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Gabriel R. Jaffe, Keenan J. Smith, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Max G. Lagally, Mark A. Eriksson, Victor W. Brar

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[Thickness-Dependent Cross-Plane Thermal Conductivity Measurements of Exfoliated Hexagonal Boron Nitride](https://mdr.nims.go.jp/datasets/6795a7b5-7b63-4911-aac4-b5bc8ac6632f)

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Thickness-Dependent Cross-Plane Thermal Conductivity Measurements of Exfoliated Hexagonal Boron NitrideThickness-Dependent Cross-Plane Thermal ConductivityMeasurements of Exfoliated Hexagonal Boron NitrideGabriel R. Jaffe,* Keenan J. Smith, Kenji Watanabe, Takashi Taniguchi, Max G. Lagally,Mark A. Eriksson, and Victor W. BrarCite This: ACS Appl. Mater. Interfaces 2023, 15, 12545−12550 Read OnlineACCESS Metrics & More Article Recommendations *sı Supporting InformationABSTRACT: Submicrometer-thick layers of hexagonal boronnitride (hBN) exhibit high in-plane thermal conductivity anduseful optical properties, and serve as dielectric encapsulationlayers with low electrostatic inhomogeneity for graphene devices.Despite the promising applications of hBN as a heat spreader, thethickness dependence of its cross-plane thermal conductivity is notknown, and the cross-plane phonon mean free paths (MFPs) havenot been measured. We measure the cross-plane thermalconductivity of hBN flakes exfoliated from bulk crystals. We findthat submicrometer thick flakes exhibit thermal conductivities upto 8.1 ± 0.5 W m−1 K−1 at 295 K, which exceeds previouslyreported bulk values by more than 60%. Surprisingly, the averagephonon mean free path is found to be several hundred nanometers at room temperature, a factor of 5 larger than previouspredictions. When planar twist interfaces are introduced into the crystal by mechanically stacking multiple thin flakes, the cross-planethermal conductivity of the stack is found to be a factor of 7 below that of individual flakes with similar total thickness, thusproviding strong evidence that phonon scattering at twist boundaries limits the maximum phonon MFPs. These results haveimportant implications for hBN integration in nanoelectronics and improve our understanding of thermal transport in two-dimensional materials.KEYWORDS: phonon, mean free path, hBN, cross-plane, thermal conductivity, twist interface■ INTRODUCTIONEffectively dissipating heat away from hotpots caused by high-power or densely packed electronic structures is an outstandingthermal management problem. Heat-spreading films mustexhibit high thermal conductivity and good dielectriccharacteristics, and form smooth clean interfaces with heat-emitting structures to reduce hotspot temperatures. Hexagonalboron nitride (hBN), a wide-bandgap dielectric two-dimen-sional (2D) material, has drawn significant research interest forits high in-plane thermal conductivity,1−3 its use as a charge-trap free encapsulation material for graphene electronics,4,5 andits optical characteristics.6 Films of hBN can be mechanicallycleaved from bulk crystals and transferred with atomicallysmooth and clean interfaces. Such transferred films havedemonstrated significant heat-spreading capability in LEDdevices and graphene electronics.7,8 The clean and conformalnature of these flexible hBN films has distinct advantages overmaterials such as diamond or SiC, which require thermallyresistive interface layers to bond to other materials and sufferfrom growth defects near the interface layer.9,10The rate at which a hotspot can be cooled is determined bythe strength of the three-dimensional heat flow through asurrounding heat-spreading film. Many 2D materials have ahigh degree of anisotropy in their thermal conductivities. Whilethey exhibit some of the highest known conductivities alongtheir in-plane directions, they often have relatively small cross-plane thermal conductivities. The high in-plane thermalconductivities make these materials excellent candidates forheat-spreading in nanoelectronics,11,12 and the anisotropicthermal transport properties have found applications inthermoelectrics and thermal isolation of temperature-sensitivecomponents.13−16 The thermal conductivities of most bulk 2Dcrystals are well-known; however, at submicrometer lengthscales, the thermal conductivity of 2D materials can exhibit astrong thickness dependence. Once the thickness of a film isless than the average phonon mean free path, the thermalconductivity begins to decrease. It is therefore necessary toknow the mean free paths (MFPs) of the phonons responsiblefor heat transport to form an accurate model of thermalReceived: December 1, 2022Accepted: February 13, 2023Published: February 27, 2023Research Articlewww.acsami.org© 2023 The Authors. Published byAmerican Chemical Society12545https://doi.org/10.1021/acsami.2c21306ACS Appl. Mater. Interfaces 2023, 15, 12545−12550Downloaded via NATL INST FOR MATLS SCIENCE (NIMS) on March 19, 2023 at 00:57:51 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Gabriel+R.