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Designing nanostructures for interfacial phonon transport via Bayesian optimization
Shenghong Ju, Takuma Shiga, Lei Feng, Zhufeng Hou, Koji Tsuda, Junichiro Shiomi
TL;DR
Controlling nanoscale interfacial thermal conductance is difficult because atomic configurations and multiple-interface interference complicate structure–transport relationships. The paper combines atomistic Green’s function with Bayesian optimization to search Si/Ge interfaces efficiently, identifying non-intuitive aperiodic superlattices whose reduced ITC reflects a balance of competing phonon-transport effects.
Problem
Coupled factors and sensitivity to detailed atomic configurations make ITC controllability difficult, especially for nanostructures with multiple interfaces.
Method
The framework combines atomistic Green’s function and Bayesian optimization to optimize Si/Ge interfacial structures for maximum or minimum ITC.
Results
The method identifies non-intuitive optimal structures, including aperiodic superlattices with ITCs significantly smaller than optimal periodic superlattices.
Takeaways & Limitations
Aperiodic structures achieve small ITC by balancing competing Fabry–Pérot interference and interface-scattering effects.
Abstract
from arXiv · showhide
We demonstrate optimization of thermal conductance across nanostructures by developing a method combining atomistic Green's function and Bayesian optimization. With an aim to minimize and maximize the interfacial thermal conductance (ITC) across Si-Si and Si-Ge interfaces by means of Si/Ge composite interfacial structure, the method identifies the optimal structures from calculations of only a few percent of the entire candidates (over 60,000 structures). The obtained optimal interfacial structures are non-intuitive and impacting: the minimum-ITC structure is an aperiodic superlattice that realizes 50% reduction from the best periodic superlattice. The physical mechanism of the minimum ITC can be understood in terms of crossover of the two effects on phonon transport: as the layer thickness in superlattice increases, the impact of Fabry-Pérot interference increases, and the rate of reflection at the layer-interfaces decreases. Aperiodic superlattice with spatial variation in the layer thickness has a degree of freedom to realize optimal balance between the above two competing mechanism. Furthermore, aperiodicity breaks the constructive phonon interference between the interfaces inhibiting the coherent phonon transport. The present work shows the effectiveness and advantage of material informatics in designing nanostructures to control heat conduction, which can be extended to other interfacial structures.
I. INTRODUCTION
At nanoscale, interfacial thermal conductance controls heat conduction, but coupled, configuration-sensitive factors and interference effects make nanostructure optimization difficult. The paper develops an AGF–Bayesian optimization framework to identify non-trivial structures that maximize or minimize ITC.
- At reduced length scales, ballistic phonon transport makes ITC determine heat conduction through the entire material.
- Reported ITC-tuning factors include roughness, vacancy defects, lattice orientation, nanoinclusions, and interfacial adhesion or bonding.
- Coupled factors and sensitivity to detailed atomic configurations make total ITC controllability difficult to identify.
- Multiple interfaces further complicate optimization because constructive and deconstructive phonon interference and resonance affect heat transport.
- Nanostructure optimization for thermal transport remains in its infancy, motivating effective optimization methods.
- The study combines atomistic Green’s function and Bayesian optimization to identify non-trivial interfacial structures realizing maximum and minimum ITC.
II. METHODOLOGY
The method represents Si/Ge interfacial structures as binary atom configurations, evaluates ITC with atomistic Green’s functions, and schedules calculations through Bayesian optimization. It targets maximum and minimum ITC under fixed composition and periodic-boundary simulation conditions.
- The simulations use a fixed 10.86 Å interfacial thickness, periodic boundary conditions, Tersoff potentials, and a converged 20×20 transverse-k-point grid.
- The interfacial structure contains 16 Si or Ge atoms with a constrained 50% fraction of each material, and the goal is to arrange them for extreme ITC.
- Binary descriptors assign ‘1’ to Ge and ‘0’ to Si, producing 12,870 possible candidates for the 16-atom configuration.
