Acoustic Phonons and Mechanical Properties of Ultra-ThinPorous Low-k Films: A Surface Brillouin Scattering Study

J. ZIZKA,1 S. KING,2 A. EVERY,3 and R. SOORYAKUMAR1,4

1.—Department of Physics, The Ohio State University, Columbus, OH 43210, USA. 2.—IntelCorporation, Logic Technology Development, Hillsboro, OR 97124, USA. 3.—School of Physics,University of Witwatersrand, Johannesburg, South Africa. 4.—e-mail: sooryakumar.1@osu.edu

To reduce the RC (resistance–capacitance) time delay of interconnects, a keydevelopment of the past 20 years has been the introduction of porous low-kdielectrics to replace the traditional use of SiO2. Moreover, in keeping pacewith concomitant reduction in technology nodes, these low-k materials havereached thicknesses below 100 nm wherein the porosity becomes a significantfraction of the film volume. The large degree of porosity not only reducesmechanical strength of the dielectric layer but also renders a need for non-destructive approaches to measure the mechanical properties of such ultra-thin films within device configurations. In this study, surface Brillouin scat-tering (SBS) is utilized to determine the elastic constants, Poisson’s ratio, andYoung’s modulus of these porous low-k SiOC:H films (� 25–250 nm thick)grown on Si substrates by probing surface acoustic phonons and their dis-persions.

Key words: Brilllouin light scattering, low-k dielectrics, ultra-thin films,acoustic phonons

INTRODUCTION

The rapid advances in device miniaturization isdriving the semiconductor industry to search con-tinually for new materials to meet the standards ofdevice performance in accordance with Moore’s law.During the recent past, material thicknesses haveentered an era of nanoscale dimensions therebyintroducing many new challenges for device fabri-cation. For example, as interconnect structuresapproach single digit nanometer length scales,interfacial properties become increasingly impor-tant and tend to dominate over bulk properties.1

Since in these cases the interconnect resistance–capacitance (RC) delay is comparable to the tran-sistor gate delay, device performance suffers due toadverse cross-talk effects.2,3 To reduce RC timedelays, low-k dielectrics have replaced the tradi-tionally used dielectric material, silicon dioxide(SiO2). Since the dielectric constant (k = 3.9) of

SiO2 was much too high to keep pace with thecontinual downscaling of device dimensions, methylgroups (CH3) were introduced to disrupt the SiO2network resulting in a lowered density and reduceddielectric constant k � 3.4 Further reduction of kwas achieved by introducing porosity typically usinga subtractive process in which the SiOC:H skeletonprecursor is mixed with an organic precursor orporogen.5 Films may also be subjected to ultraviolet(UV) cure in order to remove porogens and improvethe mechanical properties with minimum damage tothe low-k matrix.6 The resulting ultra-low-k porousSiOC:H has typical k values of 2–2.5, with porosityand pore sizes of 30–50% and 2–3 nm, respectively.7

Although ultra-low-k dielectrics are promisingmaterials for future technology, additional chal-lenges have arisen as the industry moves to sub22 nm technology nodes in which thicknesses of thelow-k materials are required to be less than 100 nm,a trend that will continue.8,9 For such nanometricthicknesses, the total free volume resulting fromporosity becomes an increasingly significant frac-tion of the film volume that leads not only to a(Received November 2, 2017; accepted March 29, 2018)

Journal of ELECTRONIC MATERIALS

https://doi.org/10.1007/s11664-018-6276-8� 2018 The Minerals, Metals & Materials Society

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decrease in mechanical and thermal stability,4,10–20

but also has the potential to be susceptible toprocess conditions.7 It is, therefore, important toinvestigate the mechanical properties of such low-kmaterials.

Traditional methods such as nano-indentation(NI) at these length scales (< 200 nm) often sufferfrom the drawback of unwanted substrate-indenterinteractions, thereby skewing the measuredmechanical properties.21 Although a recent efforthas been made to improve the NI technique,22 it isgenerally unreliable for materials with high porosi-ties where film cracking and delamination mayoccur.13,23,24 In contrast, surface Brillouin scatter-ing (SBS), as well as other methods such aspicosecond laser ultrasonics offer proven non-inva-sive approaches to measure mechanical propertiesof thin fragile films where measurements are notskewed by substrate effects.25 Probing surfaceacoustic waves (SAW) by SBS is advantageous forfilms of thickness less than 100 nm since theirbehavior in laminar geometries are well under-stood.26 Moreover, SBS allows for a clear distinctionbetween contributions from the film and substrateon the elastic properties by studying the dispersionof phonons with varying in-plane wave vector kk.Both dense and porous low-k SiOC:H films ofvarying porosity and thickness have been previ-ously studied using SBS.19,20,27 In these investiga-tions, the thinnest reported film was 94 nm thickwith a porosity of 45%.20