+Jaffe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Keenan+J.+Smith"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kenji+Watanabe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takashi+Taniguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Max+G.+Lagally"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Mark+A.+Eriksson"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Mark+A.+Eriksson"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Victor+W.+Brar"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acsami.2c21306&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?ref=pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?goto=supporting-info&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?fig=tgr1&ref=pdfhttps://pubs.acs.org/toc/aamick/15/9?ref=pdfhttps://pubs.acs.org/toc/aamick/15/9?ref=pdfhttps://pubs.acs.org/toc/aamick/15/9?ref=pdfhttps://pubs.acs.org/toc/aamick/15/9?ref=pdfwww.acsami.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acsami.2c21306?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://www.acsami.org?ref=pdfhttps://www.acsami.org?ref=pdfhttps://creativecommons.org/licenses/by-nc-nd/4.0/https://creativecommons.org/licenses/by-nc-nd/4.0/https://creativecommons.org/licenses/by-nc-nd/4.0/https://creativecommons.org/licenses/by-nc-nd/4.0/https://acsopenscience.org/open-access/licensing-options/conductivity in the submicrometer regime.17 Recently, thephonon MFP spectra of graphite and MoS2 were measured,and the phonon MFPs were found to be hundreds ofnanometers at room temperature, far exceeding kinetic-theoryestimates.18,19 It is currently not known whether other two-dimensional materials also exhibit these long phonon MFPsand to what degree scattering mechanisms such as grainboundaries limit the maximum phonon MFPs.For bulk hBN (>10 μm thick), the cross-plane thermalconductivity has been measured to be ∼2−5 W m−1 K−1,3,20,21and the average cross-plane phonon MFP has been predictedfrom first-principles calculations to be ∼18 nm at 300 K.21This prediction is an order of magnitude lower than theaverage MFPs measured in graphite and MoS2 and has notbeen verified experimentally. An empirical estimate of theaverage cross-plane phonon mean free path, Λavg, can becalculated from kinetic theory using κbulk = (1/3)CvgΛavg,where κbulk is the bulk cross-plane thermal conductivity, C isthe heat capacity, and vg is the average group velocity of thecross-plane acoustic phonon modes. When we use κ = 2−5 Wm−1 K−1, C = 1.8 J cm−3 K−1,20 and vg = 3800 m s−1,21 thisresults in an average MFP estimate of 0.9−2.2 nm, an order ofmagnitude below predictions.In this Article, we report cross-plane thermal-conductivitymeasurements of submicrometer-thick exfoliated hBN flakes asa function of thickness and temperature. The cross-planethermal conductivity of a 585 nm thick flake is measured to be60% larger than the highest conductivity of bulk hBN reportedin the literature. The thin flakes and high-quality samplesenable measurements of the physics governing short and long-mean-free-path phonons. We find that the flake thermalconductivity exhibits a strong thickness dependence, decreas-ing by a factor of 40 from 8.1 ± 0.5 W m−1 K−1 for a 585 nmthick flake to 0.20 ± 0.06 W m−1 K−1 for a 7 nm thick flake.Fits to the data indicate that the majority of the heat is carriedby phonons with mean free paths >100 nm. This value farexceeds the MFPs estimated from kinetic theory, whichpredicts MFPs of only a few nanometers, as well as theprediction from first-principles calculations that ∼80% of theheat is carried by phonons with MFPs between 3−90 nm.3 Wefurther demonstrate that stacking faults can drastically reducethe cross-plane thermal conductivity of hBN by mechanicallystacking five ∼15 nm exfoliated flakes. The stacked structure isfound to have a cross-plane thermal conductivity a factor of 7below that of individual flakes with the same total thickness asthe stack. This result suggests that variations in the densities ofstacking faults in bulk samples could explain the differences inreported hBN bulk thermal conductivities and the