function experiences only a marginal decrease of 0.1 eV when strained up to 10%. In the cases of SnS2 , MoSe2 and MoTe2 , tensile strain first increases the work function in a more pronounced way before reaching it reaches a maximum and begins to decrease. In all cases, however, tensile strain eventually works to lower the work function. It is also worth noting that all species considered (aside from VS2 )remain in a semiconducting state for strains up to 10% with the exception of MoTe2 , which becomes metallic beyond a compressive strain of 6% and MoS2 , which becomes metallic beyond a tensile strain of 9%. Any changes observed in the work function when strain is applied should be reflected by changes in either the Fermi energy, the vacuum potential energy, or both. For two representative cases, MoS2 and MoSe2 , we have plotted both of these quantities as a function of strain in figure 3. We see that for both MoS2 and MoSe2 that the vacuum potential energy increases almost linearly with increasing compressive strain, which is in accord with earlier work on the effect of strain on the work function of graphene [16]. This result is not surprising, since compressive strain brings the valence electrons closer to the ionic cores, thereby increasing the overall potential energy (including the potential energy at the vacuum level). The Fermi energy decreases as a function of compressive strain, giving rise to smaller work functions. Note that because the Fermi energy is a negative number, a decrease will result in an increase in the quantity EF −EF0 . This is also the case for tensile strain in the MoS2 , WS2 and VS2 systems. For the other three structures, namely SnS2 , MoSe2 and MoTe2 , we see that the Fermi energy increases for small values of tensile
strain. Because the Fermi energy changes more rapidly than the change in the vacuum potential energy in this region, the net effect is to increase the work function (as seen in figure 2). However, once the tensile strain is increased beyond a few percent, the Fermi energy again begins to decrease and likewise the work function becomes smaller. The more pronounced behavior with respect to tensile strain in the SnS2 , MoSe2 and MoTe2 monolayers may be related to the larger atomic radii of the constituent Sn, Se and Te atoms relative to the smaller Mo, W and V atoms. The top valence band is expected to show modulation upon the application of compressive and/or tensile strain and the work function reflects the ease with which an electron in this state can be removed from the system. The modulation of the top valence band correlates with electrons in occupied energy states re-arranging themselves to minimize the electrostatic potential energy between atoms. We plot the valence band maximum wavefunction at select K points for monolayer MoS2 in the limiting cases of 4 percent compressive strain ( = −.04), zero strain and 4 percent tensile strain ( = +0.04) in figure 4. We note first that as the atoms are moved farther apart from one another (decreasing compressive strain and then increasing tensile strain) that the wavefunction of the valence band maximum attains a more symmetrical shape. Also, the location of the valence band maximum changes from the Kpoint to the -point as the crystal is stretched. The position of the valence band at the -point steadily increases as the tensile strain is increased and we find it becomes energetically degenerate with the energy at the K-point at around 1% tensile strain. The values of strain for which these energies are nearlydegenerate correlates with the values of tensile strain for which the work function initially increases before decreasing steadily. A similar competition amongst points along the VB plays out with SnS2 and correlates with the changes in work function. As another representative monolayer, we plot the band structure and valence band wavefunctions for MoSe2 for compressive and tensile strains of 8% in figure 5. 3
J. Phys.: Condens. Matter 27 (2015) 175501
N A Lanzillo et al
1.5
1.2
MoS 2
1 0.8
Energy (eV)
Energy (eV)
1
0.5 EF - E0F 0
-0.5 0.1
MoSe 2
0.4
-0.2 0
Strain (ε)
0.05
-0.4 -0.1
0.1
EF - E0F
0.2 0
Evac - E0vac
-0.05
0.6
Evac - E0vac
-0.05
0
Strain (ε)
0.05
0.1
Figure 3. The scaled values of the Fermi energy and the vacuum potential as functions of strain for monolayer MoS2 and MoSe2 .
(a)
(b)
(c)
Figure 4. The electronic band structure and wavefunction corresponding to the valence band maximum of MoS2 for (a) 4% compressive strain (b) 0% strain and (c) 4% tensile strain.
