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Acta Materialia 60 (2012) 682–691

Fracture properties of hydrogenated amorphous silicon carbidethin films

Y. Matsuda a, S.W. King b, J. Bielefeld b, J. Xu b, R.H. Dauskardt a,⇑

a Stanford University, Stanford, CA 94305, USAb Intel Corporation, Hillsboro, OR 97006, USA

Received 12 July 2011; received in revised form 4 October 2011; accepted 8 October 2011

Abstract

The cohesive fracture properties of hydrogenated amorphous silicon carbide (a-SiC:H) thin films in moist environments are reported.Films with stoichiometric compositions (C/Si � 1) exhibited a decreasing cohesive fracture energy with decreasing film density similar toother silica-based hybrid organic–inorganic films. However, lower density a-SiC:H films with non-stoichiometric compositions (C/Si � 5)exhibited much higher cohesive fracture energy than the films with higher density stoichiometric compositions. One of the non-stoichi-ometric films exhibited fracture energy (�9.5 J m�2) greater than that of dense silica glasses. The increased fracture energy was due tocrack-tip plasticity, as demonstrated by significant pileup formation during nanoindentation and a fracture energy dependence on filmthickness. The a-SiC:H films also exhibited a very low sensitivity to moisture-assisted cracking compared with other silica-based hybridfilms. A new atomistic fracture model is presented to describe the observed moisture-assisted cracking in terms of the limited SiAOASisuboxide bond formation that occurs in the films.� 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Thin films; Fracture; Plasticity; Moisture-assisted cracking; Dielectrics

1. Introduction

Hydrogenated amorphous silicon carbide (a-SiC:H) thinfilms are a class of organic–inorganic hybrid glasses whichcontain inorganic network bonds and terminal groups suchas methyl and hydrogen. a-SiC:H films exhibit excellentthermal and chemical stabilities and unique optical andelectrical properties, which are adjustable by controllingthe chemical composition [1], the number of terminalgroups [2,3] and the film porosity. Perhaps their most sig-nificant advantage is that they have molecular structureswithout SiAOASi bonds, which make them insensitive tomoisture-assisted cracking. Moisture-assisted crackingresults from a stress-enhanced reaction at the crack tip

1359-6454/$36.00 � 2011 Acta Materialia Inc. Published by Elsevier Ltd. All

doi:10.1016/j.actamat.2011.10.014

⇑ Corresponding author. Present address: 496 Lomita Mall, DurandBldg., Rm. 121, Stanford University, Stanford, CA 94305, USA. Tel.: +1650 725 0679; fax: +1 650 725 4034.

E-mail address: dauskardt@stanford.edu (R.H. Dauskardt).

between water molecules and strained moisture-sensitiveSiAOASi bonds, which leads to accelerated bond ruptureand crack propagation [4]. Such cracking is a serious reli-ability issue for devices containing silica-based films, suchas widely used classes of organosilicate hybrid glasses[5–7]. These advantages make a-SiC:H films promising can-didates for replacing silica-based materials in applicationssuch as etch stop layers in microelectronic devices andanti-reflective coatings in photovoltaics.

The integration of a-SiC:H films into device technolo-gies, however, is limited by their decreased fracture resis-tance due to the presence of terminal groups andporosity, which reduce film network connectivity similarto the case of organosilicate glasses [8–10]. Surprisingly,there has been no study of the fracture resistance nor ofthe sensitivity to moisture-assisted cracking of a-SiC:Hfilms. There have only been studies of these fracture prop-erties for the other forms of SiC. For example, chemicalvapor deposition (CVD) polycrystalline SiC has been

rights reserved.

Table 1Material properties of a-SiC:H and SiCN films, including film density, Young’s modulus, Yield strength, dielectric constant, film stress and film porosity;parenthesized S and NS in film designation represent stoichiometric and non-stoichiometric composition, respectively.

Filmdesignation

Density, q(g cm�3)

Young’s modulus, E

(GPa)Yield strength(MPa)

Dielectricconstant,k

Film stress(MPa)

Film porosity(vol.%)

SiC-A (S) 1.93 99.0 – 6.2 �64 0SiC-B (S) 1.76 57.1 – 5.2 �9 0SiC-C (S) 1.62 35.8 – 4.8 21 0SiC-D (S) 1.42 15.6 – 4.4 21 0SiC-E (S) 1.3 11.5 – 4.0 60 0SiC-F (NS) 1.09 6.4 792 ± 43 3.2 10 2SiC-G (NS) 1.17 5.0 153 ± 13 2.8 50 12 with porogenSiCN 2.25 120 – 5.8 �350 0

Y. Matsuda et al. / Acta Materialia 60 (2012) 682–691 683

reported to exhibit insensitivity to moisture-assisted crack-ing [11,12], although bulk sintered SiC has been reported toshow a low sensitivity [13–19]. Understanding these frac-ture properties is therefore critical for their successful inte-gration into nanoscience and energy technologies.

