Proceedings of the ASME/JSME 2011 8th Thermal Engineering Joint ConferenceAJTEC2011

March 13-17, 2011, Honolulu, Hawaii, USA

AJTEC2011-44333

THERMAL BOUNDARY CONDUCTANCE BETWEEN THIN METAL FILMS ANDGRAPHITE SUBSTRATES

Justin L. SmoyerDept. of Mech. and Aero. Engr.

University of VirginiaCharlottesville, Virginia 22904

Email: jls5ra@virgina.edu

John C. DudaDept. of Mech. and Aero. Engr.

University of VirginiaCharlottesville, Virginia 22904

Email: duda@virgina.edu

Pamela M. NorrisDept. of Mech. and Aero. Engr.

University of VirginiaCharlottesville, Virginia 22904Email: pamela@virgina.edu

Arthur W. LichtenbergerDept. of Elec. and Comp. Engr.

University of VirginiaCharlottesville, Virginia 22904Email: arthurw@virgina.edu

ABSTRACT

Due to the high intrinsic thermal conductivity of graphiticstructures, much interest has developed in incorporating thesematerials into modern nano-devices for improved thermal abate-ment. In order to be integrated successfully, thermal energymust be able to transport efficiently through the graphitic materi-als and into the surrounding structure, most commonly a metal.However, thermal boundary conductance at metal-graphite in-terfaces is traditionally poor in comparison to non-graphitic sub-strates, due in large part to the weak van der Waals adhesionforce between the metal and underlying carbon structure. To beapplicable as thermal abatement materials, an enhanced under-standing of the role of the metal-carbon interface is required.This paper reports the changes to phononic thermal transportacross the interface between metallic thin films and highly ori-ented pyrolitic graphite (HOPG) substrates due to changes ininterface structure and chemistry. The temperature dependentthermal boundary conductance is measured using transient ther-moreflectance from 100 K to 400 K. It is found that the differ-ences in metal-carbon bonding and structure at the interfacehave a significant impact on the thermal conductance betweenthe metallic thin films and the HOPG substrates.

INTRODUCTIONWith increasing power densities in modern micro- and nano-

devices, thermal abatement has moved to the forefront as themajor limiting factor in the continued development of smallerdevices and is ultimately inhibiting device performance. Due totheir intrinsically high thermal conductivity, allotropes of car-bon, i.e. carbon nanotubes (CNTs) and graphite, have become ofgreat interest for thermal management solutions. In-plane ther-mal conductivity in highly oriented pyrolitic graphite (HOPG) is∼2,100 W/m-K at room temperature [1], and the room tempera-ture thermal conductivity of single walled and multiwalled CNTshas been measured between 1,750-5,800 W/m-K [2–4]. Incorpo-ration of these allotropes into thermal abatement solutions hasalready shown promising results, specifically with CNT-basedthermal interface materials (TIMs) [5, 6], and carbon reinforcedmetallic heat spreaders [7, 8].

While there is currently very little literature on experi-mental measurements of thermal boundary conductance, (hBD),between metallic films and HOPG [9, 10], current results showgenerally low hBD compared to typical metal-semiconductorsystems [11]. The low hBD of the metal-HOPG system canbe attributed to many contributing factors including the large

1 Copyright c© 2011 by ASME

vibrational spectrum mismatch between the metallic thin filmand the underlying sp2 carbon bonded HOPG substrate [12],and the weak adhesion forces between the metal and carbonstructure [13]. It has been shown that increased vibrationalmismatch between two materials comprising an interface, oftensummarized by a difference in Debye temperature, results indecreased hBD [11]. The sp2 bonding between carbon atomsis responsible for high elastic stiffness, and thus, high phonongroup velocities and vibrational cutoff frequencies in the basalplane when compared to metals. Thus, it can be expected thatthe large vibrational mismatch between metals and CNT’s orHOPG will create a situation for rather low hBD. Additionally,the adhesion between metals and graphite has been shown to bevery weak due to a lack of chemical bonding between metals andpristine HOPG [14, 15]. Instead, the bonding can be describedas a van der Waals type interaction [16]. However, the presenceof oxygen or defects on the surface can lead to the formationof carbides at the metal-graphite interface. These defects canbe induced through ion bombardment of the HOPG surfaceprior to metal deposition [14, 15]. There have been attempts toquantify the reduction in sp2 bonds during ion bombardmentof the pristine HOPG surface, which is approximately a 2 %reduction after a 230 s dose of ions (2 keV, ∼ 10 µA/cm2) [17].This bonding is of direct importance to thermal transport, asmolecular dynamics simulations have been used to show thatthe addition of a single covalent bond at the interface betweena CNT and Si substrate increased the hBD nearly two orders ofmagnitude [18].

