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j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 0 ( 2 0 0 8 ) 205–211

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

inite element analysis of thermal stress inagnetron sputtered Ti coating

ipin Chawlaa, R. Jayaganthana,∗, Ramesh Chandrab

Department of Metallurgical and Materials Engineering and Centre of Nanotechnology, Indian Institute of Technology Roorkee,oorkee-247667, IndiaInstitute Instrumentation Center and Centre of Nanotechnology, Indian Institute of Technology Roorkee, Roorkee-247667, India

r t i c l e i n f o

rticle history:

eceived 23 January 2007

eceived in revised form

6 July 2007

ccepted 7 September 2007

a b s t r a c t

The thermal, shear and radial stresses generated in the Ti coating deposited on glass and

Si substrates were investigated by finite element analysis (ANSYS). The four-node struc-

tural and quadratic element PLANE 42 with axisymmetric option were used to model the Ti

coating on glass and Si substrates. The influence of deposition temperature, substrate and

coating properties on the generation of thermal stress in Ti is analyzed. It is found that the

thermal stress of Ti coating exhibits a linear relationship with deposition temperature and

Young’s modulus of the coating, but it exhibit an inverse relationship with the coating thick-

eywords:

i coating

hermal stress

hear stress

EM

ness. The results of simulated thermal stress are in accordance with the analytical method.

The radial stress and shear stress distribution of the coating–substrate combination are cal-

culated. It is observed that high tensile shear stress of Ti coating on glass substrate reduces

its adhesive strength but high-compressive shear stress of Ti on Si substrate improves its

adhesive strength.

the coating. The deformation of hard coatings occurs by

. Introduction

itanium-based thin hard coatings such as TiN, Ti–Si–N andi–Al–N exhibit excellent mechanical and tribological proper-ies and provides superior wear resistance over the materialsn which they are coated. However, the residual stressesenerated in the thin hard coatings during the deposition pro-esses, physical and chemical vapor deposition, significantlynfluence their hardness, adhesion and wear resistance. Theesidual stress in the coating is dependent on growth stressnd thermal stress, which are affected by the deposition pro-esses. The presence of growth stress or intrinsic stress inhin coating is due to the influence of particle flux and energy

triking the condensing film on the substrate during the sput-ering process. The energy of bombardment and the structuref the coatings are sensitive to the deposition parameters such

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

924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.jmatprotec.2007.09.036

© 2007 Elsevier B.V. All rights reserved.

as substrate temperature, pressure, sputtering current, biasvoltage and substrate orientation. The intrinsic stress in sput-tered thin coatings can be related to the structure zones. Alow-density zone I possess voids between columns leading tocoating under tensile stress. The tensile stress arises from theinteraction of open columnar boundaries in the coatings. Ifthe coating is bombarded by energetic particle such as ionor reflected neutral species during sputtering at low argonpressure and bias, compressive stresses are generated due toion-peening mechanism. It will result in higher density zonewith fewer voids (Teixeira, 2001). The growth stress affectsadhesion, hardness and generation of crystalline defects in

stress relaxation mechanism namely; adhesive failure due todelamination at the interface and cohesive failure caused byspallation with the coating. It is well known from the literature

n g t e c h n o l o g y 2 0 0 ( 2 0 0 8 ) 205–211

Table 1 – Properties of coating and substrates materials

Properties Materials

Ti Glass Silicon

Poisson’s ratio 0.31 0.24 0.3

2003). The four-node structural and quadratic element PLANE42 with axisymmetric option has been used to model the Ticoating on glass and Si substrates. The model was meshed