highconductivity reported here.Taken together, the long MFPs and strong interfacescattering we report have two important implications. First,the long phonon MFPs in hBN impact its use in heat-spreading applications in nanoelectronics, because the cross-plane thermal conductivity of hBN will decrease dramaticallyas the film thickness is reduced below the phonon MFPs. Heatdissipation from hotspots in electronics flows both in-planeand cross-plane through a heat-spreading film. It is oftendesirable to make heat-spreading films as thin as possible so asto maximize their cross-plane thermal conductance. Our resultsdemonstrate that the cross-plane thermal conductance of hBNdoes not significantly increase for films <300 nm thick. Second,these results demonstrate that two-dimensional materials are apromising model system for studying coherent phonontransport behavior, because heterostructures of dissimilarmaterials with layer thicknesses far below the typical phononMFPs can be fabricated with smooth and pristine interfaces bystacking different exfoliated flakes at arbitrary angles.The thermal conductivity of hBN, κ (units of W m−1 K−1),as a function of thickness, d, can be expressed as=×d dR d A( )( )therm (1)where Rtherm(d) (units of m2 K GW−1) is the total cross-planethermal resistance and A is the surface area of a hBN flake ofthickness d. We measure Rtherm(d) using a differential three-omega measurement where the temperature of a referenceheating wire on the bare sample substrate is subtracted fromthe temperature rise of a heating wire on an hBN flake, as seenin Figure 1b.22−27 This temperature difference can beconverted to a measure of thermal resistance, Rtherm, fromwhich the thermal conductivity can be calculated using eq 1.For this technique, a metal four-probe wire is fabricated acrossthe film of interest and is then used as both a heater and athermometer. Figure 1a shows an optical image of a heatingwire on an hBN flake. The heating wires are 2 μm wide, thedistance between the voltage probes is 20 μm, and the voltageFigure 1. (a) An optical image of a four-probe heating wire fabricated across an AlOx-encapsulated hBN flake that has been exfoliated from a bulkcrystal and mechanically transferred to a SiO2/Si substrate. (b) A cross-sectional schematic diagram of a reference heating wire on the AlOx coveredSiO2 substrate and a second wire on a hBN sample. The encapsulating AlOx layer and underlying hBN are etched into a mesa as shown usingBCl3Ar and SF6 plasma etches, respectively. During a measurement, the heat from the wire flows cross-plane through the hBN and dissipates intothe substrate. (c) The measured cross-plane thermal conductivity of a 585 nm thick hBN flake as a function of temperature. The cross-planethermal conductivity of bulk hBN crystals (>10 μm thick) is shown as “■” and “◇” for comparison.20,21ACS Applied Materials & Interfaces www.acsami.org Research Articlehttps://doi.org/10.1021/acsami.2c21306ACS Appl. Mater. Interfaces 2023, 15, 12545−1255012546https://pubs.acs.org/doi/10.1021/acsami.2c21306?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?fig=fig1&ref=pdfwww.acsami.org?ref=pdfhttps://doi.org/10.1021/acsami.2c21306?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asprobe widths are 300 nm where they make contact with theheating wire. Bond pads are fabricated >400 μm away from thesection of wire between the voltage probes to prevent heatdissipating out through the wire bonds from affecting theexperiment.The hBN flakes are exfoliated in a glovebox with nitrogenatmosphere and transferred onto SiO2/Si substrates. The flakesare vacuum annealed under an Ar/H2 flow at 350 °C for 1 h.An atomic force microscope is used to measure the flakethicknesses and surface roughnesses. The flakes are encapsu-lated in a 20 nm thick layer of AlOx deposited by atomic-layerdeposition to protect the interface between the flake andsubstrate from solvent contamination during processing. Metalfour-probe heater/thermometer wires are fabricated on thesample surface using electron-beam lithography. The Au wiresare 65 nm thick with a 5 nm Ti adhesion layer. Small metalinterconnects are patterned on the edges of flakes withthicknesses >60 nm to connect the wires over the large jumpsin the surface topography. To ensure that the heat flowing outof the wire through the hBN flakes is entirely cross-plane, thehBN flakes are etched into mesas, as shown in Figure 1b, usingfirst a BCl3Ar plasma etch to remove the AlOx layer, and then aSF6 plasma etch to remove the hBN.