We observe that similar to the case of MoS2 , the wavefunctions at the valence band maximum become more symmetric as the atoms are stretched farther apart from one another. However, unlike the case of MoS2 , we observe that the location of the valence band maximum shifts from the Mpoint under compressive strain to the K-point for intermediate values of strain and finally to the -point under tensile strain. The transition from the K-point to the -point occurs around 5% tensile strain, which is just beyond the point at which tensile strain works to decrease the work function rather than increase it. We observe that as compressive biaxial strain increases (or tensile strain decreases) that the orbital becomes more focused around the interstitial regions halfway between two neighboring sulfur atoms. Bringing the atoms closer together will push the electrons closer to the ionic cores, increasing the
total energy of the system as well as the electrostatic potential. This increase in electrostatic potential results in higher vacuum energy levels as a function of strain, which accounts for the steady increase in potential energy for all systems as the strain is increased. If the Fermi level were to remain constant, this would result in larger work functions under compressive strain and smaller work functions under tensile strain. However, because the Fermi Level also modulates with both tensile and compressive strain, the net effect is a decreased work function for compressive strain and an overall decrease in the work function for strains greater than a few percent. To investigate the effects of more general strains, including uniaxial strain applied along the zigzag or armchair directions, we calculate the work function for monolayer MoS2 under these types of strain. The results are shown for compressive and tensile strain up to 5% in figure 6. 4
J. Phys.: Condens. Matter 27 (2015) 175501
N A Lanzillo et al
(a)
(b)
(c)
Figure 5. The electronic band structure and wavefunction corresponding to the valence band maximum of MoSe2 for (a) 8% compressive strain (b) 0% strain and (c) 8% tensile strain.
observe the work function to begin decreasing after initially increasing from the equilibrium value. The direct-to-indirect transition occurs at larger values of tensile strain for the heavier MDC systems and likely we observe larger thresholds for which the work function begins decreasing under tensile strain for these systems (MoS2 and MoTe2 ). Thus, the value of tensile strain at which the work function begins decreasing upon the application of additional strain is closely tied to the direct-toindirect band gap transition in monolayer MDC systems. Lastly, we mention the possibility of modulating the work function in monolayer MDC systems through the application of out-of-plane strain, as suggested by work atomically-think MoS2 [29] as well as on graphene-MoS2 heterostructures [30]. Modification of the S-plane distance through this type of strain can result in changes in the valence band maximum energies, thereby modifying the work function and band gap of MDC systems. Investigation of such effects in MDCs with metals other than Mo, as well as studying the effect of layer thickness on the work function, will be the subject of future study.
0.1 0.05
biaxial zigzag armchair
φ - φ0 (eV)
0 -0.05 -0.1 -0.15
AC ZZ
-0.2 -0.25 -0.05
0
0.05
Strain (ε )
Figure 6. The work function for monolayer MoS2 calculated for biaxial, uniaxial zigzag and uniaxial armchair strain.
A common theme emerges regardless of what direction the strain is applied and that is the fact that the work function decreases by several tenths of an eV for both compressive and tensile strain. One interesting feature is that for all uniaxial strains considered, the maximum work function occurs at a value of 1–2% tensile strain, whereas it is closer to the equilibrium lattice constant in the case of biaxial strain. However, in all cases considered, the work function decreases overall once a strain of 2–3% is reached. The shift in the location of the maximum work function is attributed to the differing and competing behaviors of the Fermi energy and the vacuum potential as a function of strain, just as we saw in case of biaxial strain for the other MDC materials. Changes in the work function resulting from strain can be correlated to the direct-to-indirect band gap transition that takes place in the monolayer MDCs [33]. Specifically, for MoS2 the direct-to-indirect band gap transition occurs at just 1–2% tensile strain, which is also the threshold at which we
4. Conclusion
In conclusion, we have examined the effect of both compressive and tensile strain on the work functions of six monolayer metal dichalcogenide materials. In each case, we find that compressive strain of up to 10% universally reduces the work function by as much as 1.0 eV. The application of tensile strain leads to a more complicated situation in which the work function initially increases but then decreases beyond a strain of a few percent. The changes observed in the work function are ultimately due to modulation of the Fermi energy under strain, while the vacuum potential energy 5
J. Phys.: Condens. Matter 27 (2015) 175501
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increases almost linearly with increasing strain for all systems considered as a result of the increased electrostatic potential energy as atoms are brought closer together. Future work will examine the effect of strain on the work function of multi-layered MDC families where interlayer interactions must be taken into account, as well as calculating quasi-particle corrections to the band gaps of MDC systems using the GW Approximation.