In the following sections, the mechanical proper-ties of four ultra-low-k dielectric films (k = 2.3) areinvestigated. While the thicknesses of two of thefilms (232 nm and 109 nm) are comparable toprevious SBS studies, two additional films are muchthinner (26 nm and 55.6 nm). In particular, one200 nm film presented in Ref. 20 had identicaldensity and porosity to several films in the currentstudy. Comparing the current and previous resultsof identical film properties provides insight to howmechanical properties may or may not change withthickness. SBS is used to probe the associated longwave acoustic phonon modal frequencies and theircoupling efficiency to photons, allowing for non-destructive determination of the elastic constants,Poisson’s ratio, and Young’s modulus of the fourdielectric films.

EXPERIMENTAL DETAILS

Surface Brillouin scattering of light, an experi-mental technique suitable for measuring the acous-tic vibrational spectrum of supported sub-micronlayers (thickness d), is employed for our study.28–30

Using a backscattering geometry, laser light offrequency x0 and wave number k ¼ x0=c is incidenton the sample surface at an angle h relative to thesurface normal (see Fig. 1). The inelastically scat-tered light having undergone a Brillouin frequencyshift, x, is collected and analyzed. Measurements

were performed with 200–300 mW of p-polarized532 nm laser light focused to a spot size of 30 lm onthe surface of a sample over the angular range of5� � h � 70�.31 A six-pass tandem Fabry–Perotinterferometer was utilized to disperse the light.The angular dependence of the modal frequencieswas recorded and the data were fit to a Green’sfunction based analysis for opaque solids outlinedpreviously.32 Scattering caused by dynamic fluctu-ations of the surface (surface ripple mechanism28,33)from the thermal distribution of bulk and surfacephonons having wave vector componentkk ¼ 2ki sin h at the surface was considered. Forsurface scattering, the Im{G33} component of thesurface elastodynamic Green’s function tensor isconsidered while other components such as Im{G11}may additionally be examined to account for anyelasto-optic contributions.28,34 It is noted that whenexamining either the Im{G11} or Im{G33} compo-nents, only the modal intensities are affected whiletheir modal frequency positions are identical.

As discussed in Ref. 20, the films were depositedon Si (100) wafers by plasma enhanced chemicalvapor deposition (PECVD) at temperature � 250�Cusing various combinations of organosilanes,alkoxysilanes, oxidizers, helium, and sacrificialpore-generating porogens.35 Post deposition, thefilms received a UV cure � 400�C to remove thesecond phase porogen material used to induceporosity and also to increase the connectivity andmechanical properties of the films.36 The filmthicknesses (d) were measured to be 232 nm,109 nm, 55.6 nm, and 26 nm using a J A Woollamvariable angle spectroscopic ellipsomter (VASE).20

The percent porosity was determined to be 33.5% forthe three thicker films (55.6 nm, 109 nm, and232 nm) and 12% for the 26 nm film by ellipsometricporosimetry37 using a vacuum system equippedwith a separate spectroscopic ellipsometer.20

Fig. 1. Selected SBS Stokes and anti-Stokes spectra for the 232 nmSiOC:H film collected at 10�, 20�, 30�, and 40�. The associated kkdfor each angle are included on the right. The scattering geometry isshown at the top.

Zizka, King, Every, and Sooryakumar

Finally, the mass density for the three thicker filmswas determined by x-ray reflectivity (XRR) to be0.9 g/cm3 while the 26 nm film has mass density1.1 g/cm3.38

