Thermal conductivity and optical phonon scattering of CMOS compatible aluminum nitride based ferroelectric thin films

Abstract

The emergence of ferroelectricity in doped aluminum nitride has positioned wurtzite nitrides as promising candidates for next-generation memory and logic devices. However, the structural modifications required to induce and stabilize ferroelectricity, including changes in bond strength, harmonicity, and crystal order, also affect phonon dynamics, creating competing pathways for polarization reversal and thermal transport. In this work, we report the contrasting roles of dopants in governing ferroelectric and thermal properties in Al_1-xB_xN and Al_1-x-yB_xSc_yN thin films where changes in composition and thickness are explored. Using time-domain thermoreflectance, the thermal conductivity reveals dopant-driven transitions between phonon-phonon, phonon-impurity, and defect-induced scattering regimes. Infrared variable-angle spectroscopic ellipsometry provides access to optical phonon lifetimes, and we show a monotonic relationship between cross-plane transverse optical phonon lifetime and cross-plane thermal conductivity measured by time-domain thermoreflectance, indicating that infrared ellipsometry can serve as a system-specific spectroscopic probe of disorder-induced vibrational damping in these aluminum nitride based ferroelectric films. The findings demonstrate that while disorder can reduce coercive fields, the same mechanism simultaneously suppresses lattice thermal conductivity, underscoring the inherent trade-off between ferroelectric performance and thermal management. This work highlights the dual, and at times conflicting, role of dopants in aluminum nitride based ferroelectrics that shape both electronic and thermal responses, defining thermal-design constraints for integrated thermally resilient electronic systems.

The authors show how boron and scandium reshape phonon scattering in aluminum nitride ferroelectrics, linking optical phonon lifetimes to thermal conductivity and revealing a key tradeoff between switching behavior and heat transport.

Introduction

The rapid growth of the Internet of Things (IoT) and big data has exposed the limitations of conventional von Neumann architectures, particularly the memory wall arising from the physical separation of logic and memory units. This bottleneck increases latency, energy consumption, and signal delays¹. In response, emerging computing paradigms such as in-memory-compute and neuromorphic architectures seek to co-locate memory and logic, reducing data transfer overhead and improving energy efficiency^2–4.

Wurtzite-based ferroelectrics, notably aluminum scandium nitride (Al_1-xSc_xN), aluminum boron nitride (Al_1-xB_xN) and aluminum scandium boron nitride (Al_1-x-yB_xSc_yN), are among the materials investigated for next-generation memory and logic technologies due to their CMOS compatibility, low deposition temperatures, and suitability for back-end-of-line integration^5–9. However, while deposition directly on Si is reported, scalability and etch capabilities are still under development^5,9–13. Their ferroelectric properties, characterized by large coercive fields and large remanent polarizations, offer potential for scalable non-volatile memory devices (e.g., ferroelectric random access memory, FeRAM), with high retention particularly under radiation and in high-temperature environments^4,9,14–16.

The practical implementation of these materials raises thermal management constraints. Ferroelectric switching dissipates instantaneous heat generated on polarization reversal and set by the area enclosed by the polarization-electric field (P–E) loop^17–19. Additionally, the compositional alloying that facilitates ferroelectricity often disrupts phonon transport and lowers thermal conductivity, increasing the risk of localized thermal hotspots and long-term reliability degradation. As such, investigating the vibrational thermal transport in aluminum nitride-based ferroelectrics on silicon is not only fundamental to advancing FeRAM technologies, but also critical to the broader effort of engineering the energy-efficient, thermally resilient computing systems.

These constraints are particularly important for wurtzite nitride ferroelectrics, which combine large remanent polarization with coercive fields that are often in the MV cm⁻¹ range^{4–6,14–16,20}. Reaching low switching voltages therefore requires nanoscale active layers, while the energy dissipated during reversal is set by the area of the polarization-electric field loop with additional contributions from leakage, electrode resistance, and, in transistor geometries, channel current. A single operating current density is not transferable across FeRAM, FeFET, and tunnel-junction architectures; instead, the relevant thermal design parameters are the switching energy density, leakage, active-layer thickness, cross-plane thermal conductivity, and the thermal boundary resistances of the adjacent interfaces. Because leakage and switching kinetics are temperature dependent²⁰, and array-level thermal crosstalk can exceed single-bit heating in nanoscale Al_1-xB_xN memory simulations¹⁴, the measured decrease in thermal conductivity with alloying is not merely a materials-property trend, but a device-level reliability and voltage-scaling constraint.

