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Transition Metal Dichalcogenide monolayers

(a) : Structure of a TMDC monolayer : M atoms are in black and X atoms are in yellow (b) : A 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 ...) and X a chalcogen atom (S, Se ...). One layer of M atoms is sandwiched between two layers of X atoms. An 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 the semimetal grahene:

  • The TMDC mononlayer crystal structure has no inversion center, which allows to access a new degree of freedom of charge carriers namely the k-valley index and to open up a new field of physics : valleytronics [4] [5] [6][7][8]
  • The strong spin-orbit coupling in TMDC monolayers leads to spin splittings in the hundreds of meV range in the valence band and a few meV in the conduction band, which allows to control the electron spin by tuning the excitation laser photon energy.

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. [6][7] [8]

Crystal structure

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Primitive cell of WSe2

In the macroscopic bulk crystal, or more precisely, for an even number of monolayers, the crystal structure has a 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 :

  • an electronic band structure with direct energy gaps, and both conduction and valence band edges are located at the non-equivalent K points (K+ and K-) of 2D hexagonal Brillouin zone. The interband transitions in the vicinity of K+ (or K-) point are coupled with right (or left) circular polarization states, which is called valley dependent optical selection rules, arising from the inversion symmetry breaking. This provides convenient method to address individual valley state (K+ or K-) by specific circularly polarized (right or left) optical excitation.Cite error: The <ref> tag has too many names (see the help page). In combination with the strong spin-splittings, the spin and valley degree of freedoms are coupled, resulting stable valley polarization. [13][14][15]

All these unique properties indicates the TMDC monolayers can be a promising platform to explore the spin and valley physics and the corresponding applications.

Properties

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Transport properties

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Representative scheme of the section of a Field Effect Transistor based on a monolayer of MoS2 [16]

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 it has zero bandgap, so a low on/off ratio, which is a limitation for electronic device. TMDC monolayers might be an alternative: they are structurally stable and show electron mobilities comparable to silicon, so they can be used to fabricate transistor.

In 2004, the first Field-effect transistor (FET) made of WSe2 was reported. It showed a mobility lower than 500 cm2.V-1.s-1 for p-type conductivity at room tempretaure compared to a FET based on silicon which has a mobility about 1000 cm2.V-1.s-1. So a FET based on TMDC heated just a little more than a FET based on silicon. It also showed a high ratio on/off, about 108. [17] FETs made of monolayer MoS2 showed an excellent on/off ratio exceeding 108. [16]

All these high carrier mobility, high on/off ratio and its extreme thickness (only 1 monolayer!) show that TMDCs might be interesting materials for the new generation of novel electronic devices.

Optical properties

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Theorical transition energy [18]
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 2.28 673
WSe2 1.52 815 2.00 619

A semiconductor can absorb light (photons) with energy larger than 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. [19] 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 spin-orbit coupling. The lowest energy and therefore most important in intensity is the A emission.[2] [20] Due to their direct band gap, TMDC monolayers could be promising materials for optoelectronics applications.

[[File:Ultrasensitive_photodetector_(MoS2).jpg|thumb|400px|left| Representative scheme of the section of an ultrasensitive Photodetector based on a monolayer of MoS2 [21]]]

MoS2 has been already used as a classical phototransistor and an ultrasensitive detectors. Phototransistors are important devices: the first with an 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 generation of devices the carrier mobility is still need 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, 10 6 greater than the first graphene photodetectors. This high degree of electrostatic control is due of the extremely thin of the active region of just one monolayer. Its simplicity and the fact it is made of only one semiconductor region, whereas the current generations of photodetectors is typically a p-n junction, make this an interesting device for industrial applications as an inexpensive, high-sensitivity and flexible photodetector. There is only one limitation : the slow photoresponse dynamics, however there are possible ways to solve this problem. [21]

Mechanical properties

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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. The first observation is that a monolayer of MoS2 can be strained to the limit of 25% which is comparable to the graphene. [22] 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%. [23] As a result, the emission efficiency of monolayers is expected to decrease for highly strained samples [24] 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

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Exfoliation

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Exfoliation is a top down approach. At the bulk state, TMDCs are crystal made of layers, which 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 sample of monolayer material, typically about 5-10 micrometer. [25]

Chemical vapor deposition

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Chemical vapor deposition is a bottom-up approach. For example, the synthesis of MoS2 is made with : SiO2 used as a substract, MoO3 and S powders used as reactants. The reactants are delivered on the susbtract 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 technical. [26]

Molecular Beam Epitaxy

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Molecular Beam Epitaxy (MBE) is an established technique for growing semiconductor devices with atomic monolayer thickness control. High quality monolayer MoSe2 samples have been grown on graphene by MBE. [27]

Electronic band structure

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Band gap

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In the bulk form, TMDC have an indirect gap in the center of the Brillouin zone whereas at the state of monolayer the gap become direct and is located in the K point.