RESULTS

Representative SBS backscattering spectrarecorded at several scattering angles h revealed upto six modes for the 232 nm film (Fig. 1). Figure 2asummarizes the frequency of measured modes inthe range 10�< h< 60� where different free spec-tral ranges were used to record the low and highfrequency modes. Additionally, a two-dimensionalgray image of the projected local density of states ofthe excitations produced by the Im{G33} componentof the surface elastodynamic Green’s function ten-sor is shown in Fig. 2b as a function of the normal-ized in-plane wave vector kkd (kk ¼ 2ki sin h) whereblack represents modes of greatest intensity. Fig-ures 3 and 4 show selected SBS spectra[10�< h< 50� (0.45< kkd< 1.97)] and the associ-ated angular (kkd) dependent frequency dispersions(Im{G11} and Im{G33}), respectively, for the 109 nmthick low-k film. Two strongly interacting modes arefound at � 5 GHz, along with one or two signifi-cantly weaker peaks around � 9 GHz and � 14GHz. Similarly, Figs. 5 and 6 include representativeSBS spectra and the associated angular (kkd)dependent frequency dispersion, respectively, forthe 55.6 nm film, recorded at selected angles10�< h< 60� (0.23< kkd< 1.14). In this case, atmost three modes were observed. In all threedispersion plots (Figs. 2a, 4a, and 6a) the modeamplitude profiles are included as insets on the leftand highlight the relative modal amplitude local-ized in the layer as depicted by components parallel(Ux) and perpendicular (Uz) to the film surface. Forlow h (< 10�), longitudinal and transverse standingmodes (LSM and TSM) have nodes or anti-nodesthat are determined by the boundary conditions atthe film interface.39 Finally, selected SBS spectraand the associated gray scale dispersion fits(Im{G11} and Im{G33}) for the 26 nm film aresummarized in Figs. 7 and 8. The SBS spectra ofthe 26 nm film are dominated by a single peak atlow angles while a secondary peak emerges forh> 30� (kkd> 0.31).

DISCUSSION

The spectra illustrated in Figs. 1, 3, and 5 can bebroadly separated into those recorded at low inci-dence angles (h< 15�), and spectra at higher h. Forh< 15�, the mode wave vector kz perpendicular tothe film surface is greater than the in-plane compo-nent kk (kz> kk). In these low h spectra, the modesare mainly composed of distinct organ pipe standingwave type excitations, where the frequencies ofnLSM and nTSM modes are given by fn ¼ð2n� 1Þv=4d; n ¼ 1; 2; . . . where v ¼

ffiffiffiffiffiffiffiffiffiffi

cij=qp

is the

longitudinal (cij= c11) or transverse (cij= c44) modevelocity.39 In Fig. 2a, the 1 LSM was calculated tohave frequency 2.1 GHz, but was not measuredexperimentally since its frequency was outside thechosen free spectral range. The lowest observedorgan pipe resonance was confirmed by simulationsto occur at � 6–7 GHz and comprised of a mixed 2LSM and 3 TSM excitation. These modes are

Fig. 2. (a) Angular dependence (h) of mode frequencies for the232 nm SiOC:H film. The SBS data are presented as thick solid dotswhile the calculated fit as small dots. Modal amplitudes are includedon the left where Ux (solid) and Uz (dashed) curves represent theTSM and LSM modes, respectively. (b) Mode frequencies repre-sented by Im{G33} plotted as a function of the product of in-planewave vector and thickness (kkd ) for the 232 nm SiOC:H film. TheSBS data are presented as thick solid dots while the calculated fit asshaded regions (white, gray, and black) of varying intensity, blackrepresenting the modes of greatest intensity.

Fig. 3. Selected SBS Stokes and anti-Stokes spectra for the 109 nmSiOC:H film collected at 10�, 20�, 30�, 40�, and 50�. The associatedkkd for each angle are included on the right.

Acoustic Phonons and Mechanical Properties of Ultra-Thin Porous Low-k Films: A SurfaceBrillouin Scattering Study

indistinguishable for h< 10� and appear as a broad,single mode in Fig. 1 for h = 10�. As h increases, the2 LSM (lower mode) and 3 TSM (higher mode) beginto split and appear as two distinct modes forh> 20�. The lower of the doublet is the 2 LSM(Fig. 2), and is relatively nondispersive for all h; it isseen to couple to a dispersive mode at h � 20� and athigher h (> 40�). Additionally, the 3 LSM wasobserved at � 11 GHz. Similar to the 2 LSM, thismode is relatively nondispersive for all h coupling todispersive modes at h � 40� and h � 60�.

At low angles (h< 15�), TSM modes were notobserved for the 232 nm film. This is expected since

at low angles the vibrations associated with TSMmodes lie almost parallel to the surface and thus donot contribute significantly to the surface ripplemechanism. This feature is consistent with themodal intensity plots (Fig. 2b), where the LSMmodes are more pronounced at low kkd (h) sincethey dominate contributions to the surface ripple.The TSM modes on the other hand begin to appearwith increasing kkd as their polarization changesfrom purely Ux to gaining a perpendicular Uzcomponent, and thus begin to couple to the incidentphotons (Fig. 2b). For example, in Fig. 2a the 4 TSMis observed for h ‡ 20� (kkd> 1.87, Fig. 2b) whichcouples to a dispersive mode at h � 30� (kkd � 2.74).For h> 60� (kkd> 4.7), additional coupling occursbetween the 4 TSM and a lower frequency disper-sive mode.