[12] Lee C, Yan H, Brus L E, Heinz T F, Hone J and Ryu S 2010 ACS Nano 4 2695 [13] Molina-Sanchez A and Wirtz L 2011 Phys. Rev. B 84 155413 [14] Qi J, Li X, Qian X and Feng J 2013 Appl. Phys. Lett. 102 173112 [15] Choi S, Jhi S and Son Y 2010 Phys. Rev. B 81 081407 [16] Peng X, Tang F and Copple A 2012 J. Phys.: Condens. Matter 24 075501 [17] Li Y, Xu C, Zhang B and Zhen L 2013 Appl. Phys. Lett. 103 033122 [18] Yu Y, Zhao Y, Ryu S, Brus L, Kim K and Kim P 2009 Nano Lett. 9 3430 [19] Shi Y, Kim K, Reina A, Hofmann M, Li L and Kong J 2010 ACS Nano 4 2689 [20] Rout C, Joshi P, Kashid R, Joag D, More M, Simbeck A, Washington M, Nayak S and Late D 2013 Sci. Rep. 3 3282 [21] Rout C, Khare R, Kashid R, Joag D, More M, Lanzillo N, Washington M, Nayak S and Late D 2014 Eur. J. Inorg. Chem. 31 5331 [22] Gonze X et al 2002 Comput. Mater. Sci. 25 478 [23] Gonze X et al 2005 Z. Kristallogr. 220 558 [24] Gonze X et al 2009 Comput. Phys. Commun. 180 2582 [25] Hohenberg P and Kohn W 1964 Phsy. Rev. 136 B864 [26] Kohn W and Sham L 1965 Phys. Rev. 140 1133 [27] Troullier N and Martins J 1991 Phys. Rev. B 43 8861 [28] Giovannetti G, Khomyakov P, Brocks G, Karpan V, van der Brink J and Kelly P 2008 Phys. Rev. Lett. 101 026803 [29] Castellanos-Gomez A, Roldan R, Cappelluti E, Busceme M, Guinea F, van der Zant H and Steel G 2013 Nano Lett. 13 5361–6 [30] Ebonnasir A, Narayanan B, Kodambaka S and Ciobanu C 2014 Appl. Phys. Lett. 105 031603 [31] Ramasubramaniam A, Naveh D and Towe E 2011 Phys. Rev. B 84 205325 [32] Ma Y, Dai Y, Guo M, Niu C, Zhu Y and Huang B 2011 ACS Nano 6 1695–701 [33] Johari P and Shenoy V 2012 ACS Nano 6 5449–56 [34] Sun Y et al 2012 Angew. Chem. Int. Edn 51 8727 [35] Seminovski Y, Palacios P and Wahnon P 2013 Thin Solid Films 535 387–9 [36] Zhuang H and Hennig R 2013 Phys. Rev. B 88 115314 [37] Rout C S, Joshi P D, Kashid R V, Joag D S, More M A, Simbeck A J, Washington M, Nayak S K and Late D J 2014 Appl. Phys. Lett. 105 043109
Acknowledgments
This work used computational resources provided by the Computational Center for Innovations (CCI) at Rensselaer Polytechnic Institute. The authors acknowledge support by the Army Research Lab Multiscale Multidisciplinary Modeling of Electronic Materials (MSME) Collaborative Research Alliance (CRA) and the Indo-US Forum. References [1] Novoselov K, Geim K, Morozov S, Jiang D, Zhang Y, Dubonos S, Grigorieva I and Firsov A 2004 Science 306 666 [2] Mak K, Lee C, Hone J, Shan J and Heinz T 2010 Phys. Rev. Lett. 105 136805 [3] Radisavljevic B, Radenovic A, Brivio J, Giacometti V and Kis A 2011 Nat. Nanotechnol. 6 147 [4] Ghatak S, Pal A and Ghosh A 2011 ACS Nano 5 7707 [5] Splendiani A, Sun L, Zhang Y, Li T, Kim J, Chim C, Galli G and Wang F 2010 Nano Lett. 10 1271 [6] Ellis J, Lucero M and Scuseria G 2011 Appl. Phys. Lett. 99 261908 [7] Li T 2012 Phys. Rev. B 85 235407 [8] Novoselov K, Jiang D, Schedin F, Booth T, Khotkevich V, Morozov S and Geim A 2005 Proc. Natl Acad. Sci. 102 10451 [9] Livneh T and Sterer E 2010 Phys. Rev. B 81 195209 [10] Lanzillo N et al 2013 Appl. Phys. Lett. 103 093102 [11] Rice C, Young R J, Zan R, Bangert U, Wolverson D, Georgiou T, Jalil R and Novoselov K S 2013 Phys. Rev. B 87 081307
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Strain engineering the work function in monolayer metal dichalcogenides
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 J. Phys.: Condens. Matter 27 175501 (http://iopscience.iop.org/0953-8984/27/17/175501) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 128.226.136.66 This content was downloaded on 07/05/2017 at 02:02 Please note that terms and conditions apply.
