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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 state-of-the-art study of thermal transport in two nanocomposite systems, Si/Ge and MoS2/WS2, which are hugely sought after for their technological applications as high-efficiency 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 two-dimensional 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.

    1. Theoretical developments: For describing thermal conductivity of bulk, and short-period nanocomposites of periodicity D shorter than 10 nm, we made three levels of theoretical development. (1) Derived a semi-ab 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 relaxation-time scheme. This involved incorporating a generalised version of the contribution of momentum-conserving three-phonon interactions as developed by the PI just before the start of this project; (3) Using (1) derived an analytic expression for four-phonon 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 multiple-scattering approach using the concepts of Green function and transition matrix, we extended the so-called 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 wave-vector 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.

    2. Computational approach: We thoroughly upgraded our existing Fortran code for thermal conductivity calculations of bulk and ultrathin nanocomposites using our semi-ab 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, temperature-dependent 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 semi-ab inito method mentioned just before.

    Broad findings and conclusion:

    We developed parameter-free state-of-the-art theoretical and computational techniques for investigating phonon transport in Si/Ge and MoS2/WS2 nanocomposites. For systems with repeat periodicity in the 1-100 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) atomic-level interface quality.

    For equal-layer 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 3-12 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 state-of-the-art theoretical and computational studies of the thermoelectric properties of nanocomposite systems.

    Publications and dissemination:


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

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

    3. G. P. Srivastava and I. O. Thomas, ‘Temperature-dependent Raman linewidths in transition-metal dichalcogenides’, Phys. Rev. B 98 (2018) 035430 (8 pp)

    4. 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)

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

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

    7. 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)

    8. G. P. Srivastava and I. O. Thomas, ‘Tunable thermal transport characteristics of nanocomposites’, Nanomaterials 10 (2020) 673:1-15

    International conference presentations:

    1. EPSRC supported Thermoelectric Workshop (Univeristy of Manchester, 14-15 Feb 2017): G. P. Srivastava; Type of presentation: Invited. Title: Theoretical ingredients for tuning thermoelectric propoerties of semiconducting materials

    2. RAMS conference (Recent Appointees in Materials Science Conference, University of Exeter, Sept 11-12, 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

    3. 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 short-period superlattice transition metal dichalcodenides

    4. 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

    5. 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

    6. 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.

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

    8. 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 transition-metal dichalcogenides.

    9. 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.

    10. 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.

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