■ RESULTS AND DISCUSSIONFigure 1c shows a comparison of the cross-plane thermalconductivity as a function of temperature of the thickest flakemeasured here (585 nm) to that of bulk hBN samples (>10μm thick) by others.20,21 The thick flake exhibits a largerthermal conductivity than previous bulk measurements acrossthe entire temperature range of ∼200−400 K. Additionally, thethermal conductivity increases by a factor of ∼2 between roomtemperature and 200 K, similar to that of other materialsknown to have large phonon mean free paths, such as Si.28 Thetemperature dependence of hBN reported here is morepronounced than previous studies of graphite where phononscattering at stacking faults limited the thermal conductivity atlow temperatures.18 In Figure 2a we report the measured cross-plane thermal resistance of the hBN flakes as a function of flakethickness at 295 K, and the calculated thermal conductivityusing eq 1 is shown in Figure 2b. Additional temperature-dependent thermal conductivity data can be found in theSupporting Information.We observe that the thermal conductivity more than doublesas the flake thickness increases from 200 to 585 nm, indicatingthat phonons with MFPs of several hundred nanometers makesignificant contributions to the thermal conductivity of thethicker flakes. Moreover, the thermal conductivity appears tobe gradually saturating with increasing thickness, consistentwith similar trends seen in graphite.18 For the thickest flakesthat we measure, the thermal conductivities exceed previouslymeasured bulk values, which are shown in Figure 2b as shadedorange, green, and red squares.3,20,21 We note that the thermalconductivity of hBN is known to vary significantly with crystaldefect density and that hBN samples with the lowest previouslymeasured cross-plane thermal conductivity (∼2 W m−1 K−1)were found to have an average crystallite size in the cross-planedirection of ∼10 nm.20 The hBN crystals studied in this workare expected to have millimeter-scale grain sizes.4,29 In Figure1a we observe flat regions of uniform thickness >50 μm across.For an infinitely thick film, the differential mean free pathcontribution function f(Λ) describes the fractional contribu-tion of phonons with mean free path Λ to the thermalconductivity.30 The contributions from phonons with longmean free paths are suppressed in a film of finite thickness. Thesuppression of phonon contributions to thermal conductivityfor the sample geometry considered here is described by thesuppression function:=S K K( ) 1 (1 e )n nK1/ n (2)where the Knudsen number Kn is defined as Kn = Λ/L and L isthe film thickness.18 The thermal conductivity of a thin film asa function of film thickness κ(L) is a convolution of f(Λ) andS(Kn) over all phonon mean free paths:=L S K f( ) ( ) ( ) dn0 (3)We find the differential mean free path contributionfunctions that best fit our thermal conductivity data at 295 Kusing a convex optimization procedure and a Gaussianquadrature discretization of the integral in eq 3.30 Additionalinformation about the fitting procedure is available in theSupporting Information. Although the thermal conductivityappears to be rolling off at large thicknesses in Figure 2b, we donot know the saturation thickness for hBN or the bulk thermalFigure 2. (a) The measured cross-plane thermal resistance of thehBN flakes multiplied by the surface area of the heating wire as afunction of flake thickness at 295 K (blue points). The phonon meanfree path contribution fits to the data assuming that the thermalconductivity eventually saturates to either 8 or 16 W m−1 K−1 areshown as black and purple lines, respectively. (b) The hBN flakecross-plane thermal conductivity at 295 K (blue points) calculatedfrom the data shown in (a). Shaded regions indicate the thermalconductivity of bulk (>10 μm) hBN measured by others.3,20,21 Theblack and purple lines show the phonon mean free path contributionfits. The dashed lines indicate the likely trend in the thermalconductivity when extrapolated to larger thicknesses. (c) Thedifferential phonon mean free path functions that best fit the datashown in (a) assuming two different values for the bulk thermalconductivity κbulk. The inset shows the corresponding thermalconductivity accumulation functions. (d) The suppression ofcontributions to thermal conductivity (eq 2) of phonons with longmean free paths for films of three different thicknesses.ACS Applied Materials & Interfaces www.acsami.org Research Articlehttps://doi.org/10.1021/acsami.2c21306ACS Appl. Mater. Interfaces 2023, 15, 12545−1255012547https://pubs.acs.org/doi/suppl/10.1021/acsami.2c21306/suppl_file/am2c21306_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsami.2c21306/suppl_file/am2c21306_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?fig=fig2&ref=pdfwww.acsami.org?ref=pdfhttps://doi.org/10.1021/acsami.2c21306?