You may also be interested in: Semiconductor to metal transition in bilayer transition metals dichalcogenides MX2 (M=Mo, W; X=S, Se, Te) Ashok Kumar and P K Ahluwalia Strain engineering in semiconducting two-dimensional crystals Rafael Roldán, Andrés Castellanos-Gomez, Emmanuele Cappelluti et al. Equibiaxial strain: tunable electronic structure and optical properties of bulk and monolayer MoSe2 C K Ghosh, D Sarkar, M K Mitra et al. Effect of strain on electronic and thermoelectric properties of few layers to bulk MoS2 Swastibrata Bhattacharyya, Tribhuwan Pandey and Abhishek K Singh Substrate dependent electronic structure variations of van der Waals heterostructures of MoSe2 or MoSe2(1x)Te2x grown by van der Waals epitaxy Horacio Coy Diaz, Yujing Ma, Sadhu Kolekar et al. Band engineering of the MoS2/stanene heterostructure: strain and electrostatic gating Wenqi Xiong, Congxin Xia, Juan Du et al. The strain effect on superconductivity in phosphorene: a first-principles prediction Yanfeng Ge, Wenhui Wan, Fan Yang et al. Control of biaxial strain in single-layer molybdenite using local thermal expansion of the substrate Gerd Plechinger, Andres Castellanos-Gomez, Michele Buscema et al.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 175501 (6pp)
doi:10.1088/0953-8984/27/17/175501
Strain engineering the work function in monolayer metal dichalcogenides Nicholas A Lanzillo1,2 , Adam J Simbeck1 and Saroj K Nayak1,3 1 Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180, USA 2 Division of Science, Mathematics and Computing, Bard College, 30 Campus Road, Annandale-on-Hudson, NY 12504, USA 3 School of Basic Sciences, Indian Institute of Technology, Bhubaneswar, Odisha 751007, India
E-mail: [email protected] Received 12 January 2015, revised 2 March 2015 Accepted for publication 5 March 2015 Published 2 April 2015 Abstract
We use first-principles density functional theory to investigate the effect of both tensile and compressive strain on the work functions of various metal dichalcogenide monolayers. We find that for all six species considered, including MoS2 , WS2 , SnS2 , VS2 , MoSe2 and MoTe2 , that compressive strain of up to 10% decreases the work function continuously by as much as 1.0 eV. Large enough tensile strain is also found to decrease the work function, although in some cases we observe an increase in the work function for intermediate values of tensile strain. This work function modulation is attributed to a weakening of the chalcogenide-metal bonds and an increase in total energy of each system as a function of strain. Values of strain which bring the metal atoms closer together lead to an increase in electrostatic potential energy, which in turn results in an increase in the vacuum potential level. The net effect on the work function can be explained in terms of the balance between the increases in the vacuum potential levels and Fermi energy. Keywords: work function, density functional theory, strain, monolayer, metal dichalcogenide (Some figures may appear in colour only in the online journal)
is a crucial quantity for opto-electronic device applications, the work function is another material-specific property that is important in field-emission based devices as well in layered heterostructures involving MDCs. There have been relatively few first-principles studies on the work function and strain-induced modulation in low-dimensional nanostructures systems [15, 16]. The effect of a backgate electric field was shown to decrease the value of the work function in bilayer MoS2 as the voltage increases from −5 V to 13 V [17]. The work function of graphene can be favorably tuned through the application of an electric field [18] and the work function of graphenebased contacts can be tuned through chemical doping [19]. Compressive strain is found to decrease the work function of armchair graphene nanoribbons, while tensile strain is found to increase the work function in both pure graphene and graphene nanoribbons [15, 16]. Changes in the work function in these materials correlates to changes in the Fermi energies and
1. Introduction
The discovery of graphene [1] has spurred enormous research interest in the field of two-dimensional materials for applications in nanoelectronics [2–5]. In particular, the metal dichalcogenide (MDC) family are attractive candidates for opto-electronic applications due to the presence of a direct band gap in monolayer samples [2, 6] and favorable structural properties [7]. Metal dichalcogenides consist of covalently bound layers of chalcogenides (for example: S, Se, Te) and metals (for example: Mo, W, V), with adjacent layers held together by the weak van der Waals interaction. Analogous to graphene, the weak interlayer interaction allows for singlelayer samples to be fabricated via mechanical exfoliation [8]. The electronic and vibrational properties of the monolayer MDCs have been studied both experimentally [2–4, 9] and theoretically [10–14, 33] while the work function has received considerably less attention. While the electronic band gap 0953-8984/15/175501+06$33.00