206 j o u r n a l o f m a t e r i a l s p r o c e s s i

that the poor adhesion of the coatings on the metal surfaceis influenced by the complex stress states manifested at theedges of the thin coatings (Islamoglu et al., 2002; Khor and Gu,2000; Teixeira et al., 1999). Thermal stress in the thin coatingsresults from the thermophysical property mismatch betweensubstrate and coating occurs during the sputtering process.The various factors such as coefficient of thermal expansion,Poisson’s ratio, Young’s modulus, thickness and thermal con-ductivity affects significantly the thermal stress of sputtereddeposited thin coatings as reported in the literature (Haideret al., 2005; Boley and Weiner, 1985; Gunnars and Wiklund,2002). Although the growth stress is substantial in physicalvapor deposition of thin coatings, thermal stress cannot beignored if the deposition temperature and CTE mismatch ishigh (Gunnars and Wiklund, 2002). Hence, analysis of resid-ual stress in thin coatings should account for both of thesestresses. It is essential to realize that the stress management isvery crucial in order to ensure the reliability of coatings in theactual applications. Analytical models are generally used todescribe the thermal stresses of the coatings constituting thelinear-elastic or elastic–plastic behavior. In recent times, finiteelement analysis (FEA) serves as potential tool to quantifythe thermal stress in the thin coatings. It may be mentionedthat FEA analysis (Ucar et al., 2001; Sarikaya and Celik, 2002;Widjaja et al., 2003) of thermal stress in thin film is quite preva-lent in device manufacturing technology to test its reliability(Okyar and Gosz, 2001) but it is very scarce in the context offailure of the coatings for the technological applications. Tithin coating is used in microelectromechanical systems, anddiffusion barrier applications due to their superior mechani-cal, thermal and chemical stability. Since the thermal stressstrongly affects the mechanical properties of the coatings, itis very essential to ensure its reliability in various applicationsby quantifying them via experimental and modeling studies.Therefore, the present work has been focused to simulate thethermal stress generated in thin Ti coatings sputter depositedon glass and Si substrates.

2. Modeling

2.1. Analytical model for thermal stress

Y.C. Tsui and T.W. Clyne (Tsui and Clyne, 1997) have pro-posed an analytical model for predicting residual stress inprogressively deposited coatings for the planar geometry con-figuration. Their analytical model in conjunction with Stoney’sequation for tension of metallic films would result in the fol-lowing equation for thermal stress in thin coating as (Stoney,1909),

�f =Eef

∫ TdTr

(˛s − ˛f)dT

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

where Eef = Ef/(1 − �f), Ees = Es/(1 − �s), h, H, ˛f, ˛s, �f, �s, Tr and Td

are effective Young’s modulus of the coating, effective Young’s

modulus of the substrate, coating thickness, substrate thick-ness, thermal expansion of coefficients of the coating, thermalexpansion of coefficients of the substrate, Poisson’s ratio of thecoating, Poisson’s ratio of the substrate, room temperature anddeposition temperature, respectively.

Young’s modulus (GPa) 120 69 167Coefficient of thermal expansion

(×10−6 ◦C−1)8.4 9 2.33

2.2. Finite element analysis

To analyze the thermal stress generated in sputter deposited Ticoating, a cylindrical shaped glass substrate of 20 mm diam-eter and 3 mm thickness, and on the top surface, Ti coatingof thickness 2.5 �m were considered. Similarly, for the siliconsubstrate, a cylindrical shape was considered but with differ-ent dimension of diameter 20 mm and thickness 0.5 mm, andcoating thickness 2.5 �m. These dimensions would allow thecoating–substrate to bend upon the development of thermalstress in the sputter deposition of Ti coating. For the simplic-ity of analysis, an isotropic and thermoelastic behavior of thecoatings and substrates were assumed. The plain biaxial stresswas considered along with the uniform temperature main-tained over the sample at the processing temperature as wellas after cooling. The orthotropic behavior of the material wasalso taken into account to analyze the thermal stress in thecoating–substrate combination. The physical and mechanicalproperties of the Ti coating and substrates (glass and Si) aregiven in Table 1.

Analyses were made to study the effect of each parame-ter on thermal stress by varying it, for example, depositiontemperature (100 to 500 ◦C), while fixing three of the otherparameters constant {Young’s modulus (120 GPa), coatingthickness (2.5 �m), substrate thickness (3 mm for glass and0.5 mm for Si)}. The identical geometry of the substrates withfixed thickness was used for the analysis. The Young’s mod-ulus values of Ti vary with in the range of 100–120 GPa asreported in the literature (Chinmulgund et al., 1995; Ogawaet al., 1997) and in the simulation the similar variations wereimposed. The axisymmetric plane parallel to XY plane wastaken into account for the two-dimensional FEA, as shown inFig. 1 in the present work.

The simulation of thermal, shear and radial stresses gen-erated in the Ti coating deposited on glass and Si substrateswere performed by ANSYS finite element analysis (ANSYS,

Fig. 1 – Schematic diagram of axisymmetric 2D solid model.

