Optical Properties of Triangular Molybdenum Disulfide Nanoflakes

Letter pubs.acs.org/JPCL

Optical Properties of Triangular Molybdenum Disulfide Nanoflakes Tsegabirhan B. Wendumu,†,‡ Gotthard Seifert,*,† Tommy Lorenz,†,§ Jan-Ole Joswig,† and Andrey Enyashin†,∥ †

Physikalische Chemie, Technische Universität Dresden, Bergstr. 66b, 01069 Dresden, Germany Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden, Germany § Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, P.O. Box 51 01 19, 01314 Dresden, Germany ∥ Institute of Solid State Chemistry, UB RAS, Pervomayskaya 91, 620990 Ekaterinburg, Russia ‡

ABSTRACT: The results from calculations of optical and electronic properties of triangular MoS2 nanoflakes with edge lengths ranging from 1.6 to 10.4 nm are presented. The optical spectra were calculated using the timedependent extension of the density-functional tight-binding method (TDDFTB). The size effect in the optical absorption spectra is clearly visible. With decreasing length of the nanoflakes edges, the long-wavelength absorption in the range of visible light is shifted toward short-wavelength absorption, confirming a quantum-confinement-like behavior of these flakes. In contrast, the edges of the nanoflakes exhibit a distinct metallic-like behavior. The relation of the absorption properties to the observed photoluminescence of MoS2 nanoflakes is discussed in a qualitative manner. SECTION: Physical Processes in Nanomaterials and Nanostructures

M

particles may be strongly influenced by varying the size of the particle. (These size effects can be described qualitatively by solving the quantum-mechanical problem of the “particle in a box”.)8 Bollinger et al.,9 Li and Galli,10 Seifert et al.,11 and Bertram et 12 al. already studied the electronic structure of small triangular MoS2 nanoflakes theoretically and experimentally. It was shown that the edges of these flakes essentially determine their electronic structure. The edges possess a metallic-like character, whereas the inner core of each flake remains semiconducting, as it has been demonstrated by scanning tunneling microscope (STM) investigations9 and explained theoretically.9−13 More recently, it even has been predicted that zig-zag edges of MoS2 nanoribbons−with the Mo edge being terminated by S atoms and the S edge being freestanding−are in a magnetic metal state.14 The results of the calculations from Li and Galli10 indicated that the blue shift observed experimentally in photoluminescence spectra of MoS2 nanoflakes1 does not originate from in-plane quantum-confinement effects in the nanoflakes. Instead, this effect was attributed to the interactions between the flakes. In light of these studies, it is our aim to present and discuss the electronic and optical properties of triangular MoS2 nanoflakes, to analyze the variation of these properties as a

olybdenum disulfide (MoS2) is a compound among the rich family of layered transition-metal dichalcogenides that has been studied most intensively in the past 40 years. Bulk MoS2 belongs to the hexagonal space group P63/mmc. It has a layered structure, and each layer consists of Mo atoms sandwiched between sulfur atoms in an S−Mo−S arrangement (see top view in Figure 1). Each Mo atom is coordinated by six sulfur atoms, and each sulfur atom is covalently bound to three Mo atoms. Consequently, adjacent S−Mo−S sandwich layers are held together by weak van der Waals forces, leading to the 2D character of MoS2.1 Recently, monolayer MoS2 has been in the focus of research because of its exceptional electronic and optical properties.2,3 Whereas bulk MoS2 is a semiconductor with an indirect band gap of 1.3 eV,4 monolayer MoS2 is a direct-gap semiconductor with a band gap of 1.8 eV.3,5 Monolayer MoS2 has been used to build transistors with a very promising electron mobility.4 Furthermore, MoS2 has been recently exploited for biosensing6 and energy-storage applications,7 and strong absorption and photoluminescence bands were observed in the visible range at ∼1.9 eV (650 nm).3,5 The electronic properties of single MoS2 layers are considered often under the assumption of an infinite 2D crystal. Thus, the real situation including the finite size of the flakes and the presence of a boundary is neglected. (Note that we will call a finite part of the infinite MoS2 monolayer a “nanoflake” throughout this contribution. We will use the phrase “nanoparticle” for general statements only.) Yet the electronic and optical properties of semiconductor nano© XXXX American Chemical Society

