Heat conduction in semiconductor nanostructures can in principle be controlled through the wave nature of thermal phonons — interference, band folding, and phononic band gaps — rather than through particle-like scattering alone. Whether and when this coherent regime can be reached and exploited, however, remains unsettled: coherent thermal-conductivity tuning has been demonstrated only below about 10 K in silicon phononic crystals; at room temperature, measured conductance reductions in lithographic nanostructures are largely attributed to incoherent boundary scattering; engineered interference stop bands in matrices with embedded nanoparticle arrays have been computed only in the zero-temperature harmonic limit; and the empirical coherence-cutoff relations used to interpret experiments lack a first-principles basis. Establish a predictive, experimentally validated account of coherent thermal-phonon transport: (1) the microscopic mechanisms and quantitative parameter conditions of the crossover between particle-like and wave-like heat conduction; (2) a quantitative, mode-resolved separation of coherent from incoherent contributions in measured nanostructures at finite temperature and realistic disorder; and (3) a demonstration of deliberate coherent control of thermal conductance — most demandingly at room temperature. Work from 2019–2026 (unified Wigner-transport theory, coherence-time formalisms, spectroscopic coherence assessment, and the first direct observation of coherently modulated phonon bands at 300–500 K in short-period superlattices) has substantially advanced the theory and evidence base but has not closed the separation and engineering question for the nanostructures at issue.

Background

In electrically insulating and semiconducting solids, heat is carried by phonons, the quantized normal modes of the crystal lattice. The textbook description is the phonon-gas picture, formalized by the Boltzmann transport equation (BTE): thermal phonons behave as particles that stream between scattering events — at rough boundaries, defects, and other phonons — each mode characterized by a wavelength and a mean free path (average distance traveled between scattering events). This particle picture becomes inadequate when the phonon wavelength is comparable to the period of a deliberately periodic nanostructure: the phonon waves then interfere, the vibrational dispersion folds into minibands, and frequency gaps can open. An artificial periodic structure engineered for this purpose is a phononic crystal, the acoustic analogue of a photonic crystal; a two-dimensional hole array etched through a suspended membrane is the canonical semiconductor realization, and the same physics appears in superlattices (periodic multilayers of two materials, e.g. GaAs/AlAs) and in nanomeshes (membranes perforated with dense hole lattices). Heat conduction that is shaped by such interference is called coherent or wave-like, in contrast to incoherent or particle-like conduction, in which each boundary or interface merely scatters phonons as particles.

The question of when heat conduction crosses over between these regimes has a long lineage. Simkin and Mahan (2000) predicted that alloy disorder in superlattices destroys wave-like interference and forces particle-like conduction, producing a minimum of the lattice thermal conductivity versus period. Luckyanova et al. (2012) demonstrated coherent phonon heat conduction in GaAs/AlAs superlattices and its destruction by alloy disorder, and Ravichandran et al. (2014) tuned the incoherent-to-coherent crossover at room temperature in epitaxial oxide superlattices. For lithographic semiconductor phononic crystals the situation is more contentious: Ravichandran and Minnich (2014) showed by frequency-dependent BTE simulation that room-temperature transport in fabricable silicon nanomeshes is dominated by incoherent boundary scattering, and Wagner et al. (2016) measured that phonon modes remain coherent only below a cutoff frequency of order tens of GHz in two-dimensional phononic crystals — roughly 50 GHz in ordered arrays and 20 GHz in disordered ones — with the cutoff degrading as hole-position disorder and surface roughness grow. Maire et al. (2017) then demonstrated thermal-conductivity tuning by hole-array order in silicon phononic crystals, with the coherent, order-dependent effect present below about 10 K and absent at 300 K; their interpretation rests on an empirical coherence-cutoff relation taken from Wagner et al. rather than a derived law, and the coherence of the low-frequency phonon population is assumed, not measured mode by mode. Liao et al. (2018) identified the Akhiezer mechanism — the damping of a phonon by the bath of all other thermal phonons — as the microscopic channel that limits coherent heat conduction in phononic crystals as temperature rises.

