Interfacial Defect Vibrations Enhance Thermal Transport In .

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CommunicationThermal Transportwww.advmat.deInterfacial Defect Vibrations Enhance Thermal Transport inAmorphous Multilayers with Ultrahigh Thermal BoundaryConductanceAshutosh Giri,* Sean W. King, William A. Lanford, Antonio B. Mei, Devin Merrill,Liyi Li, Ron Oviedo, John Richards, David H. Olson, Jeffrey L. Braun, John T. Gaskins,Freddy Deangelis, Asegun Henry, and Patrick E. Hopkins*conductivity have been driven by additionaltemperature drops occurring at each interface. These temperature drops are quantified by the thermal boundary conductance(TBC), which is traditionally assumed tobe related to the phonon states in eachmaterial comprising the interface. Whilelowering effective thermal conductivity byadding interfaces is great for thermoelectricand thermal barrier coating applications, itis highly undesirable for microelectronicapplications where there is a need to dissipate ever increasing amounts of wasteheat thanks to continued miniaturizationleading to increased device and interfacedensity. More specifically, increased interface density may be good for thermalinsulation applications but is bad from athermal perspective for microelectronicdevices. Thus, the approach of engineeringmaterials with high densities of interfacesto achieve ultralow thermal conductivitysolids requires a fundamental understanding of how atomic vibrations interactand exchange energy at interfaces, which, with the advent of disorder and other nanoscale features, is arguably lacking.While including disorder in a crystalline system can lead toreductions in thermal conductivity, this same phenomena maynot hold true at interfaces. Recent theories have suggested thatThe role of interfacial nonidealities and disorder on thermal transportacross interfaces is traditionally assumed to add resistance to heat transfer,decreasing the thermal boundary conductance (TBC). However, recent computational studies have suggested that interfacial defects can enhance thisthermal boundary conductance through the emergence of unique vibrationalmodes intrinsic to the material interface and defect atoms, a finding that contradicts traditional theory and conventional understanding. By manipulatingthe local heat flux of atomic vibrations that comprise these interfacial modes,in principle, the TBC can be increased. In this work, experimental evidenceis provided that interfacial defects can enhance the TBC across interfacesthrough the emergence of unique high-frequency vibrational modes thatarise from atomic mass defects at the interface with relatively small masses.Ultrahigh TBC is demonstrated at amorphous SiOC:H/SiC:H interfaces,approaching 1 GW m 2 K 1 and are further increased through the introductionof nitrogen defects. The fact that disordered interfaces can exhibit such highconductances, which can be further increased with additional defects, offers aunique direction to manipulate heat transfer across materials with high densities of interfaces by controlling and enhancing interfacial thermal transport.Heterogeneous interfaces between two adjacent solids haveenabled the realization of ultralow thermal conductivity materials,[1–5] with reduction to thermal conductivity often fallingbelow the corresponding minimum limit traditionally attributed to a pure amorphous solid.[6] These reductions in thermalDr. A. Giri, D. H. Olson, J. L. Braun, Dr. J. T. Gaskins,Prof. P. E. HopkinsDepartment of Mechanical and Aerospace EngineeringUniversity of VirginiaCharlottesville, VA 22904, USAE-mail: ag4ar@virginia.edu; peh4v@virginia.eduDr. S. W. King, Dr. A. B. Mei, Dr. D. Merrill, Dr. L. Li, R. Oviedo,J. RichardsIntel CorporationLogic Technology Development5200 NE Elam Young Parkway, Hillsboro, OR 97124, USAThe ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/adma.201804097.Prof. W. A. LanfordDepartment of PhysicsUniversity at AlbanyState University of New YorkAlbany, NY 12222, USAF. Deangelis, Prof. A. HenryThe George W. Woodruff School of Mechanical EngineeringGeorgia Institute of TechnologyAtlanta, GA 30332, USAProf. A HenryDepartment of Mechanical EngineeringMassachusetts Institute of TechnologyCambridge, 02139 Massachusetts, USADOI: 10.1002/adma.201804097Adv. Mater. 2018, 30, 18040971804097 (1 of 6) 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

