Internal stress in titanium nitride coatings: Modelling of complex stress systems

Surface and Coatings Technology, 36 (1988) 661 - 674

661

INTERNAL STRESS IN TITANIUM NITRIDE COATINGS: MODELLING OF COMPLEX STRESS SYSTEMS* D. S. RICKERBYt, A. M. JONES and B. A. BELLAMY Materials Development Division, Harwell Laboratory, Didcot OX11 ORA (U.K.) (Received April 5, 1988)

Summary The internal stress in sputter-ion-plated titanium nitride coatings has been measured by the well-known sin2 ~i method. In such measurements it is usual to assume that the true stress state approximates to a biaxial state which requires that there is a linear variation in lattice strain with sin2 ~‘. However, this is not always the case, and it is shown that appreciable errors in the calculated values of the principal stresses u~and 022 result if effects such as ri,D splitting and curvature in the e~ vs. sin2 ~(i plots are ignored. Results are presented which compare the values of stress calculated using the simple biaxial approximation with those obtained from a more detailed analysis. As these physical-vapour-deposited coatings thicken it is shown that the levels of internal stress decrease owing to a combination of grain size and porosity effects. These changes in coating microstructure cause curvature in the 0~, vs. sin2 ~(i stress plots and the stress state can be modelled by assuming that the stress varies exponentially with coating thickness.

1. Introduction Recently a number of papers have appeared in the literature which have been concerned with the measurement, by X-ray diffraction methods, of residual stresses in physical-vapour-deposited (PVD) coatings such as titanium nitride [1 8]. In all cases it has been assumed that the stress state which exists in the coating is one of biaxial stress, which requires a linear variation in lattice strain with sin2 t~i.However, several workers have reported behaviour such as curvature [3 7] and ~i splitting [4] in the lattice strain vs. sin2 ~.fiplots which are inconsistent with this biaxial stress approximation. In this paper we consider PVD coatings deposited by sputter ion plating -

-

*paper presented at the 15th International Conference on Metallurgical Coatings, San Diego, CA., U.S.A., April 11 - 15, 1988. tTo whom correspondence should be addressed.

0257-8972/88

Elsevier Sequoia/Printed in The Netherlands

662

(SIP); examples are given to illustrate how the sin2 ~ method may be extended from the simple biaxial approximation to allow for the determination of the full stress tensor which can then be related to changes in coating microstructure with deposition time (that is, film thickness). 2. Experimental details 2.1. Sputter ion plating The titanium nitride coatings were produced by sputter ion plating (SIP) [9], which is a soft vacuum d.c. sputtering process developed at the Harwell Laboratory of the United Kingdom Atomic Energy Authority. Further details on the process can be found in the literature [10]. For the coatings considered here a deposition temperature of approximately 500 °C was used and the coating thickness was varied in the range 1 10 j~mfor a range of stainless and tool steels. -

2.2. Instrumentation for X-ray stress measurement The measurements were made using a Harwell-designed APEX goniometer which was interfaced to a Hewlett-Packard 9816 control microcomputer using Harwell 6000 series electronics. Both Cu Ka and Cr Ka Xradiations were used, incorporating a curved graphite crystal secondary monochromator. The raw data generated from point scans over high angle diffraction peaks (for example the 422 reflection for Cu Ka radiation) were then transferred to an IBM 3084 mainframe computer, and corrections were applied for Lorentz polarization, absorption and background before peakprofile fitting. A number of peak shapes were available for fitting, but a Pearson VII function appeared to give the best fits to the data. Once the peak position had been obtained, it was converted to an interplanar spacing which was then used in the stress analysis. Further details of the technique used at Harwell can be found elsewhere [11]. 2.3. Scanning electron microscopy Both fracture sections and the surface topography of as-deposited coatings were examined by scanning electron microscopy using a Hitachi S520 scanning electron microscope operated at 20 30 keV. -

3. Stress measurement by X-ray techniques 3.1. Simple biaxial stress analysis The internal stress present in the coatings was determined by the wellknown sin2 i~(i method in which an interplanar spacing d serves as an internal strain gauge [12]. Following the convention established by Dölle [13], the strain measured along the L 3 direction (see Fig. 1, which also defines the angles of 0 and ~i) may be represented as

663

Coating Substrate

Fig. 1. Definition of the angles

0 and

~‘

and orientation of the laboratory system L~with

respect to the sample system P~and the measurement direction L

3 (after Dölle [13]).