Traditional theoretical models for predicting hBD at the in-terface between two dissimilar materials such as the diffuse mis-match model (DMM) generally only consider the phonon spec-trum mismatch in the consideration of thermal transport [19].Several groups have made modifications to the DMM in orderto better describe certain physical conditions: interface mix-ing [20, 21], contributions of inelastic scattering [22, 23], andanisotropy [24, 25]. In order to better quantify the effect of pooradhesion on thermal transport across interfaces, Prasher devel-oped an acoustic mismatch model for van der Waals interactions,v-AMM [13]. In his work, Prasher shows a significant reduc-tion in hBD for low adhesion energies. Specifically, the v-AMMpredicts for a reduction in adhesion energy from 500 mJ/m2 to100 mJ/m2, a nearly 80% reduction in hBD. However, severalstudies have shown that comparison of experimental results andpredictions of the DMM can vary by up to an order of mag-nitude [11, 26]. One significant possibility for the discrepancybetween theoretical calculations and the experimental results isthe lack of consideration of the interface structure and chemistry.Even for the same material system, the conditions at the materialinterface can vary significantly due to deposition conditions andpost deposition annealing [27]. This work begins to investigatethe role that interface chemistry and structure have on the mea-

sured value of hBD for a system which is traditionally believedto have the same phononic properties, i.e. all samples tested areAu-HOPG. However in each sample, the HOPG is subjected to adifferent surface pre-treatment prior to deposition of the metallicfilm. In this way, the role of the interface in thermal transportis studied. Different surface treatments should have a significantimpact on the condition of the Au-HOPG interface, as it has beendemonstrated that contaminants and defects can lead to increasedinteraction between metals and HOPG [14, 15].

EXPERIMENTIn order to investigate the effect of interfacial structure and

chemistry on hBD, three metal-on-graphite samples were pre-pared for experimental thermal characterization. The three sam-ples consisted of thin Au films on 12 mm x 12 mm x 1 mmgrade 1 highly-ordered pyrolytic graphite substrates (HOPG)from Structure Probe Incorporated. Gold was chosen over otherpossible metals in order to reduce the number of variables af-fecting thermal transport across the interface. Previous work hasshown that Au does not wet HOPG or other carbon-based sub-strates. As a result, the Au-HOPG surface interaction is charac-terized by weak van der Waals adhesion [16, 28, 29].

Prior to metal deposition, each substrate underwent a differ-ent surface pretreatment to influence the interfacial structure andchemistry. The first substrate was cleaved using the “scotch tapemethod” to remove the first few layers of graphene, and no otherpretreatment or cleaning method was used. The second substratewas cleaved in the same manner and subsequently ion cleaned. A3 cm ion source, located 14 cm from the substrate, with a beamvoltage of 300 V was used to surface etch the substrate, for a totalexposure time of 7 minutes. As a means of comparison, expos-ing a SiO2 wafer to these conditions removes approximately 5-10nm of material from the surface and creates a disordered surface.The third substrate was again cleaved in the same manner andwas subsequently electron cleaned. The conditions of the elec-tron cleaning were the same as the ion cleaning, however, thebeam voltage was turned off. It is presumed the electron heat-ing from both the cathode filament and the neutralizer filament(which sits outside/at the end of the ion source) helps to removesurface water from the substrate. After all surface pretreatments,50 nm of Au was deposited on the HOPG surfaces by DC sput-tering.

