Journal of Materials Processing Technology 168 (2005) 36–41

Simulation of thermal stress in magnetron sputtered thin coatingby finite element analysis

Julfikar Haidera,∗, Mahfujur Rahmana, Brian Corcoranb, M.S.J. Hashmia,b

a NCPST and MPRC, Dublin City University, Dublin-9, Irelandb School of Mechanical and Manufacturing Engineering, Dublin City University, Dublin-9, Ireland

Received 25 August 2004; accepted 22 September 2004

Abstract

Stresses due to thermal mismatch develop in thin coatings deposited by physical vapour deposition (PVD) processes when cooled down toroom temperature from deposition temperature. Despite having lower processing temperature, thermal stress can be significant when a largedifference in physical and thermal properties of the bonded materials exists. A 2D finite element (FE) model for coating substrate system (TiNon stainless steel) has been investigated to simulate thermal mismatch stress. Several parametric effects i.e., deposition temperature, substratet rmal stresss stress werec©

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hickness, coating thickness, Young’s modulus, and thermal expansion coefficient were studied to get the description of the thetates. The effect of interlayer material on thermal stress has also been studied. FEA results in terms of radial, shear and axialompared with the analytical results and good agreement was found.2004 Elsevier B.V. All rights reserved.

eywords:Thermal stress; FEM; Thin coating; TiN; PVD

. Introduction

Residual stress is very common in coating deposition tech-iques such as plasma spraying, physical vapour depositionnd chemical vapour deposition. The stress state in coating

s very complicated and could vary within the thickness ofhe coating. Higher stress gradient between the coating andubstrate is observed in case of thin coating system. Residualtress can strongly influence coating quality and performancef a coated system since it is directly related to other coat-

ng properties such as hardness, adhesion, fatigue strength,tc. [1]. They can give rise to deformation of coated work-ieces by several stress relaxing mechanisms such as adhe-ive failure (delamination at the interface) or cohesive failurespalling or micro-cracking within the coating) of the coat-ng or subsurface fracture (substrate failure)[2,3]. In most ofhe cases the first two mechanisms are very likely to occurecause thin coatings on metal surface usually have poor ad-esion. Near the edges, a complex stress state will be present,

∗ Corresponding author. Tel.: +353 1 7007674; fax: +353 1 7005345.

but away from the edges, this appears to be a simplestate where the stresses normal to the substrate and thestresses are zero[4–6].

Residual stress in thin PVD coatings is a stress undexternal loading and is the sum of growth stress andmal stress. Thermal mismatch stress results from the pcal and thermal property mismatch between the coatingthe substrate when cooled to the room temperature fromdeposition temperature. The various physical parameteboth the coating and the substrate on which thermal strepends can be listed as coefficient of thermal expansion (CYoung’s modulus, Poisson’s ratio, thickness, thermalductivity, temperature histories during deposition and cing and stress relaxation mechanisms. In general, thestresses develop at the interface between coating andstrate[7]. From the literature, it is evident that major comnent of the residual stress in PVD deposited coatings cfrom growth stress. Usually the thermal stresses are negfor approximation. But sometimes the thermal stress walso be significant (as high as 20–25% of the total st[8] if the deposition temperature or the mismatch of ela

E-mail address:haiderm2@mail.dcu.ie (J. Haider). properties and CTE of coating and substrate materials are

924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved.oi:10.1016/j.jmatprotec.2004.09.093

J. Haider et al. / Journal of Materials Processing Technology 168 (2005) 36–41 37

high. Therefore, the residual stresses in the sputtered coatingcannot be regarded as entirely due to growth. Stress manage-ment has been an essential aspect of coating manufacturingand stress estimation has increasingly become a matter ofgreat importance for the soundness of the coating.

Generally, analytical equations have been developed todescribe the biaxial thermal stress states in coating substratesystem for linear–elastic or simple elastic–plastic materials[9]. Recently, for a more general 2D or 3D problem numer-ical methods such as finite element analysis (FEA) has beenaccepted as an attractive tool to simulate thermal stress incoating substrate systems[2,10–14]. Sometimes the resultsare verified against the experimental results if thermally in-duced stresses are the major contributor in total stress. Mostof these studies are done for thick coating deposited mainlyby thermal spraying. Thermal stress simulation using FEAin thin coating is often performed in wafer processing tech-nology [15] to test the wafer reliability. There are very fewstudies of thermal stress modelling in thin hard coating formechanical applications[16–18]. The objective of this studyis to study the distribution of thermal stress developed in thinTiN coating on stainless steel substrate due to cooling fromdeposition to room temperature by FEA.