—

d~ —d0 U0

where d~ is the interplanar spacing of crystal planes which lie perpendicular to the i~idirection in the stressed condition and d0 is the interplanar spacing in the unstressed condition. If a biaxial stress state exists the strain is related to the principal stresses ~ and a22 by [14] 20 + 022 sin2Ø) sin2~i+ S = (52/2)(a11 cos 1(a11 + 022) (1) where S~and S2/2 are the X-ray elastic constants for a particular (hkl) reflection. For an elastically isotropic solid then S2 = 1+v 2(hkl)

E

Si(hkl)=—j~ where E is Young’s modulus and v is Poisson’s Figure represents the 2 ~i ratio. according to2 eqn. (1) from idealized variation in lattice strain with sin which values for the principal stresses a~and 022 can be derived or, as is more commonly reported, values for U~since a~,= a~cos20 + a 20. It must be remembered that these measured stresses are thought of22assin surface stresses and eqn. (1) takes no account of the penetration depth of the X-ray beam into the coated surface. It is this averaging of the stress elements a~ which has important consequences when considering the general stress tensor. 3.2. Triaxial stress analysis It is generally recognized that two effects are responsible for deviations from linearity in the e 2 ~liplots. The first is termed (i splitting. With 0~vs. sin

664 0-004

_________________

_

(a)

~

05

C4J

0-004

::OT0r

02

03 2 ~

(b) Sin Fig. 2. (a) An example of ~1i splitting in the

vs. sin~t/iplot for a 2

4Um titanium nitride coating deposited onto an austenitic stainless steel at a bias voltage of —35 V. The broken line represents the biaxial stress approximation, whilst the stress tensor was derived following the analysis of Noyan [15]. (b) Analysis of the data presented in (a) using the method of Dölle and Hauk [16]. The full lines represent the fit to the data for both negative and positive ~I inclinations derived from the partial stress solution at 0 = 0: •, ,Ji> 0;•, j/ < 0.

reference to Fig. 1 if, in addition to the normal stress 033, stresses 013 and 023 exist in the direction 2ofji the normal (P3), 2(a), then for ~(‘splitting is plot.surface As shown in Fig. a titanium observed in thedeposited e~ us. sin nitride coating onto an austenitic stainless steel, the plot separates into two branches for positive and negative ~ inclinations with a large curvature near ~1’= 0. With reference to Fig. 1, approximation of the true triaxial stress state to one of biaxial stress requires that the stress components in the direction of the sample normal (P 3) are negligible in the

665 0

-0001

—

“\

•I

c73~2350MPo

V •0

0002

D~3040MPa

-0-003

—

0

I 0-I

I 0-2

2

Sin

I 03

I 0-4

I 0-5

2li plot for a 4.5 #m titanium nitride coating deposited onto tool steel Fig. 3. vs. sin (M2) with a substrate bias voltage of —35 V. The internal stress value determined using Cu Ka radiation (.) differs from that measured with Cr Ka radiation (•) due to the presence of a stress gradient normal to the surface.

volume sampled by the X-ray beam and, in addition, that the components ~ and ~22 do not vary with depth. However, as Fig. 3 shows, this is not always the case. Measurements of internal stress a~,using different Xradiations vary according to the volume sampled by the X-ray beam since this depends on wavelength according to the penetration depths given in Table 1. In addition, for a given X-radiation, the average value of internal stress within the irradiated volume will change at each i,1i inclination. With increasing tilt, averaging of the stress occurs closer to the surface and the stress decreases with tilt angle D. The effect of this is to cause curvature in the e~ us. sin2 (i plot as shown in Fig. 4 for a titanium nitride coating deposited onto martensitic 420 stainless steel. These observations are important since it has been shown by Noyan [15] that even a small curvature in the e~,us. sin2 li plot can cause an appreciable error in the calculated stress when the true stress state is approximated to that of a biaxial stress system. The degree of such curvature depends on the steepness of the gradient in 033. Since 033 is a stress normal to the surface, by definition it is zero at the surface, and consequently it must exhibit a gradient in the outer regions of the surface (coating). If the unstressed lattice spacing d 0 is known it is possible to estimate the magnitude of the normal stress averaged over the penetration depth (033) and hence the likely effects on a,~,.Table 2 lists the lattice parameters of titanium nitride coatings which have been removed from their respective substrates. In all cases the unit cell dimensions agree with that published for

666

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+~

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L(L

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•0

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2 I~Iplot for a 12Mm coating of titanium Fig. 4. An example of curvature in the c~ vs. sin nitride deposited onto a martensitic 420 stainless steel. Measurements were made with Cr Ka radiation and the broken line represents the biaxial approximation (0~ —2770 MPa): ., (‘ < 0;•, /i> 0.