1
© 2015 IOP Publishing Ltd Printed in the UK
J. Phys.: Condens. Matter 27 (2015) 175501
N A Lanzillo et al
vacuum potential energies. The effect of both compressive and tensile strain on the work functions of monolayer MDC materials remains an open question and the ability to control the work function would have enormous implications on the engineering of field-emission based devices fabricated from MDC materials [20, 21]. In this work, we investigate the effect of strain on the work functions of MoS2 , WS2 , MoSe2 , MoTe2 , VS2 and SnS2 . These choices of metal dichalcogenides allow us to study any effects that may arise between different metals (i.e. Mo, W,V) and different chalcogenides (i.e. S, Se, Te). We also examine the effect of strain on a metallic MDC (VS2 ) as well as an MDC with a different crystal structure (SnS2 ) relative to the others. We find that for all systems considered, compressive strain decreases the work function while tensile strain may initially increase the work function but will ultimately lead to a decrease when the lattice is stretched more than a few percent. The changes in the work function can be traced back to the balance between electrostatic potential energy and Fermi level modulation as the lattice is strained.
(b)
(c)
(d)
Figure 1. The top views of metal dichalcogenide crystal structures with (a) P6 3/mmc and (b) P3m1 space groups, as well as the side views of (c) P6 3/mmc and (d) P3m1 space groups. Table 1. The values of the equilibrium lattice constants (in Å) and associated zero-strain work functions (in eV).
a0 MoS2 WS2 VS2 SnS2 MoSe2 MoTe2
2. Computational methods
Calculations were performed using the ABINIT [22–24] software package, which is a plane-wave pseudopotential implementation of density functional theory [25, 26]. Troullier–Martins [27] norm-conserving pseudopotentials were used with plane wave cut off energies of 40.0 Hartree for MoS2 , MoSe2 , MoTe2 and VS2 and a cutoff of 42.0 Hartree for SnS2 and WS2 . We used k-point sampling of 12 × 12 × 1 and simulated the effect of compressive/tensile strain by decreasing/increasing the lattice constants in increments of 1%. The geometry of each monolayer system was relaxed at each value of strain until the forces on the atoms were less than 10−2 eV Å−1 . This procedure was repeated for every value of strain considered. The values of strain are reported in the form 0 = a−a where a0 is the equilibrium lattice constant. Positive a0 values of correspond to tensile strain, while negative values correspond to compressive strain. The work function φ is calculated as the energy difference between the Fermi energy EF and the vacuum potential Evac . φ = Evac − EF
(a)
3.20 3.18 3.22 3.44 3.29 3.52
——
φ 6.11 5.89 5.45 6.86 5.49 5.15
3. Results and discussion
Before discussing the effects of strain on the work function, we present the optimized values of lattice constants and work functions for each monolayer MDC system considered. These results are summarized in table 1. The values of lattice constants considered here for MoS2 , WS2 , MoSe2 and MoTe2 are very close to ( within 0.08 Angstrom)—and in some cases identical to—the values presented in other works studying monolayer dichalcogenides [6, 13, 31]. Our lattice constant for VS2 is 3.22 Angstrom, which is slightly larger but comparable to the value of 3.174 Angstrom obtained in other work [32]. Both the crystal structure and the lattice constant of SnS2 agree well with earlier works [34–37]. It is worth noting that the work function of each MDC monolayer generally lies in the range of 5–7 eV, slightly larger than the reported value of 4.5 eV for graphene [28]. Upon applying biaxial compressive and/or tensile strain to each system, the total energy is expected to increase as the structure is moved away from equilibrium. We observe the general trend that as the lattice constant is reduced, the M–X bond becomes shorter while the X–M–X bond angle becomes larger. The corresponding total energies increase parabolically, as indicated in figure 2. The effect of strain on the work function will depend on how strain affects both the Fermi energy and the vacuum potential energy. We see that compressive strain decreases the work function for all species considered, while tensile strain may at first increase but eventually decreases the work function. These results are also shown in figure 2.
