Callaway Model Research Articles

Enhancing thermal dissipation ability and electrical performance in GaN-on-GaN HEMTs through stepped-carbon buffer design

This study investigates the thermal dissipation ability and electrical performance of GaN-on-GaN HEMTs through a stepped-C buffer design. We analyzed the relationship between impurity (C and Fe) concentrations and the thermal conductivity of the GaN material by fitting Debye–Callaway model. A stepped-C buffer design is proposed to avoid the Fe impurity and its tailing effect on thermal conduction in GaN epitaxial layers. In addition, the high concentration of C doping is designed to suppress the epitaxial interface leakage in GaN-on-GaN structures. The transducer-less transient thermoreflectance (TL-TTR) technique revealed that the stepped-C structure significantly improves thermal conductivity of epitaxial layers compared with that of Fe/C co-doped structure. Due to the optimization of heat dissipation ability, the peak temperature of the stepped-C sample decreased by ∼30 °C compared to the Fe/C co-doped sample at PDC = 10.4 W/mm. Consequently, the GaN-on-GaN HEMTs with the stepped-C buffer achieved a record output power density (Pout) of 14.8 W/mm and a power-added efficiency (PAE) of 48.2% at 3.6 GHz, underscoring the critical role of thermal management in advancing GaN-on-GaN HEMT RF performance.

The role of grain boundary and alloy scattering within the Callaway model to calculate lattice thermal conductivity in GaN/AlN superlattice

The grain boundary and alloy scattering within the Debye-Callaway model were introduced to calculate the temperature-dependent lattice thermal conductivity (LTC) in the GaN/AlN superlattice. The superlattice layers are assumed to be grains, and the sample is then treated as a multigrain material. The computations include various physical parameters related to Aluminum alloy compositions, such as Debye temperature, atomic mass, lattice volume, density, alloy scattering factor and deformation energy. In general, the sample size effect on LTC in this superlattice structure was similar to any single component solids, but it has a significant influence from the grain boundaries represented by the thickness of layers in the form of LTCPeakpoint.=5.9925e0.0005L2 at the peak point maximum and LTC(600K)=0.344L at 600K, L is the sample size. The dislocations in these samples are controlled by the inbuilt AlN layers with the dependence of NDisl.=−0.542LAlN+7.4.

Optimization of the thermoelectric performance of aluminum-doped zinc oxide-graphene heterojunctions under high temperature and high pressure

High-pressure effects can be used to effectively optimize the thermoelectric performance of wide-bandgap oxides. We build upon this finding to show that the synergistic effects of doping with aluminum and graphene composite give excellent thermoelectric performance under high pressure. By employing the parabolic band model, the Pisarenko curves are derived at different pressures, coupled with the band structure of Al-doped ZnO. An analysis indicates that pressure-induced narrowing of the bandgap in Al-doped ZnO reduces the electron excitation energy, thereby optimizing the electrical properties of the samples. The Debye Callaway model is also used to fit the lattice thermal conductivity of the samples, thus enabling an in-depth analysis of the phonon scattering mechanisms. Our analysis suggests that graphene composites significantly enhance point defect scattering and Umklapp scattering, thus increasing the phonon relaxation time and effectively reducing the lattice thermal conductivity of the samples. The improvement in the figure of merit (zT) of ZnO is attributed to the simultaneous enhancement of its electrical properties under high pressure and the synergistic optimization of reducing the lattice thermal conductivity through doping and composites. In this work, we consider a fixed doping ratio of Al and a constant proportion of graphene composite, and analyze the microstructure and thermoelectric properties of 0.1C–ZnAl0.04O (C–ZnAlO) samples synthesized under pressures ranging from 1 to 5 GPa, with the aim of elucidating the influence of pressure and graphene composite on the electro-acoustic transport properties of ZnO. We find that the zT value for a sample synthesized at 5 GPa is increased to 0.27 at 973 K.

