Experiments on strain-compensated InAs/AlAs superlattices (alternating layers whose lattice strains cancel over each period) with atomic-monolayer periods demonstrated coherent, wave-like phonon heat conduction up to 500 K, with first-principles calculations matching the measured thermal conductivity only after introducing a simplified uniform 5% interfacial mixing of In and Al atoms. The open problem is the quantitative, predictive accounting of realistic interfacial imperfections — non-uniform and graded mixing, atomic-scale roughness, disordered periodicity, and point and extended defects — in coherent phonon transport: how such disorder modifies phonon coherence lengths, mode-resolved lifetimes and mean free paths, the cross-plane thermal conductivity and its dependence on period and temperature, and the balance between wave-like tunnelling and particle-like scattering. The required deliverables are atomistic models of real interface structure validated by direct comparison with measurements on structurally characterized samples, and the disorder limits of coherence in device-relevant regimes.

Background

Heat in semiconductors and insulators is carried mainly by phonons, the quanta of lattice vibration. In a superlattice — a crystal grown as a periodic stack of ultrathin layers of two materials, here InAs and AlAs deposited one to five atomic monolayers (ML) at a time by molecular beam epitaxy (MBE, an ultrahigh-vacuum beam technique that controls layer thickness to single atomic planes) — heat flowing across the layers can be transported in two qualitatively different ways. In incoherent, particle-like transport, each interface scatters phonons like a diffuse wall, so the cross-plane thermal conductivity falls as interfaces are added. In coherent, wave-like transport, phonons traverse many interfaces with their phase preserved, so the stack behaves as a phononic crystal (an artificial periodic medium for phonons): the vibrational spectrum is folded into mini-bands separated by mini band gaps, and at periods of roughly a nanometre phonon tunnelling through thin barriers can raise rather than lower the conductance. The standard experimental signatures are a minimum of the thermal conductivity as a function of superlattice period (marking the crossover between the two regimes) and a conductivity that increases as the period shrinks below the phonon coherence length (the distance over which a phonon maintains a definite phase, so that successive interfaces interfere rather than scatter independently). The relevant microscopic quantities are the phonon mean free path (MFP, the product of group velocity and lifetime), the mode-resolved lifetime (limited by anharmonic phonon-phonon Umklapp scattering, which strengthens with temperature), and the fraction of heat carried by long-wavelength phonons. Thermal conductivity is measured contactlessly by time-domain thermoreflectance (TDTR), which tracks the cooling of a laser-heated metal film deposited on the sample.

The theory predates the experiments: transfer-matrix calculations of phonon wave heat conduction predicted conductance enhancement by tunnelling at sub-nanometre layer thickness (G. Chen, 1999), and the conductivity minimum marking the incoherent-to-coherent crossover was predicted by Simkin and Mahan (2000), who also showed that interface roughness erases the minimum. Molecular-dynamics studies then quantified how idealized imperfections degrade transport: interfacial roughness (Chen et al., 2005) and uniform interfacial species mixing (Landry and McGaughey, 2009). Experimentally, coherent heat conduction was demonstrated in GaAs/AlAs superlattices at low temperature (Luckyanova et al., 2012) and in perovskite oxide superlattices at room temperature (Ravichandran et al., 2014).

Geng et al. (2024) pushed the phenomenon into a regime of direct device relevance. In strain-compensated InAs/AlAs superlattices (InAs and AlAs layers carry opposite signs of lattice strain, combined so that the accumulated strain cancels over each period) with periods from 1/1 to 5/5 ML — a record interface density — the cross-plane thermal conductivity rises as the period shrinks, grows linearly with the number of periods for the 1/1 and 2/2 ML stacks, and maintains this coherent trend from 100 K up to 500 K, because low-frequency phonons below about 4 THz carry more than 90% of the heat. First-principles (density-functional) phonon Boltzmann transport calculations — which solve the semiclassical transport equation mode by mode, with scattering lifetimes computed from first principles — reproduce the trends and show that band folding lowers not only the phonon group velocity (a wave effect) but also the phonon lifetime (a scattering effect), a direct manifestation of phonon wave-particle duality. Crucially, however, the calculations agree with the measured conductivity quantitatively only after a uniform 5% mixing of In and Al atoms in the interfacial layers is introduced as an effective imperfection. The authors caution that practical interfacial imperfection is considerably more complicated than this single parameter — growth also produces roughness, graded composition, and point and extended defects — and that these additional imperfections lower the thermal conductivity further. Quantifying the effect of realistic disorder on coherent phonon transport is the open problem this work leaves behind.

Problem Statement

Determine quantitatively how realistic interfacial imperfections and material defects modify coherent phonon transport in semiconductor superlattices, as left open by the InAs/AlAs experiments of Geng et al. (2024). Concretely: (i) construct predictive atomistic models of real superlattice interfaces that go beyond a single uniform mixing parameter — incorporating non-uniform and graded mixing profiles, atomic-scale roughness, disordered periodicity, and point and extended defects in the layers; (ii) use them to compute how each class of imperfection modifies the cross-plane thermal conductivity and its dependence on period length and temperature up to the device-relevant range of about 500 K, the phonon coherence length, the mode-resolved lifetimes, mean free paths and group velocities, and the balance between wave-like tunnelling and particle-like interface scattering; and (iii) validate the account by direct quantitative comparison with experimental measurements on structurally characterized samples, thereby establishing the limits within which phonon coherence survives realistic growth-related disorder. All three components (i)–(iii) are required, and each class of imperfection is to be characterised by the full set of quantities listed in (ii); together they serve one overarching objective — a validated quantitative accounting of disorder in coherent phonon transport. The problem is complete when that account, computed from the modelled real interface structure rather than a fitted uniform mixing parameter, quantitatively reproduces the measured cross-plane thermal conductivity of the structurally characterized InAs/AlAs stacks of Geng et al. (2024) and its dependence on period length and temperature — agreement being judged by the trend and magnitude of those measured dependences — and thereby accounts for the residual deviation between ideal-interface calculations and experiment that the 5% mixing parameter currently absorbs.

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