Given the thermal bottlenecks of most conventional ferroelectric materials driven by their intrinsically low thermal conductivities as overviewed in Fig. 1(a), the search for high thermal conductivity ferroelectric materials is challenging. To this end, in 1973, Slack proposed criteria for achieving high lattice thermal conductivity, emphasizing the importance of maximizing phonon group velocities while suppressing intrinsic resistive scattering processes^21,22. These criteria translate to: (i) low atomic mass, (ii) strong interatomic bonding, (iii) simple crystal structure, and (iv) low anharmonicity in the material. Within this framework, materials composed of light elements forming strong (predominantly) covalent bonds in structurally simple lattices are particularly favorable for efficient phonon transport. As shown in Fig. 1(a), most ferroelectric materials would not fall into this category. However, with the emergence of wurtzite ferroelectrics, these Slack criteria can be partially satisfied given the presence of Al–N bonds, as both aluminum and nitrogen are light elements that form highly directional, stiff, largely covalent bonds. These structural and chemical features promote high phonon velocities and suppress phonon-phonon scattering, in agreement with Slack’s model for Al_1-xB_xN samples with low boron concentrations.

Fig. 1. Composition dependent thermal transport in wurtzite aluminum nitride ferroelectrics.

a The Ashby plot of thermal conductivity versus remnant polarization, P_r, for various ferroelectric materials (ref. ⁴): Thermal conductivity of Al_1-xB_xN (“AlBN”, measured in this work and (ref. ¹⁴); Hf_1-xZr_xO₂ (“HZO”, ref. ⁵⁹); In₂Se₃ (ref. ⁶⁰); PbZr_1-xTi_xO₃ (“PZT”, refs. ^61–63); polyvinylidene fluoride (“PVDF”, refs. ^64,65); Al_1-xSc_xN (“AlScN”, ref. ¹⁵); BaTiO₃ (“BTO”, refs. ^66–69). Within the literature comparison shown in panel (a), Al_1-xB_xN ferroelectrics exhibit the largest thermal conductivity values. b Schematic of Al_1-xB_xN and Al_1-x-yB_xSc_yN sample geometry and pump-probe experiment. c Room temperature thermal conductivity of Al_1-xB_xN and Al_1-x-yB_xSc_yN as a function of boron concentration, x. Data from Kang et al¹⁴. from ~400 nm Al_1-xB_xN films on sapphire substrate is presented for comparison. d Sound velocity in Al_1-xB_xN and Al_1-x-yB_xSc_yN as a function of boron concentration, x. Error bars in (c) and (d) represent measurement uncertainties described in the Supplementary Information.

This framework is useful as a qualitative starting point for lightly substituted Al_1-xB_xN because the Al-N backbone is retained and the films remain strongly textured wurtzite nitrides. The Slack criteria are used here as qualitative motivation for why the AlN parent lattice provides an comparatively high thermal conductivity baseline. First-principles calculations and thermal measurements on crystalline AlN show that its high thermal conductivity originates from stiff bonding, high acoustic group velocities, and long mean-free-path acoustic phonons, while vacancies, impurities, and alloy disorder strongly reduce thermal conductivity^23–27. The present data are consistent with this picture. Lightly boron-substituted AlN retains a comparatively high conductivity among ferroelectric thin films, while increased boron and scandium incorporation progressively introduces mass disorder, bond-length disorder, and microstructural disorder that reduce phonon mean free paths. Thus, the Slack criteria explain why AlN-based ferroelectrics begin from an unusually favorable thermal-transport baseline.

Results and discussion

To examine composition-dependent thermal conductivities in wurtzite ferroelectrics, six boron-substituted Al_1-xB_xN samples with boron concentrations x ≤ 0.01, 0.02, 0.06, 0.08, 0.13, and 0.17 and five Al_1-x-yB_xSc_yN samples with boron concentrations x ≤ 0.01, 0.02, 0.06, 0.08, and 0.13 and a scandium concentration y = 0.2 are investigated. The thermal conductivities of the Al_1-xB_xN and Al_1-x-yB_xSc_yN samples are measured at room temperature and at elevated temperatures up to 400 °C using time-domain thermoreflectance (TDTR)^28–30. The schematic of the TDTR measurement and the sample geometry is shown in Fig. 1(b). Under the present spot sizes and modulation frequency, the TDTR signal is dominated by through thickness heat flow. The reported film conductivities are therefore cross plane values.

Figure 1(c) presents the room-temperature thermal conductivity as a function of composition for Al_1-xB_xN and Al_1-x-yB_xSc_yN on n-type Si. The thermal conductivities span from 33 ± 7 W m⁻¹ K⁻¹ for Al_0.99B_0.01N, with further reductions observed at higher dopant concentrations. Specifically, Al_0.83B_0.17N exhibits a thermal conductivity of 3.7 ± 1.7 W m⁻¹ K⁻¹, while Al_0.67B_0.13Sc_0.2N reaches 2 ± 1.8 W m⁻¹ K⁻¹. For comparison, data from Kang et al.¹⁴ on ~400 nm Al_1-xB_xN films grown on Al₂O₃ substrates are also included. The two datasets show the effect of dopant concentration on the reduction of the thermal conductivity of these films. Within the ferroelectric materials grown directly on silicon and literature values compared in Fig. 1(a), Al_1-xB_xN films lie at the upper end of the reported thermal conductivity range. The observation of such high thermal conductivity is consistent with theoretical expectations by Slack discussed above.