The fracture properties of a range of a-SiC:H films inmoist environments are described with particular attentionto cohesive fracture energy and sensitivity to moisture-assisted cracking. The molecular structure of the a-SiC:Hfilms is characterized using Fourier transform infraredspectroscopy (FTIR). The cohesive fracture energy of thea-SiC:H films is then presented as a function of density,and an observed fracture path transition from cohesive toadhesive fracture is analyzed. It is demonstrated that thecohesive fracture energy can be increased significantly bycrack tip plasticity. It is then shown that the a-SiC:H filmsexhibit a very low sensitivity to moisture-assisted crackingin moist environments. This low sensitivity is related to theformation of SiAOASi suboxide bonds through hydrationand subsequent condensation reactions at SiAHx with dif-fused water molecules into the films. Finally, a new atom-istic fracture model is proposed, which incorporates therole of moisture-insensitive bonds to explain the mois-ture-assisted cracking of the a-SiC:H films.

2. Experimental

a-SiC:H films were deposited on a 300-mm (100) siliconwafer using a manufacturing plasma-enhanced CVD (PEC-VD) system at 250 and 400 �C, similar to methodsdescribed elsewhere [20–22]. Targeted film compositionswere obtained by finely tuning the amount of precursors,including methylsilanes, phenylsilanes, He and H2.Depending on the Si and C ratio, deposited a-SiC:H filmswere classified into stoichiometric (C/Si � 1) and non-stoi-chiometric films (C/Si � 5). One of the non-stoichiometricfilms was modified to have �12 vol.% porosity by introduc-ing additional phenyl organic porogen precursors duringdeposition. The porogen precursors were removed afterfilm deposition by e-beam cure to generate porosity. Depo-sition time was adjusted to have nominal film thickness of500 nm, and the bottom and top sides of the a-SiC:H films

were capped with 25-nm silicon carbon nitride layers(SiCN), which were deposited by the same PECVD system.

Material properties of a-SiC films were determined byvarious characterization techniques. Low-frequency dielec-tric constants of the films were measured using a Hg probeat the frequency of 100 kHz. Film density was determinedby X-ray reflectivity technique [23]. The Young’s modulusof films was determined by nanoindentation [24] with Pois-son’s ratio 0.25, using the film thickness of 2000 nm to min-imize substrate effects. Using nanoindentation, the yieldstress of non-stoichiometric films was additionally mea-sured based on Johnson’s spherical cavity model [25].The film stresses of a-SiC:H films were measured by a wafercurvature technique with Stoney’s equation and opticallymeasured film thickness. Film porosity was measured byspectroscopy ellipsometry with toluene solvent. Thesematerial properties, including those of SiCN films, are sum-marized in Table 1.

The chemical compositions and molecular structures ofthe a-SiC:H films were characterized by X-ray photoelec-tron spectroscopy (XPS, VersaProbe, Physical Electronics)and FTIR, Nicolet Magna-IR 860 and Bio-Rad QS-3300spectrometers) with a transmission mode in the wavenum-ber range from 400 to 4000 cm�1. Details on FTIR charac-terization of the a-SiC:H films are described elsewhere [22].

The fracture energy Gc (J m�2) of a-SiC films was mea-sured by double cantilever beam (DCB) fracture mechan-ics-based testing with a delaminator test system (DTS,Menlo Park, CA). In sample preparation, a-SiC:H filmswith additional metal layers were bonded to silicon waferswith epoxy adhesives (Fig. 1), which were then diced by ahigh-speed wafer saw to fabricate DCB geometry speci-mens 5 mm wide, 1.56 mm in total thickness and 50 mmin length. The DCB specimens were loaded in pure modeI, and displacement was measured to determine Gc in a lab-oratory air test environment at �25 �C and �40% RH. Themethod for calculating Gc is detailed elsewhere [26].

