Chemistry Reference
In-Depth Information
Fig. 14.4
Energy per MoS
2
unit cell as a function of
interlayer distance for
different values of
E
ext
(V/Å).
The
vertical solid line
indicates the equilibrium
interlayer distance
z
o
=
6
.
70 Å. The
inset
shows
the van der Waals barrier
(
E
vdW
) per atom as a function
of
E
ext
. (Adapted from Santos
et al.
2013b
)
of layers. As
ε
is calculated by the ratio of the external and internal fields to the slabs,
the enhancement in the value of the dielectric constant with the number of layers
N
is directly related to the reduction of the field in the innermost regions of the structure
which leads to lower
ε
values for lower values of
N
. This decay of field with the
layer thickness is in good agreement with recent electrostatic force microscopy and
Kelvin probe microscope measurements performed for MoS
2
(Castellanos-Gomez
et al.
2013
;Lietal.
2013
) and graphene (Datta et al.
2009
).
14.5
Electrostatic Exfoliation on Graphene and MoS
2
Layers
In this section we analyze the possibility to use an electrostatic gate that can be used
to exfoliate graphene and MoS
2
layers at different bias. We note that there is an upper
limit on the magnitude of
E
ext
that can be applied to the systems as the bias induces
a shift of the equilibrium position of the layers to higher interlayer separations.
Figure
14.4
displays the total energy for MoS
2
2 L as a function of the interlayer
distance
z
. We focus on MoS
2
since similar effects are observed for graphene. At
E
ext
=
0
.
0 V/Å, a van der Waals barrier
E
vdW
of 30 meV/atom prevents the separation
of the two layers from
z
o
to infinity. At finite
E
ext
, the value of
E
vdW
decreases,
indicating that the MoS
2
-layers become less bound. At
E
ext
=
2
.
0 V/Å, the two
dichalcogenide layers can be easily separated with a barrier of only 0.45 meV/atom.
This indicates that an electrostatic gate can be utilized for exfoliating and printing
few-layers MoS
2
in pre-pattern form similarly to that observed for graphene (Liang
et al.
2009
). Since several challenges of making industrially available large-scale
areas of 2D-crystals and fabricating atomic features with precise electronic structure
are still to be overcome, the electrostatic exfoliation shown in our calculations could
open new avenues for the achievement of such desired properties.