TABLE 2 As-deposited and relaxed lattice parameters for titanium nitride coatings deposited onto a range of substrates Coating—substrate system

Lattice parameter (A) As-deposited

Free-standing

Titanium nitride— tool steel (M2)

4.250

4.242

Titanium nitride— cemented carbide (A30)

4.242

4.242

Titanium nitride— martensitic 420 stainless steel

4.249

4.242

Titanium nitride— austenitic stainless steel

4.256

4.242

“bulk” titanium nitride [17]. Therefore it is reasonable to use these values for the unstressed lattice spacing d 0. only It can eqn. stress (1) that 2 ~1/is proportional to be 04, seen whenfrom a biaxial statethe is slope of 4, ~ US. sin if we assume a triaxial stress tensor of the form assumed. However,

668 [au

01

I[0

033]

I

(2)

then eqn. (1) is replaced by [15] I1+v\

(C4,4,)

~—~——)(0ii

—

Oil

=

cos20 +

-~-(a~~ + +

022

sinO

(G33)~)

sin2i~+ 1+v\ E (3)

(033)4,)

Furthermore, for the coatings considered here it can be shown that a~and eqn. (3) can be simplified to give [18] =

~—~)(0ii

(033)4,)

p

sin2 t 4L’ +

~

E

)(033)4,

—

~(~0~)4,

+

2a~~)(4)

Clearly, when a stress tensor of will the form (eqn. (2)) exists in the coating, 2~iplot be proportional to a~ (033)4, and the slope there will of bethe an ~4,4, errorus.insin the stress ~ii, determined from the slope by the conventional (biaxial) analysis, equal in magnitude to (033)4,. For the simplified analysis represented by the stress tensor (eqn. (2)) this error can be estimated for one arbitrary 0 rotation by using the intercept in addition to the slope of the line. Typical results are given in Table 3. —

3.3. Full stress tensor analysis with depth gradient In all cases the average stress measured normal to the surface is tensile in nature and much smaller in magnitude when compared with the compressive stresses acting in the plane of the coating. However, as Fig. 4 indicates, when significant stress gradients exist in the coating then curvature in the 04, vs. sin2 ~ plot is observed and the simple analysis represented by eqn. (4) is no longer valid. To overcome this problem assumptions as to the variation in stress a~ 1with penetration depth z have to be made and a number of approaches have been adopted. We have based our analysis on a stress equation of the form a,1

=

a~,° + ~a~1[G]

(5)

where o~° is a stress in the surface of the sample and the term [G] represents a gradient contribution to the total stress together with ~ Using eqn. (5) a complete stress tensor fit was achieved to the experimental data shown in Fig. 5 and the following gradient terms were considered. (i) No gradient with internal stress averaged over the penetration depth as described by Dölle and Hauk [16]. (ii) A linear gradient using two constants of the form G = G,~z.G11 G12 = G22 and G13 = G23 = G33 with the surface condition that

669 TABLE 3 Estimates for the stress components

a~and (033)4, following the analysis of Noyan [15]

Coating system

Stress elements (MPa)a Biaxial stress

01i

(033)4,

3 Mm TiN deposited ontob austenitic stainless steel

—6320

—5890

+430

4 ~m TiN deposited ontob austenitic stainless steel

—5690

—5570

+120

9Mm TiN deposited ontob tool steel (M2)

—3520

—3020

+500

12.3MmTiNdepositedc onto 1.4301 stainless steel

—6440

—6120

+320

-

5All measurements from the (422) family of planes using Cu Ka radiation. b Sputter-ion-plated titanium nitride films deposited with a substrate bias voltage of —35 V. C Data taken from ref. 4 and refers to ion-plated titanium nitride.

~

Fig. 5. vs. sin20 plot for a 12 Mm coating of titanium nitride deposited onto a martensitic 420 stainless steel. The full line respresents the predicted behaviour for Cu Ka radiation when the stress tensor is of the form listed in Table 4 and assumes that an exponential stress gradient exists normal to the surface of the coating: •, i~i< 0;•, ~> 0. 013

o_ o_ O__ ~O23 033

z is defined below in eqn. (6) as the penetration depth. (iii) An exponential gradient using the two constants and the boundary conditions listed in (ii) to give G

11

= =

G12 = G22 = z exp(k11z) G23 = G33 = z exp(k33z)

670 TABLE 4 Values for the stress components a~as a function of penetration depth z for a 12 Mm titanium nitride coating deposited onto martensitic stainless steel

Tilt angle 111 (deg)

a,j(MPa)

0 ±40

—2121 —1889

022

012

013

~23

033

—2137 —1889

—50 +1

—114 —81

—114 —81

—157 —112

Penetration depthza (Mm)