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asconductivity of an infinitely thick flake. We therefore provide,in Figure 2b, the mean-free-path fits to the data assuming abulk conductivity of either 8 or 16 W m−1 K−1, which both canprovide good fits to our measurements depending on theassumed phonon MFP distribution. The accompanying best-fitphonon mean-free-path contribution functions are shown inFigure 2c. In both fits, we find that phonons with mean freepaths >100 nm are responsible for the majority of the thermaltransport. The thermal conductivities as a function of thicknesscalculated from the fits are shown as lines in Figure 2b. We findthat all of the fits are in close agreement for thicknesses <200nm and begin to diverge at larger thicknesses.The measured thermal resistance of the hBN likely includessome small contributions from the interfacial thermalresistances (ITRs) between the hBN and surroundingmaterials.18,19 The thermal conductivity reported in Figure 2therefore represents a conservative lower bound. We accountfor possible ITR contributions by expressing the measuredtotal thermal resistance, Rtherm(d), as= +R d R d R( ) ( )therm hBN ITR (4)where RhBN(d) is the thermal-resistance contribution ofphonon scattering within the hBN layer and RITR is theinterfacial-thermal-resistance contribution given by= +R ITR ITR ITRITR (Al O /hBN) (hBN/SiO ) (Al O /SiO )x x2 2 2 2(5)Here, ITR(Al O /hBN)x2and ITR(hBN/SiO )2are the interfacialthermal resistances on the top and bottom surfaces of the hBNflake, respectively, and ITR(Al O /SiO )x2 2is the interfacial thermalresistance between the two oxide layers under the referenceheater. To our knowledge, there are no published measure-ments of these interfacial thermal resistances. Furthermore, theITRs are dependent on the microscopic conditions of theinterface and will vary from sample to sample.While we cannot directly measure these interface resistances,we can leverage the fact that interfacial thermal resistances donot vary significantly with temperature,31 whereas the thermalresistance of the hBN decreases with temperature.21 We set anupper bound on the interface resistances in our data byassuming that at low temperatures the hBN thermal resistanceis negligible, RhBN = 0, and therefore all thermal resistance wemeasure arises purely from interface scattering. The lowest-temperature data we report are at 198 K, seen in Figure 3a asred points. The measured thermal resistance at 198 K issubtracted from the resistance measured at 295 K, whichproduces the trend show in Figure 3b (orange points). InFigure 3c we show the thermal conductivities as a function ofthickness calculated using eq 1 (orange points) and fit the datawith differential mean-free-path contribution functions, assum-ing the bulk conductivity is either 8, 16, or 32 W m−1 K−2(solid lines). The conductivities calculated without consideringthe ITRs are shown as blue points for comparison. It is clearthat removing the ITR contribution increases the calculatedthermal conductivity and that the data are now only welldescribed by the fits using the higher bulk thermalconductivities of 16 or 32 W m−1 K−2 (purple and bluelines). The average phonon mean free paths from these fits are87 and 343 nm, respectively. In summary, this interfaceanalysis raises the expected bulk thermal conductivity of hBNand does not significantly reduce the extracted phonon meanfree paths.Phonon grain boundary scattering at stacking faults (planartwist interfaces) has been proposed as a limiting factor for themaximum possible phonon MFPs in two-dimensional materi-als. Studies of graphite correlated the maximum observedphonon MFPs with the average spacing between twist grainboundaries found in cross-sectional TEM images.18 Thishypothesis is further supported by studies of WSe2 crystalsgrown with random rotational mismatches between eachsuccessive layer that found that twist interfaces reduced thecross-plane thermal conductivity by a factor of 30 below that ofsingle-crystal samples.32 Molecular-dynamics simulations oftwist interfaces of both graphite and hBN have also shown thatsuch grain boundaries can significantly reduce the cross-planethermal conductivity.33To investigate the effects of grain boundary scattering inhBN, we introduce twist interfaces into a hBN crystal bymechanically stacking five exfoliated hBN flakes. The totalstack thickness is