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 0 ( 2 0 0 8 ) 205–211 207

epos

wmatatulmm

ssisct2t

3

Tdsi

Fig. 2 – Thermal stress variation as a function of d

ith mapped meshing using the quadrilateral-shaped ele-ents. The element size across the plane was decreased ingraded fashion near the coating–substrate interface, since

his area was under very high stress concentration (Wright etl., 1999). The fine mesh was imparted near the edge acrosshe thickness of the coating and substrate and it was refinedntil the results are consistent with only small changes. The

eft side of the model corresponds to the axis of the axisym-etric model and to restrict any movement, left corner of theodel was pinned so that bending occurs during cooling.The verification of the model was carried out by sub-

tituting the value of different properties of coating andubstrate in the analytical equation (1). The thermal stressn the FEM calculation is computed as maximum von Misestress in the coating. The thermal load is applied over theoating–substrate combination by fixing deposition tempera-ure as 500 ◦C and uniform temperature as room temperature,5 ◦C. The average value of radial stress components gives thehermal stress values in the coating–substrate combination.

. Results and discussion

he variation of thermal stress generated in Ti coatingeposited on glass and Si substrates as a function of depo-ition temperature is shown in Fig. 2(a) and (b), respectively. Its observed that thermal stress varies linearly with deposition

Fig. 3 – Thermal stress variation as a function of coa

ition temperature (a) on glass and (b) Si substrate.

temperature and the values calculated by FEA analysis are inaccordance with analytical model, in the present work.

The thermal stress of Ti on Si substrate induces a com-pressive stress as shown in Fig. 2(b) against tensile stress onglass substrate. Due to the high CTE mismatch between Tiand Si substrate, the induced thermal stress in the coatingis substantial. The linear relationship observed between ther-mal stress and deposition temperature of the Ti coating onglass and Si substrate is due to the increase in thermal gra-dient occurs during deposition process. The induced thermalstress in the coating is high at higher deposition temperaturedue to the influence of thermal gradient and CTE mismatchbetween coating and substrate. The thermal stress in the Ticoatings can be relieved by post-annealing treatment.

The influence of coating thickness on the thermal stressof Ti coated on glass and Si substrates is shown in Fig. 3.The decrease in thermal stress with the increase of coat-ing thickness is evident from this Fig. 3(a) and it is due tothe stress relaxation caused by the bending strain induced athigher thickness of the coating. The stress is reduced in thecoating and substrate in proportion to the bending strain asreported in the literature (Mencik, 1995). The bending effectis insignificant for the very thin coating with low stiffness

but it is well pronounced for the coating with higher thick-ness values. It may be mentioned that the bending curvaturein the coating–substrate manifests if the coating thickness isincreased, which in turn would result in the lower stress in the

ting thickness (a) on glass and (b) Si substrate.

208 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 0 ( 2 0 0 8 ) 205–211

n of

Fig. 4 – Thermal stress variation on Si substrate as a functiocoating thickness.

coating. The thermal stress of Ti coating on Si substrate is com-pressive in nature and it decreases with increase in coating

thickness.

When orthotropic behavior of the materials was taken in toaccount for the FEM analysis as shown in Fig. 4(a–c), it is evi-dent that there is a slight deviation in thermal stress values as

Fig. 5 – Comparison of thermal stress variation as a function of sthickness and (b) 0.1–0.5 mm substrate thickness.

(a) deposition temperature, (b) Young’s modulus and (c)

a function of coating thickness from the values calculated forthe isotropic case. However, they exhibit similar trends with

respect to deposition temperature and Young’s modulus.

The identical geometry of the substrates was assumed tocalculate the thermal stress of Ti coating and the results areshown in Fig. 5. It is evident that thermal stress in the coating is

ubstrate thickness of glass and Si (a) 1.0–3.0 mm substrate

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 0 ( 2 0 0 8 ) 205–211 209

f You

osTttttm

mawidttg

ctasoa

Ft

Fig. 6 – Thermal stress variation as a function o

f tensile in nature in the case of glass substrate but compres-ive for the Si substrate with increasing in substrate thickness.he thermal stress of Ti coating increases with glass substrate

hickness and the stress relaxation at the lower thickness ofhe coating is due to bending effect, which would reduce thehermal stress. The higher substrate thickness would preventhe bending effect and therefore it can affect directly the ther-

al stress generated in the coatings.The variation of thermal stress in Ti coating with Young’s

odulus (E), on the glass and Si substrates is plotted in Fig. 6(a)nd (b), respectively. The thermal stress of Ti coating increasesith increase in Young’s modulus. The E value of the Ti coat-

ng depends on the sputtering process parameters such aseposition pressure, power and deposition rate. The impuri-ies and porosity of the Ti films may affect its E value andhe porosity of the coating thereby reduces the thermal stressenerated.