(1)
The Fermi energy is determined self-consistently in a ground state electronic structure calculation and the vacuum potential is calculated as the limiting value of the electrostatic potential in the direction perpendicular to the surface at a distance far away, generally 10 or more Å for the systems considered here. Note that the Fermi energy is taken to be the top of the valence band. While the most stable crystal structure of almost all MDC monolayers is a hexagonal lattice with space group P6 3/mmc, SnS2 crystallizes with a cadmium iodide structure (space group P3m1.) In both cases, however, the metallic atom remains sixfold coordinated to neighboring chalcogenide atoms atoms. In figure 1, we show the top and side views of both crystal structures. 2
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1
1 E-E
0
E-E0
0
0
0
Energy (eV)
1 E-E0
φ-φ 0
WS 2
MoS2
-1 -0.1
φ-φ
0
0.1
1
-1 -0.1
φ-φ 0
0
-0.1
1
SnS2 0
1
0
0
φ-φ 0
0
0.1
-1 -0.1
φ-φ
φ-φ
0
0
0
MoSe2 0
0.1 E-E0
E-E0
E-E0
VS 2 -1 -0.1
-1 -0.1
0
0.1
-1 -0.1
MoTe2 0
0.1
Strain (ε) Figure 2. Calculated relative work functions (φ − φ0 ) and relative energies (E − E0 ) as functions of strain for six metal dichalcogenides monolayers.
The plots of total energy for each monolayer MDC system show the expected parabolic behavior as the structure is moved away from equilibrium. We also see that compressive strain universally decreases the work function by as much as 1.0 eV for all six monolayer MDC systems. The application of tensile strain, however, shows mixed results. In the cases of MoS2 , WS2 and VS2 , tensile strain reduces the work function although at a lesser rate than compressive strain. This is especially highighted for VS2 , in which the work function experiences only a marginal decrease of 0.1 eV when strained up to 10%. In the cases of SnS2 , MoSe2 and MoTe2 , tensile strain first increases the work function in a more pronounced way before reaching it reaches a maximum and begins to decrease. In all cases, however, tensile strain eventually works to lower the work function. It is also worth noting that all species considered (aside from VS2 )remain in a semiconducting state for strains up to 10% with the exception of MoTe2 , which becomes metallic beyond a compressive strain of 6% and MoS2 , which becomes metallic beyond a tensile strain of 9%. Any changes observed in the work function when strain is applied should be reflected by changes in either the Fermi energy, the vacuum potential energy, or both. For two representative cases, MoS2 and MoSe2 , we have plotted both of these quantities as a function of strain in figure 3. We see that for both MoS2 and MoSe2 that the vacuum potential energy increases almost linearly with increasing compressive strain, which is in accord with earlier work on the effect of strain on the work function of graphene [16]. This result is not surprising, since compressive strain brings the valence electrons closer to the ionic cores, thereby increasing the overall potential energy (including the potential energy at the vacuum level). The Fermi energy decreases as a function of compressive strain, giving rise to smaller work functions. Note that because the Fermi energy is a negative number, a decrease will result in an increase in the quantity EF −EF0 . This is also the case for tensile strain in the MoS2 , WS2 and VS2 systems. For the other three structures, namely SnS2 , MoSe2 and MoTe2 , we see that the Fermi energy increases for small values of tensile
strain. Because the Fermi energy changes more rapidly than the change in the vacuum potential energy in this region, the net effect is to increase the work function (as seen in figure 2). However, once the tensile strain is increased beyond a few percent, the Fermi energy again begins to decrease and likewise the work function becomes smaller. The more pronounced behavior with respect to tensile strain in the SnS2 , MoSe2 and MoTe2 monolayers may be related to the larger atomic radii of the constituent Sn, Se and Te atoms relative to the smaller Mo, W and V atoms. The top valence band is expected to show modulation upon the application of compressive and/or tensile strain and the work function reflects the ease with which an electron in this state can be removed from the system. The modulation of the top valence band correlates with electrons in occupied energy states re-arranging themselves to minimize the electrostatic potential energy between atoms. We plot the valence band maximum wavefunction at select K points for monolayer MoS2 in the limiting cases of 4 percent compressive strain ( = −.04), zero strain and 4 percent tensile strain ( = +0.04) in figure 4. We note first that as the atoms are moved farther apart from one another (decreasing compressive strain and