l modes unique to the interfaces that do not existintrinsically in any of the homogeneous materials can in factcontribute substantially to the TBC.[7–11] Therefore, judiciouslyselected defects near the interface could in principle be usedto increase the TBC by enhancing these interfacial modes. Inthis case, disordered interfaces could lead to higher TBCs thanmore “perfect” interfaces. Indeed, recent computational workshave demonstrated that the TBC at amorphous/amorphous andamorphous/crystalline interfaces can be higher than that at crystalline/crystalline interfaces composed of the same material.[12,13]This reasoning cannot be explained by conventional phononTBC theories[14–16] and offers a unique picture of how vibrationalenergy couples across defected or disordered interfaces. However, experimental demonstrations of the existence of these interfacial defect modes and their contributions to TBC are lacking.In this work, we report on the thermal conductivity of a seriesof amorphous multilayers (AMLs) composed of alternating layersof hydrogenated amorphous silicon carbide (a-SiC:H) and hydrogenated amorphous silicon oxycarbide (a-SiOC:H) with varyinginterface densities. One of the main reasons for studying thesematerial systems stems from a practicality standpoint, as theexistence of these particular amorphous systems is widespread inhigh density, highly integrated microelectronic products mainlydue to their low dielectric constants.[17] This is particularly thecase in metal interconnect structures where multiple layers ofamorphous dielectric materials are stacked upon one anotherand inlaid with Cu lines. In this regard, the SiC:H/SiOC:Hsystem investigated is highly relevant as SiC:H represents the Cucapping/etch stop layer and the SiOC:H material represents theinterlayer dielectric material that isolates the Cu lines.As the heat transport in these AMLs is completely diffusive,we extract a TBC across the a-SiC:H/a-SiOC:H interface thatapproaches 1 GW m 2 K 1, the highest diffusive TBC measuredto date. Through an in situ plasma exposure, we introduce N2defects at and near the interface in each layer of the AML. Theintroduction of these defects causes the thermal conductivity ofthese AMLs to become independent of interface density; inother words, the resistance at the interfaces becomes negligible,or the TBC increases beyond the ability to measure a quantifiable value. Supported with both vibrational spectroscopy andmolecular dynamics simulations, we identify interfacial defectmodes that arise in the thermal phonon regime only in theN2-processed AMLs.The amorphous SiOC:H/SiC:H multilayer samples weredeposited on crystalline silicon substrates via plasma-enhancedchemical vapor deposition (PECVD). A sample series with N2plasma-treated multilayers, carried out in situ during growthbetween the deposition of either the SiOC:H or the SiC:Hlayers, were also fabricated to understand the effect of interfacial nonidealities that arise due to lighter atoms at the interfaceon mediating thermal transport across disordered interfaces. Aschematic of the sample used for our thermal measurementsis shown in Figure 1a. The film and period thicknesses weredetermined via X-ray reflectivity (XRR) and cross-section scanning electron microscopy (XSEM) measurements; exampleXSEM and XRR measurements are shown in Figure 1b,c, fora SiOC:H/SiC:H multilayer with N2 plasma treatments carriedout on the surface of the SiOC:H layers, and for a multilayerwith N2 plasma treatments carried out on the surface of theAdv. Mater. 