Refractory and thermoelectric properties of stabilized Tricalcium aluminate allotrope: A first-principles calculation approach

Tricalcium aluminate (Ca3Al2O6) is an indispensable component of Portland cement due to its high strength and reactivity. This study investigates the equilibrium lattice structure as well as the electronic and refractory properties of a newly discovered allotrope of Ca3Al2O6 using density functional theory and random phase approximation methods. Using density functional perturbation theory, we investigate the phonon dispersion of the refined structure’s experimental stability. In addition, the lattice thermal conductivity and thermoelectric figure of merit are computed by solving the Boltzmann Transport Equation with the modified Debye Callaway model and the Relaxation time Approximation methods. The computed Figure of merit, determined by the carrier concentration, indicates a substantial enhancement of 40 to 100-fold, leading to a superior figure of merit of 0.25 and 0.6 when appropriately doped. As a result, we anticipate that stable allotropes of Ca3Al2O6 in the Pm3̄m phase will be useful as energy-harvesting, convective cooling and infrared radiation shield-based cement materials in the cement and concrete industries.

Thermoelectric properties of Gd and Se double substituted tetrahedrite.

The compound Cu12Sb4S13, known as tetrahedrite, is an eco-friendly p-type thermoelectric material with earth-abundant, low-cost, and less toxic constituents. This contemporary work studied the thermoelectric properties of Gd and Se double-substituted tetrahedrites. The samples with nominal composition Cu11.95Gd0.05Sb4S13-xSex (where x = 0, 0.2, 0.4, 0.6, and 0.8) were prepared using the solid-state synthesis and sintered using high vacuum hot pressing. The structural analysis using X-ray diffraction revealed a successful tetrahedrite phase formation, and the systematic increase of lattice parameters with the selenium content (x) indicated successful Se substitution. The electron probe microanalysis revealed the presence of secondary phases Cu3SbS4, CuSbS2, and CuGdS2. The Raman spectroscopy showed a weakening Sb-S/Se bond with increased Se content in the samples. The +3 and -2 oxidation states of Gd and Se, respectively, were confirmed from the XPS study. Gd3+, a higher valence substituent at the Cu+/Cu2+ tetrahedral site, helped reduce the carrier concentration. On the other hand, the isoelectronic substitution of Se2- for S2- enhanced the thermopower and power factor by introducing resonant energy states near the Fermi level. Consequently, a maximum power factor of ∼1.35 (±0.08) mW m-1 K-2 at ∼729 K was obtained for the sample x = 0.4. The sample x = 0.4 also exhibited the lowest thermal conductivity ∼ 1.18 (±0.04) W m-1 K-1 at 729 K. The Callaway model indicates that the lowering in the lattice thermal part of conductivity of this sample is due to the combined effect of point defect and Umklapp scattering. The simultaneous improvement of carrier concentration and thermal conductivity resulted in a relatively high zT of ∼0.83 (±0.09) in the x = 0.4 sample.

Achieving high quality factor and enhanced thermoelectric performance in polycrystalline SnS by Ag doping and Se alloying

The polycrystalline SnS with a similar layered crystal structure and band structure to SnSe exhibits enormous commercial thermoelectric potential due to its lower cost and environmentally friendly characteristics. However, the wider bandgap of SnS leads to low carrier concentration and inferior electrical transport performance. The two-dimensional interlayer hinders carrier transport, leading to interesting and mysterious anisotropic thermoelectric properties. Herein, we reported the optimized electron–phonon transport in anisotropic polycrystalline SnS by Ag doping and Se alloying, realizing a high quality factor B by multiple strategies of optimizing carrier concentration, modifying band structure, and introducing various defects; further potential performance is predicted by the single parabolic band model. Specifically, Ag-doped SnS not only significantly increases the carrier concentration and weighted mobility μw in both directions but also induces multi-scale precipitates proven by the Debye–Callaway model to suppress phonon transport. Moreover, additional Se alloying optimizes the electronic band structure and increases the Seebeck coefficient, further improving μW and boosting the maximum power factor to ∼3.72 μW cm−1 K−2 at 873 K in the out-of-plane direction. Consequently, the synergistic optimization of carrier and phonon transport achieved a high B of 0.7 and a maximum zTmax of ∼0.8 at 873 K in Ag0.02Sn0.98S0.99Se0.01. Additionally, the high B predicted a high zTmax∼1.5 based on optimized carrier transport characteristics, demonstrating the potential great-performance polycrystalline SnS. This work provides a promising avenue for optimizing the zT of polycrystalline SnS by transport engineering.