then increasing tensile strain) that the wavefunction of the valence band maximum attains a more symmetrical shape. Also, the location of the valence band maximum changes from the Kpoint to the -point as the crystal is stretched. The position of the valence band at the -point steadily increases as the tensile strain is increased and we find it becomes energetically degenerate with the energy at the K-point at around 1% tensile strain. The values of strain for which these energies are nearlydegenerate correlates with the values of tensile strain for which the work function initially increases before decreasing steadily. A similar competition amongst points along the VB plays out with SnS2 and correlates with the changes in work function. As another representative monolayer, we plot the band structure and valence band wavefunctions for MoSe2 for compressive and tensile strains of 8% in figure 5. 3
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1.5
1.2
MoS 2
1 0.8
Energy (eV)
Energy (eV)
1
0.5 EF - E0F 0
-0.5 0.1
MoSe 2
0.4
-0.2 0
Strain (ε)
0.05
-0.4 -0.1
0.1
EF - E0F
0.2 0
Evac - E0vac
-0.05
0.6
Evac - E0vac
-0.05
0
Strain (ε)
0.05
0.1
Figure 3. The scaled values of the Fermi energy and the vacuum potential as functions of strain for monolayer MoS2 and MoSe2 .
(a)
(b)
(c)
Figure 4. The electronic band structure and wavefunction corresponding to the valence band maximum of MoS2 for (a) 4% compressive strain (b) 0% strain and (c) 4% tensile strain.
We observe that similar to the case of MoS2 , the wavefunctions at the valence band maximum become more symmetric as the atoms are stretched farther apart from one another. However, unlike the case of MoS2 , we observe that the location of the valence band maximum shifts from the Mpoint under compressive strain to the K-point for intermediate values of strain and finally to the -point under tensile strain. The transition from the K-point to the -point occurs around 5% tensile strain, which is just beyond the point at which tensile strain works to decrease the work function rather than increase it. We observe that as compressive biaxial strain increases (or tensile strain decreases) that the orbital becomes more focused around the interstitial regions halfway between two neighboring sulfur atoms. Bringing the atoms closer together will push the electrons closer to the ionic cores, increasing the
total energy of the system as well as the electrostatic potential. This increase in electrostatic potential results in higher vacuum energy levels as a function of strain, which accounts for the steady increase in potential energy for all systems as the strain is increased. If the Fermi level were to remain constant, this would result in larger work functions under compressive strain and smaller work functions under tensile strain. However, because the Fermi Level also modulates with both tensile and compressive strain, the net effect is a decreased work function for compressive strain and an overall decrease in the work function for strains greater than a few percent. To investigate the effects of more general strains, including uniaxial strain applied along the zigzag or armchair directions, we calculate the work function for monolayer MoS2 under these types of strain. The results are shown for compressive and tensile strain up to 5% in figure 6. 4
J. Phys.: Condens. Matter 27 (2015) 175501
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(a)
(b)
(c)
Figure 5. The electronic band structure and wavefunction corresponding to the valence band maximum of MoSe2 for (a) 8% compressive strain (b) 0% strain and (c) 8% tensile strain.
observe the work function to begin decreasing after initially increasing from the equilibrium value. The direct-to-indirect transition occurs at larger values of tensile strain for the heavier MDC systems and likely we observe larger thresholds for which the work function begins decreasing under tensile strain for these systems (MoS2 and MoTe2 ). Thus, the value of tensile strain at which the work function begins decreasing upon the application of additional strain is closely tied to the direct-toindirect band gap transition in monolayer MDC systems. Lastly, we mention the possibility of modulating the work function in monolayer MDC systems through the application of out-of-plane strain, as suggested by work atomically-think MoS2 [29] as well as on graphene-MoS2 heterostructures [30]. Modification of the S-plane distance through this type of strain can result in changes in the valence band maximum energies, thereby modifying the work function and band gap of MDC systems. Investigation of such effects in MDCs with metals other than Mo, as well as studying the effect of layer thickness on the work function, will be the subject of future study.
