Residual stress in physically vapor deposited films: A study of deviations from elastic behavior

Thin Solid Films, 171 (1989) 197-216

197

RESIDUAL STRESS IN PHYSICALLY VAPOR DEPOSITED FILMS: A STUDY OF DEVIATIONS FROM ELASTIC BEHAVIOR A. J. PERRY AND M. JAGNER

G TE Valenite Corporation, 1711 Thunderbird, Troy, M148084 (U.S.A.) (Accepted November 23, 1988)

The residual stress in films made by plasma-enhanced physical vapor deposition is generally very high, of the order of 1~o of the shear modulus. The present work is a report of a study of the lattice parameter and the residual stress as measured by X-ray diffraction (XRD) methods on different crystal planes. ZrN films are studied on stainless steel substrate; these films are considered typical of group IVB nitride films and were used as a model system of practical significance. Deviations from simple behavior after a heat treatment are found on the (111) and (200) families of planes but not on high index planes. The deviations are discussed in terms of plastic deformation, shear stresses and.microcracking on these planes which are the primary and secondary slip systems respectively. The residual stress in the substrate is low, in contrast to what would be expected from the high stress in the film. The XRD data appear to indicate that the effect of this stress is absorbed, at least in part, by plastic deformation on the (200) planes of the stainless steel substrate; unfortunately the present experimental arrangement did not permit the (111) primary slip plane to be studied.

1. INTRODUCTION The use of X-ray diffraction (XRD) methods to determine and interpret residual stresses in polycrystalline materials has a long and distinguished history. Much of the theory and interpretation has been incorporated into the recent book by Noyan and Cohen 1. The use of the method to study thin films made by vapor deposition methods is comparatively recent: a number of groups has measured stress both in the films themselves and also in their substrates 2-14. The residual stresses in films made specifically by plasma-enhanced physical vapor deposition (PVD) methods are extremely high and can be of the order of 1~o of the shear modulus. They are related to the low temperature of the deposition process and are not found in similar films made at higher temperatures by chemical vapor deposition methods 8. The stresses can be altered by thermal treatment with the resultant values being affected by the mismatch between the coefficients of thermal expansion of film and substrate 7'9-12. Further, the strain distribution in the films, as 0040-6090/89/$3.50

© ElsevierSequoia/Printedin The Netherlands

198

A. J. PERRY, M. JAGNER

determined from a Williamson-Hall plot LS, also depends on the deposition conditions, as does its behavior when the substrate is removed to leave a freestanding film 11 13 The various effects have been summarized ~ 13 as being due to (i) growth and thermal mismatch which causes a change in the average lattice parameter, (ii) growth defect strains which affect the local lattice parameter and (iii) pseudomacrostrains resulting from the mutual impingement and yield anisotropy of the grains during growth, as postulated by Cullity 16. The latter affect both the lattice parameters and line broadening and it is such effects which are studied here. It has also been found that the high stresses in PVD films can lead to plastic deformation and also to microcracking on preferred crystal planes1 ~,~2.1-7.18 In the present work, X R D measurements on a model film of practical importance]9 24, namely ZrN, as deposited onto stainless steel, are discussed in terms of strain, deformation and microfracture. 2. EXPERIMENTAL DETAILS

The Z r N films studied here have two advantages from the point of view of X R D studies. There is no diffraction peak overlap with the stainless steel substrate, such as is found with TiN. In addition, the actual films chosen here do not have a strong texture (Fig. 1) so that not only are all the X R D peaks available for study but there are no texture effects which could otherwise potentially affect the interpretation of the results. The composition of the films was determined by electron probe microanalysis (EPMA); the additional numbers on the abscissa of Fig. 1 are the reference numbers of the samples themselves. The EPMA as well as subsidiary Auger electron spectroscopy analyses showed no evidence of the presence of impurities such as oxygen or carbon, or indeed of trapped argon, so that the socalled solid solution effects 13 on the lattice parameters can be neglected here. 3 o (111) o (200) (220)

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In contrast to the film, the stainless steel substrate was strongly textured, presumably as a result of cold rolling during its production. It was possible to measure all the lattice parameters by integrating over a sufficient period of time and deconvoluting if necessary. The (222) diffraction peak fell between the (331) and

RESIDUALSTRESSIN PVD FILMS

199

(420) peaks of the Z r N film, and was also of very low intensity. As a result it could not be used during the residual stress study of the substrate, as discussed below. The films studied were part of the series whose lattice parameter, reflectance and color properties were discussed elsewhere 25. Four of the films were chosen here. All were about 5 p.m thick and had been deposited onto D I N 1.4301 stainless steel by reactive magnetron sputtering with a target input power of 8 kW. One sample (sample 74 in Fig. 1) of about stoichiometric composition ZrNl.o2 was studied in detail; the other three were studied sufficiently to ensure that the one sample is typical of the whole set, irrespective of the composition. This sample had been cut in half and was studied both in the as-received condition and also after 1 h of vacuum heat treatment at 900 °C which is considered 9 to bring it close to an equilibrium lattice condition. The X R D measurements were carried out using a Scintag P A D V computercontrolled diffractometer. C u K ~ radiation was used with the Kct 1 wavelength assumed to be 0.154 059 nm for the measurements of lattice parameter and peak width at half-maximum, the background and K~ 2 contributions having been subtracted numerically. The instrumental peak broadening was measured using a silicon standard (NBS 640 silicon powder). The residual stress was measured in an goniometer mode. The peaks were not K0c2 deconvoluted so that a mean wavelength of 0.15418nm was taken for the lattice parameter derivation. The sin2qj plots (SSPPs) for ZrN were interpreted initially using bulk values of 0.2, 460 G P a and 0.4578 nm as the Poisson ratio, elastic modulus 26 and equilibrium lattice parameter 27 respectively. The value returned by the Nelson-Riley (NR) (Taylor-Sinclair) extrapolation of the ZrNLo 2 sample after heat treatment and in the free-standing condition is 0.4574 nm. The values used for stainless steel were 0.3 and 190 G P a as before 8 and 0.3589 nm respectively as extrapolated from the N R plot from the present heat-treated sample (Fig. 2(a)). The analysis of the lattice parameter data given below assumes that these are not affected by instrumental effects. To avoid such, the alignment of both the incident and the diffracted beams (equipped with Soller slits) was set as accurately as possible. By way of confirmation, the N R plot of the silicon standard is given in Fig. 2(b) and is seen to be flat. A further set of experiments was completed where silicon standard power stainless