Measurements of the thermal boundary conductance of theprepared samples were conducted using a transient thermore-flectance, TTR, method. Transient thermoreflectance reflectancetechniques [30–32] and similar variations [33, 34] are opticalpump-probe thermometry techniques that allow for simultane-ous heating and measurement of the thermal decay of thin filmmetallic systems. From the characteristic thermal decay mea-sured as a function of time and the appropriate thermal models,the thermophysical properties of the material system, including

2 Copyright c© 2011 by ASME

Figure 1: Schematic of the transient thermoreflectance experi-ment at the University of Virginia

the hBD across the system interface, can be determined.The TTR setup used in this experiment consists of a Co-

herent RegA 9000 regenerative amplifier seeded by a Mira 900oscillator (see Fig. 1). Both the oscillator and the amplifier areoptically pumped by a Coherent Verdi V18 with the output powersplit 5W:13W to the oscillator and amplifier, respectively. Thetotal output of the system produces a laser pulse train at 800 nmwith pulse energy on the order of µJ/pulse, a FWHM pulse widthof τp = 177 fs ± 7 fs, all at a rep rate of 250 kHz. The pump beamis modulated by a Conoptics Electro-Optical Modulator (EOM)at a frequency of 125 kHz, setting up a one-pulse-on/one-pulse-off heating scheme. The pump pulses are then passed throughan Inrad 5-035C frequency doubling system to improve filteringof scattered pump light off the sample surface before reachingthe signal photodetector, and improving the signal to noise ra-tio. The pump beam is focused down onto the sample with afinal spot size of 236 µm ± 2 µm. The temporal resolution ofthe probe beam is provided by a Newport 600 mm linear delaystage, with a total delay of 4 ns, and producing less than 2 µmdrift along the vertical and horizontal direction along the lengthof the stage. The probe beam is focused at the center of the pumpspot down to a spot size of 26 µm ± 0.6 µm. All data was takenwith a pump fluence of ∼ 2 J/m2.

In order to determine the measured hBD, a thermal modelis iteratively fit to the decay of the measured thermoreflectancesignal. In this work the model used was Carslaw and Jaeger’s so-lution for surface temperature of a multilayered system, assum-ing 1D thermal flow due to periodic steady heating [35], as im-plemented by Feldman [36], and detailed for thermoreflectance

(a) (b)

Figure 2: (a) Metal film deposited parallel to the a-axis of theHOPG with thermal probing perpendicular to the interface. (b)Thermal circuit showing thermal flow following the path of leastresistance.

experiments by Hopkins et al. [37]. The model is scaled to themeasured data starting at 1,000 ps to ensure that electron-phononnon-equilibrium processes have ceased and diffusive transportdominates. In the thermal model the hBD is treated as a sin-gle free parameter and iteratively incremented to minimize thesquare of the difference between the experimental data and thethermal model. An inverse parabolic interpolation scheme isused to reduce the number of subsequent iterations needed forthe model and data to converge.

The anisotropic nature of the thermophysical properties ofthe HOPG substrates, namely the thermal conductivity, requiresadditional consideration when fitting the thermal model to thedata as compared to more traditional isotropic systems. The in-plane vs. cross-plane thermal conductivity of HOPG can differby 3 orders of magnitude, 2,096 W/m-K vs. 5.59 W/m-K at roomtemperature, respectively [1]. Due to the low rep rate of our TTRsystem, (250 kHz), produced by using the regenerative amplifier,our heating scheme is transient rather then modulated as in mostsystems. Traditional high rep rate systems (76-80 MHz) using anoscillator alone deal with modulated heating, and therefore theprimary direction of heat flow and the sensitivity to directionalthermal conductivity is dependent on the ratio of pump-to-probespot sizes and the pump modulation rate [37, 38]. However, inthe transient system, an individual heat pulse is allowed to fullydissipate before the arrival of a subsequent pulse. Therefore thethermal energy is not “driven” as in a modulated system, butrather follows the path of least resistance (see Fig. 2). In thecase of the anisotropic nature of the HOPG, this would be thehigh thermal conductivity in-plane direction. Therefore, for theapplication of the thermal model in this study, the in-plane ther-mal conductivity is used for the thermophysical properties of thesubstrate.

