Transition metal dichalcogenide monolayers

(a) Structure of a hexagonal TMDC monolayer. M atoms are in black and X atoms are in yellow. (b) A hexagonal TMDC monolayer seen from above.

Transition metal dichalcogenide (TMDC) monolayers are atomically thin semiconductors of the type MX2, with M a transition metal atom (Mo, W, etc.) and X a chalcogen atom (S, Se, etc.). One layer of M atoms is sandwiched between two layers of X atoms. A MoS2 monolayer is 6.5 Å thick.

The discovery of graphene shows how new physical properties emerge when a bulk crystal of macroscopic dimensions is thinned down to one atomic layer. Like graphite, TMDC bulk crystals are formed of monolayers bound to each other by Van-der-Waals attraction. TMDC monolayers have properties that are distinctly different from those of the semimetal grahene:

The work on TMDC monolayers is an emerging research and development field since the discovery of the direct bandgap[1][2] and the potential applications of the very peculiar electron valley physics.[5][6][7]

Crystal structure

Primitive cell of WSe2

In the macroscopic bulk crystal, or more precisely, for an even number of monolayers, the crystal structure has an inversion center. In the case of a monolayer (or any odd number of layers), the crystal has no inversion center. There are two important consequences of that:

The above properties indicate that TMDC monolayers represent a promising platform to explore the spin and valley physics with the corresponding possible applications.

Properties

Transport properties

Representative scheme of the section of a field effect transistor based on a monolayer of MoS2[15]

The reduction of the size of electronics components (Moore's law) is a problem when arriving at very small scales. 3D materials have no longer the same behavior when they are in 2D form, which can be turned into an advantage. For example, graphene has a very high carrier mobility, so lower losses through the Joule effect. But graphene has zero bandgap, which results in a low on/off ratio in transistor applications, which is a limitation. TMDC monolayers might be an alternative: they are structurally stable and show electron mobilities comparable to those of silicon, so they can be used to fabricate transistors.

In 2004, the first field-effect transistor (FET) made of WSe2 was reported. It showed a mobility below 500 cm2 V−1 s−1 for p-type conductivity at room tempretaure, about half that of a silicon FET. So an FET based on TMDC heated just a little more than an FET based on silicon. It also showed a high on/off ratio of ~108.[16] FETs made of monolayer MoS2 showed an excellent on/off ratio exceeding 108.[15]

High carrier mobility, high on/off ratio and small thickness (one monolayer) of TMDC devices are potentially interesting for applications.

Optical properties

Theorical transition energy[17]
A (eV) A (nm) B (eV) B (nm)
MoS2 1.78 695 1.96 632
MoSe2 1.50 825 1.75 708
WS2 1.84 673 2.28 544
WSe2 1.52 815 2.00 619

A semiconductor can absorb light (photons) with energy larger than or equal to its bandgap. Semiconductors are typically efficient emitters if the minimum of the conduction band energy is at the same position in k-space as the maximum of the valence band, i.e., the band gap is direct. The band gap of the bulk TMDC material down to a thickness of two monolayers is still indirect, so the emission efficiency is lower compared to the monolayer case. There is a factor of about 104 in emission efficiency between TMDC monolayer and the bulk material.[18] The band gaps of TMDC monolayers are in the visible range (between 400 nm and 700 nm). The direct emission shows two transition called A and B, separated by the spin-orbit coupling energy. The lowest energy and therefore most important in intensity is the A emission.[2][19] Owing to their direct band gap, TMDC monolayers are promising materials for optoelectronics applications.

Representative scheme of the section of an ultrasensitive Photodetector based on a monolayer of MoS2[20]

Atomic layers of MoS2 have been used as a phototransistor and ultrasensitive detectors. Phototransistors are important devices: the first with a MoS2 monolayer active region shows a photoresponsivity of 7.5 mA W−1 which is similar to graphene devices, 6.1 mA W−1. Multilayer MoS2 show higher photoresponsivities, about 100 mA W−1, which is similar to silicon devices. For future generations of devices the carrier mobility still needs to be increased. By simply making a gold contact at the far edges of a monolayer, an ultrasensitive detector can be fabricated. This new detector has a photoresponsivity reaching 880 A W−1, 106 greater than the first graphene photodetectors. This high degree of electrostatic control is due of the extremely thin active region of just one monolayer. Its simplicity and the fact it is made of only one semiconductor region, whereas the current generation of photodetectors is typically a p-n junction, makes this an interesting device for possible industrial applications as an inexpensive, high-sensitivity and flexible photodetector. There is only one limitation for currently available devices: the slow photoresponse dynamics, however there are possible ways to solve this problem.[20]

