Reducing Interfacial Thermal Resistance Between Metal And .

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Reducing interfacial thermal resistancebetween metal and dielectric materials by ametal interlayerCite as: J. Appl. Phys. 125, 045302 (2019); https://doi.org/10.1063/1.5079428Submitted: 30 October 2018 . Accepted: 07 January 2019 . Published Online: 25 January 2019Xiangyu Li, Wonjun Park, Yan Wang, Yong P. Chen, and Xiulin RuanARTICLES YOU MAY BE INTERESTED INPhonon properties and thermal conductivity from first principles, lattice dynamics, and theBoltzmann transport equationJournal of Applied Physics 125, 011101 (2019); https://doi.org/10.1063/1.5064602Phonon thermal transport in encapsulated copper hybridsJournal of Applied Physics 125, 045106 (2019); https://doi.org/10.1063/1.5082191Nanoscale thermal transport. II. 2003–2012Applied Physics Reviews 1, 011305 (2014); https://doi.org/10.1063/1.4832615J. Appl. Phys. 125, 045302 (2019); https://doi.org/10.1063/1.5079428 2019 Author(s).125, 045302

Journal ofApplied PhysicsARTICLEscitation.org/journal/japReducing interfacial thermal resistance betweenmetal and dielectric materials by a metalinterlayerCite as: J. Appl. Phys. 125, 045302 (2019); doi: 10.1063/1.5079428Submitted: 30 October 2018 · Accepted: 7 January 2019 ·Published Online: 25 January 2019Xiangyu Li,1,2Wonjun Park,1,3 Yan Wang,4View OnlineExport CitationCrossMarkYong P. Chen,1,3,5 and Xiulin Ruan1,2,a)AFFILIATIONS1Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA2School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, USASchool of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA34School of Mechanical Engineering, University of Nevada, Reno, Nevada 89557, USA5Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USAa)Email: ruan@purdue.eduABSTRACTInterfacial thermal resistance between metal and dielectric materials is a bottleneck of the thermal management for modernintegrated circuits as interface density increases with thinner films. In this work, we have observed that the interfacial resistanceacross gold and aluminum oxide can be reduced from 4.8 10 8 m2 K W to 1.4 10 8 m2 K W after adding a nickel layer inbetween, which represents a 70% reduction. The two temperature model is applied to explain the reduction of interfacial resistance, and the results show that the nickel layer functions as a bridge that reduces the phonon mismatch between gold and aluminum oxide. Moreover, nickel has strong electron-phonon coupling, which reduces the thermal resistance caused by the weakelectron-phonon coupling in gold.Published under license by AIP Publishing. https://doi.org/10.1063/1.5079428I. INTRODUCTIONAs the thickness of thin films shrinks to micro/nanoscales, the interfacial resistance between metal and dielectricmaterials1–5 ( 10 8 m2 K W) becomes comparable to or dominant over the thermal resistance of thin films ( 10 nm) invarious engineering applications.6–8 In these scenarios, interfacial thermal resistance has become a bottleneck for thermalmanagement of nano-scale electronic devices. It is crucial toreduce such interfacial thermal resistances. For example, goldthin films have been widely used in electronic devices and thenext generation data storage technology called heat-assistedmagnetic recording (HAMR)9–11 due to its high conductance,low loss, and chemical stability. The thin films are typicallydeposited on dielectric substrates which serve as heat sinks.Low interfacial thermal resistance and high thermal conductivity of the dielectric are desired for better thermal management. Unfortunately, the interfacial thermal resistanceJ. Appl. Phys. 125, 045302 (2019); doi: 10.1063/1.5079428Published under license by AIP Publishing.between gold and dielectric materials is still high. Reportedresults are around 2 10 8 m2 K W when gold is deposited