2018, 30, 1804097SiC:H layers, respectively. The chemical compositions of themultilayer films and homogeneous samples were determinedusing nuclear reaction analysis and Rutherford backscattering(RBS) spectroscopy (details in the Supporting Information). Thepercent composition of C, N, O, Si, and H is tabulated in TableS1 (Supporting Information). Along with the chemical compositions, the densities of the films were determined by combiningthe film compositions (in atoms cm 2) with the measured filmthicknesses and are tabulated in Table S1 (Supporting Information). The vibrational properties of the samples were studiedusing Fourier transform infrared (FTIR) spectroscopy. Figure 1dshows example spectra for different period thicknesses ofSiOC:H/SiC:H multilayers with and without N2 plasma. Incomparison to the SiOC:H/SiC:H sample, the similaritiesbetween the FTIR spectra of the sample in which the SiC:Hwas treated with N2 versus the sample in which the SiOC:H wastreated with plasma suggests the N2 plasma is enhancing thevibrations in the 20–30 THz range, as discussed in detail later.To measure the thermal properties, we employed the timedomain thermoreflectance (TDTR) technique, which is a noncontact optical pump-probe technique (details are given in the Supporting Information). First, we measure the thermal conductivityand heat capacity of individual SiOC:H and SiC:H films as a function of film thickness (as shown in Figure S7, Supporting Information). The lack of film thickness dependence on the thermalconductivity for the a-SiOC:H and a-SiC:H films suggests thatheat conduction is mostly driven by vibrations that are nonpropagating (e.g., diffusons and locons).[18–20] This is in contrast torecent experimental results demonstrating size effects and anisotropic thermal conductivity of amorphous Si thin films and nanostructures,[21–23] where a significant portion of heat flow is dueto propagons that represent delocalized propagating modes. Thelack of size effects in the thermal conductivity of a-SiOC:H canbe attributed to the Si O Si network structure confirmed fromthe FTIR measurements (Figure S3a, Supporting Information),which is similar to the structure found in SiO2; the lack of sizeeffects in SiO2 is primarily due to the weak bonding that existsbetween the SiO4 tetrahedra, whereas the thickness dependentthermal conductivity in a-Si is a result of strongly bonded tetrahedra.[18] Although cross-plane thermal conductivity measurements on thin amorphous SiO2 films have revealed a lack of sizeeffects,[21,23] we note that a recent study has observed ballisticpropagation of thermal phonons across amorphous SiO2 layersthat are up to 5 nm thick. In this regard, although our SiOC:Hand SiC:H films demonstrate lack of size effects in the crossplane direction, ballistic transport of phonons across thin layersof SiOC:H and SiC:H could be observed with the correct experimental techniques, such as that reported in ref. [24].For the a-SiC:H films, the FTIR results show that the network structure mostly consists of Si C stretching modessimilar to a-SiC systems (as shown in Figure S3b, SupportingInformation);[25,26] the lack of size effects in the a-SiC:H is consistent with size independent thermal conductivities measuredfor amorphous SiC in ref. [27]. These findings along with themeasurement of heat capacities for the amorphous SiOC:H andSiC:H films and the measured thermal conductivities of amorphous SiOC:H/SiC:H SLs with varying period thicknesses areused to derive a mean TBC across a single SiOC:H/SiC:H interface as detailed in the discussions below.1804097 (2 of 6) 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