After fracture energy measurements, all fracture pathswere carefully characterized by XPS survey scan to identifythe fracture paths. The fracture paths were classified eitheras cohesive fracture within the a-SiC:H films or as adhesivefracture between SiCN and metal layers (Fig. 1). In

Fig. 1. Schematic illustration of multi-layered thin film structures, andcohesive and adhesive fracture paths (not to scale).

Fig. 2. FTIR spectrum of a-SiC:H films: (a) overall spectrum from 400 to4000 cm�1; (b) CHx vibration from 2700 to 3200 cm�1 [22].

684 Y. Matsuda et al. / Acta Materialia 60 (2012) 682–691

addition, the roughness of cohesively fractured surfaceswas measured by atomic force microscopy (XE-70, ParkSystems) with a 1 � 1 lm area.

To characterize sensitivity to moisture-assisted crackingof the a-SiC:H films, crack growth velocity v was measuredwith the DCB technique in widely varying humid air envi-ronments. To measure crack growth velocity, DCB speci-mens were loaded at a constant loading rate (2 lm s�1) toa predetermined load at which the displacement was fixed.Then automated analysis of the load relaxation withincreasing compliance of the specimens determined thecrack growth velocity over the range �10�11–10�4 m s�1

as a function of applied strain energy release rate G, to pro-duce a characteristic v–G curve. General methods of crackgrowth measurements are described elsewhere [27]. Thesemeasurements were conducted at 25 �C and in air humidenvironments ranging from dry nitrogen to 90% RH in acontrolled chamber. For tests in dry nitrogen, the chamberwas purged by N2 gas with the flow rate �6.0 L min�1 forat least 9 h prior to the measurements to remove waterresidues.

3. Results and discussion

3.1. Molecular structure characterization by FTIR

The molecular structure of the a-SiC:H films were char-acterized by measuring the absorbance from wavenumber400–4000 cm�1 with FTIR (Fig. 2a). The main absorbancepeaks consist of SiAC stretching modes at �790 cm�1

[22,28,29], SiACH2ASi wagging modes and SiAO asym-metric stretching modes between 1000 and 1050 cm�1

[22,29], SAHx stretching modes between 2000 and2300 cm�1 [28,29] and various complex CAHx stretchingmodes between 2850 and 3100 cm�1 [28–31]. Note that,while oxygen was not introduced during the deposition,SiAO bonds were probably formed through chemical reac-tions after film deposition, which is discussed further inSection 3.5. The minor absorbance peaks consist ofSiACH3 symmetric bending modes at �1260 cm�1

[22,29], SiACH2ASi symmetric bending modes at

�1350 cm�1 [22,29] and SiACH3 asymmetric bendingmodes at �1400 cm�1 [22,29]. There is a small peak at�1590 cm�1 due to sp2 carbon bonds [22,29] in two non-stoichiometric films (SiC-F and SiC-G). There are addi-tional CAH2 symmetric bending modes at �1375 cm�1,and CAHx bending modes at �1456 cm�1 [22,29,30] onlyin SiC-G, indicating the existence of sp3 carbon chains iso-lated from Si.

The more complex absorbance peaks between 2700 and3200 cm�1 corresponding to CAHx stretching modes werefurther characterized (Fig. 2b). The two main peaks consistof sp3 CAH3 symmetric stretching modes at �2890 and sp3

CAH3 asymmetric stretching modes at �2950 cm�1

[22,29,30]. There is a sp3 CAH2 symmetric stretchingmodes peak at �2870 cm�1 [22]. There are sp2 CAHx

symmetric stretching modes at �3000 cm�1 and sp2 CAHx

asymmetric stretching modes at �3050 cm�1 in two non-stoichiometric films [22]. There is also a sp3 CAH2

asymmetric stretching mode at �2923 cm�1 only in SiC-G, indicating the existence of sp3 carbon chains isolatedfrom Si.

3.2. Cohesive fracture energy

The fracture energies as a function of density for a widevariety of the a-SiC:H films are shown in Fig. 3. The errorbars in these and all subsequent figures represent one

Fig. 3. Fracture energy of a-SiC:H films as a function of film density.Solid line represents cohesive fracture energy of MSSQ organosilicatehybrid glass counterparts [5].