onthe sapphire substrate.2,12 However, when it comes to semiconductor devices, most aluminum oxide thin films for electrical insulation are amorphous.13,14 The interfacial thermalresistance further increases to 1.1 10 7 m2 K W if amorphousaluminum oxide is used.15 English et al.16 predicted, usingmolecular dynamics, that an intermediate layer to help bridgephonon spectra mismatch led to lower total resistancebetween metal and dielectric materials. Jeong et al.17 insertedan interlayer of Cu and Cr between gold and sapphire substrates, reducing interfacial thermal resistance considerably,and they attributed the reduction to the bridging of phononspectra mismatch. Recognizing that gold has weakelectron-phonon coupling which introduces high electronphonon non-equilibrium resistance, Wang et al.18 proposed toinsert a metal interlayer that has stronger electron-phonon125, 045302-1

Journal ofApplied PhysicsARTICLEscitation.org/journal/japcoupling to reduce this resistance. However, the possible roleof electron-phonon coupling has not been evaluated inexperiments. Also, such studies have not been done on amorphous aluminum oxide.In this work, we have fabricated three layered structureson silicon substrates, consisting of gold, nickel, and aluminumoxide layers. The nickel layer was selected primarily becauseof its higher electron-phonon coupling factor. The interfacialthermal resistance characterization is done by the 3ωmethod. A 70% reduction of total interfacial resistance isobserved after adding the nickel layer. The two-temperaturemodel is used to explain the change of interfacial resistance,and the modeling results show similar trends with experimental data.II. SAMPLE FABRICATIONThree structures, including reference sample A and twosandwich structures B and C, are fabricated to determine theinterfacial thermal resistance between metal and aluminumoxide layers, as shown in Fig. 1 with TEM (TransmissionElectron Microscope) images and schematic views. Thesilicon substrate is first cleaned with the RCA19 (the RadioCorporation of America) method, and HF (Hydrogen Fluoride)is used to remove any oxidation layer and contaminations.This is crucial due to low thermal conductivity of silicondioxide. Reference sample A has a 40 nm aluminum oxidelayer on the silicon substrate. Sample B consists of a 20 nmaluminum oxide layer, 50 nm gold layer, and another 20 nmaluminum oxide layer on top, preserving the total thickness ofthe aluminum oxide layer. By splitting the aluminum oxidelayer into two thinner ones, two gold-aluminum oxide interfaces are created for better measurement sensitivity, withoutintroducing unwanted ones, such as gold-silicon interface.The surface also remains electrically insulating for the 3ωmeasurement. Sample C inserts 20 nm nickel layers inbetween the gold and aluminum oxide layers. The aluminumoxide layers are deposited with atomic layer deposition toensure a consistent thickness, and metal layers are depositedby thermal evaporation. During FIB (Focused Ion Beam)lift-off for TEM images, a Pt layer is deposited on the surfaceto protect the sample during milling, which is still present inFig. 1 as the unlabeled top layer above aluminum oxide.III. INTERFACIAL THERMAL RESISTANCECHARACTERIZATIONThe differential 3ω method20–22 is used to characterizethe interfacial resistance in our work. It was developed tomeasure thin film thermal conductivity and interfacial resistance. In this work, a 30 μm wide and 3 mm long metal line isdeposited using photolithography. Because of the small sizeof the metal line, the radiation loss even at high temperatureis insignificant. With the joule heating of the metal line underAC current with frequency ω, the surface of the sample experiences a frequency-dependent temperature oscillationamplitude of ΔT(ω), and the voltage has a frequency of 3ω.Detailed mathematic deviations can be found in theJ. Appl. Phys. 125, 045302 (2019); doi: 10.1063/1.5079428Published under license by AIP Publishing.FIG. 1. Sandwich structures fabricated with multiple layers. (a) Sample A.(b) Sample B. (c) Sample C.125, 045302-2