0.1 0.05
biaxial zigzag armchair
φ - φ0 (eV)
0 -0.05 -0.1 -0.15
AC ZZ
-0.2 -0.25 -0.05
0
0.05
Strain (ε )
Figure 6. The work function for monolayer MoS2 calculated for biaxial, uniaxial zigzag and uniaxial armchair strain.
A common theme emerges regardless of what direction the strain is applied and that is the fact that the work function decreases by several tenths of an eV for both compressive and tensile strain. One interesting feature is that for all uniaxial strains considered, the maximum work function occurs at a value of 1–2% tensile strain, whereas it is closer to the equilibrium lattice constant in the case of biaxial strain. However, in all cases considered, the work function decreases overall once a strain of 2–3% is reached. The shift in the location of the maximum work function is attributed to the differing and competing behaviors of the Fermi energy and the vacuum potential as a function of strain, just as we saw in case of biaxial strain for the other MDC materials. Changes in the work function resulting from strain can be correlated to the direct-to-indirect band gap transition that takes place in the monolayer MDCs [33]. Specifically, for MoS2 the direct-to-indirect band gap transition occurs at just 1–2% tensile strain, which is also the threshold at which we
4. Conclusion
In conclusion, we have examined the effect of both compressive and tensile strain on the work functions of six monolayer metal dichalcogenide materials. In each case, we find that compressive strain of up to 10% universally reduces the work function by as much as 1.0 eV. The application of tensile strain leads to a more complicated situation in which the work function initially increases but then decreases beyond a strain of a few percent. The changes observed in the work function are ultimately due to modulation of the Fermi energy under strain, while the vacuum potential energy 5
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increases almost linearly with increasing strain for all systems considered as a result of the increased electrostatic potential energy as atoms are brought closer together. Future work will examine the effect of strain on the work function of multi-layered MDC families where interlayer interactions must be taken into account, as well as calculating quasi-particle corrections to the band gaps of MDC systems using the GW Approximation.
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Acknowledgments
This work used computational resources provided by the Computational Center for Innovations (CCI) at Rensselaer Polytechnic Institute. The authors acknowledge support by the Army Research Lab Multiscale Multidisciplinary Modeling of Electronic Materials (MSME) Collaborative Research Alliance (CRA) and the Indo-US Forum. References [1] Novoselov K, Geim K, Morozov S, Jiang D, Zhang Y, Dubonos S, Grigorieva I and Firsov A 2004 Science 306 666 [2] Mak K, Lee C, Hone J, Shan J and Heinz T 2010 Phys. Rev. Lett. 105 136805 [3] Radisavljevic B, Radenovic A, Brivio J, Giacometti V and Kis A 2011 Nat. Nanotechnol. 6 147 [4] Ghatak S, Pal A and Ghosh A 2011 ACS Nano 5 7707 [5] Splendiani A, Sun L, Zhang Y, Li T, Kim J, Chim C, Galli G and Wang F 2010 Nano Lett. 10 1271 [6] Ellis J, Lucero M and Scuseria G 2011 Appl. Phys. Lett. 99 261908 [7] Li T 2012 Phys. Rev. B 85 235407 [8] Novoselov K, Jiang D, Schedin F, Booth T, Khotkevich V, Morozov S and Geim A 2005 Proc. Natl Acad. Sci. 102 10451 [9] Livneh T and Sterer E 2010 Phys. Rev. B 81 195209 [10] Lanzillo N et al 2013 Appl. Phys. Lett. 103 093102 [11] Rice C, Young R J, Zan R, Bangert U, Wolverson D, Georgiou T, Jalil R and Novoselov K S 2013 Phys. Rev. B 87 081307
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