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Materials Chemistry and Physics 114 (2009) 290–294

Contents lists available at ScienceDirect

Materials Chemistry and Physics

journa l homepage: www.e lsev ier .com/ locate /matchemphys

nalysis of thermal stress in magnetron sputtered TiN coating by finitelement method

ipin Chawlaa,b, R. Jayaganthana,∗, Ramesh Chandrab

Department of Metallurgical and Materials Engineering & Centre of Nanotechnology, Indian Institute of Technology Roorkee, IIT Roorkee Campus,oorkee 247667, Uttarakhand, IndiaNano Science Laboratory, Institute Instrumentation Centre, Indian Institute of Technology Roorkee, Roorkee 247667, India

r t i c l e i n f o

rticle history:eceived 7 June 2008eceived in revised form 9 September 2008ccepted 13 September 2008

eywords:

a b s t r a c t

The thermal stress generated in the sputter deposited TiN coating on glass and silicon substrates wasinvestigated by finite element analysis (ANSYS). The four-node structural and quadratic element PLANE42 with axisymmetric option were used to model the thermal stress induced in the TiN coating. Theinfluence of substrate temperature, Young’s modulus, substrate and coating properties on thermal stresswere analyzed. It was found that the thermal stress in TiN coating, for the planar substrate, exhibits a linear

itridesinite element analysishermal properties

relationship with substrate temperature, substrate thickness and Young’s modulus of the coating, butshowed an inverse relationship with the coating thickness. The simulated thermal stress of TiN coating wasin tandem with the analytical method. The thermal stress induced in the coatings for the rough substrateis higher as compared to that of the planar substrate. The radial stress and shear stress distribution of thecoating–substrate combination were calculated. The low and high compressive shear stresses observedin the TiN coating on glass and Si substrate, respectively indicate a low adhesive strength of the coating

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. Introduction

Thin hard coatings such as TiN, Ti–Si–N, and Ti–Al–N exhibitxcellent mechanical and tribological properties and provide supe-ior wear resistance over the materials on which they are coated.he mechanical reliability of these hard coatings, deposited byarious physical vapor deposition techniques (PVD), is stronglynfluenced by residual stress which originates from growth stresses,eometrical constraints, thermal gradients and service stress.hen a coating is deposited at higher temperature and cooled

own to room temperature, thermal residual stress generates dueo thermal expansion mismatch between the coating and sub-trate. When the coating–substrate combination is subjected tohermal gradients, the thermal expansion mismatch (CTE) betweenhem causes a variation of thermal stress through the thickness ofhe coating. Subsequently, it transforms into a shear at the inter-ace between coating–substrate, causing the coated substrates to

ontract, elongate or bend [1]. The failure of coating may occury cracking and spalling, which are dependent on magnitudef the residual stress and the relative strengths of coating andoating–substrate interface. The preexisting defects in the coatings,

∗ Corresponding author. Tel.: +91 1332 285869; fax: +91 1332 285243.E-mail address: rjayafmt@iitr.ernet.in (R. Jayaganthan).

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254-0584/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.matchemphys.2008.09.023

atter.© 2008 Elsevier B.V. All rights reserved.

nder tensile conditions, causes the formation of through thicknessracks, which generate shear stresses along the interface resultingn de-adhesion of the coatings. The spallation of the coating, underompressive stress, may occur either from the growth of a tensile,edge crack along the interface or by buckling and cracking of the

oating [2–4].The thermal residual stress of the sputter deposited thin coat-

ngs is influenced by various factors such as CTE, Poisson’s ratio,oung’s modulus, thickness and thermal conductivity of coatingnd substrates as reported in the literature [5–6]. If the CTE mis-atch and substrate temperature of thin hard coatings are very

igh, the induced thermal residual becomes a vital issue to ensurehe reliability of the coatings for its various structural and func-ional applications. Wiklund et al. [5] investigated the influence ofesidual stress on fracture and delamination of thin hard coatingsuch as TiN, TiC, and CrN on the different substrates with differenteometries by FEM analysis. They have shown that normal stresscross the interface of the coating comparable to that of residualtress is induced at a critical coating thickness, which causes theelamination of the coatings. According to their analyses, the inter-

ace stress state becomes independent of the coating thickness ifhe coating is thicker than about three times the amplitude of thenterface roughness and it scales linearly with maximum inclina-ion of the surface profile. The experimental study [5] has shownhat the high residual stress results in fracture and delamination of