Journal ofApplied 21,22ΔT(ω) ¼pR þ Co (ω),2bl(1)where p, b, and l are the power consumption, half width, andlength of the metal line, repectively. Co is dependent on frequency but remains the same across all three samples. R represents thermal resistance above the substrate. Thermalresistances of Ni and Au layers are neglected due to highthermal conductance and so is the interfacial resistancebetween them. The amorphous aluminum oxide thin filmswithin 60 nm show similar thermal conductivity, reported byDeCoster et al.23 Thus, the thermal resistance of aluminumoxide films is the same across all samples. The thermal resistance above the silicon substrate for each sample isRA ¼ 2RAl2 O3 þ RSi Al2 O3 ,(2)RB ¼ 2RAl2 O3 þ RSi Al2 O3 þ 2RAu Al2 O3 ,(3)RC ¼ 2RAl2 O3 þ RSi Al2 O3 þ 2RNi Al2 O3 þ RAu Ni :(4)Subtracting reference sample A from samples B and C, we canassociate thermal resistance difference ΔR1 and ΔR2 withΔT(ω) from the 3ω measurement, as shown below,20ΔR1 ¼ RB RA ¼ 2RAu Al2 O3 ΔT(ω)ΔT(ω)¼ 2bl ,ppBAΔR2 ¼ 2RNi Al2 O3 þ 2RAu Ni 2RNi Al2 O3 ΔT(ω)ΔT(ω),¼ 2bl ppCA(5)(6)FIG. 2. 3ω measurement for three sandwich structures.tool for interfacial resistance estimation,24–29 assuming twodifferent temperatures for phonons and electrons, respectively, in the metal side. Wang et al.29 combined the two temperature model with molecular dynamics to illustrate theimpact of the electron-phonon coupling effect. The overallinterfacial resistance consists of a phonon-phonon component R pp , an electron-phonon nonequilibrium component Rep ,as well as an electrical inelastic scattering component, Rei , asshown in Fig. 3.30 The third component Rei is estimatedaround 3431 10 9 m2 K W for Au and 4:3 5:9 where ΔT(ω) from the 3ω measurement regarding to differentsamples as well as various frequencies are shown in Fig. 2.Sample B has an overall higher ðΔT pÞ, representing highertotal resistance than Sample A due to the added Au layer.Sample C sits between Samples A and B, indicating total resistance is lowered as the nickel interlayer is added. All threeðΔT pÞ curves are relatively parallel to each other. The thermalresistance difference is calculated from the average of thegaps between the curves at different frequencies. We obtainedthat the interfacial resistance between gold and aluminumoxide is 4:8 0:5 10 8 m2 K W, and that between the nickeland aluminum oxide is 1:4 0:1 10 8 m2 K W. This indicatesa 70% reduction of resistance after inserting the Ni layer. Theuncertainties are evaluated based on the variation of thesegaps at different frequencies in Eqs. (5) and (6). In this case,sample B yields an uncertainty around 11.5%, and sample C anuncertainty of 7.9%.IV. THEORETICAL ESTIMATION ON INTERFACIALRESISTANCEBecause our metal-dielectric system involves both electrons and phonons, the two-temperature model suits as theJ. Appl. Phys. 125, 045302 (2019); doi: 10.1063/1.5079428Published under license by AIP Publishing.FIG. 3. Thermal resistance network between nickel and aluminum oxide.125, 045302-3