In order to visualize further the dispersive behav-ior of modes that occurs as a result of the elasticdiscontinuity introduced by the film-substrate inter-face, Fig. 9 summarizes their phase velocities as afunction of kkd for the 232 nm thick film. Modeslying above the bulk transverse (T) velocity (VT =5.7 km/s) of silicon are broadened and damped due

to their interaction with the bulk T wave of silicon.Below VT, the LSM and TSM modes transform intotrue dispersive guided Sezawa modes. This transi-tion from standing modes to dispersive modes is alsoevident in Fig. 2b in which the VT threshold isrevealed as the linear segment separating thecalculated modal response and distinctive dampingabove the bulk transverse velocity. Several higherorder Sezawa modes exist due to the sufficientlythick SiOC:H film which loads the silicon substrate.Because of the presence of LSM and TSM modes,mode coupling with the Sezawa-type modes occurbelow the T threshold. In Fig. 9, the lowest mode isthe Rayleigh mode which approaches the Raleighvelocity of silicon (VR = 4.9 km/s) for kkd fi 0.Similar behavior is evident for the 109 nm and55.6 nm films (Figs. 10 and 11) as kkd fi 0. Atkkd � 1.4 in Figs. 9, 10, and 11, the Rayleigh modeinteracts with the 1 LSM and, as kkd approacheslarger values, the lowest lying mode levels off and

Fig. 4. (a) Angular dependence (h) of mode frequencies for the109 nm SiOC:H film. The SBS data are presented as thick solid dotswhile the calculated fit as small dots. Modal amplitudes are includedon the left where Ux (solid) and Uz (dashed) curves represent theTSM and LSM modes, respectively. (b) Mode frequencies repre-sented by Im{G33} plotted as a function of the product of in-planewave vector and thickness (kkd ) for the 109 nm SiOC:H film. TheSBS data are presented as thick solid dots while the calculated fit asshaded regions (white, gray, and black) of varying intensity, blackrepresenting the modes of greatest intensity. (c) Mode frequenciesrepresented by Im{G11} plotted as a function of the product of in-plane wave vector and thickness (kkd) for the 109 nm SiOC:H film.

Fig. 5. Selected SBS Stokes and anti-Stokes spectra for the55.6 nm SiOC:H film collected at 10�, 25�, 35�, 45�, and 60�. Theassociated kkd for each angle are included on the right.

Zizka, King, Every, and Sooryakumar

approaches the Rayleigh velocity associated withthe film (VR = 1.1 km/s) for kkd J 4.

The mode dispersions are comparatively simplerfor the thinner 109 nm and 55.6 nm films wherefewer standing wave modes are observed (Figs. 3and 5) due to their greater separation in frequency.As the film thickness d decreases, standing wave-type modes occur at higher frequencies, resulting infewer observable modes within a given free spectralrange, a property dictated by the Fabry–Perotinterferometer mirror spacing. In the 109 nm film,the 1 LSM was observed at 5.3 GHz (Fig. 4). Forh � 15� (kkd � 0.67, Fig. 4b), the 1 LSM couplesweakly to a Sezawa-type mode that evolves from the

1 TSM. For increasing h, the 1 LSM interactsstrongly with the Rayleigh mode at h � 30�(kkd � 1.3). Additionally, the 3 TSM observed forh> 20� (kkd> 0.88), exhibits nondispersive behav-ior with increasing h (kkd), while coupling to aSezawa mode at h � 45� (kkd � 1.82). The interac-tions of the various modal branches for the 109 nmfilm may also be visualized in Fig. 10 which showsthe phase velocity as function of kkd and the degreeof damping that each modal branch experiences as aresult of interactions with bulk Si.

