5 Enabling Materials By Dimensionality: From 0D to 3D Carbon-Based. . .
191
size graphene sheets at low temperature via our in-house SuMBE growth technique.
While we did not succeed for technological limitations to lower the working
temperature down to room conditions at variance with the case of SiC growth,
however SuMBE was capable of synthesizing a fairly even coating of graphenelike material in a single layer at 645 ◦ C using H 2 as carrier gas. This temperature
is remarkably smaller than that of other widely used approaches, such as CVD (in
excess of 900 ◦ C), MBE of C 60 on Ru(0001) (725 K for the cage thermal break
and 1200 K for complete monolayer formation) [140] or on noble metals (1050 K)
[141]. Graphene nano-islands, even according to our metadynamics simulations, are
not made of regular hexagons, like in pristine graphene, but also contain pentagons,
which come from the original buckyball structures. We notice that this characteristic
is potentially useful, because the pentagonal defects introduce a band gap into the
material, something materials scientists have longed hoped to create in graphene.
Although at this stage we believe that our results represent a proof of principle,
the technique looks interesting, not least because it produces relatively high-quality
films and could also be applied using a wide range of materials as a substrate, such as
semiconductors and insulators avoiding the graphene layer transfer from the growth
substrate to different substrates for producing high-end electronic devices.
We then discussed a systematic approach for generating bi-dimensional all-sp 2
carbon allotropes, aiming at decreasing the density of graphene without depleting
its unique mechanical properties. This method proceeds by augmenting the number
of congruent discs under the constraint of local stability. The daughter structures
share the common drawbacks of having lower stability and smaller cohesive energy
than graphene, while their density is reduced by 45% with respect to graphene.
In particular, we conclude that (i) flakene may represent the least dense possible
architecture among the families of bi-dimensional all-sp 2 carbon allotropic forms
under the local stability constraints; (ii) the augmentation increases the metallicity
character of the daughter structures with respect to parent ones; (iii) while the
absolute stress-strain characteristics are definitely depleted by augmentation, also
a threshold exists below which one cannot reduce further the density without a
considerable performance loss of the specific mechanical properties; (iv) tilene
parent displays a specific strength higher than graphene; and (v) finally, graphene
presents one of the highest specific modulus ever found, and the quest for finding a
better replacement in mechanical engineering applications is still open.
Graphene can be also rolled in the shape of nanotubes, and we have showed,
using a GW approach based on the expansion of the polarizability operator in
an optimal basis, how the electronic band gap of semiconducting CNTs evolves
by increasing the tube size. This approach allows one to avoid the explicit sum
over the unoccupied states while allowing for good accuracy. We showed that an
accurate estimate of the excitation binding energies can be achieved by coupling
optical measurements with theoretical modelling [93, 95]. We extrapolated the gap
vs. diameter function for large dimensions showing that this dependence can be
modelled by E gap = 1.54 eV× nm. This relation is found to be in good agreement
with a recent direct measurement of the electronic gap performed via STS for the
case of 1.4 nm diameter CNT [91].
191
size graphene sheets at low temperature via our in-house SuMBE growth technique.
While we did not succeed for technological limitations to lower the working
temperature down to room conditions at variance with the case of SiC growth,
however SuMBE was capable of synthesizing a fairly even coating of graphenelike material in a single layer at 645 ◦ C using H 2 as carrier gas. This temperature
is remarkably smaller than that of other widely used approaches, such as CVD (in
excess of 900 ◦ C), MBE of C 60 on Ru(0001) (725 K for the cage thermal break
and 1200 K for complete monolayer formation) [140] or on noble metals (1050 K)
[141]. Graphene nano-islands, even according to our metadynamics simulations, are
not made of regular hexagons, like in pristine graphene, but also contain pentagons,
which come from the original buckyball structures. We notice that this characteristic
is potentially useful, because the pentagonal defects introduce a band gap into the
material, something materials scientists have longed hoped to create in graphene.
Although at this stage we believe that our results represent a proof of principle,
the technique looks interesting, not least because it produces relatively high-quality
films and could also be applied using a wide range of materials as a substrate, such as
semiconductors and insulators avoiding the graphene layer transfer from the growth
substrate to different substrates for producing high-end electronic devices.
We then discussed a systematic approach for generating bi-dimensional all-sp 2
carbon allotropes, aiming at decreasing the density of graphene without depleting
its unique mechanical properties. This method proceeds by augmenting the number
of congruent discs under the constraint of local stability. The daughter structures
share the common drawbacks of having lower stability and smaller cohesive energy
than graphene, while their density is reduced by 45% with respect to graphene.
In particular, we conclude that (i) flakene may represent the least dense possible
architecture among the families of bi-dimensional all-sp 2 carbon allotropic forms
under the local stability constraints; (ii) the augmentation increases the metallicity
character of the daughter structures with respect to parent ones; (iii) while the
absolute stress-strain characteristics are definitely depleted by augmentation, also
a threshold exists below which one cannot reduce further the density without a
considerable performance loss of the specific mechanical properties; (iv) tilene
parent displays a specific strength higher than graphene; and (v) finally, graphene
presents one of the highest specific modulus ever found, and the quest for finding a
better replacement in mechanical engineering applications is still open.
Graphene can be also rolled in the shape of nanotubes, and we have showed,
using a GW approach based on the expansion of the polarizability operator in
an optimal basis, how the electronic band gap of semiconducting CNTs evolves
by increasing the tube size. This approach allows one to avoid the explicit sum
over the unoccupied states while allowing for good accuracy. We showed that an
accurate estimate of the excitation binding energies can be achieved by coupling
optical measurements with theoretical modelling [93, 95]. We extrapolated the gap
vs. diameter function for large dimensions showing that this dependence can be
modelled by E gap = 1.54 eV× nm. This relation is found to be in good agreement
with a recent direct measurement of the electronic gap performed via STS for the
case of 1.4 nm diameter CNT [91].