Mechanical properties

By depositing a sample of monolayer MoS2 on a plastic flexible substrate and bending it mechanically, studies of the material's flexibility can be done. A monolayer of MoS2 can be strained to the limit of 25% which is comparable to the graphene.[21] Under the application of strain, a decrease in the direct and indirect band gap is measured that is approximately linear with strain. Importantly, the indirect bandgap increases faster with applied strain to the monolayer than the direct bandgap, resulting in a crossover from direct to indirect band gap when the strain is around 1%.[22] As a result, the emission efficiency of monolayers is expected to decrease for highly strained samples.[23] This property allows mechanical tuning of the electronic structure and also the possibility of fabrication of flexible electronics i.e. on flexible substrates.

Fabrication of TMDC monolayers

Exfoliation

Exfoliation is a top down approach. In the bulk form, TMDCs are crystals made of layers, which are coupled by Van-der-Waals forces. These interactions are weaker than the chemical bonds between the Mo and S in MoS2, for example. So TMDC monolayers can be produced by micromechanical cleavage, just as graphene.

The crystal of TMDC is rubbed against the surface of another material (any solid surface). In practice, adhesive tape is placed on the TMDC bulk material and subsequently removed. The adhesive tape, with tiny TMDC flakes coming off the bulk material, is brought down onto a substrate. On removing the adhesive tape from the substrate, TMDC monolayer and multilayer flakes are deposited. This technique produces small samples of monolayer material, typically about 5–10 micrometers in diameter.[24]

Chemical vapor deposition

Chemical vapor deposition is a bottom-up approach. For example, the synthesis of MoS2 is made using: SiO2 as a substrate, MoO3 and S powders used as reactants. The reactants are delivered on the substrate and the whole is heated to 650 Celsius degrees in the presence of N2. The size of the sample is larger than obtained with the exfolation technique.[25]

Molecular beam epitaxy

Molecular beam epitaxy (MBE) is an established technique for growing semiconductor devices with atomic monolayer thickness control. As a promising demonstration, high-quality monolayer MoSe2 samples have been grown on graphene by MBE.[26]

Electronic band structure

Band gap

In the bulk form, TMDC have an indirect gap in the center of the Brillouin zone, whereas in monolayer form the gap becomes direct and is located in the K point.[1][2]

Spin-orbit coupling

Theorical energy of the spin-orbit coupling[27]
Valence band

splitting (eV)

 Conduction band

splitting (eV)

MoS2 0.148 0.003
WS2 0.430 0.026
MoSe2 0.430 0.007
WSe2 0.466 0.038

For TMDCs, the atoms are heavy and the outer layers electronic states are from d-orbitals that have a strong spin-orbit coupling. This spin orbit coupling removes the spins degeneracy in both the conduction and valence band i.e. introduces a strong energy splitting between spin up and down states. In the case of MoS2, the spin splitting in conduction band is in the meV range, it is expected to be more pronounced in other material like WS2.[28][29] The spin orbit splitting in the valence band is several hundred meV.

Spin-valley coupling and the electron valley degree of freedom

Spin splittings and optical selection rules[27]
Photoluminescence (PL) of a MoS2 monolayer at 4 K excited by a σ+ polarized laser

By controlling the charge or spin degree of freedom of carriers, as proposed by spintronics, novel devices have already been made. If there are different conduction/valence band extrema in the electronic band structure in k-space, the carrier can be confined in one of these valleys. This degree of freedom opens up a new field of physics: the controlling of carriers k-valley index, also called valleytronics.[12]

For TMDC monolayers crystals, the parity symmetry is broken, there is no more inversion center. K valleys of different directions in the 2D hexagonal Brillouin zone are no longer equivalent. So there are two kinds of K valley call K+ and K-. Also there is a strong energy degeneracy of different spin states in valence band. The transformation of one valley to another is described by the time reversal operator. Moreover, crystal symmetry leads to valley dependent optical selection rules: a right circular polarized photon (σ+) initialize a carrier in the K+ valley and a left circular polarized photon (σ-) initialize a carrier in the K- valley.[5] Thanks to these two properties (spin-valley coupling and optical selection rules), a laser of specific polarization and energy allows to initialize the electron valley states (K+ or K-) and spin states (up or down).