Upon further inspection of the experimentalBrillouin data from the 109 nm film shown inFig. 3, it is evident that as h is increased to 40�and 50�, the modal intensity of the 1 LSM andRayleigh modes are essentially identical. Thesecomparable intensities, however, are not reflectedin the intensity plot (Fig. 4b) of the Im{G33} compo-nent in which the intensity of the lower frequencymode is much larger at kkd J 1.3 than the higherfrequency mode. To account for this discrepancy, theIm{G11} component was examined and revealed thatthe higher frequency mode had a greater intensity.Since the experimental results yielded essentiallyidentical intensities for these two modes, bothIm{G33} and Im{G11} must contribute to the scatter-ing cross section. Moreover, since Im{G33} is largelyassociated with surface ripple scattering andIm{G11} is indicative of elasto-optic scattering, bothmechanisms must be contributing to the observedBrillouin modal intensities for the 109 nm film.

For the 55.6 nm film, the 1 LSM at 9.7 GHz(Fig. 6) is approximately twice the frequency of the1 LSM supported in the 109 nm film (Fig. 4), afeature consistent with the inversely proportionaldependence of modal frequencies with d. The evo-lution and interaction of modes supported in the55.6 nm layer are illustrated in Fig. 11 where the 1

Fig. 6. (a) Angular dependence (h) of mode frequencies for the55.6 nm SiOC:H film. The SBS data are presented as thick solid dotswhile the calculated fit as small dots. Modal amplitudes are includedon the left where Ux (solid) and Uz (dashed) curves represent theTSM and LSM modes, respectively. (b) Mode frequencies repre-sented by Im{G33} plotted as a function of the product of in-planewave vector and thickness (kkd ) for the 55.6 nm SiOC:H film. TheSBS data are presented as thick solid dots while the calculated fit asshaded regions (white, gray, and black) of varying intensity, blackrepresenting the modes of greatest intensity. (c) Mode frequenciesrepresented by Im{G11} plotted as a function of the product of in-plane wave vector and thickness (kkd ) for the 55.6 nm SiOC:H film.

Fig. 7. Selected SBS Stokes and anti-Stokes spectra for the 26 nmSiOC:H film collected at 15�, 20�, 30�, 40�, and 50�. The associatedkkd for each angle are included on the right.

Acoustic Phonons and Mechanical Properties of Ultra-Thin Porous Low-k Films: A SurfaceBrillouin Scattering Study

TSM evolves into a Sezawa mode below VT of Si, andeventually couples to the 1 LSM at kkd � 0.4�0.5As kkd increases, the 1 LSM approaches theRayleigh mode (Fig. 11), where the two modes beginto interact strongly at kkd � 1.2. For further anal-ysis of the 55.6 nm film, the two dimensional grayscale image in Fig. 6c shows the results of theIm{G11} component of the surface elastodynamicGreen’s function tensor. While Im{G33} explains thelow angle behavior, particularly the intensities ofthe organ pipe resonances (Fig. 6b), the intensitiesassociated with the higher angle modes agree moreclosely with Im{G11} (Fig. 6c), indicative of bothelasto-optic and surface ripple contributions to theoverall scattering cross section.

Finally, the 26 nm film is dominated by a singlepeak for low h (< 30�) where a secondary peakemerges for higher h (> 30�) (Fig. 7). Additionally,no low angle organ pipe resonances were observed.The lack of observed modes in the given frequency

range is due to the greater separation of modalfrequency as well as a reduced scattering volume inthe film, both the result of the ultra-thin filmthickness. Similar to the 109 nm and 55.6 nm films,both the Im{G33} and Im{G11} components wereexamined to gain insight into the nature of thescattering mechanism (Fig. 8). In the case of the26 nm film, both components separately fit the dataaccounting for the relative modal intensity. There-fore, both surface ripple and elasto-optic scatteringmust be contributing to the observable modalintensities in this ultra-thin film. In addition, the

Fig. 8. Mode frequencies for (a) Im{G33} and (b) Im{G11} plotted as afunction of the product of in-plane wave vector and thickness (kkd )for the 26 nm SiOC:H film. The SBS data are presented as thick soliddots while the calculated fit as shaded regions (white, gray, andblack) of varying intensity, black representing the modes of greatestintensity.

Fig. 9. Mode phase velocity plotted as a function of the product of in-plane wave vector and thickness (kkd ) for the 232 nm SiOC:H film.The SBS data are presented as thick solid dots while the calculatedfit as shaded regions (white, gray, and black) of varying intensity,black representing the modes of greatest intensity. The longitudinaland transverse threshold velocities of Si are marked by L (VL = 8.3km/s) and T (VT = 5.7 km/s), respectively.