A prediction of the thermodynamic, thermophysical, and mechanical properties of CrTaO4 from first principles

AbstractIt is reported that the self‐forming CrTaO4 oxide scale can protect refractory high‐entropy alloys from oxidation, superior to Cr2O3. In this paper, the phase stability, mechanical, and thermal properties of three polymorphous phases of CrTaO4 are systematically investigated from first‐principles density functional theory calculations. The mechanical properties predicted using the strain–energy methods indicated that all three phases are mechanically stable. The temperature dependence of elastic constants and polycrystalline moduli of three phases demonstrated the thermal softening as temperature increase. The Helmholtz‐free energies as a function of volume and temperature are derived from phonon dispersions within the quasi‐harmonic approximation at six strained volumes. The calculated apparent bulk coefficients of thermal expansion of these three phases are evaluated, the highest value approximately 13.4× 10−6 K−1 within a temperature range of 500–2000 K for the rutile I41md phase. The lattice thermal conductivity calculated by the Debye–Callaway model suggested that the rutile type I41md phase has the lowest value of approximately 2.1 W/m/K at 1800 K. The other two phases, C2/m and P2/c, exhibit higher values due to relatively lower Grüneisen parameters and larger phonon velocities. The melting point of CrTaO4 is predicted to be between 1975 and 2449 K using ab initio molecular dynamics simulations. This work provides a comprehensive theoretical understanding of the thermodynamic, mechanical, and thermal properties for the new material CrTaO4 and serves as an example of a viable computational design strategy for improved oxidation resistance of refractory alloys at high temperatures.

Thermal conductivity of type-Ib HPHT synthetic diamond irradiated with electrons

The effect of irradiation with 3 MeV electrons and subsequent high-temperature annealing on the thermal conductivity κT of synthetic HPHT diamond containing impurity nitrogen at a concentration of about 100 ppm was studied at temperatures from 5 to 410 K. At each stage of the experiment, the optical absorption and photoluminescence spectra, magnetization and thermal conductivity were measured on two plates from the same diamond single crystal. Color centers and their concentration in different locations in the samples were determined from the optical spectra. The concentration of paramagnetic impurities in the samples was determined from the temperature and field dependencies of the paramagnetic magnetization. Thermal conductivity is suppressed by two orders of magnitude at temperatures from 35 to 50 K after irradiation to a fluence of 5×1018 cm−2. Annealing at a temperature of 1800° C restored the thermal conductivity of diamond at moderate and high temperatures, but not at temperatures below 120 K. The measured data on thermal conductivity were analyzed within the framework of the phenomenological Callaway model in order to understand the role of various phonon scattering processes and how it changes during irradiation and annealing.

Four-phonon and normal scattering in 2D hexagonal structures

Comprehensive understanding of phonon transport will facilitate the exploration of materials. Four-phonon scattering is find to be important to determine thermal conductivity in many materials, and normal scattering (N process) could lead to some unique phonon transport behaviors, especially in 2D materials. In this work, we studied four-phonon and normal scattering in hexagonal structures, both of which were found to be significant. With the increase of atomic mass ratio, the relative four-phonon scattering is gradually enhanced, whereas N process is weakened. Callaway model and Allen’s modified models were used to approximate the thermal conductivity, and we find that the models are applicable in some cases with relative weak N scattering intensity.

Analytical model for two-channel phonon transport engineering

The reduction of vibrational contributions to thermal transport and the search for material classes with intrinsically low lattice thermal conductivities are at the heart of thermoelectric research. Both engineering the heat transport of known thermoelectrics and searching for new material candidates is guided by understanding the physics of low thermal conduction. Spectral analytical models (e.g., the Callaway model) for propagating phonon transport have proved to be a powerful tool for interpreting experimental results and providing metrics for materials design. Now, however, it is known that another mechanism of phonon heat transport can occur in complex crystalline materials. Called diffusons, they describe the non-propagating atomic scale random-walk of thermal energy between energetically proximal phonon modes. While analytical models exist to describe both transport behaviors independently, an analytical model accounting for both transport channels simultaneously is necessary to interpret and design so-called 2-channel thermal transport. In this work, we propose an analytical 2-channel transport model that partitions the vibrational density of states into two transport regimes and subsequently accounts for both transport mechanisms. The model is then used to explain the experimental thermal conductivities of the solid solution series Ag9-xGa1-xGexSe6. In this series, substitution leads to the stabilization of a highly vacant Ag+ substructure, which is expected to induce strong point-defect phonon scattering. While the propagating phonons are strongly scattered at low temperatures, the diffuson channel is apparently unaffected. By establishing materials design metrics for 2-channel thermal transport from analytical theory, experimental investigations of materials with astonishingly low lattice thermal conductivities can now be better guided and informed.