States in brillouin center zone (Γ point) originate from the combination of pz antibonding orbital of chalcogen atoms and d orbitals of transition metal atoms. These orbitals are delocalized so the interaction between the layers is strong in this zone. The states in the edge zone (K point) are due of d orbitals of transition metal atoms with less interactions between layers. As we reduce the layer, we reduce inter-layer interactions so we increase the band-gap of the center zone. But states of the edge zone are not affected by this modification. When there is only one atomic layer, the band gap moves in the edge zone and become direct. [17]

Spin-orbit coupling

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Theorical energy of the spin-orbit coupling[28]
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 degeneration of 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 tens of meV range, it is expected to be more pronounced in other material like WS2. [29] [30]

Spin-valley coupling and the electron valley degree of freedom

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The two valleys K and the spin-orbit coupling
 
Photoluminescence of a MoS2 monolayer at 4 Kelvin 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 more than two conduction/valence band extrema on 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. [13]

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 transition of one valley to another is describe by the time reversal operator, which reverse the spin, with the same energy, from one valley to another. 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.[6] 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/absorption of light: excitons

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A single layer of TMDC can absorb more than 10% of light, which is unprecedented. 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 the bound state exciton. This results in practice an important energy difference between the bandgap observed in optical experiments ('optical bandgap') and the true bandgap for free carrier absorption i.e. bandgap renormalization. The energy difference also called binding energy, which is important to determine the other key properties of excitons. In atomically thin 2D systems there exist a strong confinement of electrons and holes in the layer plane. [20] This confinement enhances dramatically the Coulomb interaction between the electron and hole in TMDC monolayers comparing to bulk situation or other quasi 2D materials, leading a large binding energy in hundreds of meV range. [12] [20] [31] [32][33] [34]