Y. Matsuda et al. / Acta Materialia 60 (2012) 682–691 685

standard deviation unless otherwise stated. A fracture pathtransition observed at �1.63 g cm�3 from cohesive to adhe-sive fracture is discussed in the following section. It wasfound that the cohesive fracture energy of a-SiC:H filmswith stoichiometric compositions decreased with decreas-ing film density and is comparable with that of MSSQorganosilicate glass counterparts [8] (Fig. 3). This decreas-ing cohesive energy is due to decreases in network connec-tivity with increasing terminal groups, similar to thephenomenon demonstrated in brittle hybrid glasses[9,10,32,33]. Conversely, the cohesive fracture energy oflower-density a-SiC:H films with non-stoichiometric com-positions (SiC-F and SiC-G) deviated from the trend andwas greater than that of higher-density stoichiometricfilms. In particular, a surprisingly high cohesive fractureenergy of �9.5 J m�2 was found for SiC-G, much higherthan that of MSSQ organosilicate film counterparts andeven dense silica glasses (�8 J m�2 [9]).

As revealed by FTIR (Fig. 2a and b), the non-stoichiom-etric a-SiC:H films were found to contain sp2 carbon dou-ble bonds (C@C). These bonds can contribute to the higherfracture energy in two possible ways. First, breaking strongC@C bonds requires more energy because C@C bondenergy (�728 kJ mol�1 in ethylene [34]) is higher than thatof SiAC bond energy (�447 kJ mol�1 in silicon carbide[34]). Second, the strong C@C bonds in the molecular net-work may cause the crack path to meander around them.While rms roughness was measured by AFM (Table 2), itis noted that these values are not at the molecular scaleneeded to observe the increased crack path meandering inthe molecular network. However, neither of these processesaccounts for the significantly increased fracture energy ofSiC-G.

A more potent mechanism for the high fracture energy ofSiC-G is related to increased crack tip plasticity. Althoughcrack tip plasticity is certainly not expected in brittlea-SiC:H films, the possibility of plasticity related to poly-meric components in a-SiC:H films has been theoretically

predicted [35]. In the present study, plasticity in SiC-Gdue to polymeric components was inferred from the FTIRpeaks corresponding to sp3 carbon chains (Fig. 2b), anddirectly indicated by the significant amount of pileup for-mation during nanoindentation (Fig. 4). In spite of a lowerindentation load used, SiC-G exhibited far more significantpileup formation than SiC-F. Moreover, SiC-G had a mea-sured yield strength of 153 ± 13 MPa, which is much lowerthan that of 792 ± 43 MPa in SiC-F (Table 1). Clearly, thelower yield strength value together with the far more signif-icant pileup formation suggest more crack tip plasticity inthe SiC-G film.

To assess further the contribution of the crack tip plas-ticity to fracture energy, the fracture energy of SiC-G andSiC-F was measured as a function of film thickness,because plasticity contribution to fracture energy usuallyincreases with film thickness [27,36]. While the fractureenergy of SiC-F was independent of film thickness, thatof SiC-G films increased dramatically with film thicknessuntil a plateau was reached (Fig. 5). This marked contrastcan be explained by the first-order estimate of the planestrain plastic zone size [37]

2rp ¼1

3pGE0

r2YS

ð1Þ

where E0 is the plane strain Young’s modulus, and rYS isthe film yield stress. The calculated plastic zone sizes were215.3 nm in SiC-G and 2.7 nm in SiC-F. The plastic zonesize of SiC-G is consistent with the magnitude of film thick-ness corresponding to the onset of plateau fracture energy(Fig. 5). The fracture energy dependence on film thicknesscan be explained in terms of constraint by the adjacent lay-ers, which suppress the plastic zone when the film thicknessis below 2rp [36]. These observations strongly suggest thatthe crack tip plasticity is the main cause of the increasedfracture energy of SiC-G.

Note the absence of a local maximum in Gc at the filmthickness of �2rp. A local maximum [36] often appears inpolymer films between elastic layers, owing to enhancedcrack tip plasticity when constrained by the elastic layers[36,38,39]. Such constraint increases mean stress ahead ofthe crack tip [38,39], which is presumed to maximize at athickness of �2rp. In the present study, the absence of sucha local maximum was attributed to yield stress insensitivityto the mean stress in SiC-G. The yielding behavior of poly-meric components surrounded by brittle SiAC bonds couldbe different from that of polymer films.

3.3. Fracture path transition analysis

The fracture path in the film sandwiched between elasticsubstrates under pure mode I loading is determined by twocompeting factors: elastic modulus mismatch between thefilm and the substrates and the weakest fracture path[40–42]. The elastic modulus mismatch generates a modeII stress intensity factor at the crack tip, which can deflectthe crack path in the film. A cohesive crack in the film is

Table 2Roughness of cohesively fractured surface, Dundur’s parameters and XPS oxygen concentration of a-SiC:H films; parenthesized S and NS in filmdesignation represent stoichiometric and non-stoichiometric composition, respectively.