5.l6’~ 3.23

a Determined for the (422) planes of titanium nitride using eqn. (6).

bAt z = 0 then Oii

= ~22

=

—1860 MPa and

0i3 = ~23

=

033

=

0.

where z is the penetration depth sufficient to generate l/e of the total diffracted signal, and is given by sin2O —sin2~!i z= (6) 2M sin 0 cos Here ~.t is the linear absorption coefficient, 0 is the Bragg angle of diffraction and t,li is defined in Fig. 1. The full lines in Fig. 5 show the predicted variation in the 4,4, VS. sin2 i~i plot for an exponential variation of a~,with respect to depth in the coating; equally good fits were also obtained with a linear stress gradient. For the exponential gradient the values of a,~at two penetration depths (tilt angles) are given in Table 4, and at the surface of the coating 0j3, 023 and 033 are constrained to be zero. The principal stresses in the plane of the coating surface (a~~ 022) were calculated to be 1860 MPa (compressive) and these increase with depth in the coating. Clearly it is possible to explain curvature effects in the ~4,4, vs. sin2 ~(i plots by the existence of gradients within the coating, and the stress elements 0jj increase towards the coating—substrate interface. It is interesting to speculate as to the likely physical characteristics of the coating which may account for this behaviour. For example, the average diameter of the columnar grains which make up the microstructure of these PVD coatings becomes much smaller close to the substrate; on this basis thinner coatings would be expected to have a greater yield strength, and consequently they should support larger elastic stresses without yielding. Evidence for such a mechanism has been reported by Rickerby et at. [19] who showed that the internal stress supported by physically vapour deposited tungsten films is a strong function of coating thickness (grain size). Alternatively, with increasing thickness, coatings become more crystallographically textured and there is an increase in the average diameter of the columnar units which cornprise the coating. This may result in a decrease in yield strength of the coatings (see Fig. 6 and ref. 20). However, perhaps more important is the decrease in film density which occurs as the coating grows outwards. This means the films are less able to generate the full thermal contribution to internal stress as they cool from deposition temperature (see Fig. 7 and ref. 21).

671

— ~iii’iuIIIi ct

~

~

I

~5im

Fig. 6. Fracture cross-sections of titanium nitride coatings deposited onto carbon steel with a substrate bias voltage of —50 V: (a) 1.5 Mm coating; (b) 10Mm coating (note the larger column diameter in (b)).

7. Scanning electron rnicrographs or the surface of titanium nitride coatings deposited as in Fig. 6: (a) 1.5 Mm coating; (b) 10 Mm coating (note the open columnar morphology in (b)). Fig.

3.4. Full stress tensor analysis by averaging We now turn to the analysis of i/i splitting. The positive and negative I//inclination data split into two distinct branches and as shown in Fig. 2 a large degree of curvature is observed near = 0 to accomodate this divergence. To illustrate the complex triaxial stress state which can exist in PVD titanium nitride coatings, and to show the errors in a~and 022 which can be introduced by approximating the true stress state to one of biaxial stress, the data of Fig. 2(a) have been analysed using a method reported by DöIle and Hauk [16]. In order to carry out this analysis eqn. (1) is no longer an adequate description of the stress state and must be replaced by the more general form (see also Fig. 1)

672 o

0035

0 0030 0- 0025 00020

° C -~

00015

4

0-0010 0 0005 0 0000 -0-0005

I

0 00

0-05

0 10

0-15

0 20

(a)

I

I

025 030 2 ~) Sill

I

0 35

0 40

&45

0-00005 0-00000

[~i~nn

NIrid. on

l~J

I

-000005 -0-00010 C -~

-0-00015

2

~ -0-00020 U

-0-00025 -0 00030 -0 00035 - 0-00040

0-0

I

02

I

04

I

06 Sin 12411

08

10

(b) Fig. 8. (a) Variation in the constant a 21~1for the data given in Fig. 2; 1 ii), of eqn. (8)the with sin the slope of the line yields values of (e while intercept gives (33). (b) Variation in the constant a 2 of eqn. (9) with sin I2~L’I for the data given in Fig. 2 from which values of the shear stresses (13> and (23> can be obtained.

d4,4, —d0 d0 =

2 1111 + 12 sin 20 e~ cos~sin + 22 sin2~sin2~’+ 23 sin

sin2~’+

0 sin 2i/i

13

+

33

cos ~ sin 2~1i cos2i~1

(7)

By introducing terms a 1 and a2 (defined below) with carats to indicate averages over the depth2i4’ of penetration it since is possible to solve for (33> from (see Fig. 8(a)) the intercept of a1 vs. sin =

and

(33) + ((11)

cos2Ø

+ (12)

sin 20 +

(22)

srn2O —(~~)) sin2 i~i

(8)