www.advancedsciencenews.comwww.advmat.deFigure 1. a) Schematic of a multilayer sample for our thermal measurements via the pump-probe TDTR technique. b) Characteristic XSEM imagefor a multilayer with 27.4 nm period thickness and N2 plasma treatment carried out on the surface of SiC:H layers. The thickness and periodicity canbe confirmed via the XSEM images. c) Characteristic XRR patterns showing superlattice reflections exemplified by the peaks in the XRR data for a(7.8 nm period thick) SiC:H/SiOC:H sample with N2 plasma treatment over SiOC:H layers. d) Characteristic FTIR spectra for two representative samples with and without N2 plasma treatment on the SiOC:H or SiC:H laminates in situ during growth.The measured thermal conductivities of the amorphousSiOC:H/SiC:H superlattices are shown as a function ofperiod lengths and interface densities in Figure 2a and 2b,respectively (square symbols). The thermal conductivity forSiC:H/SiOC:H SLs monotonically decreases with decreasingperiod thickness and increasing interface density. This suggeststhat the interfaces in the amorphous SLs contribute nonnegligibly to thermal resistance across the thin films. To determinethe TBC across the SiC:H/SiOC:H interface, we apply the widelyused thermal circuit model,[28] which describes the resistivity, ρ,of a SL as a superposition of the thermal resistances of the individual layers and the resistances at the individual interfaces asρ κ 1 1 LL 2RK L 2κ SiOC:H 2κ SiC:H (1)where κSiOC:H and κSiC:H are determined from the measurements of the thickness series for the respective homogeneous samples. Equation (1) is fit to the experimentaldata with RK as the fitting parameter. Using this approach,we determine RK 1.1 m2 K GW 1 (alternatively the TBC,hK 1/RK 909 MW m 2 K 1), resulting in the best-fit lineshown in Figure 2.This intrinsic TBC across our amorphous SiC:H/SiOC:Hinterfaces is considerably higher than mostly all TBCs reportedin the literature for crystalline/crystalline interfaces as shown inFigure 3, which plots the experimentally measured TBCs acrossAdv. Mater. 2018, 30, 1804097various interfaces as a function of the ratio of elastic modulibetween the two constituents. Typical TBCs at crystalline/crystalline interfaces range from 20 to 300 MW m 2 K 1 and are shownin Figure 3 (in the shaded region in Figure 3). A better matchbetween the elastic moduli of the crystalline materials formingthe interface and a high quality of interface usually results in ahigher TBC. For example, in ref. [40], it is shown that by controlling the surface condition between crystalline silicon nanomembranes mechanically joined on to silicon substrates through vander Waals interactions, the TBC can be tuned by as much as300%. However, for interfaces comprising of amorphous solids,the measured TBCs can be relatively higher even for interfacesbetween materials with highly mismatched elastic moduli.The high TBCs at these amorphous SiC:H/SiOC:H interfacesare in line with those predicted via molecular dynamics simulations (refs. [12] and [39]), experimentally measured acrossSiO2/Al2O3 interfaces reported from a single AML at roomtemperature ( 0.67 GW m 2 K 1),[45] and the lower limit toTBC measured across an amorphous SiO2/crystalline Si interface.[29] In ref. [39], we showed that the TBC across a genericLennard Jones (LJ)-based amorphous/amorphous interface ishigher than that of their crystalline counterpart, suggestingthat TBC associated with amorphous interfaces are, in general,much higher than those across their corresponding crystallineinterfaces. An analysis to predict the spectral contributions atthe LJ-based amorphous/amorphous and crystalline/crystalline interfaces (as detailed in the Supporting Information)1804097 (3 of 6) 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1.4N2 plasma over SiC:H(a)0.80.60.4Eq. 1,hK 909 MW m-2 K-1;RK 1.1 m2 K GW-10.2051015202530Period Length, L (nm)1.4(b)N2 plasma over SiOC:H1.21SiC:H/SiOC:Hamorphous/amorphous(this work)800SiO /Al O22SrRuO3 /SrTiO33amorphous/amorphousCoSi 2 /SiSiO /GaN0ZnO/HQ/ZnONiSi/SiAl/Si00.2Pt/Al O20.4Pt/Si3Au/SiBi/Si0.60.811.2Ratio of Elastic Modulus0.8Figure 3. Experimentally measured thermal boundary conductanceversus ratio of the elastic moduli of the two constituent materials (forSi/SiO2,[29] Al/diamond, Pt/diamond,[30] Al/SiC,[31] Au/GaN,[32] Al/Ge,[33]GaN/SiC,[34] TiN/MgO,[35] SrRuO3/SrTiO3,[36] Pt/Al2O3,[37] ZnO/GaN,[38]ZnO/HQ/ZnO,[39] Si/vdW (van der Waals interface)/Si,[40] Bi/Si,[41] Mo/Si, Al/Si, Ni/Si,[42] Cr/Si, Pt/Si, Au/Si,[43] NiSi/Si, and CoSi2/Si[44]).0.60.4Eq. 1,hK 909 MW m-2 K-1;RK 1.1 m2 K