Film designation Rms roughness (nm) Dundurs’ parameters XPS oxygen concentration after film deposition (at.%)

a b

SiC-A (S) – 0.261 0.026 –SiC-B (S) – 0.495 0.122 –SiC-C (S) 1.94 0.650 0.186 2.3SiC-D (S) 3.51 0.831 0.262 3.4SiC-E (S) 4.64 0.873 0.280 2.6SiC-F (NS) 3.0 0.927 0.302 1.1SiC-G (NS) 6.72 0.943 0.309 2.8

Fig. 4. Cross-section of SiC-G and SiC-F after nanoindentation.Fig. 5. Cohensive fracture energy dependence of non-stoichiometric a-SiC:H films on film thickness. 2rSiC-G

p represents the plastic zone size ofSiC-G.

686 Y. Matsuda et al. / Acta Materialia 60 (2012) 682–691

stable when the film is less stiff than the adjacent substrates.Conversely, a crack tends to deflect away from the filmwhen the film is stiffer than the substrates. Note that thecrack path in the film is also affected by film stresses,depending on their sign and magnitude [40,41]. However,in the present study, the effect of such stresses on the crackpath was minor compared with that of the elastic modulusmismatch.

The effect of the elastic modulus mismatch on the crackpath can be analyzed quantitatively using Dundurs’sparameters, a and b, which measure the elastic modulusmismatch between the film and the substrates [43]:

a ¼ E0substrate � E0filmE0substrate þ E0film

ð2Þ

b ¼ 1

2

lsubstrateð1� 2mfilmÞ � lfilmð1� 2msubstrateÞlsubstrateð1� mfilmÞ þ lfilmð1� msubstrateÞ

ð3Þ

where E0 is plane strain Young’s modulus (E/(1 � m2)), m isPoisson’s ratio, l is the shear modulus (E0/2(1 + m)), andthe subscripts represent either film or substrate. To calcu-late the Dundurs’ parameters, the multi-layered structureswere simplified by excluding SiCN, metal and epoxy layers.Then, the Dundurs’ parameters for the multi-layered struc-tures are given by substituting elastic properties of a-SiC:Hfilms and Si substrates into Eqs. (2) and (3). The Poisson’sratios for the films and Si [110] were 0.25 and 0.064,

respectively. All the multi-layered structures were foundto have positive values for a, and more importantly for b(Table 2), suggesting a stable cohesive crack in the a-SiC:Hfilms [40,42]. These results suggest that the crack path tran-sition is not related to the elastic modulus mismatch, butrather to the weakest fracture path. The film cohesive frac-ture strength most likely exceeded the interfacial fracturestrength above the transition densities, thus leading to theobserved crack path transition.

3.4. Sensitivity to moisture-assisted cracking

The sensitivity to moisture-assisted cracking of a-SiC:Hfilms was characterized by measuring crack growth velocityv as a function of applied G in different humid air environ-ments (Fig. 6). All the films exhibited crack growth belowthe cohesive fracture energy, resulting in characteristicv–G curves, except for SiC-C, which did not exhibit anysubcritical cracking. The measured v–G curves were verysteep and confined to a narrow range of G values. The posi-tion of the v–G curves did not change with humidity. Crackgrowth thresholds Gth, below which crack growth is inac-tive (technically defined around v = 10�9–10�10 m s�1),were also observed. SiC-C exhibited a sudden load dropat a critical load corresponding to Gc with no evidence of

Fig. 6. Crack growth velocity of a-SiC:H films as a function of applied strain energy release rate at 20% and 70% RH: (a) SiC-D; (b) SiC-E; (c) SiC-F; (d)SiC-G.

Y. Matsuda et al. / Acta Materialia 60 (2012) 682–691 687

stable crack growth. These results are in marked contrastto silica-based materials, such as organosilicate glasses [8]and silicate glasses [4,44,45]. However, it is still not clearwhether all a-SiC:H films are sensitive to moisture-assistedcracking.