Emission and absorption of light: excitons

Graphene-MoS2 enhanced SPR biosensor.[30]

A single layer of TMDC can absorb 5-10% of light,[30] which is unprecedented for such a thin material. When a photon of suitable energy is absorbed by a TMDC monolayer, an electron is created in the conduction band, the electron now missing in the valence band is assimilated by a positively charged quasi-particle called hole. The negatively charged electron and the positively charged hole are attracted via the Coulomb interaction, forming a bound state called exciton. This results in practice in an important energy difference between the bandgap observed in optical experiments ('optical bandgap') and the true bandgap for free carrier absorption. This referred to as bandgap renormalization and occurs, albeit on smaller energy scales, in semiconductor like GaAs and ZnO. The energy difference between the optical bandgap and the free carrier bandgap is called exciton binding energy. In atomically thin 2D systems there exist a strong confinement of electrons and holes in the layer plane.[19] This confinement enhances dramatically the Coulomb interaction between the electron and hole in TMDC monolayers comparing to the bulk situation or other quasi 2D materials, leading to a large binding energy in the hundreds of meV range.[11][19][31][32][33]

References

  1. ↑ 1.0 1.1 1.2 Mak, K. F.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. F. (2010). "Atomically Thin MoS2: A New Direct-Gap Semiconductor". Physical Review Letters 105 (13). arXiv:1004.0546. doi:10.1103/PhysRevLett.105.136805.
  2. ↑ 2.0 2.1 2.2 2.3 Splendiani, A.; Sun, L.; Zhang, Y.; Li, T.; Kim, J.; Chim, C. Y.; Galli, G.; Wang, F. (2010). "Emerging Photoluminescence in Monolayer MoS2". Nano Letters 10 (4): 1271–5. doi:10.1021/nl903868w. PMID 20229981.
  3. ↑ Ross, J. S.; Klement, P.; Jones, A. M.; Ghimire, N. J.; Yan, J.; Mandrus, D. G.; Taniguchi, T.; Watanabe, K.; Kitamura, K.; Yao, W.; Cobden, D. H.; Xu, X. (2014). "Electrically tunable excitonic light-emitting diodes based on monolayer WSe2 p–n junctions". Nature Nanotechnology 9 (4): 268–72. arXiv:1312.1435. doi:10.1038/nnano.2014.26. PMID 24608230.
  4. ↑ Rycerz, A.; Tworzydło, J.; Beenakker, C. W. J. (2007). "Valley filter and valley valve in graphene". Nature Physics 3 (3): 172. arXiv:cond-mat/0608533. doi:10.1038/nphys547.
  5. ↑ 5.0 5.1 5.2 Cao, T.; Wang, G.; Han, W.; Ye, H.; Zhu, C.; Shi, J.; Niu, Q.; Tan, P.; Wang, E.; Liu, B.; Feng, J. (2012). "Valley-selective circular dichroism of monolayer molybdenum disulphide". Nature Communications 3 (6): 887. doi:10.1038/ncomms1882. PMC 3621397. PMID 22673914.
  6. ↑ 6.0 6.1 Mak, K. F.; He, K.; Shan, J.; Heinz, T. F. (2012). "Control of valley polarization in monolayer MoS2 by optical helicity". Nature Nanotechnology 7 (8): 494–8. doi:10.1038/nnano.2012.96. PMID 22706698.
  7. ↑ 7.0 7.1 7.2 Zeng, H.; Dai, J.; Yao, W.; Xiao, D.; Cui, X. (2012). "Valley polarization in MoS2 monolayers by optical pumping". Nature Nanotechnology 7 (8): 490–3. arXiv:1202.1592. doi:10.1038/nnano.2012.95. PMID 22706701.