Journal ofApplied Physics10 9 m2 K W for Ni.30–32 Thus, Rei for Au will be neglectedwhile that for Ni will be accounted.The first part R pp happens across both metaldielectric and dielectric-dielectric interfaces. Acousticmismatch model (AMM)33,34 and diffuse mismatch model(DMM)34 are two models widely used on different interface conditions. The former works mostly for ideal interfaces at low temperatures, which rarely happens inexperiments. Hence, we use DMM here, which assumesphonons lose their correlations and randomize directionsacross the interface. We chose the [100] direction for Niand Au, and [1010] for aluminum oxide for heat flux direction across the interface. The phonon density of states isshown for aluminum oxide, gold and nickel, respectively,in Fig. 4. To calculate phonon dispersion and density ofstates, we assume crystalline structures of metals and aluminum oxide layer for simplification. Since the metallayers are polycrystalline and an aluminum oxide layer isamorphous in our structures, the theoretical results wouldunderestimate interfacial resistance. With film thicknesseshigher than the phonon mean free path, the bulk phonondensity of states is calculated for Au and Ni.35 Amorphousalumina is reported with a different phonon density ofstates, though most of the differences are at frequenciesover 10 THz, beyond the phonon frequency ranges of Niand Au.36 Please also note that our DMM and TTM resultsshould be understood on a qualitative basis since they areintended for crystal alumina rather than amorphousalumina. In Fig. 4, both nickel and gold phonons overlapwith aluminum oxide phonons at low frequencies whereacoustic phonons dominate. Compared with gold, nickelphonons show a larger overlap with aluminum oxide, dueARTICLEscitation.org/journal/japTABLE I. Properties for Ni and Au for Rei calculation.γ ( J m 3 K 2)τ e ph (ps)ul 3AuNito its smaller lattice constant and lighter atom mass, functioning as a phonon bridge between aluminum oxide andgold phonon frequencies. DOS can be affected by latticeconstant, atom mass, and bonding strength, while a quantitative relation is rather complicated. For phonon transmission coefficient α, αA!B ¼ αB!A is satisfied. With that, R ppcan be calculated as37ð1 X@f hωMA (ω)αA!Bdω,(7)hA!B ¼2πAc j@TP0αA!B (ω ) ¼ PMB (ω)P,j MB (ω) þj MA (ω)jM ¼ πAc v K(ω)2g2 2π 2 vg(8),(9)where M is the number of phonon modes, j stands forphonon modes, Ac stands for contact region area, vg isthe group velocity, K is wavevector, and f is theBose-Einstein distribution function. The results are shownin Table II.For the resistance due to electron-phonon coupling, thetwo temperature model considers the electron-phonon coupling effect by assigning two temperatures for electrons andphonons. Since electrons are main carriers for heat transferin most metals, the interfacial resistance based on the twotemperature model can be written as24,29" 3 2 1 2 #1ke1Ri ¼ Rei (R pp þ Rep ) ¼ Rei þh ppGep kpke þ kp" 1 2 #11,þ Rei h ppGep kp(10)where Gep is the electron-phonon coupling factor formetals,26,38 ke and kp are the electron and lattice thermal conductivity of the metal, respectively, Ri is the overall interfacialthermal resistance, R pp and h pp are lattice mismatch resistanceTABLE II. Comparison between the TTM and 3ω measurement.Au-Al2 O3Ni-Al2 O3FIG. 4. Phonon density of states for Ni, Au, and aluminum oxide.J. Appl. Phys. 125, 045302 (2019); doi: 10.1063/1.5079428Published under license by AIP Publishing.aR pp aRep aRi aExperimenta20.66.74.30.224.92.948.414.010 9 m2 K W.125, 045302-4

Journal ofApplied Physicsand conductance, respectively, and Rep is the interfacial resistance with regard to the electron-phonon coupling effect. Gep isset as 2:88 1017 W m3 K for nickel and 2:6 1016 W m3 K forgold. kp ¼ 18:5 W m K for 20 nm nickel film and kp ¼ 1:5 W m Kfor 50 nm gold film from first principles calculations.39We adopted the work of Sergeev31 to estimate Rei , theinelastic electron-boundary scattering in our system. Theequation is as follows:" 3 #3π hγululel1þ2σK ¼,(11)35ζ(3)kB τ e phutin which h is the reduced Planck constant, ζ is the Riemann Zetafunction, kB is the Boltzmann constant, γ is the Sommerfeldconstant, τ e ph is the electron phonon relaxation time, and u isthe sound velocity with the subscript l denoting longitudinalphonon and t for transverse waves. We used the propertieslisted in Table I in