2.2 Fundamentals of 2D Materials
25
spin attributed to each valley and makes K and K
valleys separately accessible to
oppositely circularly polarised light [30, 31].
Mechanical Exfoliation and Production of Heterostructures
The intralayer MX bonds are mainly covalent in nature, whereas the sandwiched
layers are coupled by weak vdW forces, thereby allowing the crystal to be readily
cleaved along the layer surface. Thus, mechanical exfoliation is the most common
lab-scale approach to deliver isolated (high-quality) monolayers to experiments. Such
monolayers can—in a simplified picture—be even stacked in a “LEGO” buildingblock fashion by means of vdW interactions between adjacent layers to form highquality homo- or heterojunction interfaces (cf. [56, 91]).
Stacking TMDC monolayers to form different heterostructures offers the unique
opportunity to design advanced electronic and optoelectronic devices [16, 56].
Commonly, dry-stamping techniques, wet-transfer or pick-and-lift techniques are
employed for the desired vertical heterostructuring [56, 141, 142], whereas chemicalvapour-deposition (CVD) growth can deliver, both, crystalline in-plane as well as
lattice-matched out-of-plane heterostructures [97]. Indeed, lateral heterojunctions
and pn-junctions are understood to also occur for manually stacked monolayers on
other 2D materials at the edge of overlap due to the influence of the environment on
the energetics and doping, respectively, in the stacked materials [143].
Confinement and Screening in Monolayers
The strong enhancement of the Coulomb interaction in the monolayer limit leads to
an indirect-to-direct band gap transition [3, 4] (see sketched ‘band structure model’,
inset in Fig. 2.5), large exciton binding energy [23, 24] (cf. table of electronic properties of 2D TMDCs in [16]), the abundance of multi-excitons [54, 55] and sensitivity to the surrounding dielectrics [40, 49, 58, 86–88, 144]. Mostly, these drastic
changes are attributed to the screening changes from bulk to single-layer crystal.
These changes do not only introduce a drastic quantum confinement of charge carriers to one single layer but also expose the excitonic dipole to harsh dielectric changes
at the interface (e.g. from monolayer to vacuum/air on two sides in the case of fully
suspended flakes) which results in a modified screening for them (the excitons and
their higher excitations, cf. [23, 88]).
Band Properties and Interlayer Coupling
In addition, the p-orbital contributions to the electronic band structure originating
from the chalcogen atoms (basically sitting at the interfaces) are more prone to
variations of the environment than the d-orbital contributions from the transition
metal (sandwiched in the central layer). This affects the indirect gap’s conduction
band minimum at the Σ and the valence band’s maximum at the Γ crystal Brillouinzone symmetry points. In contrast, little happens at the d-orbital dominated K and K
points, at which the direct gap is given in the monolayer regime [4, 145]. Furthermore,
a strong spin–orbit coupling leads to a degeneracy lifting of, both, the highest valence
and lowest conduction bands, whereas the splitting of the valence band is typically
much larger and is the main source of the energy difference between A and B excitons
(cf. Fig. 2.4b) corresponding to these spin-opposite optical transitions. Thereby, spin
25
spin attributed to each valley and makes K and K
valleys separately accessible to
oppositely circularly polarised light [30, 31].
Mechanical Exfoliation and Production of Heterostructures
The intralayer MX bonds are mainly covalent in nature, whereas the sandwiched
layers are coupled by weak vdW forces, thereby allowing the crystal to be readily
cleaved along the layer surface. Thus, mechanical exfoliation is the most common
lab-scale approach to deliver isolated (high-quality) monolayers to experiments. Such
monolayers can—in a simplified picture—be even stacked in a “LEGO” buildingblock fashion by means of vdW interactions between adjacent layers to form highquality homo- or heterojunction interfaces (cf. [56, 91]).
Stacking TMDC monolayers to form different heterostructures offers the unique
opportunity to design advanced electronic and optoelectronic devices [16, 56].
Commonly, dry-stamping techniques, wet-transfer or pick-and-lift techniques are
employed for the desired vertical heterostructuring [56, 141, 142], whereas chemicalvapour-deposition (CVD) growth can deliver, both, crystalline in-plane as well as
lattice-matched out-of-plane heterostructures [97]. Indeed, lateral heterojunctions
and pn-junctions are understood to also occur for manually stacked monolayers on
other 2D materials at the edge of overlap due to the influence of the environment on
the energetics and doping, respectively, in the stacked materials [143].
Confinement and Screening in Monolayers
The strong enhancement of the Coulomb interaction in the monolayer limit leads to
an indirect-to-direct band gap transition [3, 4] (see sketched ‘band structure model’,
inset in Fig. 2.5), large exciton binding energy [23, 24] (cf. table of electronic properties of 2D TMDCs in [16]), the abundance of multi-excitons [54, 55] and sensitivity to the surrounding dielectrics [40, 49, 58, 86–88, 144]. Mostly, these drastic
changes are attributed to the screening changes from bulk to single-layer crystal.
These changes do not only introduce a drastic quantum confinement of charge carriers to one single layer but also expose the excitonic dipole to harsh dielectric changes
at the interface (e.g. from monolayer to vacuum/air on two sides in the case of fully
suspended flakes) which results in a modified screening for them (the excitons and
their higher excitations, cf. [23, 88]).
Band Properties and Interlayer Coupling
In addition, the p-orbital contributions to the electronic band structure originating
from the chalcogen atoms (basically sitting at the interfaces) are more prone to
variations of the environment than the d-orbital contributions from the transition
metal (sandwiched in the central layer). This affects the indirect gap’s conduction
band minimum at the Σ and the valence band’s maximum at the Γ crystal Brillouinzone symmetry points. In contrast, little happens at the d-orbital dominated K and K
points, at which the direct gap is given in the monolayer regime [4, 145]. Furthermore,
a strong spin–orbit coupling leads to a degeneracy lifting of, both, the highest valence
and lowest conduction bands, whereas the splitting of the valence band is typically
much larger and is the main source of the energy difference between A and B excitons
(cf. Fig. 2.4b) corresponding to these spin-opposite optical transitions. Thereby, spin