Received: July 31, 2014 Accepted: October 4, 2014

3636

dx.doi.org/10.1021/jz501604j | J. Phys. Chem. Lett. 2014, 5, 3636−3640

The Journal of Physical Chemistry Letters

Letter

Figure 1. Construction of triangular structures of sulfur-terminated MoS2 nanoflakes from an MoS2 slab: (a) infinite slab; the lines indicate the cuts for the construction of the MoS2 nanoflakes; (b) corresponding flake of type tri-1 (resulting from blue-line cut) with zig-zag-like edges of bridging S atoms; and (c) corresponding flake of type tri-2 (resulting from black-line cut) with antenna-like S atoms.

characterized by the number of Mo atoms (l) along each edge. The total number of Mo atoms is given then by n = l(l + 1)/2. Correspondingly, the number of sulfur atoms is m = 2n + 2(l + 1). In agreement with previous calculations on MoS 2 nanoflakes,10 geometry optimizations of all studied nanoflakes reveal that they have similar bond lengths and bond angles as the infinite MoS2 monolayer. The calculated density of states of nanoflakes with zig-zag edges and edge lengths between 2.2 and 7.8 nm are shown in an energy window around the Fermi energy in Figure 2 in

function of particle size, and to show that these systems indeed exhibit a considerable quantum-confinement effect that is visible in their absorption spectra. A density-functional tight-binding (DFTB) method15 was utilized for calculating the electronic properties of a series of triangular MoS2 nanoflakes. The method is based on the density functional theory of Hohenberg and Kohn in the formulation of Kohn and Sham. The single-particle Kohn− Sham eigenfunctions ψi(r) are expanded with a set of localized atom-centered basis functions φj(r). These functions are determined by self-consistent density functional calculations on the isolated atoms employing a large set of Slater-type basis functions. The effective one-electron potential in the Kohn−Sham Hamiltonian is approximated as a superposition of the potentials of neutral atoms. Additionally, only one- and twocenter integrals are calculated to set up the Hamilton matrix. We have taken a minimal valence basis, including the 5s, 5p, and 4d orbitals for molybdenum and the 3s and 3p orbitals for sulfur. States below these levels were treated within a frozencore approximation. Moreover, we have used time-dependent density functional response theory for the calculations of the excitation spectra.16 The coupling matrix, which gives the response of the potential with respect to a change in the electron density, has to be built to obtain the excitation energies. This is also referred to as a linear response16 theory. In our scheme, we approximate the coupling matrix in the so-called γ-approximation,16 which allows for an efficient calculation of the excitation energies and the required oscillator strengths within the dipole approximation. The spectrum calculations were performed using a linear-response extension to the DFTB method as implemented in an experimental version of the deMon computer code.17 The structure generation is shown in Figure 1a. Sulfurterminated triangular nanoflakes can be obtained from cuts of the MoS2 monolayer along [100] directions. Two types of sulfur termination may be considered: zig-zag-like edges with bridging (double-coordinated) sulfur atoms (labeled “tri-1”, Figure 1b) and a sulfur-rich termination with antenna-like (single-coordinated) sulfur atoms (labeled “tri-2”, Figure 1c). Experimentally, Lauritsen et al.13 showed that the edge type of such flakes varies as a function of size and sulfur coverage. Variation of the edge type leads to subtle changes of the electronic density of states (DOS) but does not affect the general behavior of the electronic structure. Hence, we restrict our investigations on nanoflakes with zig-zag-like edges (tri-1). The calculations were performed for a continuous set of triangular nanoflakes with different edge lengths varying from 1.6 to 10.4 nm. The size of the tri-1 MonSm nanoflakes can be

Figure 2. (a) Calculated DOS of nanoflakes with zig-zag edges and edge lengths between 2.2 and 7.8 nm in comparison with (b) the DOS of the infinite MoS2 layer. The energy is given with respect to the Fermi energy. The gray-shaded areas indicate contributions resulting only from the Mo atoms along the edges of the flakes.

