Phonon engineering in nanostructures: Controlling interfacial thermal resistance in multilayer-graphene/dielectric heterojunctions Page: 1
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APPLIED PHYSICS LETTERS 101, 113111 (2012)
Phonon engineering in nanostructures: Controlling interfacial thermal
resistance in multilayer-graphene/dielectric heterojunctions
R. Mao,1 B. D. Kong,1 K. W. Kim,1 T. Jayasekera,2 A. Calzolari,3'a)
and M. Buongiorno Nardelli4,b)
IDepartment of Electrical and Computer Engineering, North Carolina State University,
Raleigh, North Carolina 27695-7911, USA
2Department of Physics, Southern Illinois University, Carbondale, Illinois 62901, USA
3lstituto Nanoscienze CNR-NANO-S3, 1-41100 Modena, Italy
4Department of Physics and Department of Chemistry, University of North Texas, Denton, Texas 76203,
USA and CSMD, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
(Received 2 July 2012; accepted 28 August 2012; published online 13 September 2012)
Using calculations from first principles and the Landauer approach for phonon transport, we study
the Kapitza resistance in selected multilayer graphene/dielectric heterojunctions (hexagonal BN
and wurtzite SiC) and demonstrate (i) the resistance variability (r50 - 700 x 10-10 m2K/W)
induced by vertical coupling, dimensionality, and atomistic structure of the system and (ii) the
ability of understanding the intensity of the thermal transmittance in terms of the phonon
distribution at the interface. Our results pave the way to the fundamental understanding of active
phonon engineering by microscopic geometry design. 2012 American Institute of Physics.
Recent progress in nanostructured materials synthesis
and device fabrication technology has brought the need for
thermal management to the forefront. For example, the
power density needed to operate an integrated circuit chip is
already nearing that of a nuclear reactor (around the
100 W/cm2 mark) and could continue its climb with size
scaling if no improvement is made.' Effective strategies for
heat transfer away from active devices and into heat sink
regions need to be engineered in future nanometer-scale ele-
ments on heterogeneous material platforms for high integra-
tion density and performance. Hence, a fundamental
understanding of thermal transport in the nanoscale environ-
ment is an essential requirement. In fact, the problem of ther-
mal transport at the nanoscale inherently demands an
atomistic, quantum-mechanical description of the complex-
ity of the nanointerfaces.
Among the most promising materials for advanced
microelectronic applications, graphene, a single plane or a
few-layers of graphite, has taken center stage for its out-
standing mechanical, electronic, and thermal properties.2-5
In particular, advances in the epitaxial growth of graphene
films on dielectric substrates, such as hexagonal BN (h-BN)
or SiC, have the potential to open new classes of device
applications that may revolutionize the semiconductor road-
map for future decades.6'7 Heat conduction between dielec-
trics can be interpreted as transport of phonons: quantized
elastic waves of lattice vibrations. When the heat flows
across interfaces, the scattering of the phonons originates a
thermal resistance often known as Kapitza resistance.8 There
are two classic models of evaluating the thermal resistance
in materials: the acoustic mismatch and the diffuse mismatch
model.9'1" Both are phenomenological approaches, assume
linear phonon dispersions, oversimplify the effects from the
a)Electronic address: email@example.com.
b)Electronic address: firstname.lastname@example.org.
interfaces, and are fitted to reproduce existing experimental
results. Beyond these simplified approaches, atomic level
methods, such as molecular dynamics," lattice dynamics,12
and non equilibrium Greens functions,13,14 have been used to
study thermal resistance in interfaces and superlattices.
These methods have in common the need for interatomic
potential functions for the evaluation of the dynamics of the
systems for which only empirical models have been used to
date. However, given the complexity of the interactions at
nanoscale systems such as graphene/substrate interfaces and
the impracticality of generating accurate potential functions
for any specific case, first principles methods are clearly the
ideal choice for these investigations.
In this letter, we have studied the heat conduction prop-
erties at the heterogeneous interface between multilayer gra-
phene and selected dielectric substrate materials using a fully
first principles approach for both the electronic and the ther-
mal properties of the systems. In particular, we combine
state-of-the-art density functional theory (DFT) and density
functional perturbation theory (DFPT)15 calculations for the
evaluation of the vibrational properties of nanoscale systems
with the general framework of the Landauer approach16,17
for ballistic phonon transport using a real-space Green's
At the nanoscale, thermal transport across a device con-
nected to two thermal baths (L and R) can be described by
extending the Landauer formalism for electrons to phonons.
In this formalism, the expression for the thermal current den-
J(TL, TR) =7 dW W Tph()[n(TL, ) - n(TR, ),
where n(TL,R, w) are the Bose-Einstein distribution functions
for the left or right lead, TL,R = T AT/2 are the temperatures
2012 American Institute of Physics
Downloaded 14 Jan 2013 to 220.127.116.11. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions
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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/m1/1/: accessed October 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.