2. Thermal stress equation in thin coating

np etryw ge d as

σ

wT ef-f f thes , sub-s ature,t coat-i con-s y thinca

3

3

oat-i teel)a ren tingq

Table 1Physical and thermal properties of coating, interlayer and substrate materials

Property Materials

Ti TiN Stainless steel

Young’s modulus (GPa) 140 600 200Poisson’s ratio 0.41 0.25 0.3Thermal expansion coefficient(× 10−6 ◦C−1)

10.48 9.4 13

3.2. Model formulation

For the modelling of residual thermal stress generated af-ter TiN coating deposition by sputtering method, a simplecylindrical shaped stainless steel sample (30 mm diameterand 0.05 mm thick) with coating on top of the sample (typi-cal thickness 5�m) was considered. Although quite thin, thissubstrate thickness was large in comparison to the coatingthickness.

These dimensions were chosen to keep the model rea-sonably sized[24] and to allow the coating substrate sys-tem bending after the development of thermal stress. For 2Danalysis an axisymmetric plane parallel to the globalXYplanewas considered as shown inFig. 1. Several assumptions weremade for simplicity of calculations[17,18]. It was assumedthat the coating and substrate materials are isotropic and lin-ear thermoelastic; perfect bonding between coating and sub-strate; plain biaxial stress; and uniform temperature was es-tablished in the body both at the processing temperature andat the temperature after cooling.

3.3. Analysis details

Numerical simulation of residual thermal stresses gener-ated after the deposition of the coating was simulated usingAs struc-t trico entsw planew stratei ressc eart strate.T ange[ f thea ym-m there placed ther 0a

ingd sub-sα to the

Combining the analytical model[9] of thermal stress irogressively deposited coating for simple planar geomith the well-known Stoney’s[19] equation, the followinquation for thermal stress in thin coating can be derive

f = Eef∫ Td

Tr(αs − αf ) dT

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

hereEef [=Ef /(1− νf )], Ees [=Es/(1− νs)], νs, νf , h, H, Td,r,αs, andαf are effective Young’s modulus of the coating,

ective Young’s modulus of the substrate, Poisson ratio oubstrate, Poisson ratio of the coating, coating thicknesstrate thickness, deposition temperature, room temperhermal expansion coefficients of the substrate and theng, respectively. The whole coating substrate system isidered as a composite beam, where the coating is verompared to the substrate. Then biaxial stress (σx=σz=σ

ndσy= 0) state can be assumed.

. Finite element considerations

.1. Material properties

The physical and thermal material properties of the cng (TiN), interlayer (Ti) and the substrate (stainless sre shown inTable 1 [8,20–23]. The coating properties aot consistent in the literature due to differences in coauality and thickness.

NSYS finite element analysis code[25]. TiN coating ontainless steel substrate was modelled using four-nodeural and quadratic element PLANE 42, with axisymmeption. Mapped meshing with quadrilateral-shaped elemas used to mesh the model. Element size across theas minimized in a graded fashion near the coating–sub

nterface (Fig. 2), as this area was very prone to high stoncentration[7,24]. Fine mesh was also introduced nhe edge across the thickness of the coating and subhe mesh was refined until results showed only small ch

22,24]. The left side of the model was used as the axis oxisymmetric model. The bottom left corner of the axisetric model was pinned to restrict any movement. All odges were free so that bending was permitted to takeuring cooling. Thermal loading was applied by settingeference temperature as the deposition temperature (50◦C)nd uniform temperature as room temperature (25◦C).

Numerical verification of the model was done by puttifferent property and dimension values of coating andtrate in the general equation of thin coating (Eq.(1)). Ass >αf coating substrate system takes convex shape due

38 J. Haider et al. / Journal of Materials Processing Technology 168 (2005) 36–41

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

developed thermal stress after cooling from deposition tem-perature. Opposite phenomenon occurs during heating fromroom temperature to deposition temperature. Both eventswere verified by FEA.

