Transition Metal Dichalcogenide monolayers

Transition Metal Dichalcogenide (TMDC) monolayers are atomically thin

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:

• TMDC monolayers
  WS₂ have a direct band gap, and can be used in electronics as transistors and in optics as emitters and detectors. ^{[1] [2][3]}

• 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
  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

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 :

• nonlinear optics phenomena : frequency doubling. When the crystal is excited by a laser, the output frequency can be doubled. ^{[9] [10] [11] [12]}

• 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

Transport properties

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

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

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

Exfoliation

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

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 p_z

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

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

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