GW-10.200.05Thermal Boundary Conductance (MW mThermal Conductivity,(W m-1 K-1 )101000-21.2www.advmat.deK -1)www.advancedsciencenews.com0.11Interface Density, N (nm -1 )Figure 2. a,b) Thermal conductivities of amorphous SiOC:H/SiC:H superlattices plotted as a function of period length (a) and interface density (b).For comparison, thermal conductivities of N2 plasma treated superlatticesare also included. The solid square symbols represent AMLs without the N2plasma treatments. The hollow triangles represent AMLs with N2 plasmatreatment on the SiC:H layers, whereas the solid triangles represent AMLswith N2 plasma treatment on the SiOC:H layers. The N2 plasma is shown toincrease the thermal conductivities of AMLs with smaller period thicknessesregardless of whether the plasma is applied on the SiC:H or SiOC:H layers.suggests that vibrations carrying heat across interfaces are verydifferent between the amorphous and crystalline phases. Alongthese lines, recent work has suggested that disorder aroundamorphous interfaces forces atomic vibrations near the interface to perturb the natural modes of vibrations in the amorphous materials, leading to higher frequency vibrations nearthe interface that effectively couple with one another.[12] Thus,in the event that the masses of these atoms are reduced, thelocal velocity that drives the cross-correlation of the heat fluxwill be increased. In this regard, the introduction of light atomimpurities at amorphous interfaces should further increase theTBC by enabling a higher heat flux across the interface.Figure 2 shows the thermal conductivity of the multilayerswith N2 plasma treatment carried out after either the SiOC:Hor SiC:H layers are deposited. For both cases, when N2 plasmais exposed on the SiOC:H layers or on the SiC:H layers, thethermal conductivity of the multilayers is independent ofperiod thicknesses, in contrast to the results for the multilayerswithout the plasma treatment.As shown in Table S1 (Supporting Information), the chemicalcompositions and the density of the multilayers do not changeAdv. Mater. 2018, 30, 1804097significantly due to the plasma treatment, which suggests thatthe varying thermal conductivity trends as shown in Figure 2 forour AMLs with/without plasma treatments is not due to densification or drastic changes in the composition and coordinationnumber for these films. Furthermore, the thermal conductivity ofsamples with plasma treatment carried out at different thicknessintervals for homogeneous SiC:H and SiOC:H films (i.e., SiC:H/N2 plasma/SiC:H/N2 plasma or SiOC:H/N2 plasma/SiOC:H/N2plasma) do not change within uncertainty compared to the oneswithout the plasma treatment (Table S1, Supporting Information).These observations suggest that there is a different mechanismleading to an increase in the thermal conductivity of the N2 plasmatreated samples at high interface densities. To investigate this phenomenon further, we turn to material specific lattice dynamics calculations for our structures to assess how the vibrational modeschange with N2 plasma treatment. Figure 4a shows the densityof states (DOS) for the interfacial modes predicted by a supercelllattice dynamics (SCLD) calculation for a short 2.5 nm periodAML structure. The SCLD calculations used the ReaxFF potentialto model the interatomic interactions[46] and the definition of an“interfacial mode” was taken to be the same as what was used previously by Gordiz and Henry.[11] Here, the interfacial region wastaken to be all atoms within 7 Å of the interface. As expected,since the two different systems contain different atom types in theinterfacial region, the structures wi

reductions in thermal conductivity, this same phenomena may not hold true at interfaces. Recent theories have suggested that The role of interfacial nonidealities and disorder on thermal transport across interfaces is traditionally assumed to add resistance to heat transfer, decreasing the thermal boundary conductance (TBC). However, recent com-

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