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Analyzing coherent phonon mode-conversion in gradient superlattices with atomistic wave-packet simulations

Evan Wallace Doe, Theodore Maranets, Yan Wang

Abstract

In this study, we have used atomistic phonon wave-packet simulations to investigate the manifestation of coherent phonons and phonon transmission in gradient superlattices (SL) based on ordered arrangements of varied SL period sizes. We specifically explore how coherent mode-conversion in these quasi-periodic structures changes as function of three key structural parameters: (1) the number of distinct period sizes, (2) the number of periods present for each distinct period size, and (3) the arrangement of period sizes in either an ascending or descending arrangement. Comparisons to periodic SLs and aperiodic SLs are highlighted, revealing that coherent phonons in gradient SLs generally exhibit behaviors characteristic of intermediate states between the fully ordered and disordered structures. Interestingly, changes to the short-range order of GMLs does not significantly influence transmission, indicating that long-range disorder is far more important to coherent mode-conversion. Our results indicate that manipulating the long-range disorder of interfaces could be an effective strategy to tailor phonon thermal conductivity of SL architectures.

Analyzing coherent phonon mode-conversion in gradient superlattices with atomistic wave-packet simulations

Abstract

In this study, we have used atomistic phonon wave-packet simulations to investigate the manifestation of coherent phonons and phonon transmission in gradient superlattices (SL) based on ordered arrangements of varied SL period sizes. We specifically explore how coherent mode-conversion in these quasi-periodic structures changes as function of three key structural parameters: (1) the number of distinct period sizes, (2) the number of periods present for each distinct period size, and (3) the arrangement of period sizes in either an ascending or descending arrangement. Comparisons to periodic SLs and aperiodic SLs are highlighted, revealing that coherent phonons in gradient SLs generally exhibit behaviors characteristic of intermediate states between the fully ordered and disordered structures. Interestingly, changes to the short-range order of GMLs does not significantly influence transmission, indicating that long-range disorder is far more important to coherent mode-conversion. Our results indicate that manipulating the long-range disorder of interfaces could be an effective strategy to tailor phonon thermal conductivity of SL architectures.
Paper Structure (11 sections, 4 equations, 5 figures)

This paper contains 11 sections, 4 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Methodology
  3. Material system
  4. Superlattice architectures
  5. Wave-packet simulations
  6. Results
  7. Number of periods for each period size
  8. Number of different period sizes
  9. Ascending vs. descending layer patterns
  10. Discussion
  11. Conclusion

Figures (5)

  • Figure 1: Schematic illustrations of wave-packet simulations domains for: (a) an ascending gradient multilayer (GML) device with 4 different SL period sizes and 4 periods for each period size, (b) a descending GML device with 4 different SL period sizes and 4 periods for each period size, (c) a periodic SL device, and (d) an aperiodic SL device. $k_0$ denotes the central wavevector of the incident LA-mode incoherent phonon wave-packet. The phonon wave-packet is generated in the left contact and is allowed to propagate into the device over the duration of the simulation. The total energies of the left and right contacts and the device are monitored to compute the energy transmission across the device using Eqn. \ref{['eqn:transmission_calc']}. Illustrations of the wavelength and spatial coherence length for the wave-packet are not to scale.
  • Figure 2: Transmission $\mathcal{T}$ versus wavevector $k$ for longitudinal-acoustic (LA) incoherent phonon wave-packets propagating through gradient multilayer (GML) and random multilayer (RML) devices. Transmission is computed using Eq. \ref{['eqn:transmission_calc']}. The GMLs are categorized by the number of distinct period sizes $N_s$ and the number of periods included for each period size $N_p$. For each 4-$N_p$ configuration, we compare the transmission spectra to that of an RML with equivalent length. Select wavevectors $k_1$, $k_2$, and $k_3$ investigated in reciprocal-space wavelet transforms in Fig. \ref{['fig:gml_wavelet']} are marked.
  • Figure 3: Snapshots of the reciprocal-space wavelet transform for $k_1$, $k_2$, and $k_3$ as the incoherent phonon wave-packets propagate through the GML devices of several configurations of $N_p$ for $N_s=7$. The dotted vertical lines indicate the position and boundaries of the GML device. Arrows and text labels identify the wavevector of the incident incoherent phonon as well as the coherent mode-conversion inside the device maranets2024prominent.
  • Figure 4: Snapshots of the reciprocal-space wavelet transform for $k_1$ as the incoherent phonon wave-packets propagate through the GML devices with $N_s=3$, 5, and 7 for differing $N_p$. The dotted vertical lines indicate the position and boundaries of the GML device. Arrows and text labels identify the wavevector of the incident incoherent phonon as well as the coherent mode-conversion inside the device maranets2024prominent.
  • Figure 5: Transmission $\mathcal{T}$ versus wavevector $k$ for longitudinal-acoustic (LA) incoherent phonon wave-packets propagating through gradient multilayer device of $N_s=7$ and $N_p=8$ in ascending vs. descending layering patterns. A comparison of simulation domains is visualized in Fig. \ref{['fig:SL-GML-RML']}a-\ref{['fig:SL-GML-RML']}b. Transmission is computed using Eq. \ref{['eqn:transmission_calc']}.