To further assess the sensitivity of the a-SiC:H films tomoisture-assisted cracking, a series of crack growth mea-surements were performed in dry nitrogen and 90% RHair test environments with a single specimen of SiC-E.The measurements were repeated twice in each conditionand started from dry nitrogen conditions to minimize inter-actions between water molecules and the films. While theposition of the v–G curves did not change with humiditychanges, the slopes of the curves in dry nitrogen were con-sistently steeper than those in 90% RH air test environ-ments (Fig. 7), which is quantified by moisture-assistedcrack growth models [45,46]

v ¼ v0 sinhaðG� 2cÞ

kT

� �ð4Þ

where v is crack growth velocity v0 is the reference velocityincluding activation energy for a kinetic bond rupture pro-cess and characteristic vibration frequency and bond sepa-ration, a is the activation area characterizing the slope ofthe v–G curve, 2c is surface energy, k is the Boltzmann con-stant, and T is the temperature in kelvin. By fitting the v–G

curves of SiC-E in the velocity range �10�8–10�5 m s�1,the slopes were characterized as activation areas (Fig. 8).The activation areas were found to decrease monotonicallywith decreasing humidity, clearly indicating that the a-SiC:H films react with water molecules, and indeed havea low sensitivity to moisture-assisted cracking.

Note here that steric hindrance related to the ability ofwater molecules to reach the crack tip was not responsible

688 Y. Matsuda et al. / Acta Materialia 60 (2012) 682–691

for the low sensitivity to moisture-assisted cracking of thea-SiC:H film. Steric hindrance occurs when crack openingdisplacements are smaller than the size of water molecules,which prevents the molecules from reaching the crack tipbonds, thereby suppressing moisture-assisted cracking[47,48]. The crack opening displacements calculated withlinear elastic fracture mechanics [5,48] were greater thanthe size of water molecules for all the films. A model toaccount for the low sensitivity of the a-SiC:H films to mois-ture-assisted cracking is described in the following section.

3.5. Model of moisture-assisted cracking

Moisture-assisted cracking occurs in materials whichcontain moisture-sensitive bonds such as SiAOASi bonds.These moisture-sensitive bonds are polar and have electronlone pairs needed to react with water molecules [44]. In thepresent a-SiC:H films, no moisture-sensitive bonds areintroduced during film deposition, so there are only mois-ture-insensitive SiAC and C@C bonds which have no elec-tron lone pairs. However, moisture-sensitive SiAOASisuboxide bonds can form after film deposition. When thea-SiC:H films are exposed to air environments, water mol-ecules can diffuse into the films because of the increasedfree volume from the terminal groups. Then, SiAOASi sub-oxide bonds can form through hydration and subsequentcondensation reactions at SiAHx groups [49,50]:

SiAHþH2O! SiAOHþH2 ð5ÞSiAOHþ SiAOH! SiAOASiþH2O ð6Þ

These reactions may be enhanced by subsequent ele-vated temperature processes. XPS high-resolution scansperformed at �60 nm below the surface detected peaks cor-responding to SiAO suboxide bonds, including bothSiAOASi and SiAOH bonds. These peaks were convertedto �1.1–3.4 at.% oxygen (Table 2). While it is not possibleto differentiate SiAOASi bonds from SiAOH bonds byXPS, it has been reported that the FTIR peak intensity cor-responding to SiAOASi suboxide asymmetric stretchingmodes (�1000–1050 cm�1) increased in the identical a-SiC:H films after exposure to air environments [51]. There-fore, the present authors believe that some of the SiAOsuboxide bonds exist as SiAOASi bonds in the a-SiC:Hfilms studied. How these SiAOASi suboxide bonds leadto the low sensitivity of the a-SiC:H films to moisture-assisted cracking below is now described.

Existing models for moisture-assisted cracking in silicateglasses [4,44–46,52,53] do not consider the role of moisture-insensitive SiAC and C@C network bonds, so these modelscannot be used directly for a-SiC:H films. A model is pro-posed which is an extension of existing kinetic brittle frac-ture models [4,44,46,52,53], particularly atomistic ones[45,46], but incorporates the role of moisture-insensitivebonds. Ideally brittle fracture is assumed, and thereforeSiC-G with plasticity is excluded. Terminal groups are alsoignored.