Fig. 10. Mode phase velocity plotted as a function of the product ofin-plane wave vector and thickness (kkd ) for the 109 nm SiOC:Hfilm. The SBS data are presented as thick solid dots while the cal-culated fit as shaded regions (white, gray, and black) of varyingintensity, black representing the modes of greatest intensity. Thelongitudinal (L) and transverse (T) threshold velocities of Si are de-fined in Fig. 9.

Zizka, King, Every, and Sooryakumar

lowest observed mode (Fig. 7) is found to be sharperand well-defined in comparison to the broad sec-ondary mode observed for h> 30�. These differingcharacteristics of the two modes are reflected in thegenerated dispersion plots shown in Fig. 8.

From the fits to the mode dispersion, the inde-pendent elastic constants were derived and theresults are summarized in Table I. The elasticconstants c11 and c44 were independently deter-mined from the modal frequency dependence oneach respective cij. The low angle behavior of theLSM modes exclusively depends on c11, allowing forprecise determination of this elastic constant. Forinstance, increasing c11 by 25% would increase theLSM frequency by 11.5%. On the other hand, c44controls the low h (< 15�) behavior of the TSMmodes, along with many of the higher frequencySezawa modes. Possion’s ratio (m) and Young’smodulus (E) were calculated via the relationshipsm ¼ c12=ðc11 þ c12Þ and E ¼ c12ð1 þ mÞð1 � 2mÞ=m,respectively.

The previously studied 200 nm SiOC:H film20 hadidentical porosity and density of 33.5% and 0.9 g/

cm3, respectively, compared to the three thickerfilms of 232 nm, 109 nm, and 55.6 nm utilized inthis study. The mechanical properties determinedfor the comparable film are additionally included inTable I. All values associated with the thickest232 nm film in the current study are comparableand lie within the error margins of the measure-ments for the 200 nm SiOC:H film reported inRef. 20. Additionally, Young’s modulus for all threefilms in the present study are consistent with eachother and the previously studied 200 nm film. TheYoung’s modulus for the 200 nm film measured byNI was reported to be 5.1 ± 0.5 GPa, which liesoutside the experimental error of the modulus foundfor the four films shown in Table I. This trend inwhich a smaller Young’s modulus reported by SBSin comparison to NI is consistent with previousfindings.19,21 SBS has the advantage that it allowsthe mechanical properties associated with the filmto be distinguished from the substrate, and thus theresults are not adversely skewed by substratecontributions.

The Poisson’s ratio (m) of the 232 nm film is inagreement with the 200 nm film from Ref. 20. Onthe other hand, although the values associated withthe 109 nm and 55.6 nm films are in agreementwith each other, they are larger (m = 0.31 and 0.30,respectively) in comparison to the values deter-mined for the 232 nm and 200 nm films and lieoutside the experimental error. These differencesare likely due to transient growth conditions inwhich the deposition takes time to reach a steadystate where RF power, pressure, and gas flows rampup during the first � 25 nm of deposition. Thesetransient conditions may lead to inconsistencies inthe final mechanical state of each film, and will havea more pronounced effect on thinner films. Morelikely though is that the observed changes inmechanical properties with thickness are relatedto the efficiency of the post deposition UV curescaling non-linearly. More specifically, the optimumUV cure times may not scale linearly with thicknessas assumed in this study. A lower Poisson’s ratiowould indicate less deformability, so it is possiblethe 55.6 nm and 109 nm films were under-curedrelative to the 232 nm film. Overall, these differ-ences emphasize the role growth processing plays in

Table I. Summary of results for SiOC:H films and comparative 200 nm film

Thickness (nm) c11 (GPa) c44 (GPa) m E (GPa)

232 3.4 ± 0.2 1.3 ± 0.2 0.19 ± 0.05 3.1 ± 0.2109 4.7 ± 0.2 1.3 ± 0.2 0.31 ± 0.04 3.4 ± 0.455.6 4.2 ± 0.3 1.2 ± 0.1 0.30 ± 0.03 3.1 ± 0.226 7.2 ± 1.3 2.4 ± 0.2 0.25 ± 0.05 6.0 ± 0.520020 3.0 ± 0.3 1.1 ± 0.2 0.22 ± 0.04 2.6 ± 0.4

m Poisson’s ratio. E Young’s modulus.

Fig. 11. Mode phase velocity plotted as a function of the product ofin-plane wave vector and thickness (kkd ) for the 55.6 nm SiOC:Hfilm. The SBS data are presented as thick solid dots while the cal-culated fit as shaded regions (white, gray, and black) of varyingintensity, black representing the modes of greatest intensity. Thelongitudinal (L) and transverse (T) threshold velocities of Si are de-fined in Fig. 9.