Two further source results frame the engineering side. Hu et al. (2020) used the atomistic Green's function method (an exact calculation of phonon transmission through a harmonic lattice region attached to ideal leads) and wave-packet molecular dynamics (simulations that launch a localized phonon wave packet and track its scattering) to show that Ge nanoparticles embedded in a silicon matrix produce sharp two-path destructive-interference resonances that coalesce into a stop band — a frequency interval of near-total phonon reflection — without requiring strict periodicity; but all their calculations are harmonic, with wave-packet amplitudes deliberately kept small to avoid anharmonicity, so finite-temperature persistence is untested. Zhang et al. (2019) patterned two-dimensional phononic-crystal hole arrays into the suspended GaAs beams of MEMS bolometers (microelectromechanical uncooled thermal detectors whose responsivity improves as the beam thermal conductance falls), gaining a factor of 2–3 in thermal sensitivity, but interpreted the conductance reduction with diffusive finite-element continuum calculations whose validity at sub-micron neck widths is undetermined.

On the theory side, Simoncelli, Marzari, and Mauri (2019, 2022) developed a unified first-principles framework — the Wigner formulation of thermal transport — that treats particle-like (Boltzmann) and wave-like (coherent tunneling) contributions on the same footing; Zhang et al. (2022) derived a thermal-conductivity expression incorporating phonon coherence times and lifetimes; and Di Lucente et al. (2023) defined a quantitative descriptor of the Boltzmann-to-Wigner crossover and applied it to filled skutterudite thermoelectrics. Yet field reviews by the source community (Xie et al. 2018; Zhang et al. 2021; Anufriev et al. 2021; Nomura et al. 2022) describe the separation of wave-like from particle-like contributions as an open controversy in which methodology-dependent conclusions, interface roughness, mass disorder, structural randomness, aperiodicity, and temperature remain uncontrolled — and very recent work (Huang et al. 2026) still debates whether band folding or intrinsic temporal coherence dominates the thermal effect in short-period superlattices.

Problem Statement

Establish a predictive and experimentally validated account of coherent (wave-like) thermal phonon transport in low-dimensional and nanostructured semiconductors, jointly comprising three linked targets. (1) Crossover mechanism and parameter conditions: identify the microscopic mechanisms and the quantitative conditions — temperature, surface roughness and positional disorder, feature size relative to the dominant thermal-phonon wavelengths and mean free paths, and structural period — under which heat conduction crosses over between particle-like and wave-like behavior, replacing the empirical coherence-cutoff relation (a cutoff frequency fc set by the sound velocity divided by a disorder-and-roughness length, of the form fc ≈ 0.043 vL/R used in the phononic-crystal literature) with a first-principles account of thermal and disorder-induced decoherence. (2) Quantitative separation: provide a mode-resolved procedure, applicable to measured nanostructures at finite temperature and realistic disorder, that quantitatively splits the thermal conductance into the coherent contribution (phonon interference, band folding and gaps, two-path resonances and stop bands, hybridization of inclusion resonances with matrix modes) and the incoherent contribution (boundary and diffuse scattering, geometric conduction-area and density-of-states reduction). (3) Predictive engineering: demonstrate a nanostructure designed from that account whose thermal conductance at room temperature — the most demanding and practically relevant case, as required for thermal management, thermoelectrics, and MEMS bolometric detection — is set by coherent phonon interference, with quantitative agreement between first-principles prediction and measurement. These targets form one objective, not independent deliverables: the separation (2) supplies the evidence on which the mechanism (1) is tested, and the mechanism supplies the design rules that the demonstration (3) must exercise. Concrete instances left open by the source literature: whether the two-path phonon-interference stop band of a Ge-nanoparticle array embedded in Si — established only in zero-temperature harmonic atomistic Green's function and wave-packet calculations — survives anharmonicity at finite temperature and real fabrication disorder; and whether coherent phonon effects or purely diffusive continuum modeling govern the conductance of phononic-crystal MEMS beams with sub-micron neck widths. An account developed for particular materials classes or device geometries must be shown to generalize through the stated parameter conditions.

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