The lattice thermal conductivity is described within the framework of kinetic theory as κ = (1/3)Cvℓ, where C represents the volumetric heat capacity, v the average phonon group velocity, and ℓ the phonon mean free path (MFP). This expression underscores that any substantial reduction in κ must arise from modifications to one or more of these underlying parameters. To explicitly quantify such contributions, picosecond ultrasonics were employed to measure the longitudinal acoustic velocity. As shown in Fig. 1(d), the cross plane longitudinal sound velocity decreases by ~18% as the total dopant concentration increases from 1% to 33%. This decrease is not negligible because acoustic velocity influences both the harmonic spectrum and intrinsic scattering rates. In Debye Slack descriptions, these combined effects can yield an approximate κ proportional to v³ sensitivity, although that limit assumes a branch averaged velocity and predominantly intrinsic phonon–phonon scattering. Our present work resolves only the cross plane longitudinal branch, and the measurement temperatures remain below the Debye temperature of crystalline AlN. Even when the v³ relation is used as a sensitivity estimate, the measured velocity decrease corresponds to a conductivity reduction of ~45%, which is smaller than the nearly 90% decrease measured across the Al_1-xB_xN series. The remaining suppression therefore requires a substantial reduction in phonon mean free path from alloy, defect, and microstructural scattering³¹. This kinetic expression is used here to organize the dominant physical contributions to the measured thermal conductivity, rather than as a complete microscopic transport model. A fully quantitative treatment would require spectral phonon transport calculations, such as first-principles Peierls-Boltzmann transport with composition-dependent force constants and realistic defect scattering.

The reduction in phonon MFP originates from enhanced scattering processes that intensify with increasing dopant concentration. Substitutional incorporation of boron and scandium into the AlN lattice introduces perturbations in both mass and bond geometry. The B–N bond length ( ~ 1.57 Å)^32,33 is shorter than the Al–N bond ( ~ 1.91 Å)^34,35, while the Sc–N bond ( ~ 2.12 Å)^35–37 is longer. These disparities in atomic mass and bond geometry generate local strain and lattice distortions, thereby increasing the overall structural disorder. These local mass and force-constant perturbations increase phonon scattering rates and reduce the mean free paths of heat-carrying modes. Thus, as impurity concentration increases, impurity-limited scattering (ℓ_impurity) progressively dominates, reducing thermal conductivity^14,15,38. We note that substituting lighter B for Al might be expected to increase acoustic velocity, but B incorporation also contracts the wurtzite unit cell and modifies the elastic constants^5,6. Because the density depends on both average mass and unit-cell volume, these effects can partially compensate. The measured acoustic velocity also probes only the cross-plane longitudinal branch and has uncertainties that are too large to resolve the small velocity increase that might be expected from local optical-mode hardening alone. We therefore use sound-speed measurements as an experimental constraint on the acoustic spectrum, rather than as a complete description of all heat-carrying branches. The large residual decrease in thermal conductivity beyond any plausible velocity effect requires strong mean-free-path suppression from substitutional disorder, force-constant disorder, and microstructural scattering.

To gain insight into the fundamental mechanisms driving the thermal conductivity of these wurtzite ferroelectrics, phonon lifetimes and infrared absorption spectra of all samples were characterized using infrared variable-angle spectroscopic ellipsometry (IR-VASE)^39,40. The films were modeled with separate in-plane and cross-plane dielectric functions, allowing the optical phonon linewidths and lifetimes to be extracted along the two principal directions of the wurtzite film. The cross-plane response primarily captures the A₁(TO) mode, while the in-plane response captures the E₁(TO) mode and a disorder-activated B₁-related feature. This separation is important because the TDTR measurements are most sensitive to cross-plane heat flow through the thin films. A detailed description of the experimental setup and measurement procedures is provided in the Supporting Information. The anisotropic imaginary dielectric functions (ε₂) for the Al_1-xB_xN and Al_1-x-yB_xSc_yN films are shown in Fig. 2(a) and 2(b), respectively.

Fig. 2. Infrared optical response and thermal conductivity across composition.