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  10. ↑ Zeng, H.; Liu, G. B.; Dai, J.; Yan, Y.; Zhu, B.; He, R.; Xie, L.; Xu, S.; Chen, X.; Yao, W.; Cui, X. (2013). "Optical signature of symmetry variations and spin-valley coupling in atomically thin tungsten dichalcogenides". Scientific Reports 3. arXiv:1208.5864. doi:10.1038/srep01608.
  11. ↑ 11.0 11.1 Wang, G. et al. (2014). "Non-linear Optical Spectroscopy of Excited Exciton States for Efficient Valley Coherence Generation in WSe2 Monolayers". arXiv:1404.0056.
  12. ↑ 12.0 12.1 Xiao, D.; Liu, G. B.; Feng, W.; Xu, X.; Yao, W. (2012). "Coupled Spin and Valley Physics in Monolayers of MoS2 and Other Group-VI Dichalcogenides". Physical Review Letters 108 (19). doi:10.1103/PhysRevLett.108.196802.
  13. ↑ Jones, A. M.; Yu, H.; Ghimire, N. J.; Wu, S.; Aivazian, G.; Ross, J. S.; Zhao, B.; Yan, J.; Mandrus, D. G.; Xiao, D.; Yao, W.; Xu, X. (2013). "Optical generation of excitonic valley coherence in monolayer WSe2". Nature Nanotechnology 8 (9): 634–8. arXiv:1303.5318. doi:10.1038/nnano.2013.151. PMID 23934096.
  14. ↑ Xu, X.; Yao, W.; Xiao, D.; Heinz, T. F. (2014). "Spin and pseudospins in layered transition metal dichalcogenides". Nature Physics 10 (5): 343. doi:10.1038/nphys2942.
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  16. ↑ Wang, Q. H.; Kalantar-Zadeh, K.; Kis, A.; Coleman, J. N.; Strano, M. S. (2012). "Electronics and optoelectronics of two-dimensional transition metal dichalcogenides". Nature Nanotechnology 7 (11): 699–712. doi:10.1038/nnano.2012.193. PMID 23132225.
  17. ↑ Ramasubramaniam, A. (2012). "Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides". Physical Review B 86 (11). doi:10.1103/PhysRevB.86.115409.
  18. ↑ Sundaram, R. S.; Engel, M.; Lombardo, A.; Krupke, R.; Ferrari, A. C.; Avouris, P.; Steiner, M. (2013). "Electroluminescence in Single Layer MoS2". Nano Letters: 130329131217003. arXiv:1211.4311. doi:10.1021/nl400516a.
  19. ↑ 19.0 19.1 19.2 Qiu, D. Y.; Da Jornada, F. H.; Louie, S. G. (2013). "Optical Spectrum of MoS2: Many-Body Effects and Diversity of Exciton States". Physical Review Letters 111 (21). arXiv:1311.0963. doi:10.1103/PhysRevLett.111.216805.
  20. ↑ 20.0 20.1 Lopez-Sanchez, O.; Lembke, D.; Kayci, M.; Radenovic, A.; Kis, A. (2013). "Ultrasensitive photodetectors based on monolayer MoS2". Nature Nanotechnology 8 (7): 497–501. doi:10.1038/nnano.2013.100. PMID 23748194.
  21. ↑ He, K.; Poole, C.; Mak, K. F.; Shan, J. (2013). "Experimental Demonstration of Continuous Electronic Structure Tuning via Strain in Atomically Thin MoS2". Nano Letters 13 (6): 2931–6. arXiv:1305.3673. doi:10.1021/nl4013166. PMID 23675872.
  22. ↑ Conley, H. J.; Wang, B.; Ziegler, J. I.; Haglund, R. F.; Pantelides, S. T.; Bolotin, K. I. (2013). "Bandgap Engineering of Strained Monolayer and Bilayer MoS2". Nano Letters 13 (8): 3626–30. arXiv:1305.3880. doi:10.1021/nl4014748. PMID 23819588.
