Back to top
SUMMARY OF RESULTS OF THE LEVERHULME TRUST FUNDED RESEARCH RPG2016186
Tuning thermal transport in nanocomposites with size, shape and interface control
PI: G. P. Srivastava
Aims and objectives of the project:
The aim of this project was to identify key physical parameters of
doped semiconductor nanocomposites (e.g. system dimensionality, sample
length, unit cell size, relative sizes of constituent materials,
interface quality and carrier doping level) which can significantly
reduce their thermal transport capability below the alloy and
amorphous limits and help enhance their thermoelectric figure of merit
ZT.
The objectives set out are to make theoretical studies for three
different nanocomposite constructs using two materials A and B of
sizes d_A and d_B within a repeat period (unit cell size D=d_A+d_B):
(1) planar composite or planar superlattice (PSL) growth of alternate
layers of A and B along a direction; (2) nanowire composites (NWSL) by
periodically embedding nanowires of A inside the B matrix; (3) nanodot
composites (NDSL) by periodically embedding small volumes of A inside
the B matrix.
For each of these constructs the range of thermal conductivity values
is predicted by exploring (a) different sample size L in the range
500nm–1mm, (b) unit cell size d in the range 1–100 nm, (c) sample
doping in the range 10^(17)10^(20) cm^(3) and (d) interface
roughness occuring in various froms, including unavoidable mass
smudging.
Research activity:
We made a systematic and stateoftheart study of thermal
transport in two nanocomposite systems, Si/Ge and MoS2/WS2, which are
hugely sought after for their technological applications as
highefficiency thermoelectric materials. Specifically, for Si/Ge
nanocomposites we considered planar superlattices (PSLs), embedded
nanowire superlattices (NWSLs) and embedded nanodot superlattices
(NDSLs) constructed from isotropically cubic constituents Si and
Ge. In order to explore quasi twodimensional nature of nanocomposites
we studied NDSLs constructed from transition metal dichalcogenides
(TMDs) MoS2 and WS2 in their bulk 2H structure. We developed many
aspects of the theoretical method without the use of any adjustable
parameters, performed numerical analysis from scratch, wrote several
new compute codes in Fortran and made calculations using computer
nodes purchased out of the grant budget. The original aims, objectives
and plans were maintained throughout the course of the grant period.
 Theoretical developments:
For describing thermal conductivity of bulk, and shortperiod
nanocomposites of periodicity D shorter than 10 nm, we made three
levels of theoretical development. (1) Derived a semiab initio
expression for cubic and quartic crystal anharmonic potential terms
which are essential for examining phonon mean free path and thus
lattice thermal conductivity; (2) Based on (1) and a linearised
Boltzmann equation, derived an analytical expression for thermal
conductivity tensor within an effective relaxationtime scheme. This
involved incorporating a generalised version of the contribution of
momentumconserving threephonon interactions as developed by the PI
just before the start of this project; (3) Using (1) derived an
analytic expression for fourphonon relaxation rate, which is required
to describe correct temperature dependence of conductivity above room
temperature.
For studying thermal conductivity of nanocomposites of periodicity
larger than 10 nm we made another three levels of theoretical
development. (4) Based on a multiplescattering approach using the
concepts of Green function and transition matrix, we extended the
socalled Modified Effective Medium Approximation (mEMA) to study
thermal conductivity of anisotropic nanocomposite materials. This
involved consideration of anisotropic nature of the conductivity of
constituent bulk materials as well that of the interface region; (5)
Developed a theoretical framework for evaluating thermal interface (or
thermal boundary) resistance. This involved using a judicious level of
mixing of the diffused mismatch model (DMM) and acoustic mismatch
model (AMM) schemes by incorporating wavevector dependent phonon
scattering rate due to surface inhomogeneity. We refer to the
development (4)+(5) as Extended Modified Effective Medium
Approximation (emEMA); (6) At the very end we developed a Generalised
Extension of the Effective Medium Approximation (GemEMA) for
conductivity by incorporating in emEMA the important effect of
unintentional mass smudging within a few atomic layers across
interfaces that takes place even when the best fabrication techniques
are employed.
 Computational approach:
We thoroughly upgraded our existing Fortran code for thermal
conductivity calculations of bulk and ultrathin nanocomposites using
our semiab initio method which includes the theoretical ingredients
mentioned in section [A] above. The starting point was lattice
dynamical calculations (i.e. phonon eigenvalues and eigenvectors)
using the quantum espresso package, based on the DFPT (density
functional perturbation theory). Using these, we computed phonon
velocities, temperaturedependent Grüneisen’s constant, and phonon
scattering rates from isotopic defects and interface mass smudging.
Detailed computation of phonon anharmonic scattering rates was
performed using the phonon eigensolutions and the Grüneisen constant.
For computing thermal conductivity of nanocomposites of practical
fabrication sizes and periodicities we wrote and used computer codes
based on the GemEMA discussed in section [B] and using bulk
conductivity inputs using the semiab inito method mentioned just
before.
Broad findings and conclusion:
We developed parameterfree stateoftheart theoretical and
computational techniques for investigating phonon transport in Si/Ge
and MoS2/WS2 nanocomposites. For systems with repeat periodicity in
the 1100 nm range, we have identified four key physical parameters
which should are capable of rendering lowest possible value of lattice
thermal conductivity. These are:
(1) difference in the conductivities of individual materials,
(2) period size,
(3) volume fraction of insertion, and
(4) atomiclevel interface quality.
For equallayer thickness Si/Ge planar superlattices of sample size
500 nm, the conductivity takes a value lower than that of the SiGe
alloy and amorphous Si when the period size lies in the range 312 nm.
This positively highlights the usefulness of nanocomposites for
achieving high figure of merit in thermoelectric applications. The
development and findings from this project on phonon transport can be
confidently employed in future stateoftheart theoretical and
computational studies of the thermoelectric properties of
nanocomposite systems.
Publications and dissemination:
Publications:

I. O. Thomas and G. P. Srivastava, ‘Anharmonic, dimensionality
and size effects in phonon transport’, J. Phys.: Condens. Matter 29
(2017) 505703 (11pp)

I. O. Thomas and G. P. Srivastava, ‘Control of thermal
conductivity with species mass in transitionmetal dichalcogenides’,
J. Appl. Phys. 123 (2018) 135703 (7 pp)

G. P. Srivastava and I. O. Thomas, ‘Temperaturedependent Raman
linewidths in transitionmetal dichalcogenides’, Phys. Rev. B 98
(2018) 035430 (8 pp)

I. O. Thomas and G. P. Srivastava, ‘Extension of the modified
effective medium approach to nanocomposites with anisotropic thermal
conductivities’, Phys. Rev. B 98 (2018) 094201 (6pp)

I. O. Thomas and G. P. Srivastava, ‘Anisotropic thermal conduction
in transition metal dichalcogenide nanocomposites with rough
interfaces’, Nanomaterials 8 (2018) 1054 (12 pp)

G. P. Srivastava and I. O. Thomas, ‘Mode confinement, interface
masssmudging, and sample length effects on phonon transport in thin
nanocomposite superlattices’, J. Phys.: Condens. Matter 31 (2019)
055303 (12 pp)

I. O. Thomas and G. P. Srivastava, ‘Effect of interface density,
quality and period on the lattice thermal conductivity of
nanocomposite materials’, J. Appl. Phys. (special topic on Advanced
Thermoelectrics) 127 (2020) 024304 (12 pp)

G. P. Srivastava and I. O. Thomas, ‘Tunable thermal transport
characteristics of nanocomposites’, Nanomaterials 10 (2020) 673:115
International conference presentations:

EPSRC supported Thermoelectric Workshop (Univeristy of Manchester,
1415 Feb 2017): G. P. Srivastava; Type of presentation: Invited.
Title: Theoretical ingredients for tuning thermoelectric propoerties
of semiconducting materials

RAMS conference (Recent Appointees in Materials Science
Conference, University of Exeter, Sept 1112, 2017): I. O. Thomas
(presenter) and G. P. Srivastava; Type of presentation: Oral. Title:
Anharmonic and dimensional effects on lattice thermal transport in Si,
Ge, and MoS2

MRS Fall 2017 conference, Boston, USA: I. O. Thomas (presenter)
and G. P. Srivastava; Type of presentation: Poster. Title: Cation and
anion controlled phonon transport in bulk, monolayer and shortperiod
superlattice transition metal dichalcodenides

MRS Spring 2018 conference, Phoenix, USA: G. P. Srivastava
(presenter) and I. O. Thomas; Type of presentation: Poster. Title:
Dimensionality dependent reduction in phonon conductivity of ultrathin
nanocomposites

MRS Spring 2018 conference, Phoenix, USA: G. P. Srivastava
(presenter) and I. O. Thomas; Type of presentation: Oral. Title:
Theoretical analysis of Raman linewidths in transition metal
dichalcogenides

International congress on the world of technology and advanced
materials, Kirsehir, Turkey, 21 Sept 2018. G. P. Srivastava; Type of
presentation: Invited talk. Title: Theoretical studies of solid
surfaces and interfaces.

Hot carriers workshop, Kavli Royal Society International Centre at
Chicheley Hall, Buckinghamshire, 1 Oct 2018. G. P. Srivastava; Type
of presentation: Invited talk. Title: Nonequilibrium phonon
dynamics.

MRS Spring 2019 conference, Phoenix, USA. G. P. Srivastava
(presenter) and I. O. Thomas; Type of presentation: Oral. Title:
Anharmonic coalescence and decay contributions for Raman linewidths in
2D transitionmetal dichalcogenides.

MRS Spring 2019 conference, Phoenix, USA: I. O. Thomas (presenter)
and G. P. Srivastava; Type of presentation: Poster. Title: Theory of
anisotropic thermal interface resistance in nanocomposite materials.

Current Trend in Material Sci. and Eng., S. N. Bose Institute,
Kolkata, India, 18 July 2019 G. P. Srivastava; Type of presentation:
Plenary talk. Title: Thermal transport in nanocomposites.