Ordered-vacancy defect chalcopyrite ZnIn2Te4: A potential thermoelectric material with low lattice thermal conductivity

An effective route towards commercializing thermoelectric devices is to explore materials with high conversion efficiency. This study investigates the thermoelectric properties of ZnIn2Te4 with the combination of first-principles calculations, Boltzmann transport theory and the modified Debye Callaway model. This vacancy-ordered defect chalcopyrite shows a direct band gap of 1.37 eV, obtained by mBJ functional with spin orbit coupling. The positive phonon dispersion curves ensure the thermodynamical stability of the material. Moreover, strong acoustic-optical coupling, Grüneisen parameter, and moderate phonon group velocity yielded the low lattice thermal conductivity (kL) of 1.46 W m−1 K−1 at 900 K. Owing to this low kL, the optimum thermoelectric figure of merit of 0.90 and 0.98 is obtained for p and n-type ZnIn2Te4. These findings will open the way for the experimentalists to attempt for its experimental realization.

Calculation of Thermal Conductivity of AlGaN/GaN Superlattices

Herein, the results of theoretical investigation of anisotropic thermal conductivity of AlGaN/GaN superlattices (SLs) are presented. For calculations, the Boltzmann transport equation in the relaxation time approximation is used. Results of computations are compared with experiment and theoretical result obtained using Callaway model. Good agreement between experimental and theoretical results is observed. Opportunity of use of the Callaway model for calculation of anisotropic thermal conductivity of SLs is discussed.

Electronic and phonon contributions to the Thermoelectric properties of newly discovered half-Heusler alloys XHfPb (X= Ni, Pd, and Pt)

In this work we calculate the thermoelectric figure of merit of XHfPb (X= Ni, Pd, and Pt) by computing the both the power factor and the lattice thermal conductivity by first principles. We make reasonable approximations: we use the Constant Relaxation Time Approximation (CRTA) to compute the electron transport contribution and the modified Debye–Callaway model to calculate the thermal lattice conductivity. We also report the dielectric properties of these semiconductors and the mode Grüneisen parameters. Not surprisingly we find that the average Grüneisen coefficient correlates with the thermal conductivity. Next, we consider a realistic relaxation time τ and carrier concentration n from experimental data on ZrHfPb and obtain the figure of merit ZT as a function of temperature. Our main finding is that despite the Pt is isoelectronic with Ni and Pd, the ZT of PtHfPb is larger and behaves differently from the other two materials, suggesting that PtHfPb is better suited for high temperature thermoelectric generators.

High-pressure and high-temperature synthesis of stable SxCo3.6Ni0.4Sb12 skutterudite compounds

Compared to Te, Ni is found in abundance in the earth's crust. At the same time, the mechanical properties of Ni atom-substituted skutterudite are significantly improved. In this study, a series of S-filled Ni-substituted skutterudite compounds were synthesized by a high-pressure and high-temperature (HPHT) method in the synthesis pressure range of 1.0–3.0 GPa. The phase composition, microscopic morphology, and electrothermal transmission properties of the SxCo3.6Ni0.4Sb12 (x = 0, 0.05, 0.10, 0.20) samples were systematically characterized. Phase composition analysis showed that the introduction of S atoms into the intrinsic pores of skutterudite can improve the solid solution limit of Ni atoms in the Co sites of skutterudite. The filling limit of S increased with the synthetic pressure. Moreover, microscopic morphology analysis revealed that the filling of S atoms inhibited the growth of grains. A large number of lattice fringes in different directions were found in the sample, containing abundant microstructures such as lattice distortions and dislocation defects. Compared with the synthesized samples, S0.05Co3.6Ni0.4Sb12 synthesized at 1.0 GPa had a maximum room temperature power factor of 7.98 × 10−4 Wm−1K−2. The electrical properties of S0.05Co3.6Ni0.4Sb12 samples stored for 6 months without any protective measures were tested at room temperature. No obvious changes in performance were observed, which proved that the HPHT method can synthesize stable samples. After several thermal cycles, the electrical properties of the S0.05Co3.6Ni0.4Sb12 sample was tested for variable temperature, and it was found that the sample still had good stability. How the substitution of S atoms with Ni atoms reduces the lattice thermal conductivity can be explained by fitting the Callaway model. The S0.05Co3.6Ni0.4Sb12 sample synthesized at 1.0 GPa had a maximum zT value of 0.46 at the test temperature of 773 K, which decreased to 0.43 after multiple thermal cycles at the same temperature.