Imaginary parts, ε₂, of anisotropic infrared dielectric responses of (a) Al_1-xB_xN and (b) Al_1-x-yB_xSc_yN. Peaks in the in-plane and cross-plane imaginary parts correspond to E₁ and A₁ transverse optical phonon modes, respectively. The in-plane response includes the disorder-activated B₁ feature in the range of 500–600 cm⁻¹. The optical modes of the ferroelectrics with higher dopant concentration are broader, indicating greater anharmonicity from defect scattering. c Polarization hysteresis progression of ~200 nm Al_1-xB_xN (top) and Al_1-x-yB_xSc_yN films (bottom) with increasing B composition. d, e Thermal conductivity versus cross-plane A₁(TO) phonon lifetime of (d) Al_1-xB_xN and (e) Al_1-x-yB_xSc_yN. A monotonic relationship is observed between the extracted phonon lifetimes and independently measured room-temperature thermal conductivities. Increasing boron and scandium content broadens the phonon resonances, shortens the extracted lifetimes, and suppresses thermal conductivity. Error bars in (d) and (e) represent measurement uncertainties described in the Supplementary Information.

At the Γ-point of the Brillouin zone, the optical phonon modes of wurtzite AlN decompose according to group theory as: Γ = A₁ + E₁ + 2E₂ + 2B₁^{35,37,41–43}. Among these, the A₁ and E₁ modes are polar and thus infrared-active, with A₁ polarized along the c-axis and E₁ polarized in the basal plane. The E₂ modes are non-polar and only Raman-active. The B₁ modes are nominally silent in the ideal wurtzite AlN and are inactive in both Raman and infrared spectroscopy. These silent modes typically have a low slope in the phonon dispersion curve and do not significantly contribute to thermal transport or optical activity in pristine AlN. However, the presence of defects, disorder, or strain can break selection rules, enabling weak activation of B₁ modes in experimental spectra^44–49.

As boron concentration increases in Al_1-xB_xN and Al_1-x-yB_xSc_yN films, both principal dielectric responses show a systemic broadening and hardening in the polar TO modes. These mode shifts reflect changes in polar bond stiffness and dynamic charge distribution. Both the A₁ peak in the cross-plane direction and the E₁ peak in the in-plane direction blue shift with increasing the boron contents, while their peak amplitudes are attenuated and the linewidths increase. Similar behavior is observed in the Sc-containing series, although the absolute ε₂ amplitude is lower and the in-plane response is broader. These trends indicate that boron and scandium substitution stiffen selected local bond environments while simultaneously increasing vibrational disorder and phonon damping. The blue shift of the A₁(TO) and E₁(TO) resonances with increasing B content is consistent with prior structural studies showing that B incorporation contracts the AlN-based wurtzite lattice and changes local bond environments^5,6. Because optical mode frequencies depend on both force constants and reduced mass, we interpret the hardening as evidence of local bonding changes rather than as a standalone measurement of macroscopic lattice compression.

These phonon hardening trends occur even though these materials exhibit a reduction in the coercive field (E_c) with increasing substituent concentration^5,6,9. This distinction is important because these ferroelectrics wurtzite structures do not display a conventional Curie temperature and do not follow the soft-mode behavior typical of many perovskite ferroelectrics. The reduction in coercive field is therefore more consistent with a disorder-assisted lowering of the switching barrier than with a softening of a zone-center polar mode. The simultaneous hardening and broadening of A₁ and E₁ modes support this interpretation because the local bonding environment stiffens while the phonon lifetime decreases through enhanced impurity and defect scattering. Previous studies, such as that by Kang et al.,¹⁴ have also reported E₂(high) hardening under similar conditions^50,51.

At higher boron concentrations, a lower wavenumber feature develops in the in-plane dielectric response of both Al_1-xB_xN and Al_1-x-yB_xSc_yNsamples in the range of 500-600 cm⁻¹, located at lower frequencies than the E₁(TO) modes. In the Sc containing series, the feature is shifted to lower wavenumber together with the broader softening of the host optical response. The spectral position of this feature is close to the calculated silent B1 branch of wurtzite nitrides; it evolves systematically with alloy composition, and no secondary crystalline phase is detected by XRD. These observations favor a disorder activated B1 related assignment over a fixed interfacial or secondary phase origin^46,48,52. However, IR-VASE measurements alone do not uniquely determine the mode eigenvector, so we describe the feature as B1 related and consistent with disorder relaxed selection rules rather than as definitive proof of a specific symmetry breaking mechanism.

The B₁-related feature appears over the same composition range in which polarization switching becomes experimentally accessible. This co-occurrence does not establish that the mode causes ferroelectric switching. Instead, both observations are consistent with the broader local structural disorder and symmetry lowering introduced by substitution. We therefore use the B₁-related feature as a spectroscopic marker of the changing vibrational environment, while the reduction in switching barrier is discussed in terms of previously reported changes in bonding, local coordination, and polarization energetics^5,6,9,53.

