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Transition metal dichalcogenide monolayers

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(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, or Te.). 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 graphene:

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 in electronics[3] and valley physics.[7][8][9] TMDCs are often combined with other 2d materials like graphene and hexagonal boron nitride to make van der Waals heterostructure devices.

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. Two important consequences of that are:

  • nonlinear optical phenomena, such as second-harmonic generation. When the crystal is excited by a laser, the output frequency can be doubled.[11][12][13][14]
  • an electronic band structure with direct energy gaps, where both conduction and valence band edges are located at the non-equivalent K points (K+ and K-) of the 2D hexagonal Brillouin zone. The interband transitions in the vicinity of the K+ (or K-) point are coupled to right (or left) circular photon polarization states. These so-called valley dependent optical selection rules arise from inversion symmetry breaking. This provides a convenient method to address specific valley states (K+ or K-) by circularly polarized (right or left) optical excitation.[9] In combination with strong spin-splitting, the spin and valley degree of freedom are coupled, enabling stable valley polarization.[15][16][17]

These properties indicate that TMDC monolayers represent a promising platform to explore 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[3]

At submicron scales, 3D materials no longer have the same behavior as their 2D form, which can be an advantage. For example, graphene has a very high carrier mobility, and accompanying lower losses through the Joule effect. But graphene has zero bandgap, which results in a disqualifying low on/off ratio in transistor applications. TMDC monolayers might be an alternative: they are structurally stable, display a band gap 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 bulk WSe2 was reported. It showed a mobility below 500 cm2 V−1 s−1 for p-type conductivity at room temperature, about half that of a silicon FET but a low on/off current ratio because the device was realised on the surface of a bulk crystal. FETs made of monolayer MoS2 showed an excellent on/off ratio exceeding 108.[3]

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

Optical properties

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
MoTe2
WS2 1.84 673 2.28 544
WSe2 1.52 815 2.00 619

A semiconductor can absorb photons with energy larger than or equal to its bandgap. This means that light with a shorter wavelength is absorbed. 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 bulk TMDC material down to a thickness of two monolayers is still indirect, so the emission efficiency is lower compared to monolayered materials. The emission efficiency is about 104 greater for TMDC monolayer than for bulk material.[4] The band gaps of TMDC monolayers are in the visible range (between 400 nm and 700 nm). The direct emission shows two transitions called A and B, separated by the spin-orbit coupling energy. The lowest energy and therefore most important in intensity is the A emission.[1][19] Owing to their direct band gap, TMDC monolayers are promising materials for optoelectronics applications.

File:Ultrasensitive photodetector (MoS2).jpg
Representative scheme of the section of an ultrasensitive Photodetector based on a monolayer of MoS2[5]

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 that reach 6.1 mA W−1. Multilayer MoS2 show higher photoresponsivities, about 100 mA W−1, which is similar to silicon devices. Making a gold contact at the far edges of a monolayer allows an ultrasensitive detector to be fabricated.[5] Such a detector has a photoresponsivity reaching 880 A W−1, 106 greater than the first graphene photodetectors. This high degree of electrostatic control is due to the thin active region of the monolayer. Its simplicity and the fact that it has only one semiconductor region, whereas the current generation of photodetectors is typically a p-n junction, makes possible industrial applications such as high-sensitivity and flexible photodetectors. The only limitation for currently available devices is the slow photoresponse dynamics.[5]

Mechanical properties

A monolayer of MoS2 can be strained at least up to 10%,[20] comparable to graphene. Under the application of strain, a decrease in the direct and indirect band gap is measured that is approximately linear with strain.[21] 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 at a strain level of 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]

Large quantities of exfoliated material can also be produced using liquid-phase exfoliation by blending TMDC materials with solvents and polymers. [25]

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.[26]

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.[27]

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.[2][1]

Spin-orbit coupling

Theorical energy of the spin-orbit coupling[28][29]
Valence band

splitting (eV)

Conduction band

splitting (eV)

MoS2 0.148 0.003
WS2 0.430 0.026
MoSe2 0.184 0.007
WSe2 0.466 0.038
MoTe2 0.219 0.034

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.[30][31][32] 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[29]
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.[15]

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.[7] 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

File:Graphene-mos2 enhanced SPR.png
Graphene-MoS2 enhanced SPR biosensor.[33]

A single layer of TMDC can absorb 5-10% of light,[33] 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 a hole. The negatively charged electron and the positively charged hole are attracted via the Coulomb interaction, forming a bound state called an exciton. This results in an important energy difference between the bandgap observed in optical experiments ('optical bandgap') and the true bandgap for free carrier absorption. This is referred to as bandgap renormalization and occurs, albeit on smaller energy scales, in semiconductors like GaAs and ZnO. The energy difference between the optical bandgap and the free carrier bandgap is called the exciton binding energy. In atomically thin 2D systems there exists a strong confinement of electrons and holes in the layer plane.[19] This confinement dramatically enhances the Coulomb interaction between the electron and hole in TMDC monolayers compared to the bulk situation or other quasi 2D materials, leading to a large binding energy in the hundreds of meV range.[14][19][34][35][36]

Trions (charged excitons)[37][38] and biexcitons[39][40] have been observed in monolayer transition-metal dichalcogenides.

References

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