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

Ramez Cheaito, Carlos A. Polanco, Sadhvikas Addamane, Jingjie Zhang, Avik W. Ghosh, Ganesh Balakrishnan, and Patrick E. Hopkins

Phys. Rev. B 97, 085306 – Published 20 February 2018

Abstract

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. We use harmonic atomistic Green's function calculations to capture incoherence in phonon transport by averaging the calculated transmission over several purely coherent simulations of independent SL with different random mixing at the AlAs-GaAs interfaces. These simulations demonstrate the significant contribution of incoherent phonon transport through the decrease in the transmission and conductance in the SLs as the number of interfaces increases. In spite of this conductance decrease, our simulations show a quasilinear increase in thermal conductivity with the superlattice thickness. This suggests that the observation of a quasilinear increase in thermal conductivity can have important contributions from incoherent phonon transport. Furthermore, this seemingly linear slope in thermal conductivity versus SL thickness data may actually be nonlinear when extended to a larger number of periods, which is a signature of incoherent effects. Indeed, this trend for superlattices with interatomic mixing at the interfaces could easily be interpreted as linear when the number of periods is small. Our results reveal that the change in thermal conductivity with period thickness is dominated by incoherent (particlelike) phonons, 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.

Received 18 June 2017

DOI:https://doi.org/10.1103/PhysRevB.97.085306

Physics Subject Headings (PhySH)

Lattice thermal conductivity Phonons

Superlattices

Nonequilibrium Green's function Thermoreflectance

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ramez Cheaito¹, Carlos A. Polanco², Sadhvikas Addamane³, Jingjie Zhang², Avik W. Ghosh², Ganesh Balakrishnan³, and Patrick E. Hopkins^1,4,5,*

¹Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, Virginia 22904, USA
²Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, Virginia 22904, USA
³Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, New Mexico 87106, USA
⁴Department of Materials Science and Engineering, University of Virginia, Charlottesville, Virginia 22904, USA
⁵Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA

^*Corresponding author: phopkins@virginia.edu

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Issue

Vol. 97, Iss. 8 — 15 February 2018

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Images

Figure 1
Literature data of cross-plane thermal conductivities of AlAs-GaAs and Si-Ge SLs plotted versus $d_{SL}$ in (a) and (c) and versus $L$ in (b) and (d), respectively. Data are taken from Refs. [6, 10] for AlAs-GaAs and Refs. [11, 12, 13] for Si-Ge. Selected data points are labeled by the corresponding value of $L$ in (a) and (c) and the corresponding value of $d_{SL}$ in (b) and (d). All data are at room temperature.
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Figure 2
(a), (b) STEM images on two of the AlAs-GaAs SL samples. (c) Cross-plane thermal conductivity measurements on three sets of AlAs-GaAs SLs of 2, 12, and 24 nm period thicknesses and a set of thin film GaAs samples plotted versus thickness, $L$ , at room temperature. The lines connecting the various data sets are guides to the eye. The figure also shows good agreement between our measurement results on samples with $d_{SL} = 24 nm$ and those by Luckyanova et al. [6]. The inset is a zoomed view of the data for samples with $L < 136$ nm plotted on a linear-linear scale. The solid lines in the inset are linear fits to the plotted data points. (d) Selected data from (c) plotted versus period thickness, $d_{SL}$ . Green left triangles represent $κ_{SL}$ in the diffusive regime obtained by taking average values of thermal conductivities of films with $L > 216$ nm for each data set $d_{SL} = 2$ , 12, and 24 nm and the two data points at $L = 2, 160 nm$ for $d_{SL} = 6$ and 18 nm. The lines are guides to the eye. (e) Thermal conductivity as a function of SL thickness, $L$ , at three different temperatures (100 and 200 K compared to room temperature). The trend at low temperatures is similar to that at room temperature suggesting that the mechanisms of heat transfer are dictated by the sample geometry even though the characteristic length and the mean free path distribution of heat carriers are significantly altered.
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Figure 3
(a) Conductance vs. number of periods for SL with atomically smooth “(S)” and mixed “(M)” interfaces. The decrease in conductance of the SLs with interatomic mixing at the interfaces results from incoherent phonon transport. (b) $M T$ per perpendicular unit cell for SL with atomically smooth “(S)” and mixed “(M)” interfaces. The decrease in $M T$ as the number of periods increases show the corresponding decrease in transmission, which is a signal of incoherent phonon transport. For these calculations, the total sample thickness is set to 12 periods of AlAs-GaAs for each sample regardless of the period. (c) Experimental data replotted as conductance vs. number of periods. The data show that conductance is independent of period for short samples with long periods.
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Figure 4
Thermal conductivity of AlAs-GaAs SLs calculated via our Green's function analysis $(κ_{SL, GF})$ vs. number of periods for SLs with atomically smooth “(S)” and mixed “(M)” interfaces. For SLs with perfect interfaces, the slope is nearly independent of the period. For SLs with mixed interfaces, the slope seems linear in spite of incoherent phonon transport. We note that this calculated value for $κ_{SL, GF}$ does not include phonon-phonon interactions.
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