Phonon Transport In Superlattices Research Articles

(Invited) Phonon Heat Transport Processes and Thermal Conductivity of II-Oxide and III-V Superlattices: Wave-like Coherent Transport in CaTiO3/SrTiO3 Superlattices and Ballistic-Diffusive Transport in GaAs/Alas Superlattices

The thermal conductivity of superlattices is strongly reduced as compared to the thermal conductivity of the individual parent materials comprising these multilayered structures due to phonon-scattering and thermal boundary resistances at the superlattice period interfaces. However, given the relatively length scale of the superlattice periods compared to typical phonon wavelengths and mean free paths, the vibrational heat transport in superlattices can give rise to unique phonon scattering processes. For example, partially ballistic and partially diffusive phonon transport in superlattices in which long wavelength phonons effectively do not “see” the interfaces on the order of the superlattice period can occur if superlattice periodicity is short enough. As another example, under certain conditions in which phonon coherence is not destroyed at superlattice interfaces, the emergence of a “minimum” in the superlattice thermal conductivity as a function of interface density can be realized. In this work, we present a series of works on III-V (e.g., GaAs/AlAs) and II-oxide (CaTiO3/SrTiO3) superlattices in which we observe unique phonon thermal transport properties based on measurements of thermal conductivity of these superlattice thin films. First, we will discuss our work on CaTiO3/SrTiO3 superlattices in which we observe coherent phonon transport based on the observation of a minimum in thermal conductivity of superlattice thin films as a function of interface density. When the period thickness decreases to below the phonon coherence length of the phonons in CaTiO3 and SrTiO3, an increase in interface density leads to an increase in thermal conductivity, a phenomenon that indicates a “particle-wave-like” crossover and coherent phonon transport influencing the in phonon thermal conductivity in superlattices. This observation is enabled by the chemically and structurally abrupt nature of the CaTiO3/SrTiO3 interfaces in these superlattices. Next, we will discuss our work on GaAs/AlAs superlattices in which we observe a ballistic-diffusive cross over based on the total thickness of the superlattice. We report on the room temperature thermal conductivity of AlAs-GaAs superlattices (SLs), in which we systematically vary the period thickness and total thickness between 2–24 nm and 20.1–2,160 nm, respectively. The thermal conductivity increases with the SL thickness and plateaus at a thickness around 200 nm, showing a clear transition from a quasiballistic to a diffusive phonon transport regime. These results demonstrate the existence of classical size effects in SLs, even at the highest interface density samples. Our results reveal that the change in thermal conductivity with period thickness is dominated by incoherent (particlelike) phonons in these III-V superlattice films, whose properties are not dictated by changes in the AlAs or GaAs phonon dispersion relations. This work demonstrates the importance of studying both period and sample thickness dependencies of thermal conductivity to understand the relative contributions of coherent and incoherent phonon transport in the thermal conductivity in SLs. “Crossover from incoherent to coherent phonon scattering in epitaxial oxide superlattices,” Nature Materials, 13, 168–172 (2014).“Interplay between total thickness and period thickness in the phonon thermal conductivity of superlattices from the nanoscale to the microscale: Coherent versus incoherent phonon transport,” Physical Review B, 97, 085306 (2018).

Phonon Surface Scattering and Thermal Energy Distribution in Superlattices

Thermal transport at small length scales has attracted significant attention in recent years and various experimental and theoretical methods have been developed to establish the reduced thermal conductivity. The fundamental understanding of how phonons move and the physical mechanisms behind nanoscale thermal transport, however, remains poorly understood. Here we move beyond thermal conductivity calculations and provide a rigorous and comprehensive physical description of thermal phonon transport in superlattices by solving the Boltzmann transport equation and using the Beckman-Kirchhoff surface scattering theory with shadowing to precisely describe phonon-surface interactions. We show that thermal transport in superlattices can be divided in two different heat transport modes having different physical properties at small length scales: layer-restricted and extended heat modes. We study how interface conditions, periodicity, and composition can be used to manipulate the distribution of thermal energy flow among such layer-restricted and extended heat modes. From predicted frequency and mean free path spectra of superlattices, we also investigate the existence of wave effects. The results and insights in this paper advance the fundamental understanding of heat transport in superlattices and the prospects of rationally designing thermal systems with tailored phonon transport properties.

An interfering Monte Carlo method for partially coherent phonon transport in superlattices

Partially coherent phonon transport has been experimentally observed in superlattices. In this paper, a holistic treatment of partially coherent phonon transport is proposed and an interfering Monte Carlo (IMC) method is developed. The IMC method is based on the conventional Monte Carlo (MC) method, but with a particle model that has amplitude and phase information. As such, in addition to diffuse scatterings, wave interference between coherent phonons can also be modeled, resulting in a method that is capable of modeling both particle and wave behavior of the phonons. Numerical study of the cross-plane heat conduction in silicon/heavy silicon superlattices shows that the IMC is able to reproduce the conventional MC results in cases when particle behavior dominates. For cases when wave effects become important, the IMC can also capture wave phenomena that have been experimentally observed or revealed in molecular dynamics simulations.