Thermal conductivity of AlxGa1−xN (0≤x≤1) epitaxial layers

${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ ternary alloys are emerging ultrawide band gap semiconductor materials for high-power electronics applications. The heat dissipation, which mainly depends on the thermal conductivity of the constituent material in the device structures, is the key for device performance and reliability. However, the reports on the thermal conductivity of ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ alloys are very limited. Here, we present a comprehensive study of the thermal conductivity of ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ in the entire Al composition range. Thick ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ layers grown by metal-organic chemical vapor deposition on GaN/sapphire and GaN/SiC templates are examined. The thermal conductivity measurements are done by the transient thermoreflectance method at room temperature. The effects of the Al composition, dislocation density, Si doping, and layer thickness on the thermal conductivity of ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ layers are thoroughly investigated. All experimental data are fitted by the modified Callaway model within the virtual crystal approximation, and the interplay between the different phonon scattering mechanisms is analyzed and discussed.

Vacancy-induced heterogeneity for regulating thermoelectrics in n-type PbTe

The fact that the thermoelectric performance is far inferior to that of p-type PbTe has inspired many strategies to develop n-type PbTe thermoelectrics. Alloying PbS in n-type PbTe effectively changes the shape of a valley to trigger a heavier conduction band for improving the Seebeck coefficient, while the resulting small orbital overlap inevitably leads to phase separation hindering electron transport. The effect of vacancies on the solubility of sulfur in n-type PbTe is ambiguous; especially, the heterostructure due to phase separation in high-content PbS-alloyed PbTe also requires sufficient modification to optimize the electroacoustic transport. This motivates the current work on the introduction of vacancies by charge-balancing doping via Sb2Te3 and discovers striking new insight that the introduced vacancies can induce a new heterostructure of Pb2Sb2S5 and suppress the aggregation of Sb and PbS in high-solubility n-type PbTe–PbS. The modification of the band structure and optimization of the electron transport give rise to a prominent enhancement in electronic performance. Furthermore, the Debye–Callaway model validates the dramatic contribution of vacancy aggregation and heterostructures to lattice thermal conductivity. As a result, the synergistic modulation of electroacoustic characteristics achieves a significant improvement in both the maximum zT and the near-room-temperature zT. Understanding such unique findings is critical for applicability to other thermoelectric materials.

Computational study of the effect of different doping elements on the thermal conduction properties of graphene nanoribbons

The dopant's atoms of various elements can be incorporated into the crystal lattice of graphene for the purpose of modulating its structural, optical and electrical properties. While the dopant's presence negatively affects the thermal conductivity, the exact effect of doping is still poorly understood and the mechanisms involved remain obscure. The effect of different doping elements on the thermal conductivity of graphene ribbons was investigated by performing molecular dynamics simulations to understand how impurities affect the thermal conduction properties of the nanostructured material. Graphene ribbons were doped with silicon, boron, or nitrogen elements to modify their nanostructure and thermal properties. The importance of edge structure was evaluated in comparison with that of doping. The Callaway model and the Einstein's model were used to provide the theoretical upper and lower bounds on the thermal conductivity. The contribution of optical phonons at different temperatures was evaluated in order to further understand the microscopic mechanisms of thermal conduction in the two-dimensional doped crystal. A computational analysis of thermal behavior was carried out in terms of the maximum density of states. The results indicated that a small number of dopant atoms can greatly change the ability to conduct heat. The thermal conductivity of the doped nanomaterial decreases successively in the order of nitrogen, boron, and silicon. Acoustical phonons still dominate the thermal conduction in the doped crystal, but the contribution of optical phonons become larger, especially at higher temperatures. The contribution of phonons in the optical branches increases with the doping concentration and can be as large as 6.0 %. In the presence of doping, the edge structure does not significantly affect the thermal conductivity and the maximum density of states. When graphene is heavily doped, the effect of ribbon length is insignificant while doping becomes dominant. The results have significant implications for the understanding of the relations between doping elements and thermal conduction properties.