measured with an atomic force microscope tobe 74 ± 2 nm, and the individual layer thicknesses areestimated using optical contrast to be (from bottom to top) 26,19, 11, 10, and 8 nm, respectively. Figure 4a shows a schematicdiagram of the stacked flakes, and Figure 4b shows an opticalimage of the heating wire fabricated over the stack before theFigure 3. (a) The measured cross-plane thermal resistance of thehBN flakes multiplied by the surface area of the heating wire as afunction of flake thickness at 295 K (blue points) and 198 K (redpoints). (b) The cross-plane thermal resistance at 198 K is subtractedfrom the resistance at 295 K to remove the interfacial thermalresistance contribution (ITR). The remaining thermal resistance(orange points) is due solely to heat conduction in the hBN flake. Thephonon mean free path contribution fits to the data assuming that thethermal conductivity eventually saturates to either 8, 16, or 32 W m−1K−1 are shown as black, purple, and blue lines, respectively. (c) Thecalculated thermal conductivity of hBN with the ITR contributionremoved (orange points) and without the subtraction (blue points).The thermal conductivity fits to the ITR removed data points areshown as solid lines. (d) The differential phonon mean free pathspectra that best fit the orange data points shown in (b) assumingthree different values for the bulk thermal conductivity κbulk. The insetshows the corresponding thermal conductivity accumulationfunctions.ACS Applied Materials & Interfaces www.acsami.org Research Articlehttps://doi.org/10.1021/acsami.2c21306ACS Appl. Mater. Interfaces 2023, 15, 12545−1255012548https://pubs.acs.org/doi/10.1021/acsami.2c21306?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?fig=fig3&ref=pdfwww.acsami.org?ref=pdfhttps://doi.org/10.1021/acsami.2c21306?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashBN is etched into a mesa. The residue present between flakesin such stacked structures has been found to clump up intolarge bubbles after annealing.34 The heating wires arespecifically designed on each sample to route around thebubbles to provide a measurement of only the atomically cleaninterface regions. Dark-field optical imaging is used to identifyregions without bubbles or residue, an example image of whichcan be found in the Supporting Information.We measure the cross-plane thermal conductivity of the five-flake stack and compare the results to the thermal conductivityof individual flakes of similar thicknesses as a function oftemperature in Figure 4c. We calculate the expected thermalconductivity of a 74 nm flake to be 2.00 W m−1 K−1 at 295 Kby averaging the values from the fits at that thickness in Figure2b. By comparison, we measure the thermal conductivity of thefive-flake stack to be 0.26 ± 0.01 W m−1 K−1, more than afactor of 7 below this estimate and equivalent to that of a single∼9 nm flake. This indicates that strong phonon scattering atthe twist interfaces has drastically reduced the phonon MFPs,thereby reducing the thermal conductivity. Furthermore, thethermal conductivity of the stack does not increase at lowertemperatures, suggesting that the thermal conductivity isdominated by interface scattering.■ CONCLUSIONOur results show that the cross-plane thermal conductivity ofhBN is higher than previously thought. We measure it to be 8.1± 0.5 W m−1 K−1, but when interfaces are considered, it can beas large as 15.6 ± 2.5 W m−1 K−1. Our low-defect-densitysamples allow us to measure the thickness dependence of thethermal conductivity, thereby providing access to the phononmean free paths, which we find to be hundreds of nanometersin length, far exceeding previous predictions. We demonstratethat the thermal conductivity of thicker films of hBN can besignificantly reduced by stacking multiple thin flakes of hBNwith arbitrary rotational mismatches between each layer. Theability to stack hBN flakes at controlled angles and potentiallyincorporate layers of other two-dimensional materials withlong phonon MFPs, such as graphite and MoS2, presentsinteresting opportunities to explore phonon interface scatteringas parameters such as twist angle, layer thickness, and phononmode mismatch between layers are varied. The data presentedhere have important implications for thermal-managementefforts to incorporate hBN as a heat-spreading material,providing the necessary information for determining how thecross-plane thermal conductivity of hBN films will scale withfilm thickness.