Acoustic Phonons and Mechanical Properties of Ultra-Thin Porous Low-k Films: A SurfaceBrillouin Scattering Study

determining the mechanical stability of thin porousfilms.

Unlike the three thicker films in which the LSMand TSM modes can be used to precisely determinethe elastic constants, the lack of observed low angleacoustic resonances resulted in a higher errormargin for c11 of the thinnest 26 nm film. Theintensity and frequency of the two lowest dispersivemodes shown in Fig. 8 were found to be particularlysensitive to c44, thus allowing this elastic constantto be determined to within ± 8%. These same twomodes (Rayleigh and first Sezawa), however, werefound to be relatively insensitive to c11 making itdifficult to achieve a high degree of accuracy for c11.As a result, the error associated with c11 wasdetermined by assuming that Poisson’s ratio liesroughly within the range of 0.2–0.3 for SiOC:H.19,20

In comparison to the elastic constants of the threethicker films, the cij’s of the 26 nm film were foundto be larger. These differences in the mechanicalproperties may again be the result of transientgrowth conditions as well as consequences of UVcure processing at these nanometric scales.

CONCLUSIONS

The mechanical properties of four low-k SiOC:Hfilms (232 nm, 109 nm, 55.6 nm, and 26 nm) wereinvestigated to demonstrate that the elastic con-stants of highly porous films with thicknesses as lowas 25 nm can be non-destructively extracted fromSBS measurements. The elastic constants weredetermined by probing the angular (kkd) dependenceof modal frequencies where the dispersion of LSMand TSM, as well as dispersive modes were studiedand compared to projected local density of phononstates. Furthermore, Possion’s ratio and Young’smodulus were determined for each film. Previousresults for a 200 nm film are consistent with thefindings for the 232 nm film where both films haveidentical density and porosity. The differences in thec11 and m parameters for the 109 nm and 55.6 nmfilms are likely the result of variations in growthparameters. Finally, a 26 nm thin film of SiOC:Hwas measured and the elastic constants extractedwhich demonstrates the capability of SBS to non-destructively measure porous SiOC:H thin films tothicknesses � 25 nm tending to the nanometer limit.

ACKNOWLEDGEMENTS

Authors would like to acknowledge the support ofthe Semiconductor Research Corp. (Contact No:2012-IN-2296).

REFERENCES

1. S.W. King, H. Simka, D. Herr, H. Akinaga, and M. Garner,APL Mater. 1, 040701 (2013).

2. M. Bohr, in Proceedings of the IEEE International Elec-tronic Devices Meeting (1995), p. 241.

3. W.Volksen,R.Miller,andG.Dubois,Chem.Rev.110,56 (2010).

4. K. Maex, M.R. Baklanov, D. Shamiryan, F. Iacopi, S.H.Brongersma, and Z.S. Yanovitskaya, J. Appl. Phys. 93,8793 (2003).

5. A. Grill, Annu. Rev. Mater. Res. 39, 49 (2009).6. L. Prager, P. Marsik, L. Wenrich, M.R. Baklanov, S. Nau-

mov, L. Pistol, D. Schneider, J.W. Gerlach, P. Verdonck,and M.R. Buchmesier, Microelectron. Eng. 85, 196(2004).

7. M. Baklanov, J. de Marneffe, D. Shamiryan, A. Urbanow-icz, H. Shi, T. Rakhimova, H. Huang, and P. Ho, J. Appl.Phys. 113, 041101 (2013).

8. G. Stan, R.S. Gates, P. Kavuri, J. Torres, D. Michalak, D.Ege, J. Bielefeld, and S.W. King, Appl. Phys. Lett. 105,152906 (2014).

9. L. Kljucar, M. Gonzalez, I. De Wolf, K. Croes, J. Bommels,and Z. Tokei, Microelectron. Reliab. 56, 93 (2016).

10. E. Andideh, M. Lerner, G. Palmrose, S. El-Mansy, T.Scherban, G. Xu, and J. Blaine, J. Vac. Sci. Technol. B 22,196 (2004).

11. A. Grill, J. Appl. Phys. 93, 1785 (2003).12. C.A. Yuan, O. Sluis, G.Q. Zhang, L.J. Ernst, W.D. Driel,

R.B.R. Silfhout, and B.J. Thijsse, Comput. Mater. Sci. 42,606 (2008).