our calculation, where the group velocities areobtained from our own first-principles calculations.2We estimate the σ elK for Au-Al2 O3 to be 291 397 W m Kwhile that for Ni-Al2 O3 to be 1:7 2:3 108 W m2 K. Afterconverting these into resistances, we obtained Rei,Au Al2 O3 ¼3431 10 9 m2 K W and Rei,Ni Al2 O3 ¼ 4:3 5:9 10 9 m2 K W.The former one can be neglected, while the latter is includedin the theoretical estimation in this revision.In our study, theoretical estimations using the TTM areshown in Table II along with experimental data. It can beseen that inserting a Ni layer significantly reduces both R ppand Rep . With a Ni interlayer, Rep almost diminishes, and R ppdominates the overall interfacial resistance. Compared withgold, phonons in nickel show a larger match with those inaluminum oxide, resulting in lower phonon-phonon resistance than gold. The difference between experiments andtheoretical estimations is mainly due to the fact that we usedcrystalline phonon properties for Al2 O3 . Adhesion betweenfilms is another significant factor leading to poor interfacialthermal resistance.15,43,44 Lahmar et al. have measured interfacial thermal resistance of 1:1 10 7 m2 K W between goldand aluminum oxide, which decreases below 10 8 m2 K Wafter improving film adhesion by thermal treatment.15 Wealso saw a rougher interface between nickel and aluminumoxide, which may have some effect on interfacial thermalresistance, but unlikely to be the major contribution. Despitethese simplifications, our model reveals the same trendsobserved in experiments.V. CONCLUSIONIn this work, we measured the interfacial thermal resistance between gold and aluminum oxide before and afterinserting a Ni interlayer. The interfacial resistance decreasesby 70%, from 4.8 10 8 m2 K W to 1.4 10 8 m2 K W.Theoretical calculations using the diffuse mismatch modeland two-temperature model show a similar trend with experimental data, indicating that the Ni layer significantly reducesboth resistances due to phonon mismatch and electronphonon non-equilibrium.J. Appl. Phys. 125, 045302 (2019); doi: 10.1063/1.5079428Published under license by AIP EDGMENTSThanks go to Tianli Feng and Zexi Lu at PurdueUniversity for their useful discussions in the two temperaturemodel and phonon dispersion.REFERENCESS.-M. Lee and D. G. Cahill, J. Appl. Phys. 81, 2590 (1997).R. J. Stoner and H. J. Maris, Phys. Rev. B 48, 16373 (1993).3R. J. Stevens, A. N. Smith, and P. M. Norris, J. Heat Transfer 127, 315(2005).4A. J. Griffin, F. R. Brotzen, and P. J. Loos, J. Appl. Phys. 75, 3761 (1994).5J. H. Kim, A. Feldman, and D. Novotny, J. Appl. Phys. 86, 3959 (1999).6B.A. Cola, J. Xu, C. Cheng, X. Xu, T. S. Fisher, and H. Hu, J. Appl. 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S. English, J. C. Duda, J. L. Smoyer, D. A. Jordan, P. M. Norris, andL. V. Zhigilei, Phys. Rev. B 85, 035438 (2012).17M. Jeong, J. P. Freedman, H. J. Liang, C.-M. Chow, V. M. Sokalski,J. A. Bain, and J. A. Malen, Phys. Rev. Appl. 5, 014009 (2016).18Y. Wang, Z. Lu, A. K. Roy, and X. Ruan, J. Appl. Phys. 119, 065103 (2016).19W. Kern and D. A. Puotinen, RCA Rev. 31, 187 (1970).20T. Borca-Tasciuc, A. R. Kumar, and G. Chen, Rev. Sci. Instrum. 72, 2139(2001).21D. G. Cahill, Rev. Sci. Instrum. 61, 802 (1990).22D. G. Cahill, J. Vac. Sci. Technol. A 7, 1259 (1989).23M. E. DeCoster, K. E. Meyer, B. D. Piercy, J. T. Gaskins, B. F. Donovan,A. Giri, N. A. Strnad, D. M. Potrepka, A. A. W

Low interfacial thermal resistance and high thermal conduc-tivity of the dielectric are desired for better thermal manage-ment. Unfortunately, the interfacial thermal resistance between gold and dielectric materials is still high. Reported results are around 2 10 8 m2 K W when gold is deposited on the sapphire substrate.2,12 However, when it .

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