■ ASSOCIATED CONTENT*sı Supporting InformationThe Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acsami.2c21306.Phonon mean free path fitting procedure, temperature-dependent thermal conductivity data for multiple flakethicknesses, and device optical characterization (PDF)■ AUTHOR INFORMATIONCorresponding AuthorGabriel R. Jaffe − Department of Physics, University ofWisconsin-Madison, Madison, Wisconsin 53706, UnitedStates; orcid.org/0000-0003-2672-0375; Email: gjaffe@wisc.eduAuthorsKeenan J. Smith − Department of Physics, University ofWisconsin-Madison, Madison, Wisconsin 53706, UnitedStatesKenji Watanabe − Research Center for Functional Materials,National Institute for Materials Science, Tsukuba 305-0044,Japan; orcid.org/0000-0003-3701-8119Takashi Taniguchi − International Center for MaterialsNanoarchitectonics, National Institute for Materials Science,Tsukuba 305-0044, Japan; orcid.org/0000-0002-1467-3105Max G. Lagally − Department of Materials Science andEngineering, University of Wisconsin-Madison, Madison,Wisconsin 53706, United StatesMark A. Eriksson − Department of Physics, University ofWisconsin-Madison, Madison, Wisconsin 53706, UnitedStatesVictor W. Brar − Department of Physics, University ofWisconsin-Madison, Madison, Wisconsin 53706, UnitedStatesComplete contact information is available at:https://pubs.acs.org/10.1021/acsami.2c21306NotesThe authors declare no competing financial interest.Figure 4. (a) A schematic diagram showing a heterostructure consisting of five exfoliated hBN flakes mechanically stacked with arbitrary rotationalmismatches between each flake. (b) An optical image of the heating wire fabricated across the five-flake stack. (c) The measured cross-planethermal conductivity as a function of temperature of the five-flake stack shown in (b), which had a total thickness of 74 nm, is shown in red. The“■” and gray “▲” are the thermal conductivities of individual flakes from Figure 2 with thicknesses of 112 and 48 nm, respectively.ACS Applied Materials & Interfaces www.acsami.org Research Articlehttps://doi.org/10.1021/acsami.2c21306ACS Appl. Mater. Interfaces 2023, 15, 12545−1255012549https://pubs.acs.org/doi/suppl/10.1021/acsami.2c21306/suppl_file/am2c21306_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?goto=supporting-infohttps://pubs.acs.org/doi/suppl/10.1021/acsami.2c21306/suppl_file/am2c21306_si_001.pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Gabriel+R.+Jaffe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0003-2672-0375mailto:gjaffe@wisc.edumailto:gjaffe@wisc.eduhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Keenan+J.+Smith"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kenji+Watanabe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0003-3701-8119https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takashi+Taniguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0002-1467-3105https://orcid.org/0000-0002-1467-3105https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Max+G.+Lagally"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Mark+A.+Eriksson"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Victor+W.+Brar"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?ref=pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsami.2c21306?fig=fig4&ref=pdfwww.acsami.org?ref=pdfhttps://doi.org/10.1021/acsami.2c21306?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as■ ACKNOWLEDGMENTSThermal transport measurements and theoretical modelingwere performed with support from US DOE Basic EnergySciences DE-FG02-03ER46028. hBN crystal exfoliation andstacking was performed with support from US DOE BasicEnergy Sciences under award #DE-SC0020313. We acknowl-edge the use of facilities supported by NSF through the UW-Madison MRSEC (DMR-1720415) and electron beamlithography supported by the NSF MRI program (DMR-1625348). K.W. and T.T. acknowledge support from JSPSKAKENHI (Grant numbers 19H05790, 20H00354, and21H05233). We thank Dr. Donald Savage for his helpfulcomments and suggestions.■ REFERENCES(1) Sichel, E. K.; Miller, R. E.; Abrahams, M. S.; Buiocchi, C. J. HeatCapacity and Thermal Conductivity of Hexagonal Pyrolytic BoronNitride. Phys. Rev. B 1976, 13, 4607−4611.(2) Jo, I.; Pettes, M. T.; Kim, J.; Watanabe, K.; Taniguchi, T.; Yao,Z.; Shi, L. Thermal Conductivity and Phonon Transport inSuspended Few-Layer Hexagonal Boron Nitride. Nano Lett. 2013,13, 550−554.(3) Yuan, C.; Li, J.; Lindsay, L.; Cherns, D.; Pomeroy, J. W.; Liu, S.;Edgar, J. H.; Kuball, M. Modulating the Thermal Conductivity inHexagonal Boron Nitride via Controlled Boron Isotope Concen-tration. Communications Physics 2019, 2, 43.(4) Dean, C. R.; Young, A. 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