3 Copyright c© 2011 by ASME

100 200 300 4000

5

10

15

20

25

30

35

40

h BD

(MW

/m2 K)

Temperature (K)

As-CleavedElectron CleanedIon Cleaned

Elastic + Inelastic

Elastic

Figure 3: Thermal boundary conductance, hBD, for each of thethree samples. Also represented are elastic and elastic + in-elastic models for thermal transport between isotropic solids andanisotropic substrates presented by Duda et al. [24, 25]

RESULTSThe temperature-dependent hBD for each of the three differ-

ent Au-HOPG samples is presented in Fig. 3. Each data pointshown represents the average over 10 scans, taken successivelyat a single location, of the best fit hBD values at the given tem-perature. The error bars represent the standard deviation of thebest fit values of hBD over the 10 scans. Also represented in Fig.3 are elastic and elastic+inelastic models for thermal transportbetween isotropic solids and anisotropic substrates presented byDuda et al. [24, 25].

It is clearly shown in Fig. 3 that the different surface prepa-rations drastically change the phonon thermal transport acrossthe Au-HOPG interface. The as-cleaved sample exhibited thehighest hBD across the temperature range, followed by the elec-tron cleaned and finally the ion cleaned. The difference in hBDbetween the as-cleaved and ion cleaned samples is over 300%,demonstrating how significantly the surface structure and chem-istry of the HOPG surface prior to metal deposition effects ther-mal transport.

In addition to the experimental data, Fig. 3 also includes theresults from theoretical models predicting the elastic and inelas-tic contributions to phononic thermal transport across the Au-HOPG interface. Comparing the theoretical models to the ex-perimental data, a few important features should be noted. First,

(a) Electron Cleaned Sample

(b) As-Cleaved Samples

(c) Ion Cleaned Sample

Figure 4: Bright field cross sectional transmission electron mi-croscopy images of the three prepared Au/HOPG samples

note that the data for the electron-cleaned sample best fits the pre-diction considering both the elastic and inelastic phonon trans-port. This can be explained as follows: considering that elec-tron cleaning effectively removed surface water and hydrocar-bon contaminants from the HOPG surface without changing thesurface structure, the Au-electron-cleaned-HOPG interface mostclosely mimics the ideal interface assumed by most theoreticalmodels, such as the diffuse mismatch model mentioned previ-ously. It has been shown that freshly cleaved graphite (cleavedin air) has an RMS surface roughness less that 1 nm [39] andthe choice of Au film (deposited on a clean surface) will onlyinteract with the surface through weak van der Waals interac-tion [16]. For the as-cleaved sample, having been cleaved inair, the presence of impurities should lead to increased reactiv-ity between the Au and the HOPG [14], suggesting increasedbonding strength, and hence and increased hBD [13]. Lastly, forthe ion-cleaned sample, the ion bombardment during cleaningshould have resulted in increased disorder and roughness of theHOPG surface prior to deposition of the metal. As shown byHopkins et al. [27], increased atomic mixing and inter-diffusionof the constituent materials at the interface can have a detrimen-tal effect of the hBD. While the trends between the experimentaldata and the literature can be inferred with confidence, in orderto have a full understanding of the effect of surface structure andchemistry on hBD further interfacial and surface characterizationis still required.

4 Copyright c© 2011 by ASME

1 2

3 4 5

6 71.5 mm

0.75 mm

1.5 mm

Figure 5: To measure repeatability of hBD measurements acrossthe sample surface a 7 spot sample grid was taken.