4. Results and discussions

4.1. Parametric studies

In order to examine the effects of the parameters on ther-mal stress (maximum von Mises stress in the coating) fivesets of analyses were performed by holding four of otherparameters constant. The constant values used for differentparameters were as follows: deposition temperature (500◦C),substrate thickness (0.5 mm), coating thickness (5�m), co-efficient of thermal expansion (9.4× 10−6 ◦C−1), and elasticmodulus (600 GPa).

Typically, deposition temperature in sputtering techniquevaries between 100 and 500◦C depending on operating pa-rameters. FromFig. 3, it is seen that the thermal stress varieslinearly with the deposition temperature. This proportionalityhas been reflected in the graph both for analytical and finiteelement analysis.

The Young’s modulus of the coating deposited by PVDtechniques depends on the processing parameters (depositionpressure, deposition current, N2 percentage in the coating,etc.). Usually understoichiometric TiN has lower Young’smodulus values whereas overstoichiometric TiN coating hashigher Young’s modulus[20]. The reported values of Young’smodulus of TiN coating in the literature vary within the rangeof 250–600 GPa mainly due to the porosity induced in thecoating. FromFig. 4, it is seen that thermal stress increaseswith coatings Young’s modulus agreeing with the analyticalequation (Eq.(1)). This plot gives an indication of the er-ror introduced in the thermal stress calculation with differentyoung’s modulus of the coating. As the porosity increases inthe coating the Young’s modulus and thermal conductivityvalues decrease and also Poisson’s ratio decreases[6,26].This result gives an indirect relation between the coatingporosity and thermal stress.

Thermal stress decreases with the increase of the coat-ing thickness[2] as seen inFig. 5. The reason for this isbending-induced stress relaxation at high coating thicknessand consistent with the analytical solution in literature[27].The stress in the coating and substrate is reduced in pro-portion to the bending strain when the coating–substratesystem is bent. This bending effect is negligible for verythin films, due to their very low stiffness; it is significant

ry cond

Fig. 2. Physical bounda itions applied in the model.

J. Haider et al. / Journal of Materials Processing Technology 168 (2005) 36–41 39

Fig. 3. Variation of analytical and FEA thermal stress with deposition tem-perature.

Fig. 4. Variation of analytical and FEA thermal stress with different Young’smodulus of coating.

as the film thickness increases. When coating thickness isincreased larger bending curvature in the coating–substratesystem occurs. This causes considerable bending-inducedstress relaxation[2] and consequently lower stress in thecoating.

Thermal stress increases with the substrate thickness asshown inFig. 6. With lower substrate thickness the stressin the coating is relaxed by the deformation of the substratewhile for higher substrate thickness bending is prevented due

Fig. 5. Variation of analytical and FEA thermal stress with coating thickness.

Fig. 6. Variation of analytical and FEA thermal stress with substrate thick-ness.

to the higher substrate thickness and consequently higherresidual stress develops in the coating.

Similar correlation for thermal stress with Poisson’s ratioand CTE has been found according to Eq.(1).

4.2. Stress distribution through thickness

The coating failure mechanisms are mainly controlled bythe magnitude and the distribution of radial stress (σx), tan-gential stress (σz), axial stress (σy) and shear stress (σxz) ator near the radial free edge of the specimen or near the spec-imen’s axis of symmetry (y-axis).Fig. 7shows the distribu-tion of radial stress (σx) through the thickness of the coat-ing and substrate at different position from the edge of thecoating substrate system. Through the thickness of the sub-strate from bottom to top surface stress gradient and stressreversals (compressive to tensile) were observed and reachedmaximum value near the interface between the coating and

F nds

ig. 7. Radial stress (σx) distribution through the thickness of coating aubstrate at different position from the edge to the center.