The TO phonon lifetimes in each direction were extracted by fitting a multi-oscillator dielectric function model to the IR-VASE spectra³⁹. The anisotropic lifetime extraction provides a clearer comparison between optical phonon scattering and thermal transport. In Al_1-xB_xN, the room-temperature cross-plane lifetime decreases from ~400 fs for Al_0.99B_0.01N to ~50 fs for Al_0.83B_0.17N as the TDTR thermal conductivity decreases from ~32 to ~3.8 W m⁻¹ K⁻¹. While the in-plane lifetime follows the same compositional trend, the cross-plane correlation is the more physically direct comparison because TDTR probes heat flow primarily normal to the film plane. This result suggests that the reduction in thermal conductivity is governed mainly by a collapse in phonon lifetime and mean free path, rather than by the small changes in sound velocity shown in Fig. 1(d). Because the TDTR geometry is primarily sensitive to cross-plane heat flow, the thermal-transport comparison is made with the cross-plane A₁(TO) lifetime extracted from the anisotropic IR-VASE model. The E₁(TO) mode and lower-wavenumber B₁-related feature appear in the in-plane dielectric response and is discussed as a marker of disorder-relaxed selection rules, not as a separate contribution to thermal conductivity.

For Al_1-x-yB_xSc_yN, scandium incorporation lowers both the thermal conductivity and the optical phonon lifetimes before additional boron is added. The Al_0.80Sc_0.20N film has a thermal conductivity near 5.8 W m⁻¹ K⁻¹ and a cross-plane lifetime of ~225 fs. With increasing boron concentration to Al_0.67B_0.13Sc_0.20N, the thermal conductivity decreases to ~2 W m⁻¹ K⁻¹, consistent with a decrease in the cross-plane lifetime to ~55 fs. The lower absolute conductivities and shorter lifetimes in the Sc-containing films show that alloy disorder from scandium is already associated with increased phonon scattering, while boron adds further bond-length and mass disorder. Across both material families, the directional lifetime analysis strengthens the interpretation that optical phonon damping is a sensitive metric for the same disorder that suppresses cross-plane thermal conductivity.

The measured A₁(TO) lifetime is not interpreted as the lifetime of the modes that dominate lattice heat conduction. Mode-resolved calculations and measurements on AlN show that most heat is carried by acoustic branches, while optical modes can influence thermal conductivity indirectly through acoustic-optic scattering and through their sensitivity to the same defect landscape that scatters heat-carrying modes^23–26,54. In the present alloy series, the cross-plane A₁(TO) linewidth provides a spectroscopic measure of disorder-induced vibrational damping. Its monotonic covariation with TDTR-measured cross-plane thermal conductivity should therefore be interpreted as a system-specific proxy for the strength of phonon scattering in Al_1-xB_xN and Al_1-x-yB_xSc_yN, not as a universal conversion from optical phonon lifetime to thermal conductivity.

Given the promise of wurtzite AlN-based ferroelectrics for high-temperature applications^4,55, thermal transport and optical behavior of these materials is characterized at elevated temperatures. Thermal conductivity is measured at temperatures up to 400 °C using TDTR, while A₁ phonon lifetimes were extracted at temperatures up to 750 °C. The details of measurements and fitting procedure is provided in the Supporting Information, and the results are presented in Fig. 3(a–b) for Al_1-xB_xN and (c–d) for Al_1-x-yB_xSc_yN films. Three distinct scattering regimes emerge as a function of dopant concentration. Although thermal conductivity could not be reliably resolved above 200 °C for films with total dopant concentrations below 5% due to the thermal resistances of the film interfaces and measured volume of the substrate, complementary IR-VASE measurements up to 750 °C reveal a clear trend of decreasing A₁(TO) lifetime with increasing temperature in these samples, primarily due to increased phonon-phonon scattering. The reduction in thermal conductivity directly reflects a shortening of the phonon mean free path driven by enhanced Umklapp processes (ℓ_Umklapp), consistent with increasing anharmonic phonon-phonon scattering at elevated temperatures.

Fig. 3. Temperature dependence of thermal conductivity and optical phonon lifetime.

Thermal conductivity (left), Cross-plane A1(TO) phonon lifetime, τ_A1, (middle), and product of heat capacity, C, times A₁ lifetime (right) as a function of temeprature for (a) Al_1-xB_xN and (b) Al_1-x-yB_xSc_yN films. Error bars represent measurement uncertainties described in the Supplementary Information.

At midrange doping levels (6% ≤ total dopant concentration (x + y) ≤ ~25%), thermal conductivity becomes nearly temperature independent. Here, phonon-impurity scattering dominates, with substitutional boron and scandium introducing further mass disorder, bond length fluctuations, and dislocation densities⁶. This defect landscape drives the phonon mean free path down, rendering additional temperature-dependent scattering negligible, which is also observed in the behavior of phonon lifetimes.