comparison with the DOS of the infinite MoS2 layer. The monolayer DOS can be characterized by a valence band determined by Mo-4d, S-3p states (not shown in Figure 2). The upper edge of the valence band is dominated by Mo-4dz2 contributions, whereas the lower edges of the conduction band are dominated by Mo-4dxy, Mo-4dx2−y2, and a contribution of S3p states can be seen at higher energies. The MoS2 monolayer shows semiconducting behavior. In contrast, the Fermi energy of the nanoflakes is located within the DOS peak corresponding to the Mo-4dz2 states. This results in an almost zero HOMO− LUMO gap, as it was already discussed in the previous studies.9−13 3637



Letter

Figure 3. (a) Projected Mo-4d density of states of a single Mo153S342 nanoflake resulting from groups of Mo atoms triangularly. (b) Color code of the groups of Mo atoms (labeled pn, n = 1−6) as used for the PDOS representation in panel a.

nanoflakes in the same size range: Wilcoxon et al.1 as well as more recently Chikan and Kelley18 observed a size dependence of the optical spectra of MoS2 nanoflakes. The observed size dependence of the optical absorption was explained by the quantum-confinement effect. To visualize the quantum confinement more clearly, we show the low-energy absorption in the visible range in Figure 5 as a

In the nanoflakes, the unoccupied states at 1 to 2 eV above the HOMO level are formally located in the band gap of the infinite monolayer. These states are composed of Mo-4dxy and Mo-4dx2−y2 orbitals being located exclusively at the edge atoms (gray-shaded areas in Figure 2). For a more detailed analysis, the partial densities of states (PDOS) of a single nanoflake resulting from Mo-4d states are only shown in Figure 3 as an example. The analysis of the PDOS shows that the occupied states near the HOMO are formed by Mo-4d orbitals, with highest contributions from the outermost edge atoms (labeled p6). This result is in accordance with the metallic edge states observed in the STM images of such nanoflakes.9 Also, the region between 1 and 2 eV above the HOMO is dominated by states from the edge atoms. Not considering these states, the PDOS profile for all Mo atoms resembles already very much that of the infinite 2D MoS2 layer with its distinct semiconductor gap between the valence band and the conduction band (see Figure 2b). This gap is also related to an absorption in the visible-light region of bulk MoS2.5 The absorption spectra of the nanoflakes resulting from the TD-DFTB calculations also show an absorption in the visiblelight region (Figure 4) blue-shifted to the corresponding absorption in MoS2 bulk at ∼650 nm. There is also a clear blue shift observable, when the flake size, that is, the edge length, d, is decreasing. Such behavior was reported already for MoS2

Figure 5. Calculated absorptions in the visible-light region of a set of MoS2 nanoflakes as a function of edge length d in comparison with the experimental results from ref 1. The results from Chikan and Kelly18 show qualitatively the same behavior. The edge length d of a triangular nanoflake can be related to the particle size (radius R) by R = d/√3 as reported in refs 1 and 18.

function of size. The data agree very well with the available experimental results; that is, the energy of the absorption in the visible-light region follows a 1/d2 behavior for flakes larger than ∼3 nm and gives asymptotically the bulk value (1.9 eV). Such behavior is also obtained for the size dependence of the quantum confinement of spherical particles as described in the Brus19 model. However, the quantum confinement in disks with radius R and fixed thickness scales as 1/R2 as well.20 For triangular flakes, the scaling should be ∼1/d2 according to the solution of the Schrödinger equation for a particle in an equilateral triangle with an edge length d.21 The actual shape of the flake is not clearly identifiable from the experimental studies,1,18 but as shown in refs 9 and 13 MoS2 nanoflakes prefer to appear in a triangular topology. Chikan and Kelly18

Figure 4. Calculated absorption spectra of a continuous set of MoS2 nanoflakes with different edge lengths as indicated. The spectra are shifted in the y direction for a better visibility. 3638



Letter

Figure 6. (a) Electron density distribution of the final state affiliated to the first absorption peak (at 563 nm) of an Mo153S342 flake illustrating the spatial contributions to the excitation. (b) Projected Mo-4d density of states from triangularly arranged groups of Mo atoms (labeled p1, ..., p6; see Figure 3 for labeling) for the final unoccupied state of the corresponding excitation. The contributions of sulfur atoms are negligible small.