To solidify the comparison between the experimental re-sults and the expected interface structure induced by the depo-sition conductions and pre-deposition surface treatments, crosssectional transmission electron microscopy, TEM, images weretaken of each sample. The TEM images were collected by EvansAnalytical Group and bright field TEM images from each of thethree samples are shown in Fig. 4. A comparison of the TEMimages of the electron cleaned and as-cleaved samples, Figs. 4aand 4b, shows that both interfaces have similar surface structures,with very little interface roughness. Therefore, again, the differ-ence in hBD between the two samples is attributed to the presenceof surface impurities and changes to the chemical structure of theinterface. The TEM image for the ion cleaned sample, Fig. 4c,shows a significant increase in surface roughness as compared tothe other two samples. It is assumed that the decreased hBD inthe ion cleaned samples is due to increased phonon scattering atthe rough interface.

In order to ensure that the data collected for each sample wasgenerally representative of the hBD across the surface of the sam-ple surface, a secondary data set was collected at 300 K acrossthe sample surface. A total of 7 scans were taken across the sam-ple surface in a grid pattern detailed in Fig. 5. At each of the 7locations a total of 5 scans were taken and the collected data av-eraged. A comparison of the data collected and reported in Fig.3 and the standard deviation of measurements across the samplesurface is shown in Table 1.

As the table shows, the standard deviation of the 10 scans ata single location is within or on the order of the standard devi-ation of measurement across the sample surface. Therefore, wehave taken the data collected for each sample to be representativeof the hBD of the entire sample.

Table 1: Comparison of the standard deviation of the 10-scanstaken at a single location and the standard deviation of the scansat 7-locations.

Sample hBD (W/m2-K) SD10−Scans SD7−Locations

As-Cleaved 3.07×107 1.42×106 1.06×106

Electron Cleaned 2.33×107 2.47×106 3.84×106

SUMMARYWhile graphite and other carbon allotropes exhibit high in-

trinsic thermal conductivity, the thermal bottleneck for their inte-gration into thermal abatement solutions is the interface betweenthe graphitic structure and surrounding metal. The results ofthis study have shown that besides the vibrational and crystal-lographic properties of the constitutive materials normally con-sidered in thermal modeling, an in-depth understanding of thesurface structure and chemistry is required for effective thermalengineering. In order to tune and manage the thermal transportproperties in nano-devices utilizing graphitic thermal abatementsystems, an enhanced understanding of the effects of surfacestructure and metal-HOPG bonding on hBD will be key.

ACKNOWLEDGMENTSThe authors acknowledge the financial support of Office of

Naval Research through a MURI grant (Grant No. N00014-07-1-0723). J.C.D. is greatly appreciative for financial support fromthe National Science Foundation through the Graduate ResearchFellowship Program.

REFERENCES[1] Incropera, F.P., and DeWitt, D.P., 2002, ”Fundamentals of

Heat and Mass Transfer,” John Wiley & Sons, p. 981.[2] Hone, J., Whitney, M., Piskoti, C., 1999, ”Thermal Con-

ductivity of Single-Walled Carbon Nanotubes,” PhysicalReview B (Condensed Matter), 59(4) pp. 2514-2516.

[3] Hone, J., Llaguno, M. C., Nemes, N. M., 2000, ”Electricaland Thermal Transport Properties of Magnetically AlignedSingle Wall Carbon Nanotube Films,” Applied Physics Let-ters, 77(5) pp. 666-668.

[4] Kim, P., Shi, L., Majumdar, A., 2001, ”Thermal Trans-port Measurements of Individual Multiwalled Nanotubes,”Physical Review Letters, 87(21) p. 215502.

[5] Xu, J., and Fisher, T. S., 2006, ”Enhancement of ThermalInterface Materials with Carbon Nanotube Arrays,” Inter-national Journal of Heat and Mass Transfer, 49(9-10) pp.1658-1666.

5 Copyright c© 2011 by ASME

[6] Tong, T., Zhao, Y., Delzeit, L., 2007, ”Dense VerticallyAligned Multiwalled Carbon Nanotube Arrays as ThermalInterface Materials,” IEEE Transactions on Componentsand Packaging Technologies, 30(1) pp. 92-100.

[7] Abel, P. B., Korenyi-Both, A., Honecy, F. S., 1994, ”Studyof Copper on Graphite with Titanium Or Chromium BondLayer,” Journal of Materials Research, 9(3) pp. 617-624.