At the highest total dopant concentrations, the measured thermal conductivity shows a weak increase with temperature. We do not interpret this trend as evidence that acoustic heat-carrying modes are absent at room temperature. Reported AlN phonon dispersions show that the acoustic spectrum lies in an energy range comparable to k_BT between room temperature and 400 °C, so many acoustic modes are already thermally populated^23,24. The films are also not interpreted as metallic; the AlN-based alloys remain wide-band-gap nitride ferroelectrics, and no free-carrier evidence is available that would support a semimetallic transport mechanism. Instead, the weak increase is treated as an apparent trend in a strongly disorder-limited regime, where impurity and microstructural scattering substantially reduce the phonon mean free path and where changes in heat capacity, mode population, and non-propagating vibrational contributions may compete with anharmonic resistive scattering.

To qualitatively examine the competing effects of heat capacity and vibrational lifetime, Fig. 3 presents the temperature dependence of C*τ_A1, where C is the volumetric heat capacity estimated through composition-weighted alloy averaging and τ_A1 is the measured cross-plane A₁-mode lifetime. At low boron concentrations, the decrease in lifetimes with increasing temperature is largely offset by the increase in heat capacity, producing a relatively weak temperature dependence of their product. At high boron concentrations, lifetime remains nearly constant, while heat capacity increases with temperature, causing the product to increase. This evolution is qualitatively similar to the measured thermal-conductivity trend. However, this product should not be interpreted as a quantitative thermal-transport model because it combines the total estimated heat capacity with the lifetime of a single optical phonon mode and does not account for mode-dependent group velocities or the full vibrational spectrum. The comparison instead illustrates how the relative temperature dependences of heat capacity and vibrational lifetime change with boron concentration.

Quantitative separation of these effects at elevated temperatures would require spectral phonon-transport calculations beyond the scope of the present work. In the highly disordered limit, a complete description may also require transport channels beyond the conventional phonon-gas picture. Wigner and unified thermal-transport formulations show that wave-like coupling between vibrational eigenstates can contribute to thermal conductivity in complex or disordered crystals, and that this contribution can increase with temperature^56,57. The present measurements do not isolate such a channel, and we therefore do not assign the high-dopant temperature trend uniquely to either heat capacity or non-phonon-gas transport. Instead, the data motivate future first-principles spectral calculations that include alloy disorder, finite size, and possible Wigner-channel contributions.

To elucidate the effective phonon mean free paths (MFPs) in AlN-based ferroelectrics, a series of Al_0.92B_0.08N thin films with thicknesses ranging from 13 to 199 nm is investigated. It is well established that increasing film thickness leads to changes in microstructure and strain in AlN-based films⁵⁸. To probe thermal transport, the thermal conductivity as well as total thermal resistance across the Al/Al_1-xB_xN /Si interfaces is measured using TDTR. Details of thermal conductivity measurements and uncertainty analyses is provided in the Supporting Information. The TDTR-measured thermal resistance across the film and its boundaries can be described by the following:

$$R_{total}=R_{Al/AlBN}+{\left(\frac{L}{\kappa }\right)}_{AlBN}+R_{AlBN/Si}$$ 1

where κ and L denote the thermal conductivity and thickness of the Al_1-xB_xN film, respectively, and R_Al/AlBN and R_AlBN/Si denote the thermal boundary resistance across the Al/Al_1-xB_xN and Al_1-xB_xN/Si interfaces, respectively. In the analysis, the thermal boundary resistance at the Al_1-xB_xN /Si interfaces is assumed to be 6.25 m² K GW⁻¹²⁴; the Al_1-xB_xN thermal conductivity and the Al/Al_1-xB_xN interfacial resistance is extracted by fitting the TDTR data.

To complement the TDTR measurements, IR-VASE is employed to extract anisotropic optical phonon lifetimes. Figure 4(a) shows the evolution of the imaginary part of the cross-plane dielectric function with increasing film thickness. Figures 4(b) and 4(c) show the thickness dependence of the thermal conductivity, cross-plane A₁ phonon lifetimes, and measured thermal resistance, respectively. The results reveal a systematic increase in phonon lifetime with increasing film thickness. This trend, in conjunction with the observed changes in thermal resistance, underscores the role of microstructural evolution in modulating phonon scattering mechanisms and overall thermal transport behavior^38,58.

Fig. 4. Thickness dependent thermal transport and optical phonon lifetime in Al_0.92B_0.08N.

a The Imaginary part of the cross-plane dielectric function for Al_0.92B_0.08N films with thicknesses from 13 nm to 199 nm. b thermal conductivity and phonon lifetime of Al_0.92B_0.08N at various thicknesses. It can be seen that thermal conductivity at thicknesses ≥ 40 nm approaches a constant value of ~7 W m⁻¹ K⁻¹. c Total thermal resistance of the Al_0.92B_0.08N films with increasing film thickness. Error bars in (b) and (c) represent measurement uncertainties described in the Supplementary Information.