The fundamental assumption is that the applied strainenergy release rate G can be separated into two compo-nents related to fracture of moisture-sensitive SiAO bonds,GSiAO, and to fracture of moisture-insensitive SiAC andC@C network bonds, GSiAC/C@C. Therefore, the appliedG may be expressed as the summation of the twocomponents:

G ¼ GSiAO þ GSiAC=C@C ð7ÞMoisture-insensitive SiAC and C@C bonds exhibit no

moisture-assisted bond rupture, because these bonds haveno electron lone pair needed to react with water. TheseSiAC and C@C bonds are ruptured when their critical frac-ture energy GSi�C=C@C

c is reached. In the a-SiC:H films, onlySiAO bonds exhibit a kinetic moisture-assisted bond rup-ture by reacting with water as follows [44]:

gH2Oþ SiAOASi! SiAOHþHOASi ð8Þwhere g is the number of water molecules. This kineticSiAO bond rupture determines the overall crack growthvelocity of the a-SiC:H films. Moisture-assisted crackingof the a-SiC:H films occurs only when GSiAC=C@C ¼GSiAC=C@C

c , and the value of GSiAO is on the v–GSiAO

Curves. Moisture-assisted cracking of the a-SiC:H films,va-SiC:H, can now be written by combining the general crackgrowth velocity expression (Eq. (4)) and GSiAO (Eq. (7))together with the condition that GSiAC=C@C ¼ GSiAC=C@C

c

and the parameters relevant to SiAO bond rupture:

va�SiC:H ¼ vSiAO0 sinh

aSiAO G� GSiAC=C@Cc � 2cSiAO

� �kT

!

¼ vSiAO0 sinh

aSiAOðG� GthÞkT

� �ð9Þ

where vSiAO0 is the reference velocity of SiAO bond rupture,

aSiAO is the activation area for SiAO bond rupture , 2cSiAO

is the surface energy of SiAO bonds, andGth ¼ GSi�C=C@C

c þ 2cSiAO is threshold G. 2cSiAO for thereaction (Eq. (8)) is given by [46]

2cSiAO ¼ N SiAO

"2lSiAOH � lSiAOASi

� g l0H2O � kT ln

P H2O

P 0H2O

! !#ð10Þ

where NSiAO is the number of SiAO bonds ruptured perunit area, l is the chemical potential of the appropriatebond, subscripts denote type of bond or molecule, P H2O iswater pressure, and superscript 0 represents standard state.

This model can explain the low sensitivity of the a-SiC:H films to moisture-assisted cracking, as demonstratedby the absence of shifts in the position of the v–G curveswith changing humidity (Figs. 6 and 7). The position ofv–G curves is characterized by Gth where only 2cSiAO ishumidity dependent. Shifts in Gth with changing humidity,DGth, are calculated from the crack growth velocity model(Eq. (9)):

Fig. 7. Crack growth velocity of SiC-E as a function of applied strainenergy release rate in dry nitrogen and 90% RH.

Fig. 8. Activation areas of SiC-E characterized from the slopes of v–G

curves at different humidities. Error bars represent maximum andminimum values.

Table 3Estimated values of shifts in the position of v�G curves, DGth, from Eq.(11) using NSiAO = 1018 bonds m�2 and g = 1 at 25 �C in selected humidityranges.

Humidity range (% RH) DGth (J m�2)

20–70 0.0051–90 0.0190.1–90 0.028

Fig. 9. v–G curves of a SiC:H films at 20% RH and model prediction usingthe fixed value vSiAO

0 and aSiAO obtained from SiC-E as reference.

Y. Matsuda et al. / Acta Materialia 60 (2012) 682–691 689

DGth ¼ G0th � Gth ¼ NSiAOgkT lnP H2O

P H2O;

� �ð11Þ

where superscripts represents different humidities. Afrequently used approximation of NSiAO is two-thirds ofthe bond density, which has recently been estimated to be�1027 bonds m�3 [51]. This yields NSiAO � 1018 bonds m�2.By assuming first-order reaction kinetics (g = 1), the valuesof DGth can be estimated at the selected humidities (Table 3)

from Eq. (11). This clearly demonstrates that shifts in theposition of v–G curves with changing humidity are verysmall. Even for a humidity change from 0.1% to 90% RH,DGth is only 0.028 J m�2, which is difficult to detectexperimentally.

The present model can also predict the relative positionsof v–G curves among the different a-SiC:H films, and itspredictive ability has implications for the role of mois-ture-insensitive SiAC and C@C network bonds in the mois-ture-assisted cracking of the films. In the crack growthvelocity (Eq. (9)), the values of parameters relevant toSiAO bond rupture, vSiAO

0 ; aSiAO and 2cSiAO, remain almostconstant among the different films. The values of vSiAO

0

depend mainly on the types of ruptured bonds [45,46]. Sim-ilar values of aSiAO and 2cSiAO are apparent from the slopesof the v–G curves (Fig. 6), and from the comparable valuesof NSiAO among the different films [51], respectively. Thecomparability of these parameter values across the differentfilms suggests that the positions of v–G curves among thedifferent films at fixed humidity are mainly determined byGSiAC=C@C

c . GSiAC=C@Cc is estimated to be �Gth from Eq.