- AGF evaluates each configuration’s ITC from phonon transmission using Green’s functions and lead self-energies.
- The heat current is computed between leads at temperatures T_L and T_R, with ITC obtained in the small-temperature-difference limit.
- Bayesian optimization learns from evaluated descriptor–ITC pairs, predicts remaining candidates, and selects the next structure by expected improvement.
- Repeating candidate selection and ITC evaluation schedules calculations efficiently so the best candidate can be found quickly.
III. RESULS AND DISCUSSIONS
Bayesian optimization identified extreme-ITC Si/Ge structures with far fewer evaluations than exhaustive search, including non-intuitive aperiodic superlattices. Their low ITC arises from balancing layer-thickness interference and interface scattering while suppressing constructive coherence.
- Optimization performance: All optimizations converged within 438 structure calculations, and exhaustive AGF evaluation confirmed the same maximum and minimum structures.
- Optimization performance: ITC maximum-to-minimum ratios are 2.4 for Si-Si and 2.2 for Si-Ge interfaces, showing strong nanostructure dependence.
- Phonon transmission: For frequencies below 3 THz, transmission is nearly structure-independent, whereas higher-frequency transmission strongly depends on interfacial structure.
- Phonon transmission: The maximum-ITC Si-Ge structure behaves like a rough interface and enhances transmission around 4–5 THz and 8–11 THz.
- Optimal structures: The minimum-ITC structures for both interfaces are aperiodic superlattices with layers perpendicular to heat flow, unlike periodic superlattices.
- Mechanism: As layer thickness increases, Fabry–Pérot interference becomes stronger while interface reflection decreases, creating competing effects that determine minimum ITC.
- Optimal structures: Fixed-fraction aperiodic superlattices reduce ITC by 20–50% relative to separately optimized periodic superlattices, while variable fractions reduce it further.
- Mechanism: Aperiodicity balances layer thickness and interface number, suppresses constructive interference, and drives transmission toward the incoherent transport limit.
IV. CONCLUSIONS
The study combines atomistic Green’s function with Bayesian optimization to identify Si/Ge-composite interfacial structures that minimize or maximize ITC using only a few percent of candidates. It finds non-intuitive aperiodic structures with reduced ITC, explained by balancing competing phonon-transport effects and suppressing constructive interference.
- The framework combines atomistic Green’s function and Bayesian optimization to minimize or maximize ITC across Si-Si and Si-Ge interfaces.
- A few percent of the total candidate structures sufficed to identify optimal Si/Ge configurations, considerably saving computational resources.
- The minimum-ITC structures are non-intuitive aperiodic superlattices whose ITCs are significantly smaller than those of optimal periodic superlattices.
- Aperiodic layer-thickness variation provides freedom to balance Fabry–Pérot wave interference against interfacial particle scattering as layer thickness changes.
- The optimal aperiodic structure restrains constructive phonon interference, making phonon transport approach its incoherent limit.
- The method’s effectiveness and advantage are demonstrated for designing nanostructures to control heat conduction, with the search extended to structures up to 8.69 nm.
FIGURES, TABLES AND CAPTIONS
The figures and tables examine optimized Si/Ge superlattice structures, their interfacial thermal conductance, and phonon transmission across interface types and structural parameters.
- The study compares optimized aperiodic and periodic Si/Ge superlattices with bare Si-Si and Si-Ge interfaces.
- The optimized aperiodic superlattice has lower ITC than the corresponding periodic superlattice with optimized period thickness.
- Phonon dispersion, density of states, and transmission are compared for three optimized superlattice structures.
- The reported comparisons include interfacial thermal conductance versus layer thickness, interface number, and Si/Ge composition.
- The supplementary comparisons show that transmission functions can differ substantially while their normalized integrated transmission converges to an almost constant value.
- Transmission functions are also examined for scattering regions with different thicknesses and for interfaces separated by different distances.