The thickness dependence of the A₁(TO) lifetime is not interpreted as direct boundary limitation of the optical phonon mean free path. Near the Brillouin zone center, the A₁(TO) group velocity is small, so its propagation length is not expected to approach tens of nanometers. Instead, the lifetime trend follows the thickness dependent microstructure. Stacked θ–2θ scans for the entire thickness series zoomed in around the (002) wurtzite reflection are presented in Fig. 5(a), and Fig. 5(b) presents FWHM rocking curve values for the same series, showing that the out-of-plane mosaic spread increases as film thickness decreases. The concurrent increase in mosaic spread and reduction in κ in the ultrathin films indicate that greater defect and orientational disorder increase vibrational damping, while heat carrying acoustic modes may also experience finite size suppression.

Fig. 5. Thickness dependent structural texture in Al_0.92B_0.08N.

a $\theta$–2$\theta$ scans for the entire thickness series zoomed in around the (002) wurtzite reflection. Starred peaks represent x-ray spectral lines. b FWHM rocking curve values for the same series, showing that the out-of-plane mosaic spread increases as film thickness decreases.

The thickness dependence does not establish a uniformly diffusive regime across the full 10 to 200 nm range. Above ~40 nm, the thermal conductivity approaches an approximately constant value while the total resistance continues to increase with thickness, which is consistent with predominantly diffusive transport in the thicker films. Below ~40 nm, thermal conductivity, A₁(TO) lifetime, and mosaic spread change concurrently, indicating that finite size effects and thickness dependent microstructure are coupled. The present data therefore identify a crossover from an ultrathin microstructure and size sensitive regime to near thickness independent conductivity at larger thickness, rather than demonstrating that the dominant phonon mean free paths are shorter than 10 nm.

In conclusion, the interplay between ferroelectricity and vibrational heat transport in boron- and scandium-substituted wurtzite AlN thin films was investigated using time-domain thermoreflectance, picosecond ultrasonics, and infrared variable-angle spectroscopic ellipsometry. The results show that while dopant incorporation facilitates polarization switching through enhanced structural complexity, it simultaneously introduces further phonon scattering mechanisms that suppresses thermal conductivity, while the B1-related feature appears over the same composition range in which polarization switching becomes accessible. Thermal transport evolves from phonon-phonon scattering at low dopant levels to impurity-limited behavior at intermediate concentrations, with non-monotonic temperature dependence at higher dopant contents. The observed covariation between optical phonon lifetimes and thermal conductivity establishes optical linewidth extraction using infrared ellipsometry as a spectroscopic probe of vibrational damping induced by defects in these AlN-based films. The thickness series also identifies a crossover from an ultrathin regime in which size and microstructure vary together to approximately thickness-independent conductivity above about 40 nm. These results define composition- and thickness-dependent constraints relevant to thermal design of aluminum nitride based ferroelectric devices.

Methods

Fabrication

Al_1-xB_xN varying B from x = 0, 0.01, 0.02, 0.06, 0.08, 0.13, and 0.17 and Al_0.8-xB_xSc_0.2N varying B from x = 0, 0.02, 0.06, 0.08, and 0.13. Thin films are grown via reactive Radio Frequency (RF) magnetron co-sputtering with a metal Al and ceramic BN target. Sc is deposited with a metal target and 200 W DC power. All samples are approximately 200 nm thick. Al_0.92B_0.08N films from 13 nm to 199 nm are also investigated. Each film is grown on 100 mm diameter (100) highly As-doped (0.001–0.005 Ohm-cm) n-type Si substrates (Nova Electronic Materials). Chamber base pressures for depositions are all below 8 × 10⁻⁸Torr. Substrates are first loaded into the vacuum chamber and heated to 600 °C for 30 min then cooled down to 350 °C for another 30 min. A plasma treatment is performed at 20 mTorr in 20 sccm Ar and 20 sccm N₂ with a 50 W substrate bias before the deposition. This step forms a Si₃N₄ layer on the Si surface to improve AlN film texture and electrical properties.

Structural characterization

Boron composition variation was quantified across the sample series using a PHI VersaProbe II X-ray Photoelectron Spectrometer (XPS). Prior to XPS analysis, a 2-minute Ar sputter at 2 keV with a 2 mm × 2 mm spot size was performed to minimize contributions from surface oxidation and hydrocarbons. Sc composition is based on deposition rates and Energy dispersive spectroscopy (EDS). Crystallinity and mosaic spread were characterized using a Panalytical Empyrean X-ray diffractometer (XRD) equipped with a Cu source and a five-axis cradle. All scans utilized a Bragg–Brentano HD incident optic and a PIXcel3D detector with programmable anti-scatter slits. An in-situ Film Sense Multiwavelength UV–Vis ellipsometer was used to measure refractive indices and verify film thickness.