[8] Datta, S. K., Tewari, S. N., Gatica, J. E., 1999, ”CopperAlloy-Impregnated Carbon-Carbon Hybrid Composites forElectronic Packaging Applications,” Metallurgical and Ma-terials Transactions A (Physical Metallurgy and MaterialsScience), 30A(1) pp. 175-181.

[9] Norris, P. M., Smoyer, J. L., Duda, J. C., 2010, ”Predic-tion and Measurement of Thermal Transport Across Inter-faces between Isotropic Solids and Graphitic Materials,”Proceedings of the 3rd Joint US-European Fluids Engineer-ing Summer Meeting and 8th International Conference onNanochannels, Microchannels, and Minichannels, ASME,pp. 1-10.

[10] Schmidt, A. J., Collins, K. C., Minnich, A. J., 2010, ”Ther-mal Conductance and Phonon Transmissivity of Metal–Graphite Interfaces,” Journal of Applied Physics, 107(10)p. 104907.

[11] Stevens, R. J., Smith, A. N., and Norris, P. M., 2005, ”Mea-surement of Thermal Boundary Conductance of a Seriesof Metal-Dielectric Interfaces by the Transient Thermore-flectance Technique,” Journal of Heat Transfer, 127(3) pp.315-322.

[12] Lyeo, H., and Cahill, D. G., 2006, ”Thermal Conduc-tance of Interfaces between Highly Dissimilar Materials,”Phys.Rev.B, 73(14) p. 144301.

[13] Prasher, R., 2009, ”Acoustic Mismatch Model for ThermalContact Resistance of Van Der Waals Contacts,” AppliedPhysics Letters, 94(4) p. 041905.

[14] Ma, Q., and Rosenberg, R. A., 1997, ”Interaction of AlClusters with the (0001) Surface of Highly Oriented Py-rolytic Graphite,” Surface Science, 391(1-3) pp. L1224-L1229.

[15] Ma, Q., and Rosenberg, R. A., 1999, ”Interaction of Ti withthe (0001) Surface of Highly Oriented Pyrolitic Graphite,”Physical Review B (Condensed Matter), 60(4) pp. 2827-2832.

[16] Dezellus, O., and Eustathopoulos, N., 1999, ”Role ofVan Der Waals Interactions on Wetting and Adhesionin metal/carbon Systems,” Scripta Materialia, 40(11) pp.1283-1288.

[17] Lascovich, J. C., Giorgi, R., and Scaglione, S., 1991, ”Eval-uation of the sp2/sp3 Ratio in Amorphous Carbon Structureby XPS and XAES,” Applied Surface Science, 47(1) pp.17-21.

[18] Hu, M., Keblinski, P., Wang, J., 2008, ”Interfacial ThermalConductance between Silicon and a Vertical Carbon Nan-

otube,” Journal of Applied Physics, 104(8) p. 083503.[19] Swartz, E. T., and Pohl, R. O., 1989, ”Thermal Boundary

Resistance,” Review of Modern Physics, 61(3) pp. 605-688.[20] Beechem, T., Graham, S., Hopkins, P., 2007, ”Role of In-

terface Disorder on Thermal Boundary Conductance usinga Virtual Crystal Approach,” Applied Physics Letters, 90(5)p. 054104.

[21] Beechem, T., and Hopkins, P. E., 2009, ”Predictions ofThermal Boundary Conductance for Systems of DisorderedSolids and Interfaces,” Journal of Applied Physics, 106(12)p. 124301.

[22] Hopkins, P. E., Norris, P. M., and Stevens, R. J., 2008,”Influence of Inelastic Scattering at Metal- Dielectric In-terfaces,” Journal of Heat Transfer, 130(2) p. 022401.

[23] Hopkins, P. E., 2009, ”Multiple Phonon Processes Con-tributing to Inelastic Scattering during Thermal Bound-ary Conductance at Solid Interfaces,” Journal of AppliedPhysics, 106(1) p. 013528.