  23. ↑ Zhu, C. R.; Wang, G.; Liu, B. L.; Marie, X.; Qiao, X. F.; Zhang, X.; Wu, X. X.; Fan, H.; Tan, P. H.; Amand, T.; Urbaszek, B. (2013). "Strain tuning of optical emission energy and polarization in monolayer and bilayer MoS2". Physical Review B 88 (12). arXiv:1306.3442. doi:10.1103/PhysRevB.88.121301.
  24. ↑ Novoselov, K. S.; Jiang, D; Schedin, F; Booth, T. J.; Khotkevich, V. V.; Morozov, S. V.; Geim, A. K. (2005). "Two-dimensional atomic crystals". Proceedings of the National Academy of Sciences 102 (30): 10451–3. doi:10.1073/pnas.0502848102. PMC 1180777. PMID 16027370.
  25. ↑ Lee, Y. H.; Zhang, X. Q.; Zhang, W; Chang, M. T.; Lin, C. T.; Chang, K. D.; Yu, Y. C.; Wang, J. T.; Chang, C. S.; Li, L. J.; Lin, T. W. (2012). "Synthesis of large-area MoS2 atomic layers with chemical vapor deposition". Advanced Materials 24 (17): 2320–5. arXiv:1202.5458. doi:10.1002/adma.201104798. PMID 22467187.
  26. ↑ Zhang, Y.; Chang, T. R.; Zhou, B.; Cui, Y. T.; Yan, H.; Liu, Z.; Schmitt, F.; Lee, J.; Moore, R.; Chen, Y.; Lin, H.; Jeng, H. T.; Mo, S. K.; Hussain, Z.; Bansil, A.; Shen, Z. X. (2013). "Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe2". Nature Nanotechnology 9 (2): 111–5. arXiv:1401.3386. doi:10.1038/nnano.2013.277. PMID 24362235.
  27. ↑ 27.0 27.1 Liu, G. B.; Shan, W. Y.; Yao, Y.; Yao, W.; Xiao, D. (2013). "Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides". Physical Review B 88 (8). arXiv:1305.6089. doi:10.1103/PhysRevB.88.085433.
  28. ↑ Kośmider, K.; González, J. W.; Fernández-Rossier, J. (2013). "Large spin splitting in the conduction band of transition metal dichalcogenide monolayers". Physical Review B 88 (24). doi:10.1103/PhysRevB.88.245436.
  29. ↑ Kormányos, A.; Zólyomi, V.; Drummond, N. D.; Burkard, G. (2014). "Spin-Orbit Coupling, Quantum Dots, and Qubits in Monolayer Transition Metal Dichalcogenides". Physical Review X 4. arXiv:1310.7720. doi:10.1103/PhysRevX.4.011034.
  30. ↑ 30.0 30.1 Zeng, Shuwen; Hu, Siyi; Xia, Jing; Anderson, Tommy; Dinh, Xuan-Quyen; Meng, Xiang-Min; Coquet, Philippe; Yong, Ken-Tye (2015). "Graphene–MoS2 Hybrid Nanostructures enhanced Surface Plasmon Resonance Biosensors". Sensors and Actuators B: Chemical. doi:10.1016/j.snb.2014.10.124.
  31. ↑ Chernikov, Alexey; Berkelbach, Timothy C.; Hill, Heather M.; Rigosi, Albert; Li, Yilei; Aslan, Ozgur Burak; Reichman, David R.; Hybertsen, Mark S.; Heinz, Tony F. (2014). "Exciton Binding Energy and Nonhydrogenic Rydberg Series in Monolayer WS2". Physical Review Letters 113 (7). arXiv:1403.4270. doi:10.1103/PhysRevLett.113.076802.
  32. ↑ Ye, Ziliang; Cao, Ting; O’Brien, Kevin; Zhu, Hanyu; Yin, Xiaobo; Wang, Yuan; Louie, Steven G.; Zhang, Xiang (2014). "Probing excitonic dark states in single-layer tungsten disulphide". Nature 513 (7517): 214–218. arXiv:1403.5568. doi:10.1038/nature13734. PMID 25162523.
  33. ↑ Ugeda, M. M.; Bradley, A. J.; Shi, S. F.; Da Jornada, F. H.; Zhang, Y.; Qiu, D. Y.; Ruan, W.; Mo, S. K.; Hussain, Z.; Shen, Z. X.; Wang, F.; Louie, S. G.; Crommie, M. F. (2014). "Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor". Nature Materials. doi:10.1038/nmat4061.