■

have already shown that synthesized particles represent most likely single layers rather than stacks of such layers. This means that the particle size can be related to the edge length of the triangles. Thus, the observed blue shift in the absorption spectra is connected to the quantum-confinement effect within the 2D structure. The absorption in the visible-light region (between 500 and 600 nm, as shown in Figure 4) corresponds to transitions from occupied states around the HOMO to unoccupied states around 2 eV above EF. The analysis of the eigenvectors of the calculated transitions within the TD-DFTB approach allows for a qualitative spatial assignment of these excitations. The calculated electron density distribution of the final state affiliated to the first absorption peak is shown for a 5.5 nm large particle in Figure 6. It can be seen in Figure 6b that the main contribution to these excitations is caused by the atoms along the edges. It decreases considerably toward the center of the flake, where almost no atoms contribute (Mo atom grouped in p1, p2, p3). This behavior can be understood easily from the high density of states at the edge atoms in the energy region around 2 eV (see Figure 3). This might also explain the strong photoluminescence observed close to the edges of such MoS2 nanoflakes as it is illustrated in Figure 6a.22 Very recent experimental investigations of triangular monolayer MoS2 nanoribbons23 indicate sub-band transitions from the valence bands to the isolated edge states. This result fits well to the existence of the first peak in the DOS at ∼1 eV above the Fermi level, which we could assign also to the Mo edge atoms (see Figures 2a and 3). In summary, we have presented a study of optical and electronic properties of triangular MoS2 nanoflakes, which were calculated employing the TD-DFTB and the DFTB methods. Special attention was given to the effect of the flake size on the optical properties. The electronic properties show a metalliclike behavior of the flake edges, whereas the inner parts behave more like a semiconductor. This result is in agreement with the findings of other studies.9−13 The electronic properties apparently resemble a coexistence of metallic and semiconducting behavior. The optical absorption spectra in the visible-light region show a distinct blue shift with decreasing flake edge length. This confirms the existence of a quantumconfinement effect. Finally, we could give a plausible explanation of the recently observed photoluminescence of MoS2 nanoflakes.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was financially supported by the European Union via grant INTIF (ERC-2008-AdG) and Max Planck Institute for the Physics of Complex Systems. The computational resources for this project were provided by ZIH Dresden. We thank Knut Vietze and Mads L. Trolle for fruitful discussions.