(9), together with the fact that the values of 2cSiAO aresmall. Then, using the fixed values of vSiAO

0 and aSiAO

obtained from SiC-E at 20% RH (Fig. 6), the v–G curvesfor the different films fit very well by only changing the val-ues of GSiAC=C@C

c (Fig. 9). The shifts in the position of thev–G curves by GSiAC=C@C

c imply that the moisture-insensitiveSiAC and C@C network bonds act to mechanically shieldthe moisture-sensitive SiAO bonds rupture from theapplied G. The present model can also be modified todescribe moisture-assisted cracking of other materials thatcontain both moisture-sensitive and insensitive bonds, suchas bridged oxycarbosilane organosilicate glasses [54].

The steep slopes of the v–G curves of the a-SiC:H films(Figs. 6 and 7) suggest that activation areas of the films(�0.2–0.4 nm2) were much greater than those reported

690 Y. Matsuda et al. / Acta Materialia 60 (2012) 682–691

for silicate glasses in moist environments (�0.01 nm2 [55]).The activation area, directly related to the activation vol-ume, is generally interpreted as the difference in the charac-teristic molecular volumes of SiAO bonds as the reactionadvances to the activated complex during SiAO bond rup-ture. It has been reported that the larger the activation vol-ume, the higher the reactivity of bonds with activeenvironmental species [56]. This suggests that while a-SiC:H films have a low sensitivity to moisture-assistedcracking, the SiAO bond reactivity of the films is actuallymuch greater than that of bulk silicate glasses. The presentauthors believe that the higher reactivity is associated witha more strained SiAO bond configuration of the a-SiC:Hfilms. It has been shown that when SiAO bond strainincreases from the equilibrium state (bond length0.163 nm, SiAOASi angle 144�, and OASiAO angle109.5� [53]), SiAO bond reactivity with water moleculesincreases over six orders of magnitude [57]. The SiAOASisuboxide bond angle in the a-SiC:H films is known to besmaller than 144� [29], thereby significantly increasing thebond strain and the reactivity.

The mechanism underlying decreased activation areawith increase in humidity (Fig. 8) is still unclear. One pos-sible explanation might be SiAO bond strain relaxationdue to water diffusion ahead of the crack tip and subse-quent adsorption on unruptured SiAO bonds in a-SiC:Hfilms, which will decrease activation area. In addition, ithas been shown that water diffusion and subsequentabsorption on nanoporosity change local strain energyrelease rate at the crack tip in nanoporous organosilicatethin films [8]. This may also decrease the activation area.At this point, however, it is not clear which mechanismchanged the activation area of the a-SiC:H films.

4. Conclusions

This paper has described the cohesive fracture propertiesof a range of a-SiC:H films in moist environments. Whilestoichiometric films exhibited a decrease in cohesive frac-ture energy with decreasing density, carbon-rich non-stoi-chiometric films with lower density showed a surprisinglyincreased cohesive fracture energy. This increased cohesivefracture energy can be explained by crack tip plasticity, asdemonstrated by significant pileup formation during nano-indentation and a fracture energy dependence on filmthickness. Elastic modulus mismatch analysis suggestedthat the observed fracture path transition was due to thecohesive fracture strength exceeding the interfacial fracturestrength between SiCN/metal layers. The films exhibited avery low sensitivity to moisture-assisted cracking, whichwas associated with the formation of SiAOASi suboxidebonds through hydrolation and subsequent condensationat SiAHx groups. We developed a new atomistic fracturemodel to explain how these SiAOASi suboxide bonds leadto the moisture-assisted cracking of the films. This modelcan be applied to other brittle materials composed of bothmoisture-sensitive and moisture-insensitive bonds.

Acknowledgements

This work was supported by the US Department of En-ergy, under Contract No. DE-FG02-07ER46391 and bythe Semiconductor Research Corporation, under Task ID1292.052 g. Y.M. was partially supported by Heiwa Nakaj-ima Foundation Fellowship, Nakagawa/Mitani Fellowshipand Stanford Graduate Fellowship. The authors would liketo thank Dr. Taek-Soo Kim at Stanford University (Cur-rently at KAIST, Korea) for helpful discussions.

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