The radial stress distribution through the thickness of theoating and substrates at different position from the edge tohe center is evaluated and plotted in Fig. 7 for both glass

nd Si substrate. The stress gradient and the stress rever-als from compressive to tensile occurs through the thicknessf the substrate from its bottom to top surface and reachesmaximum value near the interface between coating and

ig. 7 – Radial stress (�s) distribution through the thickness of cohe center (a) on glass and (b) Si substrate.

ng’s modulus (a) on glass and (b) Si substrate.

glass substrate. The radial stress is very high at a distance of−5 h from the glass substrate edge. Through the thickness ofthe coating, in the case of glass substrate, compressive radialstress is observed from the bottom to top surface. The mini-mum radial stress is noticed at the edge of the coating but itincreases with the distances, such as −5 h, −10 h and −15 haway from the edges. The large compressive radial stress inthe coating is due to the higher substrate-to-coating thick-ness ratio. It is observed that the stress reversal from tensileto compressive occurs through the thickness of Si substrate,and reaches a maximum at the interface between substrateand coating. The compressive stress is very high at a distanceof −5 h from the edge of Si substrate. The radial stress in thecoating increases upon moving at a distance of −5 h, −10 h and−15 h from the coating edge and it is of tensile in nature in thecase of Si substrate.

The shear stress distribution of Ti coating on glass and Sisubstrate are shown in Fig. 8(a) and (b), respectively. The max-imum tensile shear stress is evident at the interface in thecoating edge in the case of glass substrate. The maximum

compressive shear stress is observed at the interface in thecoating deposited on Si substrate. The CTE mismatch betweenSi and Ti is responsible for the higher compressive shear stressat the coating edge and the decreasing trend of compressive

ating and substrate at different position from the edge to

210 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 0 ( 2 0 0 8 ) 205–211

Fig. 8 – Shear stress (�xz) distribution through the thickness of coating and substrate at different position from the edge to

r

the center (a) on glass and (b) Si substrate.

shear stress is noticed at a distance of −5 h, −10 h and −15 hfrom the coating edge.

The tensile shear stress of Ti coating on glass substrateshows a decreasing trend upon moving away −5 h, −10 h and−15 h from the coating edge. The very small value of tensileshear stress at the top surface of the coating is due to the freesurface phenomenon (Teixeira et al., 1999). There is no stressreversal in the coating away from its edges. At the edge ofthe glass substrate, the maximum tensile stress is observedat the interface and it decreases to the small value at the bot-tom surface of the substrate. The stress reverses from tensileat the interface to compressive at the bottom surface of theglass substrate as seen in Fig. 8(a). The shear stress decreasesat the interface when we move away from the coating edge.The shear stress is of compressive in nature in the case of Ticoating on Si substrate as shown in Fig. 8(b). The shear stressvalue can determine an adhesive strength of the coatings, asthey are equivalent to each other. It may be inferred basedon the reported literature (Ward and Wiliams, 1999) that theadhesive strength of Ti coating on glass substrate is less dueto the higher tensile shear stress in the coating obtained inthe present work. However, the compressive shear stress ofTi coating on Si substrate is beneficial in improving adhesivestrength of the coating. The de-adhesion of the coating is dueto through thickness cracks develops from the pre-existingdefects in the coating and generates shear stress along theinterface which exceeds the bond strength between the coat-ing and substrate (Teixeira, 2001).

4. Conclusion

The thermal stress of Ti coating sputter deposited on glassand silicon substrate has been simulated by finite elementsimulation package ANSYS and compared with that of ana-lytical model. The thermal stress of coatings exhibits a linearrelationship with deposition temperature and Young’s modu-lus of the coating, but it exhibit an inverse relationship with

the coating thickness due to the stress relaxation. The radialstress of the coating–substrate exhibits a maximum value atthe interface near the edge and it determines the failure of thecoatings. The radial stress in the Ti coating is of compressive

in nature on the glass substrate but tensile on the Si substrate.The higher shear stress of the Ti coating is observed along theinterface at the edge due to the higher stress concentration.The tensile and compressive shear stresses are observed for Ticoating on glass and Si substrates, respectively. The spallationof the coatings from the edge is heavily dependent on theseshear stresses. The adhesive strength of the Ti coating on Sisubstrate is higher when compared to glass substrate due tothe high compressive stress in the former.

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