■

REFERENCES

(1) Wilcoxon, J. P.; Newcomer, P. P.; Samara, G. A. Synthesis and Optical Properties of MoS2 and Isomorphous Nanoclusters in the Quantum Confinement Regime. J. Appl. Phys. 1997, 81, 7934. (2) Radisavljevic, B.; Radenovic, A.; Brivio, J.; Giacometti, V.; Kis, A. Single-Layer MoS2 Transistors. Nat. Nanotechnol. 2011, 6, 147−150. (3) Splendiani, A.; Sun, L.; Zhang, Y.; Li, T.; Kim, J.; Chim, C.-Y.; Galli, G.; Wang, F. Emerging Photoluminescence in Monolayer MoS2. Nano Lett. 2010, 10, 1271−1275. (4) Kam, K. K.; Parkinson, B. A. Detailed Photocurrent Spectroscopy of the Semiconducting Group VI Transition Metal Dichalcogenides. J. Phys. Chem. 1982, 86, 463−467. (5) Mak, K. F.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. F. Atomically Thin MoS2: A New Direct-Gap Semiconductor. Phys. Rev. Lett. 2010, 105, 136805. (6) Narayanan, T. N.; Vusa, C. S. R.; Alwarappan, S. Selective and Efficient Electrochemical Biosensing of Ultrathin Molybdenum Disulfide Sheets. Nanotechnology 2014, 25, 335702. (7) Stephenson, T.; Li, Z.; Olsen, B.; Mitlin, D. Lithium Ion Battery Applications of Molybdenum Disulfide (MoS2) Nanocomposites. Energy Environ. Sci. 2014, 7, 209. (8) Yoffe, A. D. Semiconductor Quantum Dots and Related Systems: Electronic, Optical, Luminescence and Related Properties of Low Dimensional Systems. Adv. Phys. 2001, 50, 1−208. (9) Bollinger, M.; Jacobsen, K.; Nørskov, J. Atomic and Electronic Structure of MoS2 Nanoparticles. Phys. Rev. B 2003, 67, 085410. (10) Li, T.; Galli, G. Electronic Properties of MoS2 Nanoparticles. J. Phys. Chem. C 2007, 111, 16192−16196. (11) Seifert, G.; Tamuliene, J.; Gemming, S. MonS2n+x Clusters magic Numbers and Platelets. Comput. Mater. Sci. 2006, 35, 316−320. (12) Bertram, N.; Cordes, J.; Kim, Y. D.; Ganteför, G.; Gemming, S.; Seifert, G. Nanoplatelets Made from MoS2 and WS2. Chem. Phys. Lett. 2006, 418, 36−39. (13) Lauritsen, J. V.; Kibsgaard, J.; Helveg, S.; Topsøe, H.; Clausen, B. S.; Laegsgaard, E.; Besenbacher, F. Size-Dependent Structure of MoS2 Nanocrystals. Nat. Nanotechnol. 2007, 2, 53−58. 3639



Letter

(14) Lu, P.; Wu, X.; Guo, W.; Zeng, X. C. Strain-Dependent Electronic and Magnetic Properties of MoS2 Monolayer, Bilayer, Nanoribbons and Nanotubes. Phys. Chem. Chem. Phys. 2012, 14, 13035−13040. (15) Seifert, G.; Porezag, D.; Frauenheim, T. Calculations of Molecules, Clusters, and Solids with a Simplified LCAO-DFT-LDA Scheme. Int. J. Quantum Chem. 1996, 58, 185−192. (16) Niehaus, T.; Suhai, S.; Della Sala, F.; Lugli, P.; Elstner, M.; Seifert, G.; Frauenheim, T. Tight-Binding Approach to TimeDependent Density-Functional Response Theory. Phys. Rev. B 2001, 63, 085108. (17) Köster, A. M.; Geudtner, G.; Goursot, A.; Heine, T.; Vela, A.; Salahub, D.; Patchkovskii, S. deMon, NRC: Ottawa, Canada, 2004. (18) Chikan, V.; Kelley, D. F. Size-Dependent Spectroscopy of MoS2 Nanoclusters. J. Phys. Chem. B 2002, 106, 3794−3804. (19) Brus, L. E. Electron−Electron and Electron-Hole Interactions in Small Semiconductor Crystallites: The Size Dependence of the Lowest Excited Electronic State. J. Chem. Phys. 1984, 80, 4403. (20) Murayama, Y. Mesoscopic Systems Fundamentals and Applications; Wiley-VCH: Berlin, 2001; p 74. (21) Li, W.-K.; Blinder, S. M. Solution of the Schrödinger Equation for a Particle in an Equilateral Triangle. J. Math. Phys. 1985, 26, 2784. (22) Gutiérrez, H. R.; Perea-López, N.; Elías, A. L.; Berkdemir, A.; Wang, B.; Lv, R.; López-Urías, F.; Crespi, V. H.; Terrones, H.; Terrones, M. Extraordinary Room-Temperature Photoluminescence in Triangular WS2 Monolayers. Nano Lett. 2013, 13, 3447−3454. (23) Yin, X.; Ye, Z.; Chenet, D. a; Ye, Y.; O’Brien, K.; Hone, J. C.; Zhang, X. Edge Nonlinear Optics on a MoS2 Atomic Monolayer. Science 2014, 344, 488−490.

3640


Optical Properties of Triangular Molybdenum Disulfide Nanoflakes

Recommend Documents