673

a2

=li

—

— 1~04,~ =

((13)

C05

0+

(~23) Sin

0) sin I2~iI

(9)

The shear components 13 and 23 are determined from the slope of Fig. 8(b). The stresses o,~are then obtained from the calculated values of strain e~jaccording to 0~j= (~~ + 22 + 33)~il (10) 1 1jJ — ~Sjj S1(hkl) .~.S 2(hkl)~ .~.S2(hkl)+ 3S1(hkl) J (

where ~ is the Kronecker delta function and the resulting stress tensor is given in Fig. 2(b). In Fig. 2(b)both thepositive full lines the 2 i,ti for and represent negative ~(‘ tilts,predicted and the behaviour of ~4,4, with sin symbols represent the experimentally determined values; the fit between experiment and theory is excellent. Also given in Fig. 2 is the stress tensor which would result from neglecting the presence of ~‘ splitting (the broken line in Fig. 2(a)); this was derived following the analysis of Noyan [15] outlined above from which a value of (033) can be determined. Clearly, it is very important to check for ~!i splitting since this can markedly affect the values derived for the stresses in the plane of the coating (0ii, ci 22) and normal to the surface (033). Again, as observed with the analysis of curvature effects discussed earlier in this paper, both stress tensors indicate that the stress gradients normal to the surface can be quite significant for sputter-ion-plated coatings, and these are tensile in nature for a titanium nitride coating deposited onto stainless steel. 4. Conclusions The internal stresses in titanium nitrideincoatings 2 ~isputter-ion-plated method. The linear behaviour the 64,4,have us. been~i measured by the on sin the basis of a biaxial stress state is not always sin2 plots predicted observed, and plots often show ~i splitting and curvature due to the presence of shear stresses and stress gradients normal to the surface. It has been shown that it is important to identify these effects, since if they are ignored and the stress state is approximated to biaxial, appreciable errors in the calculated values for the principal stresses can result. As these PVD coatings thicken it has been demonstrated that the internal stress levels decrease owing to a combination of grain size and porosity effects. Acknowledgment The authors wish to gratefully acknowle”lge financial support from the Department of Trade and Industry.

674

References 1

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

M. Wong, Thin Solid Films, 53 (1978) 65. S. Skladnikiewitz, Krist. Techn., 15 (1980) 921. A. J. Perry, L. Simmen and L. Chollet, Thin Solid Films, 118 (1984) 271. L. Chollet and A. J. Perry, Thin Solid Films, 123 (1985) 223. L. Chollet, H. Boving and H. E. Hintermann, J. Mater. Energy Syst., 6 (1985) 293. A. J. Perry and L. Chollet, J. Vac. Sci. Technol., A4 (1986) 2801. D. S. Rickerby, J. Voc. Sci. Technol., A4 (1986) 2813. D. T. Quinto, G. J. Wolfe and P. C. Jindal, Thin Solid Films, 153 (1987) 19. J. P. Coad and R. A. Dugdale, Proc. mt. Conf. on Ion Plating and Allied Techniques, CEP Consultants, Edinburgh, 1979, p. 186. D. S. Rickerby and R. B. Newbery, Vacuum, 38 (1988) 161. A. M. Jones, AERE Rep. R12275, 1986 (Atomic Energy Research Establishment, Harwell, U.K.). B. D. Cullity, Elements of X-ray Diffraction, Addison-Wesley, Reading, MA, 2nd edn., 1978, p. 447. H. Dölle, J. Appi. Crystallogr., 12 (1979) 489. J. B. Cohen, H. DSlle and M. R. James, Proc. Symp. on Accuracy in Powder Diffraction, Nat. Bur. Stand. (U.S.) Spec. Pub., 567 (1980) 453. I. C. Noyan,Metall. Trans., 14A (1983) 249. H. Dölle and V. Hauk, Haerterei-Tech. Mitt., 31 (1976) 165. 5. Nagakura, T. Kusunoki, F. Kakimoto and Y. Hirotsu, J. Appi. Crystallogr., 8 (1975) 65. D. S. Rickerby, A. M. Jones and B. A. Bellamy, Surf. Coat. Technol., to be published. D. S. Rickerby, G. Eckold, K. T. Scott and I. M. Buckley-Golder, Thin Solid Films, 154 (1987) 125. U. Helrnersson, J.-E. Sundgren and J. E. Green, J. Vac. Sci. Technol., A4 (1986) 500. D. S. Rickerby and P. J. Burnett, Thin Solid Films, 157 (1988) 195. S.