PE loop characterization

Polarization hysteresis measurements were carried out with an aixACCT TF 3000 Analyzer in combination with a 150 V high voltage amplifier. Triangular bipolar waveforms are used at 10 Hz, 200 Hz, and 1 kHz, respectively. 100 nm circular W top electrodes are sputtered using 100 µm diameter shadow masks. Optical microscopy is used to determine relative electrode size for each electrical measurement. The highly doped n-Si substrate acts as the bottom electrode in each measurement.

Thermal conductivity and sound speed

Time-domain thermoreflectance (TDTR) is a non-contact optical technique in which a modulated pump beam induces an oscillatory temperature rise at the sample surface, while a probe beam monitors the corresponding changes in thermoreflectance caused by this thermal excitation. In the two-tint TDTR setup, the output of an 80 MHz Ti:sapphire femtosecond pulsed laser (center wavelength 808 nm) is split into pump and probe paths. The pump beam is modulated at 8.4 MHz using an electro-optic modulator, whereas the probe beam is routed through a mechanical delay stage to generate a time-dependent signal relative to the pump pulses. The probe is then passed through a high-pass filter before being recombined with the pump, and both beams are focused onto the sample surface using a 10× objective lens, yielding spot radii of approximately 20 µm (pump) and 11 µm (probe). For room-temperature measurements, the uncertainty is estimated by accounting for a 5% variation in the transducer thickness, the substrate thermal conductivity, and the thermal boundary conductance. The film thicknesses measured in this study are 10–200 nm, which are much smaller than the pump and probe radii. Sensitivity analysis confirms that the fitted film parameter is dominated by cross plane heat transport. In-plane thermal conductivity is not independently extracted, so possible conductivity anisotropy is not included as a measured quantity.

Picosecond acoustics measurements were performed using the same optical setup described for TDTR. In this configuration, the pump beam generates a rapid thermal expansion of the metal transducer layer, which launches coherent acoustic strain pulses into the underlying sample. The time-delayed probe beam detects the returning acoustic echoes through transient changes in the surface reflectivity, enabling the determination of layer thicknesses and acoustic properties of buried interfaces. The pump and probe beams, derived from the 80 MHz Ti:sapphire femtosecond laser (center wavelength 808 nm), were modulated and delayed in the same manner as for TDTR. Both beams were focused onto the sample surface using a 10× objective, resulting in spot diameters of ~20 μm and 11 μm for the pump and probe, respectively. The reflected probe signal was monitored as a function of time delay to resolve acoustic oscillations and reflections associated with the multilayer structure. Analysis of the periodicity and amplitude of these features allowed for extraction of film thicknesses, sound velocities, and interface quality.

Spectroscopic ellipsometry

Spectroscopic ellipsometry measurements were carried out using a JA Woollam IR-VASE Mk II in order to characterize the anisotropic dielectric function of AlN based ferroelectrics across the mid-infrared spectral range. To ensure robust and reproducible data, measurements were acquired at two angles of incidence at 50° and 70° at room temperature, and at a 60° angle under elevated-temperature conditions. The spectral resolution was set to 16 cm⁻¹ ( ~ 2 meV), providing sufficient sensitivity to resolve the subtle spectral features associated with phonon and electronic contributions to the dielectric response. The films were modeled as optically anisotropic uniaxial layers on Si with separate in-plane and cross-plane dielectric functions. Lorentz oscillators were used to describe the A₁(TO) and E₁(TO) polar phonon modes, and the B₁-related oscillator was included only in the in-plane dielectric response. The optical phonon lifetimes were extracted from the fitted damping parameters for each oscillator. Lifetime uncertainties were determined by refitting the spectra around the optimum solution and identifying the parameter bounds that increased the mean squared error by 10%. The backside of each Si substrate was roughened before measurement to suppress backside reflections and ensure that the extracted dielectric functions represent the intrinsic response of the films.

Author contributions

S.M., I.M. and S.Z. contributed equally to this work. J.F.I., S.T.M., J.P.M. and P.E.H. conceived of the study and oversaw the research. S.M., M.S.L. and S.Z. conducted the IR-VASE measurements and analysis; S.M., T.W.P., W.H., D.H. and E.A.S. conducted and contributed to the TDTR and sound speed measurements and analysis. I.M. conducted sample fabrication, structural characterization, and PE loop measurements.

Peer review

Peer review information

Nature Communications thanks Riley Hanus and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

This work was supported as part of the Center for 3D Ferroelectric Microelectronics Manufacturing (3DFeM²), an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences under Award No. DE-SC0021118.

Data availability

All data supporting the findings of this study are available within the Article and its Supplementary Information.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41467-026-77264-y.