V. Chawla et al. / Materials Chemistry a

Table 1Properties of coating and substrates materials

Serial no. Properties Materials

TiN Glass Silicon

1 Poisson’s ratio 0.25 0.24 0.323

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2

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is3nTdcwcthe sample at the processing temperature as well as after cool-ing. Both isotropic and orthotropic behaviors of the materialwere taken into account to analyze the thermal stress in thecoating–substrate combination. The physical and mechanical prop-

Young’s modulus (GPa) 600 69 167Coefficient of thermalexpansion (×10−6 ◦C−1)

9.4 9 2.33

eramic coatings at the tip of an edge or rough substrate surfaces,hen the thickness of the coatings was higher than that of the edge

adius. Bielawski and Seo [7] have measured the residual stress gen-rated in sputter deposited TiN coatings on Si and steel substratesy using the surface curvature method. They observed that the TiNoatings sputter deposited on steel substrates at high bias and loweposition pressure are highly stressed. It was attributed to intense

on bombardment producing high compressive residual stress inhe coatings. The residual stress in TiN coating on steel substrateas larger than that of the TiN coating on Si substrate due to its

arge difference in CTE. It was shown in their work that critical post-nnealing treatment, above the substrate temperature, is requiredo relieve the residual stress present in the as deposited coatings.he residual stress in DC and pulsed DC unbalanced magnetronputtered TiN thin films on cemented carbide substrate was inves-igated under different deposition conditions such as bias, targetower and pulsed power through XRD/Sin2� method by Benegrat al. [8]. They observed the higher compressive residual stress inhe coatings deposited with higher negative bias and the pulsedower. The microstructural characteristics and mechanical proper-ies of the PVD deposited TiN coating are strongly influenced byhe residual thermal stress in the coatings. Therefore, the presentork has been focused to simulate the thermal stress generated in

he sputter deposited TiN coatings on Si and glass substrate underifferent conditions by finite element analysis.

. Modeling

.1. Analytical model for thermal stress

Tsui and Clyne [9] have used an analytical model for calculatinghe residual stress in progressively deposited coatings for the planareometry configuration. By combining their analytical model andtoney’s equation for tension of metallic films, the thermal stress

n thin coating can be obtained as [10]:

f =Eef

∫ TdTr

(˛s − ˛f)dT

1 + 4(Eef/Ees)(h/H)(1)

Fig. 1. A schematic of axisymmetric 2D solid model of plane and rough substrates.Fa

nd Physics 114 (2009) 290–294 291

here Eef = Ef/(1 − �f), Ees = Es/(1 − �s), Ef, Es, h, H, ˛f, ˛s, �f, �s, Tr andd are effective Young’s modulus of the coating, effective Young’sodulus of the substrate, Young’s modulus of the coating, Young’sodulus of the substrate, coating thickness, substrate thickness,

hermal expansion of coefficients of the coating, thermal expan-ion of coefficients of the substrate, Poisson’s ratio of the coating,oisson’s ratio of the substrate, room temperature and substrateemperature, respectively.

.2. Finite element analysis

The thermal stress generated in sputter deposited TiN coat-ng was analyzed by FEM with the following dimension of theamples. A cylindrical shaped substrate of 30 mm diameter and.0 mm thickness, and on the top surface, TiN coating of thick-ess 3.0 �m were considered for both glass and silicon substrates.hese dimensions allow the coating–substrate to bend upon theevelopment of thermal stress in the sputter deposition of TiNoating. Thermoelastic behavior of the coatings and substratesere assumed during the analysis. The plain biaxial stress was

onsidered along with the uniform temperature maintained over

ig. 2. Thermal stress variations as a function of substrate temperature on (a) glassnd (b) silicon substrate.

292 V. Chawla et al. / Materials Chemistry and Physics 114 (2009) 290–294

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ig. 3. Thermal stress variations as a function of coating thickness on (a) glass andb) silicon substrate.

rties of the TiN coating and substrates (glass and silicon) are givenn Table 1.

Analyses were performed to study the effect of each parametern thermal stress by varying it, for example, substrate temperature100–600 ◦C), while fixing three of the other parameters constantuch as Young’s modulus (600 GPa), coating thickness (3.0 �m), andubstrate thickness (3.0 mm). The Young’s modulus values of TiNary with in the range of 350–600 GPa as reported in the literature11,12] and therefore in the simulation, the similar variations weremposed. The axisymmetric plane parallel to XY-plane was takennto account for the two dimensional FEA, as shown in Fig. 1 in theresent work.