References

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  1. ^ a b Kin Fai Mak, Chang gu Lee, James Hone, Jie Shan, Tony F. Heinz "Atomically thin MoS2  : a new Direct-Gap Semiconductor", 24 September 2010
  2. ^ a b c Andrea Splendiani, Liang Sun, Yuanbo Zhang, Tianshu Li, Jonghwan Kim, Chi-Yung Chim, Giulia Galli, Feng Wang "Emerging Photoluminescence in Monolayer MoS2 ", 15 March 2010
  3. ^ Jason S. Ross, Philip Klement, Aaron M. Jones, Nirmal J. Ghimire, Jiaqiang Yan, D. G. Mandrus, Takashi Taniguchi, Kenji Watanabe, Kenji Kitamura, Wang Yao, David H. Cobden, Xiaodong Xu "Electrically tunable excitonic light-emitting diodes based on monolayer WSe2 p–n junctions ", 9 March 2014
  4. ^ A. Rycerz, J. Tworzydlo, C. W. J. Beenakker "Valley filter and valley valve in graphene", 18 February 2007
  5. ^ Di Xiao, Wang Yao, and Qian Niu "Valley Contrasting Physics in Graphene: Magnetic Moment and Topological Transport", 7 December 2007
  6. ^ a b c Ting Cao, Gang Wang, Wenpeng Han, Huiqi Ye, Chuanrui Zhu, Junren Shi, Qian Niu, Pingheng Tan, Enge Wang, Baoli Liu, Ji Feng. "Valley-selective circular dichroism of monolayer molybdenum disulphide", 6 Jun 2012
  7. ^ a b Kin Fai Mak, Keliang He, Jie Shan, Tony F. Heinz "Control of valley polarization in monolayer MoS2 by optical helicity", 17 June 2012
  8. ^ a b Hualing Zeng, Junfeng Dai, Wang Yao, Di Xiao, Xiaodong Cui "Valley polarization in MoS2 monolayers by optical pumping", 17 June 2012
  9. ^ N. Kumar, S. Najmaei, Q. Cui, F. Ceballos, P. M. Ajayan, J. Lou, H. Zhao “ Second harmonic microscopy of monolayer MoS2”, 9 April 2013
  10. ^ Leandro M. Malard, Thonimar V. Alencar, Ana Paula M. Barboza, Kin Fai Mak, and Ana M. de Paula "Observation of Intense Second Harmonic Generation from MoS2 Atomic Crystals", 13 May 2013
  11. ^ Hualing Zeng, Gui-Bin Liu, Junfeng Dai, Yajun Yan, Bairen Zhu, Ruicong He, Lu Xie, Shijie Xu, Xianhui Chen, Wang Yao, Xiaodong Cui. "Optical signature of symmetry variations and spin-valley coupling in atomically thin tungsten dichalcogenides", 11 April 2013
  12. ^ a b G.Wang, X. Marie, I.Gerber, T. Amand, D. Lagarde, L. Bouet, M. Vidal, A. Balocchi, B. Urbaszek “Non-linear Optical Spectroscopy of Excited Exciton States for Efficient Valley Coherence Generation in Wse2 Monolayers”, 31 March 2014
  13. ^ a b Di Xiao, Gui-Bin Liu, Wanxiang Feng, Xiaodong Xu, Wang Yao "Coupled Spin and Valley Physics in Monolayers of MoS2 and Other Group-VI Dichalcogenides", 7 May 2012
  14. ^ Aaron Mitchell Jones, Hongyi Yu, Nirmal Ghimire, Sanfeng Wu, Grant Aivazian, Jason Solomon Ross, Bo Zhao, Jiaqiang Yan, David Mandrus, Di Xiao, Wang Yao, Xiaodong Xu"Optical Generation of Excitonic Valley Coherence in Monolayer WSe2", 11 August 2013
  15. ^ Xiaodong Xu, Wang Yao, Di Xiao, Tony F. Heinz "Spin and pseudospins in layered transition metal dichalcogenides", Published online 30 April 2014
  16. ^ a b B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, A. Kis "Single-layer MoS2 transistors ", 30 January 2011
  17. ^ a b Qing Hua Wang, Kourosh Kalantar-Zadeh, Andras Kis, Jonathan N. Coleman and Michael S. Strano. " Electronics and optoelectronics of two-dimensional transition metal dichalcogenides", 6 November 2012
  18. ^ Ashwin Ramasubramaniam “Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides”, 6 September 2012
  19. ^ R. S. Sundaram, M. Engel, A. Lombardo, R. Krupke, A. C. Ferrari, Ph. Avouris, M. Steiner “Electroluminescence in Single Layer MoS2” , 19 November 2012
  20. ^ a b c D. Y. Qiu, F. H. da Jornada, S. G. Louie “Optical Spectrum of MoS2 Many-Body Effects and Diversity of Exciton States”, 5 November 2013
  21. ^ a b O. Lopez-Sanchez, D. Lembke, M. Kayci, A. Radenovic, A. Kis “Ultrasensitive photodetectors based on monolayer MoS2” , 9 June 2013
  22. ^ K. He, C. Poole, K. F. Mak, J. Shan "Experimental Demonstration of continuous Electronic Structure Tuning via Strain in Atomically Thin MoS2" , 21 Jun 2013
  23. ^ H. J. Conley, B. Wang, J. I. Ziegler, R. F. Haglund, Jr., S. T. Pantelides, K. I. Bolotin “Bandgap Engineering of Strained Monolayer and Bilayer MoS2”, 20 September 2013
  24. ^ C.R Zhu, G.Wang, B.L.Liu, X. Marie, X. F. Qiao, X. Zhang, X. X. Wu, H. Fan, P. H. Tan, T. Amand, B. Urbaszek tuning of optical emission energy and polarization in monolayer and bilayer MoS2 ”, 9 September 2013
  25. ^ K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, A. K. Geim "Two-dimensional atomic crystals", 7 Jun 2005
  26. ^ Y-H. Lee, X-Q. Zhang, W. Zhang, M-T. Chang, C-T. Lin, K-D. Chang, Y-C. Yu, J. T-W. Wang, C-S. Chang, L-J. Li, T-W. Lin “Synthesis of Large-Area MoS2 Atomic Layers with Chemical Vapor Deposition ”, 30 March 2012
  27. ^ Y. Zhang, T-R. Chang, B. Zhou, Y-T. Cui, H. Yan, Z. Liu, F. Schmitt, J. Lee, R. Moore, Y. Chen, H. Lin, H-T. Jeng, S-K. Mo, Z. Hussain, A. Bansil, Z-X. Shen“Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoS2”, 14 January 2014
  28. ^ Giu-Bin Liu, Wen-Yu Shan, Yugui Ya, Wang Yao, Di Xiao "Three-band tight-binding model for monolayers of group of VIB transition metal dichalcogenides", 24 January 2014
  29. ^ K. Kosmider, J. W. Gonzalez, J. Fernandez-Rossier “Large spin splitting in the conduction band of transition metal dichalcogenide monolayers”, 5 November 2013
  30. ^ A. Kormanyos, V. Zolyomi, N. D. Drummond, G. Burkard “Spin-orbit coupling, quantum dots, and qubits in monolayer transition metal dichalcogenides”, 4 February 2014
  31. ^ A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, O. B. Aslan, D. R. Reichman, M. S. Hybertsen, T. F. Heinz “Non-Hydrogenic Exciton Rydberg Series in Monolayer WS2”, 24 March 2014
  32. ^ Bairen Zhu, Xi Chen, Xiaodong Cui"Exciton Binding Energy of Monolayer WS2", 20 Mar 2014
  33. ^ Ziliang Ye, Ting Cao, Kevin O'Brien, Hanyu Zhu, Xiaobo Yin, Yuan Wang, Steven G. Louie, Xiang Zhang"Probing Excitonic Dark States in Single-layer Tungsten Disulfide", 21 Mar 2014
  34. ^ Miguel M. Ugeda, Aaron J. Bradley, Su-Fei Shi, Felipe H. da Jornada, Yi Zhang, Diana Y. Qiu, Sung-Kwan Mo, Zahid Hussain, Zhi-Xun Shen, Feng Wang, Steven G. Louie, Michael F. Crommie"Observation of giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor", 8 Apr 2014
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