Anisotropy and boundary scattering in the lattice thermal conductivity of silicon nanomembranes

We present a calculation of the full thermal conductivity tensor for 001, 111, and 011 surface orientations of the silicon-on-insulator SOI nanomembrane, based on solving the Boltzmann transport equation in the relaxation-time approximation with the full phonon dispersions, a momentum-dependent model for boundary scattering, as well as three-phonon and isotope scattering. The interplay between strong boundary scattering and the anisotropy of the phonon dispersions results in thermal conduction that strongly depends on the surface orientation and exhibits marked in-plane vs out-of-plane anisotropy, as well as slight in-plane anisotropy for the low-symmetry 011 SOI. In-plane thermal conductivity is highest along 100 on Si011 and lowest in Si001 due to the strong scattering of the highly anisotropic TA modes with 001 surfaces. The room-temperature in-plane conductivities in 011 and 001 nanomembranes with thicknesses around 10 nm differ by a factor of 2, and the ratio can be much higher at lower temperatures or in rougher samples. We discuss surface facet orientation as a means of tailoring thermal conduction in low-dimensional nanostructrures and address the role of out-of-plane thermal conductivities in predicting vertical phonon transport in superlattices.

Thermal conductivity measurement of InGaAs/InGaAsP superlattice thin films

The thermal conductivities of InGaAs/InGaAsP superlattices with different period lengths were measured from 100 to 320 K using 3θ method. In this temperature range, the thermal conductivities were found to decrease with an increase in temperature. For the period length-dependant thermal conductivity, the minimum value does exist at a certain period length, which demonstrates that at a short period length, superlattice thermal conductivity increases with a decrease in the period length. When the period is longer than a certain period length, the interface thermal resistance dominates in phonon transport. The experimental and theoretical results confirmed the previous predictions from the lattice dynamics analysis, i.e. with the increase in period length, the dominant mechanisms of phonon transport in superlattices will shift from wave mode to particle mode. This is crucial for the cutoff of the phonons and lays a sound foundation for the design of superlattice structures.

Molecular dynamics study of the lattice thermal conductivity of Kr/Ar superlattice nanowires

The nonequilibrium molecular dynamics (NEMD) method has been used to calculate the lattice thermal conductivities of Ar and Kr/Ar nanostructures in order to study the effects of interface scattering, boundary scattering, and elastic strain on lattice thermal conductivity. Results show that interface scattering poses significant resistance to phonon transport in superlattices and superlattice nanowires. The thermal conductivity of the Kr/Ar superlattice nanowire is only about 1 3 of that for pure Ar nanowires with the same cross-sectional area and total length due to the additional interfacial thermal resistance. It is found that nanowire boundary scattering provides significant resistance to phonon transport. As the cross-sectional area increases, the nanowire boundary scattering decreases, which leads to increased nanowire thermal conductivity. The ratio of the interfacial thermal resistance to the total effective thermal resistance increases from 30% for the superlattice nanowire to 42% for the superlattice film. Period length is another important factor affecting the effective thermal conductivity of the nanostructures. Increasing the period length will lead to increased acoustic mismatch between the adjacent layers, and hence increased interfacial thermal resistance. However, if the total length of the superlattice nanowire is fixed, reducing the period length will lead to decreased effective thermal conductivity due to the increased number of interfaces. Finally, it is found that the interfacial thermal resistance decreases as the reference temperature increases, which might be due to the inelastic interface scattering.

Multiscale simulation of phonon transport in superlattices

A particle-based model for phonon transport and the scattering of phonon wave packets at interfaces is developed. The model, which incorporates the interference effects associated with the wave nature of phonons, is parametrized with frequency-dependent scattering rates obtained from molecular-dynamics simulations of the interaction of phonon wave packets with a single interface. From simulations of scattering of phonon wave packets from superlattices, we find that when the interference effects are not included there is qualitative disagreement between the molecular-dynamics and particle simulations. Moreover, we show that such interference effects tend to result in a larger amount of energy being transmitted through a superlattice.

Phonon engineering in nanostructures for solid-state energy conversion

Solid-state energy conversion technologies such as thermoelectric and thermionic refrigeration and power generation require materials with low thermal conductivity but good electrical conductivity, which are difficult to realize in bulk semiconductors. Nanostructures such as quantum wires and quantum wells provide alternative approaches to improve the solid-state energy conversion efficiency through size effects on the electron and phonon transport. In this paper, we discuss the possibility of engineering the phonon transport in nanostructures, with emphases on the thermal conductivity of superlattices. Following a general discussion on the directions for reducing the lattice thermal conductivity in nanostructures, specific modeling results on the phonon transport in superlattices will be presented and compared with recent experimental studies to illustrate the potential approaches and remaining questions.