The thermal, shear and radial stresses generated in the TiN coat-ng deposited on glass and silicon substrates were simulated byNSYS finite element analysis [13]. The thermal stress in TiN coatedlass and Si substrate was simulated using the four-node structuralnd quadratic element PLANE 42 with axisymmetric condition.apped meshing was carried out using the quadrilateral-shaped

lements. The element size across the plane was decreased in araded fashion near the coating–substrate interface due to its veryigh stress concentration [14]. The fine mesh was imparted near the

dge across the thickness of the coating and substrate and it wasefined until the results are consistent with only small changes. Theeft side of the model corresponds to the axis of the axisymmetric

odel and to restrict any movement, left corner of the model wasinned so that bending occurs during cooling. The similar axisym-

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ig. 4. Thermal stress variations as a function of substrate thickness on (a) glass andb) silicon substrate.

etric configuration was used for the coating on rough substrates shown in Fig. 1.

The substrate temperature of 600 ◦C and uniform tempera-ure of 25 ◦C were fixed as reference temperature and uniformemperature, respectively for applying the thermal load over theubstrate-coating system. The verification of the model was car-ied out by substituting the value of different properties of coatingnd substrate in the analytical equation (1). The thermal stress inhe FEM calculation is computed as maximum von Mises stress inhe coating. The coefficient of thermal expansion mismatch (CTE)etween coating and substrate causes a variation of thermal stresshrough the thickness of the coating, which transforms into a sheart the interface between coating–substrate. Similarly, the radialtress is also caused by CTE mismatch, difference in mechanicalroperties and thickness effect of coating and substrate. Therefore,he induced thermal stress in the coating due to the thermal loadpplied over the coating–substrate combination is computed as theum of average value of radial and shear stress components.

. Results and discussion

For the isotropic behavior of the materials, the following resultsere obtained by the FEM analysis. The variation of thermal stress

enerated in TiN coating deposited on glass and Si substrates asfunction of substrate temperature is shown in Fig. 2(a) and (b),

V. Chawla et al. / Materials Chemistry and Physics 114 (2009) 290–294 293

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ig. 5. Thermal stress variations as a function of Young’s modulus on (a) glass andb) silicon substrate.

espectively. It is evident that the thermal stress varies linearlyith substrate temperature for the plane substrate and the values

alculated by FEA analysis are in accordance with analytical model.The thermal stress of TiN on silicon substrate induces a high

ompressive stress as shown in Fig. 2(b) against low compressivetress on glass substrate (Fig. 2(a)). Due to the high CTE mismatchetween TiN and silicon substrate, the induced thermal stress inhe coating is substantial. The linear relationship observed betweenhermal stress and substrate temperature of the TiN coating on glassnd silicon substrate is due to the occurrence of increased thermalradient during deposition process. The thermal stress in the TiNoatings can be relieved by post-annealing treatment. The influ-nce of plane and rough surface topography of substrates (glassnd Si) on the thermal stress induced in the coating is compared inig. 2(a) and (b). It is evident that the compressive stress induced inhe coating due to the thermal stress is higher with rough substratehen compared to planar substrate. The rough substrate affects the

dhesion of the coating–substrate interface and its thermal expan-ion behavior, thereby influencing the induced thermal stress in theeposited coatings at high temperature. It is well known that theough substrate influence the differential nucleation and growth of

eposited atoms on the substrate surface and subsequently lead tohe intrinsic stress during the growth of the thin films [15].

The influence of coating thickness on the thermal stress ofiN coated on glass and silicon substrates is shown in Fig. 3. The

nic

ig. 6. Radial stress (�s) distribution through the thickness of coating and substratet different position from the edge to the center on (a) glass and (b) silicon substrate.

ecrease in thermal stress with the increase of coating thicknesss evident from this Fig. 3(a) and it is due to the stress relaxationaused by the bending strain induced at higher thickness of theoating. The stress is reduced in the coating and substrate in pro-ortion to the bending strain as reported in the literature [16].he bending effect is insignificant for the very thin coating withow stiffness but it is well pronounced for the coating with higherhickness values. The bending curvature in the coating–substrate

ay occur if the coating thickness is increased, which result in theower stress in the coating. The thermal stress of TiN coating onoth glass and silicon substrates is compressive in nature and itecreases with increase in coating thickness. The influence of pla-ar and rough surface topography of substrates (glass and Si) on thehermal stress induced in the coating as a function of coating thick-ess is shown in Fig. 3(a) and (b). The rough substrate contributeso very high compressive stress in the coating as observed in thisgure. The substrate roughness may influence the thickness of theeposited coatings, which in turn affect the induced thermal stress

n the coatings.