Thermal decay in the one-dimensional transient thermal grating experiment using modified Debye-Callaway model

We calculate the thermal decay in the one-dimensional transient thermal grating (TTG) experiment by solving the transient Boltzmann-Peierls transport equation (BPTE) within the framework of the single-mode relaxation time approximation and using modified Debye-Callaway model in which both longitudinal and transverse phonon modes are included explicitly. We consider surface heating of an opaque thick semiconductor (SC) crystal film that we assume to have a cubic symmetry and is treated as a continuum, elastic, isotropic, and dispersionless medium. We obtain a nonuniversal spectral suppression function (SSF) in the integrand of the effective apparent thermal conductivity that is similar to the one obtained by Chiloyan et al. [Phys. Rev. B 93, 155201 (2016)] using the standard single-mode relaxation time approximation (RTA) model. Therefore, the nonuniversal character of the SSF in the TTG experiment does not depend on the form of the collision operator approximation in the BPTE: Callaway's or standard. Moreover, the analysis of the behavior of the thermal decay rate shows how the peculiar crystal momentum shuffling effect of phonon-phonon scattering Normal processes (N processes) that is captured by Callaway's model influences the onset of the nondiffusive (quasiballistic) regime in the phonon transport process in SC crystals. This effect tends independently from the other phonon scattering processes to favor the maintenance of the phonon diffusive regime over a large length-scale range, a remarkable feature that cannot be put into light with the standard RTA model used in previous works. Hence, the implicit effect of N processes has certainly an important impact on the extraction of the phonon mean-free path spectrum distribution, especially in the high-temperature regime.

Thermoelectric properties of a series of polycrystalline Mo(Se1−xTex)2

AbstractTransition metal dichalcogenides have being actively studied on the account of their large density‐of‐state effective mass and low lattice thermal conductivity. Herein, thermoelectric and electrical transport properties of MoSe2–MoTe2 system are investigated. A series of Mo(Se1−xTex)2 (x = 0, .25, .5, .75, and 1) polycrystalline samples was synthesized by conventional solid‐state reaction. Single hexagonal phase was identified for each sample without secondary phase, confirming the formation of complete solid solutions between MoSe2 and MoTe2. The electrical conductivity and magnitude of the Seebeck coefficient increased simultaneously with increasing Te content x at high temperatures, with the power factor following the same trend. As results, the MoTe2 sample exhibited the maximum power factor of .014 mW/(m K2) at 823 K. The lattice thermal conductivities of the alloyed samples (x = .25, .5, and .75) significantly decreased compared to MoSe2 and MoTe2 owing to point defect phonon scattering via anion substitution, which is verified by the Debye–Callaway model. A maximum zT of .0044 was obtained for MoTe2 sample at 773 K; however, the calculated quality factor B values of the samples with x = .75 and 1 at 773 K were almost identical, suggesting that a further enhancement of zT can be achieved by optimizing an nH of the Mo(Se0.25Te0.75)2 sample.

Hydrodynamic signatures in thermal transport in devices based on two-dimensional materials: An ab initio study

We investigate the features arising from hydrodynamic effects in graphene and phosphorene devices with finite heat sources, using ab initio calculations to go beyond Callaway's model and inform a full linearized scattering operator, and solving the phonon Boltzmann transport equation through energy-based deviational Monte Carlo methods. We explain the mechanisms that create those hydrodynamic features, showing that boundary scattering and the relation of sample dimensions to the nonlocal length $\ensuremath{\ell}$ are the determinant factors, regardless of the relative importance of normal versus resistive scattering. From this point of view, the nonlocal length $\ensuremath{\ell}$ reflects the ability of scattering to randomize the heat flux, and we show that approximations made on the scattering operator may have, through the value of $\ensuremath{\ell}$, qualitative consequences on the signatures of hydrodynamic behavior.