13. A. Volinksy, J. Vella, and W. Gerberich, Thin Solid Films429, 201 (2003).

14. M. Hussein and J. He, IEEE Trans. Semicond. Manuf. 18,69 (2005).

15. S.W. King and J.A. Gradner, Microelectron. Reliab. 49, 721(2009).

16. T. Scherban, B. Sun, J. Blaine, C. Block, B. Jin, and E.Andideh, in Proceedings of the IEEE International Inter-connect Technology Conference (2001), p. 257.

17. E.G. Linger and E.E. Simonyi, J. Appl. Phys. 96, 3482(2004).

18. K. Yonekura, S. Sakamori, K. Goto, M. Matsuura, N.Fujiwara, and M. Yoneda, J. Vac. Sci. Technol. B 22, 548(2004).

19. W. Zhou, S. Bailey, R. Sooryakumar, S. King, G. Xu, E.Mays, C. Ege, and J. Bielefeld, J. Appl. Phys. 110, 043520(2011).

20. S. Bailey, E. Mays, D.J. Michalak, R. Chebiam, S. King,and R. Sooryakumar, J. Phys. D Appl. Phys. 46, 1(2013).

21. M.F. Doerner and W.D. Nix, J. Mater. Res. 1, 601(1986).

22. H. Li, K. Lin, and C. Ege, J. Appl. Phys. 117, 115303 (2015).23. R.J. Nay, O.L. Warren, D. Yang, and T.J. Wyrobek, Mi-

croelectron. Eng. 75, 103 (2004).24. D. Morris and R. Cook, J. Mater. Res. 23, 2428 (2008).25. B. Daly, S. Bailey, R. Sooryakymar, and S.W. King, J.

Nanophotonics 7, 073094 (2013).26. G.W. Farnell and E.L. Adler, Physical Acoustics, vol. 9, ed.

W.P. Mason and N. Thurston (New York: Academic Press,1972), p. 35.

27. A. Link, R. Sooryakumar, R.S. Bandhu, and G.A. Antonelli,J. Appl. Phys. 100, 013507 (2006).

28. J.D. Comins, Handbook of Elastic Properties of Solids,Liquids, and Gases, vol. 1, ed. M. Levy, H. Bass, and R.Stern (New York: Academic Press, 1972), p. 349.

29. M.G. Beghi, A.G. Every, V. Prakapenka, and P.V. Zinin,Ultrasonic and Electromagnetic NDE for Structure andMaterial Characterization, ed. T. Kundu (Boca Raton: CRCPress, 2012), p. 539.

30. X. Zhang, J.D. Comins, A.G. Every, P.R. Stoddart, W.Pang, and T.E. Derry, Phys. Rev. B 58, 13677 (1998).

31. J.M. Karanikas and R. Sooryakumar, Phys. Rev. B 39,1388(R) (1989).

32. J. Zizka, S. King, A.G. Every, and R. Sooryakumar, J. Appl.Phys. 119, 144102 (2016).

33. R. Loudon and J.R. Sandercock, J. Phys. C 13, 2609(1980).

34. A. Pinczuk and E. Burstein, Light Scattering in Solids, vol.1, ed. M. Cardona (Heidelberg: Springer, 1983), p. 23.

Zizka, King, Every, and Sooryakumar

35. V. Rouessac, L. Favennec, B. Remiat, V. Jousseaume, G.Passemard, and J. Durand, Microelectron. Eng. 82, 333(2005).

36. V. Jousseaume, A. Zenasni, L. Favennec, G. Gerbaud, M.Bardet, J.P. Simon, and A. Humbert, J. Electrochem. Soc.154, G103 (2007).

37. M.R. Baklanov, K.P. Mogilnikov, V.G. Polovinkin, and F.N.Dultsev, J. Vac. Technol. B 18, 1385 (2000).

38. S. King, R. Chu, G. Xu, and J. Huening, Thin Solid Films518, 4898 (2010).

39. X. Zhang, R. Sooryakumar, A.G. Every, and W.H.Manghnani, Phys. Rev. B 640, 081402 (2001).

Acoustic Phonons and Mechanical Properties of Ultra-Thin Porous Low-k Films: A SurfaceBrillouin Scattering Study

Acoustic Phonons and Mechanical Properties of Ultra-Thin Porous Low-k Films: A Surface Brillouin Scattering StudyAbstractIntroductionExperimental DetailsResultsDiscussionConclusionsAcknowledgementsReferences