The thermal stress of TiN coating increases with substrate thick-

ess as shown in Fig. 4. It is evident that thermal stress withncreasing substrate thickness is compressive in nature in bothases (glass and silicon substrates), with a higher value for the sili-

294 V. Chawla et al. / Materials Chemistry a

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ig. 7. Shear stress (�xz) distribution through the thickness of coating and substratet different position from the edge to the center on (a) glass and (b) silicon substrate.

on substrate. The higher substrate thickness prevents the bendingffect and therefore it can affect directly the thermal stress gen-rated in the coatings. The rough surface topography of substratesglass and Si) increases the thermal stress, which becomes highlyompressive in the coating with increasing thickness of substrate asompared to the planar surface of the substrates shown in Fig. 4(a)nd (b).

The variation of thermal stress in TiN coating with Young’s Mod-lus (E), on the glass and silicon substrates is plotted in Fig. 5(a) andb), respectively. The thermal stress of TiN coating increases withncrease in Young’s Modulus. The E value of the TiN coating dependsn the sputtering process parameters such as deposition pressure,ower and deposition rate. The impurities and porosity of the TiNlms may affect its E value and the porosity of the coating therebyeduces the thermal stress generated. The higher thermal stress inhe coating is observed for the rough substrates (glass and Si) thanhat of the planar substrates, and exhibited a linear relationshipith increase in Young’s modulus.

The radial stress distribution through the thickness of the coat-ng and substrates at different position from the edge to the centers evaluated and plotted in Fig. 6 for both glass and silicon substrate.he stress gradient and its transition from tensile to compressiveccurs through the thickness of the substrates and reaches a maxi-

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nd Physics 114 (2009) 290–294

um value near the interface between coating and substrates. Theadial stress is very high at a distance of −5 h from the substratedge. Through the thickness of the coating, in case of both sub-trates, tensile radial stress is observed from the bottom to topurface. The minimum radial stress is noticed at the edge of theoating but it increases with the distances, such as −5 h, −10 h and15 h away from the edges. In between the two substrates, coatingn silicon substrate exhibit high tensile radial stress as comparedo coating on glass substrate The large tensile radial stress in theoating is due to the higher substrate-to-coating thickness ratio.

The shear stress distribution of TiN coating on glass and siliconubstrates are shown in Fig. 7(a) and (b), respectively. The max-mum compressive shear stress is evident at the interface in theoating edge in the case of both glass and silicon substrates. TheTE mismatch between substrates (glass and Si) and TiN is respon-ible for the compressive shear stress at the coating edge and itxhibited a decreasing trend at a distance of −5 h, −10 h and −15 hway from the edge in both substrates.

There is no stress reversal in the TiN coating away from its edges.he adhesive strength of TiN coating on glass substrate may be lessue to the less compressive shear stress observed in the presentork. However, the high compressive shear stress of TiN coating

n Si substrate is beneficial in improving adhesive strength of theoating.

. Conclusion

The thermal stress of TiN coating sputter deposited on glassnd silicon substrate has been simulated by finite element analysisANSYS) and compared with that of analytical model. The thermaltress of coatings exhibits a linear relationship with substrate tem-erature, substrate thickness and Young’s modulus of the coating.owever, it exhibits an inverse relationship with the coating thick-ess due to the stress relaxation. The thermal stress induced in theoatings for the rough substrate is higher as compared to that ofhe planar substrate. The radial stress of the TiN coating is tensilen nature on both substrates but it is high on the silicon substrate.he higher shear stress of the TiN coating is observed along thenterface at the edge due to the higher stress concentration. Theompressive shear stresses are observed for TiN coating on glassnd silicon substrates. The spallation of the coatings from the edges heavily dependent on these shear stresses. The adhesive strengthf the TiN coating on silicon substrate is higher when compared tolass substrate due to the high compressive stress in the former.

eferences

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Cannon, Mater. Sci. Eng. A 262 (1999) 246.15] M. Ohring, Materials Science of Thin Films, Academic Press, New York, 2002.16] J. Mencik, Mechanics of Components with Treated or Coated Surfaces, Kluwer

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