24
2 Entering a Two-Dimensional Materials World
Fig. 2.5 Top: Typical schematic side-view of a monolayer (ML) TMDC with metal atoms sandwiched between chalcogen atom layers, rendering the monolayer semiconductor a covalentlyconfigured three-layer crystalline system. Left box: Sketch of the local coordination (top) in the
monolayer crystal lattice with a primitive unit cell (bottom), indicated in black (dashed line). Note
the two-element basis. An exemplary translation of that cell to the next lattice point is shown in
grey. Also, note that the chalcogen atoms are not in the same plane as the transition metal. Right
box: Common representation of a real-space (top) and momentum-space (bottom) elementary unit
cell for a monolayer TMDC indicating a three-fold rotation symmetry of a hexagonally-arranged
unit cell and of the corresponding Brillouin zone, respectively. Differently coloured balls indicate
atoms in the unit cell (in sum containing one W and two Se atoms), and K and K denote the two
distinguishable high-symmetry points on the corners of the hexagonally-shaped Brillouin zone.
Note that a three-fold symmetry exists in both the real space and the k space. Central figure with
inset: Schematic comparison of a natural multilayer configuration (a) with indirect electronic band
gap (cf. inset, left) and a monolayer (b) with direct gap (cf. inset, right). The inset shows a simplified sketch of the band structure model for bulk and monolayer (Mo/W)(S/Se) 2 . Arrows mark
a momentum-indirect (unlikely) valence-to-conduction-band transition for bulk and a direct gap
transition for the monolayer case (K –K ). Energy scales according to [4, 93]
mobilities up to 350,000 cm
2 /(Vs) [140], graphene has become an ideal candidate
for high-mobility devices, while monolayer TMDCs address the demand on the
optoelectronics side due to their semiconducting nature (see for instance [16] and
references therein).
Structural Properties of TMDCs
One single TMDC layer typically has a thickness of about 0.6–0.7 nm which consists of a hexagonally-packed layer of metal atoms sandwiched between two layers
of chalcogen atoms (see Fig. 2.5). However, a three-fold crystal symmetry—and correspondingly k-space symmetry—renders the corners of the hexagonally-shaped 2D
Brillouin zone distinguishable, in a way that K and K
valleys are located next to
each other. Time-reversal-symmetry exists between these high-symmetry points of
the Brillouin zone. From this, the valley degree of freedom gives rise to a pseudo-
2 Entering a Two-Dimensional Materials World
Fig. 2.5 Top: Typical schematic side-view of a monolayer (ML) TMDC with metal atoms sandwiched between chalcogen atom layers, rendering the monolayer semiconductor a covalentlyconfigured three-layer crystalline system. Left box: Sketch of the local coordination (top) in the
monolayer crystal lattice with a primitive unit cell (bottom), indicated in black (dashed line). Note
the two-element basis. An exemplary translation of that cell to the next lattice point is shown in
grey. Also, note that the chalcogen atoms are not in the same plane as the transition metal. Right
box: Common representation of a real-space (top) and momentum-space (bottom) elementary unit
cell for a monolayer TMDC indicating a three-fold rotation symmetry of a hexagonally-arranged
unit cell and of the corresponding Brillouin zone, respectively. Differently coloured balls indicate
atoms in the unit cell (in sum containing one W and two Se atoms), and K and K denote the two
distinguishable high-symmetry points on the corners of the hexagonally-shaped Brillouin zone.
Note that a three-fold symmetry exists in both the real space and the k space. Central figure with
inset: Schematic comparison of a natural multilayer configuration (a) with indirect electronic band
gap (cf. inset, left) and a monolayer (b) with direct gap (cf. inset, right). The inset shows a simplified sketch of the band structure model for bulk and monolayer (Mo/W)(S/Se) 2 . Arrows mark
a momentum-indirect (unlikely) valence-to-conduction-band transition for bulk and a direct gap
transition for the monolayer case (K –K ). Energy scales according to [4, 93]
mobilities up to 350,000 cm
2 /(Vs) [140], graphene has become an ideal candidate
for high-mobility devices, while monolayer TMDCs address the demand on the
optoelectronics side due to their semiconducting nature (see for instance [16] and
references therein).
Structural Properties of TMDCs
One single TMDC layer typically has a thickness of about 0.6–0.7 nm which consists of a hexagonally-packed layer of metal atoms sandwiched between two layers
of chalcogen atoms (see Fig. 2.5). However, a three-fold crystal symmetry—and correspondingly k-space symmetry—renders the corners of the hexagonally-shaped 2D
Brillouin zone distinguishable, in a way that K and K
valleys are located next to
each other. Time-reversal-symmetry exists between these high-symmetry points of
the Brillouin zone. From this, the valley degree of freedom gives rise to a pseudo-