Phonon engineering in nanostructures: Controlling interfacial thermal resistance in multilayer-graphene/dielectric heterojunctions Page: 3
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Appl. Phys. Lett. 101, 113111 (2012)
values) interfacial thermal resistance in this system indicates
a sizable permeability of the system to heat transport and can
be clearly understood in terms of the similarity of the phonon
dispersions in the two sub-systems and the transferability of
the force constants due to the similar masses of the B, N, and
C atoms (mass approximation29). Our values are in good
agreement with the experimentally observed thermal resist-
ance of exfoliated (weakly coupled) graphene on SiO2 at
room temperature (56 - 120 x 10-10 m2 K/W).5 The inter-
face indeed acts as a barrier to the transmission of phonons
from one side of the device to the other.
The situation changes drastically when we consider
interfaces with 3-D materials such as SiC. Looking at the
results for the G/SiC and G/H:SiC cases, shown in Figs.
2(b) and 2(c), it is clear that the thermal resistance depends
critically on the microscopic details of the interfaces. For
instance, the interfacial thermal resistance of the SiC/G at
300K is 361.1 x 10-10 m2 K/W one order of magnitude
higher than in the G/h-BN case. This is due to the substan-
tial difference between the phonon distribution functions in
a 3-D bulk vs. a 2-D layered system. Even more drastic is
the variation due to the microscopic modification of the
interface by hydrogenation. Now the thermal resistance
increases by a factor of 2 (712.4 x 10-10 m2 K/W), indicat-
ing a strengthening of the interfacial barrier to phonon
In order to understand the thermal conductance features
of these three systems, we have carried out a microscopic
analysis of the transmittance in terms of the most relevant
contribution from the vibrational normal modes at the inter-
face. The results are summarized in Fig. 3 (left panel). A
general feature, common to all the systems, is the suppres-
sion of the phonon modes for energies above ~100 cm-1,
which can be attributed to the lack of matching between the
graphene layers and the substrate modes in the same energy
region (see Figs. S4-S6 in supplementary material).24 More-
over, the individual analysis of the atomic displacements for
the low energy modes (< 100 cm-1) that correspond to high
transmittance values allows us to identify the general shape
of the transport eigenchannels for the heat flux at those ener-
!i747ZI XX X
FIG. 3. Left panel: total transmittance for (a) G/h-BN, (b) G/SiC, and (c)
G/H:SiC. Right panel: sketch of the atomic displacement patterns of the rele-
vant normal modes that are mainly responsible for the phonon transmission
at the interface. The corresponding energies of modes (d), (e), and (f) are
indicated by arrows in panels (a), (b), and (c), respectively.
gies (Fig. 3, right panel). In the G/h-BN case, we find two
representative sets of collective modes that are efficiently
transmitted across the interface: at low frequencies (up to
r25 cm-1), the modes have out-of-plane displacements as
in Fig. 3(d).
In the intermediate energy range (25 - 100 cm-1), the
modes have in-plane displacements (shear modes, parallel to
the interface) and are more weakly coupled (hence the lower
transmittance). In the SiC case [Fig. 3(b)], this transmission
channel is inhibited by the 2-D to 3-D transition across the
heterojunction. Now, only out-of-plane modes can transmit
across the interface [Fig. 3(e)]. This effect is clearly a mani-
festation of the possibility of engineering phonon transport
across an interface by the selective modification of the inter-
face geometry. Indeed, this is further exemplified by the case
of transmission through the G/H:SiC interface. The addition
of a H atom on the Si lonely atom at the interface layer
blocks the transmission of the out-of-plane mode responsible
for most of the heat transfer around ~40 cm-'. The H-Si
bond makes the interface rigid to out-of-plane modes and
effectively blocks the transmission in the low energy range,
as displayed by the displacement pattern of the correspond-
ing mode (now red-shifted at ~25 cm-1) and shown in Fig.
3(f). This is clearly interpretable in view of the breaking of
the mass approximation by the insertion of a "mass defect,"
the light H atoms. Moreover, in addition to the mass effect,
there is a slight variation of the interlayer distance between
G and SiC upon H adsorption in the buffer layer (3.89 A in
SiC vs. 4.13 A in H:SiC), which induces a further weakening
of the IFCs. Recent experiments have already shown that
hydrogen functionalization can play an important role in
manipulating thermal conductance in graphene-metal inter-
faces,30 an indirect confirmation of the validity, significance,
and timeliness of our investigation.
These results point to the paramount importance of
interfacial geometry for the control of thermal properties of a
heterojunction: Indeed, interfaces can be engineered as to
prevent or enhance heat transfer from one system to another
and thus select the directionality of the heat dissipation chan-
nel. Depending on the application for any particular device,
one should be able to design the desired phonon distribution
function. For instance, in systems where one needs to capture
thermal energy, e.g., solar thermal devices or thermoelectric
systems, it would be desirable to collect the heat in the active
layer, with negligible dissipation (as in G/H:SiC). If instead
heat dissipation is essential for maintaining high charge or
spin carrier mobility in a device, a heterojunction like G/SiC
or G/h-BN would be the ideal choice. Finally, we would like
to stress once again that this type of analysis is only possible
because we are using a fully first principles approach where
all the individual contributions are evaluated explicitly at a
quantum mechanical level.
We would like to thank Yifeng Chen for his technical
support and useful discussions. This work was supported, in
part, by the DARPA/HRL CERA, SRC/NRI SWAN, and US
ARO. M.B.N. wishes to acknowledge partial support from the
Office of Basic Energy Sciences, U.S. Department of Energy
at Oak Ridge National Laboratory under Contract No.
DE-AC05-000R22725 with UT-Battelle, LLC. Calculations
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113111-3 Mao et al.
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Mao, R.; Kong, Byoung Don; Kim, Ki Wook; Jayasekera, Thushari; Calzolari, Arrigo & Buongiorno Nardelli, Marco. Phonon engineering in nanostructures: Controlling interfacial thermal resistance in multilayer-graphene/dielectric heterojunctions, article, September 13, 2012; [College Park, Maryland]. (digital.library.unt.edu/ark:/67531/metadc132984/m1/3/: accessed September 26, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.