40 J. Haider et al. / Journal of Materials Processing Technology 168 (2005) 36–41

Fig. 8. Shear stress (σxz), distribution through the thickness of coating andsubstrate at different position from the edge to the center.

substrate. Compressive radial stress exists through the thick-ness of the coating from bottom to top surface with slightstress gradient but no stress reversal was observed. Radialstress distribution through the thickness of the coating andsubstrate at different distances away from the edge showedthat minimum radial stress value in the coating appeared atthe edge while stress values increased away from the edge. Ataround a distance of 5h (whereh is coating thickness) stressesreached the maximum value. Since the substrate-to-coatingthickness ratio was very large, the compressive radial stressin the coating was much larger than the tensile stress in thesubstrate[24]. Similar stress distribution was found for tan-gential stress (σz) component, which confirmed the biaxialstress state in the coating.

The shear stress values were far less than the other stresscomponents except near the edge as shown inFig. 8. Themaximum tensile shear stress appeared at the interface nearthe edge of the coating and decreased to very small compres-sive stress at the top surface of the coating. But away fromthe edge no stress reversal in the coating was observed andthe tensile stress at the top surface of the coating reached tovery small value due to the free surface phenomenon. Whileat the edge of the substrate, the maximum tensile stress at theinterface decreased to very small value at the bottom surface.Stress reversal from tensile at the interface to compressive to-wards the bottom surface was also observed. Away from thee d. But atinga ivalents d subs fromt dings dt etricl

Fig. 9. Shear stress (σxz) distribution through the thickness of coating andsubstrate at the edge without and with interlayer.

4.3. Effect of interlayer

It is generally acknowledged that Ti interlayer betweenTiN coating and steel is used to enhance the adhesion of thecoating to substrates and to reduce the thermal mismatch be-tween them, as well as prolong the service life of the coating[16,29]. Chemically, diffused mixing of elements forming abroad interface and strong epitaxial relation between the TiNand Ti layers is attributed for better adhesion with Ti inter-layer. Mechanically, the titanium interlayer acts as a soft flex-ible layer, reducing the shear stresses at the coating–substratecontact and stopping the propagation of cracks in the inter-surface area. The shear stress distribution through the thick-ness of the coating and substrate at the edge of the coat-ing substrate model with and without interlayer is shown inFig. 9. A significant reduction of shear stress at the interfaceis evident with introducing Ti interlayer. Smooth transitionof thermal properties from TiN to stainless steel and accom-modation of shear stress by the deformation of soft Ti layerwould be recognised as the possible reasons for the reductionof shear stress. The increase of Ti interlayer thickness couldreduce the shear stress levels but not very significant reduc-tion was observed. The reduction of other stress componentse.g., radial or tangential and axial stress was also observedby introducing the Ti interlayer.

5

thinT beenp YSa Thew tressv ions.T ther-m elas-t . The

dge the shear stress values at the interface decreasehe general trend for shear stress distribution in the cond substrate remained same. The shear stress is equ

o the adhesion strength of the coating[5]. As the maximumhear stress is at the interface between the coating antrate, the spallation of the coating is expected to occurhis position if the shear stress is greater than the bontrength between the coating and substrate[28]. As expectehere was very small shear stresses along the axisymmine.

t

t

-

. Conclusion

A method for analysing thermal stress developed iniN sputtered coating on stainless steel substrate haserformed using finite element simulation package ANSnd validated by appropriate analytical calculations.ide ranging parametric studies show how thermal saries with the various material properties and dimenso obtain minimum peak stress, coating thickness andal expansion coefficient should be increased whilst the

ic modulus should be reduced as much as practicable

J. Haider et al. / Journal of Materials Processing Technology 168 (2005) 36–41 41

highest radial stress values found at the interface between thecoating and substrate, which indicates that the interface be-tween the coating and substrate is the critical location fromthe failure point of view. Along the interface higher shearstresses were found at the edge because of stress concentra-tion. This will cause the start of the spallation of the coatingfrom the edge. Results also showed that insertion of Ti inter-layer between the TiN coating and substrate can significantlyreduce the stress components especially the shear stress. Theinterlayer thickness has little effect on stress reduction. Fi-nally, FEM analysis provides detailed information about allstress components and proves very useful in providing bet-ter understanding of thermal stress developed during coolingdown of the thin coating substrate system.

Acknowledgement

The funding from Material Processing Research Center(MPRC) and National Center for Plasma Science and Tech-nology (NCPST) to carry out this research is greatly acknowl-edged.

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