[24] Duda, J. C., Smoyer, J. L., Norris, P. M., 2009, ”Exten-sion of the Diffuse Mismatch Model for Thermal Bound-ary Conductance between Isotropic and Anisotropic Mate-rials,” Applied Physics Letters, 95(3) p. 031912.

[25] Duda, J. C., Hopkins, P. E., Beechem, T. E., 2010, ”Inelas-tic Phonon Interactions at Solid-Graphite Interfaces,” Su-perlattices and Microstructures, 47(4) pp. 550-555.

[26] Stoner, R. J., and Maris, H. J., 1993, ”Kapitza Conductanceand Heat Flow between Solids at Temperatures from 50 to300 K,” Physical Review B, 48(22) pp. 16373-16387.

[27] Hopkins, P. E., Norris, P. M., Stevens, R. J., 2008, ”Influ-ence of Interfacial Mixing on Thermal Boundary Conduc-tance Across a chromium/silicon Interface,” Journal of HeatTransfer, 130(6) pp. 1-10.

[28] Lopez-Salido, I., Lim, D. C., Dietsche, R., 2006, ”Elec-tronic and Geometric Properties of Au Nanoparticles onHighly Ordered Pyrolytic Graphite (HOPG) Studied us-ing X-Ray Photoelectron Spectroscopy (XPS) and Scan-ning Tunneling Microscopy (STM),” Journal of PhysicalChemistry B, 110(3) pp. 1128-1136.

[29] Lee, J., Tanaka, T., Seo, K., 2006, ”Wetting of Au andAg Particles on Monocrystalline Graphite Substrates,” RareMetals, 25(5) pp. 469-472.

[30] Smith, A. N., Hostetler, J. L., and Norris, P. M., 2000,”Thermal Boundary Resistance Measurements using aTransient Thermoreflectance Technique,” Microscale Ther-mophysical Engineering, 4(1) pp. 51-60.

[31] Norris, P. M., Caffrey, A. P., Stevens, R. J., 2003, ”Fem-tosecond Pump-Probe Nondestructive Examination of Ma-terials,” Review of Scientific Instruments, 74(1) pp. 400-406.

[32] Stevens, R. J., Smith, A. N., and Norris, P. M., 2006, ”Sig-nal Analysis and Characterization of Experimental Setupfor the Transient Thermoreflectance Technique,” Review of

6 Copyright c© 2011 by ASME

Scientific Instruments, 77(8) p. 84901.[33] Cahill, D. G., Goodson, K., and Majumdar, A., 2002,

”Thermometry and Thermal Transport in micro/nanoscaleSolid-State Devices and Structures,” Journal of Heat Trans-fer, 124(2) pp. 223-241.

[34] Cahill, D. G., Ford, W. K., Goodson, K. E., 2003,”Nanoscale Thermal Transport,” Journal of AppliedPhysics, 93(2) pp. 793-818.

[35] Carslaw, H.S., and Jaeger, J.C., 1959, Oxford UniversityPress, New York, pp. 109-112.

[36] Feldman, A., 1999, ”Algorithm for Solutions of the Ther-mal Diffusion Equation in a Stratified Medium with a Mod-ulated Heating Source,” High Temperatures - High Pres-sures, 31(3) pp. 293-298.

[37] Hopkins, P. E., Serrano, J. R., Phinney, L. M., 2010, ”Crite-ria for Cross-Plane Dominated Thermal Transport in Multi-layer Thin Film Systems during Modulated Laser Heating,”Journal of Heat Transfer, 132(8) p. 081302.

[38] Schmidt, A. J., Chen, X., and Chen, G., 2008, ”PulseAccumulation, Radial Heat Conduction, and AnisotropicThermal Conductivity in Pump-Probe Transient Thermore-flectance,” Review of Scientific Instruments, 79(11) p.114902.

[39] Yang, S., Kooij, E. S., Poelsema, B., 2008, ”Correlationbetween Geometry and Nanobubble Distribution on HOPGSurface,” Europhysics Letters, 81(6) p. 64006.

7 Copyright c© 2011 by ASME