Chemistry Reference
In-Depth Information
can be characterized by dielectric constant,
ε
. Indeed, screening effects based on
ε
play a fundamental role in determining the electron dynamics, the optical exciton
binding energy, the electron and hole mobilities as well as charge storage features. In
this context the Coulomb interactions are confined in a two-dimensional geometry
which can give place to a new set of dielectric properties depending on the electronic
nature of the 2D crystal.
Graphene, a semimetal with zero bandgap, and MoS
2
, a low-dimension direct
band gap semiconductor, are two representative members of the 2D family that have
been receiving much attention in many fields due to their remarkable chemical and
physical properties (Castro Neto et al.
2009
; Wang et al.
2012a
). One of the main
features that influences all these properties is the layer thickness, which determines
the charge distribution in the device as well as the electronic structure through the
band gap. In particular, graphene can become a semiconductor with a band gap of
several tenths of millielectronvolts at a bilayer structure subjected to high electric
gate bias (Castro et al.
2007
). MoS
2
, in its turn, has a sizable band gap that varies
as a function of the number of layers which reaches values of about 1.8 eV at the
monolayer limit (Mak et al.
2010
). In both situations the electric-field screening
is observed to change as the dielectric response depends on the intrinsic electronic
properties as well as on
ε
.
In fact, the large range of values for
ε
found by different experiments on graphene
(Elias et al.
2011
; Siegel et al.
2011
; Bostwick et al.
2010
; Reed at al.
2010
; Wang
et al.
2012b
; Sanchez-Yamagishi et al.
2012
; Fallahazad et al.
2012
; Jellison et al.
2007
) and MoS
2
(Zhang et al.
2002
; Kim et al.
2012
; Bell et al.
1976
; Frindt et
al.
1963
; Beal et al.
1979
) has become a subject of considerable discussions. More
factors, apart from the external electric fields and layer thickness, indicate that
ε
might
depend on the underneath substrate as recently measured for graphene (Hwang et al.
2012
) and MoS
2
layers (Bao et al.
2013
). In practical terms, the dielectric constant
is defined by
ε
ε
vac
)/2, with
ε
sub
and
ε
vac
the dielectric constant values
for the substrate and vacuum, respectively. However, this approach suggests that the
environment could play a role in the determination of the intrinsic dielectric constant
of these 2D materials. Therefore, it is paramount to determine the intrinsic value of
ε
despite of external screening environments.
In the present Chapter, we provide a review of some of our recent computational
studies on the effect of electric fields on multilayer graphene and MoS
2
. We will
consider both layered systems at different field magnitudes (0-1.0 V/Å) and number
of layers (2-10 L). Some differences on the dielectric response between graphene
and MoS
2
will be discussed based on simple electrostatic concepts, which will give
generality to the calculations for other 2D-layers still to be explored.
=
(
ε
sub
+
14.2
Electrical Field Tuning of the Dielectric Constant
Figure
14.1
a, c display how
ε
evolves with external fields for different number of
graphene and MoS
2
layers, respectively. At low fields,
E
ext
≤
0
.
001 V/Å,
ε
is almost
independent of the number of layers having a value close to
4 for both two-
dimensional crystals. As the external field
E
ext
is increased,
ε
reaches larger values,
∼