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RESIDUAL STRESS 1N PVD FILMS

was added to the surface of the ZrN sample to act as an "internal" standard. The lattice parameter data for the silicon standard, the steel and ZrN, as given in Figs. 2 and 3(a), were thereby duplicated. Consequently, it is assumed that all the data given below are free from instrumental effects. Finally, sample 74 (ZI:N1.02 in the as-received and heat-treated conditions) was studied after dissolving away the substrate to give free-standing films. 3.

SOME CONSIDERATIONS ON X-RAY STRESS MEASUREMENTS

In this section the relationships between various aspects of X-ray stress measurements are emphasized. In general practice, a diffraction peak at a high 20 value is chosen for study to give a high precision of measurement s. The shift in the location of the diffraction peak with the angle ~9 is interpreted according to the classical strain equation I

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(2)

Given v and E, the residual stress can be derived. However, this is only true if a straight-line plot is obtained. In practice, deviations from linearity are often encountered. Simple curvature of the plot results from a stress gradient through the film, whereas the splitting of the plot into two curves for positive and negative angles 0 is due to the presence of shear stressesL Both effects can be found together in a given system 4. Finally, strongly textured materials can give rise to the so-called serpent's tail curve which is often found in cold-rolled materials 2s but which has

202

A.J. PERRY, M. JAGNER

also been observed in thin films 9'1°. The stress situation present when deviations from linearity are found can be analyzed, and practical examples have been reported 29, where it has been shown that the state of zero strain at the sample surface, assumed in the theoretical derivation ofeqn. (1), need not correspond to the situation found in reality. In materials which are not elastically isotropic, the elastic constants for the different crystal planes need to be discussed, as mentioned above. The elastic constants for single crystals of many materials are known. The random agglomeration of crystals of random orientation which, when bonded together, constitute the polycrystalline solid has elastic constants which are related to those of the single crystal. In theoretical studies, b o t h t h e state of constant strain in all the grains of a polycrystalline material a° as well as that of constant stress 31 have been considered. These represent the upper and lower bounds respectively and they do not necessarily assume crystalline contiguity to be maintained at the grain boundaries. A more realistic approach has been considered 32 where grain boundary contiguity is forced. The result lies between the previous two cases, as might have been expected. Using these models and the available elastic constants, the XECs s 1 and is 2 for polycrystalline material can be calculated. The relationship between the XECs and the standard X R D stress equation can be seen from the theoretical equation "~:00 = SI(O'I 1 -I-0"22 ) -t-1S20",~ sin'- q)

(3)

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with E hk~and vhk~the values for any (hk/). It should be noted that s~ and the slope of the SSPP have opposite signs. The theoretical studies 3°-32 (as indicated in Figs. 3(c) and 3(d) for TiN) show a linear relationship between the XEC and a crystallographic orientation parameter 3F. This parameter is given by the relationship 3h2k 2 q- k a l 2 + 12h 2 3F = .

(h2q._k2q_12)2

which is zero for the (h00) family of planes and is at the maximum of unity for the ( h h h ) family of planes. It is generally assumed 33 that a value of 3F equal to 0.6 corresponds to the condition found in massive randomly oriented material. As remarked above, the oft-used high 20 peaks of (420), (422) and (331) have 3F values of 0.48, 0.75 and 0.81 respectively which are sufficiently close to the bulk 3F value of 0.6. It is thus now apparent how the single-crystal elastic constants, the XECs and those for bulk randomly oriented material are related. Unfortunately, single-crystal

203

RESIDUAL STRESS IN PVD FILMS

data for ZrN are not available so results for TiN have been taken ~3 for comparison purposes as a near approximation to ZrN in the present work. As discussed below, the (h00) and (hhh) diffraction peaks from the present films are thought to exhibit deviant behavior. The XECs for TiN have been normalized onto Figs. 3(c) and 3(d) by forcing them through the average of the values from the remaining ZrN diffraction peaks, and set at the bulk value of 3F equal to 0.6. It is understood that this approach although admittedly somewhat arbitrary does nevertheless allow an effective comparison between experiment and theory. A final relation needs to be considered here. This is the plot as used by Rickerby 1~ which describes the relation between the measured residual stress and the measured intercept lattice parameter (i.e. the intercept at ~ = 0). This follows from the above under the condition that ax~ = 0"22 = 0"~, the residual stress. The plot of residual stress vs. intercept lattice parameter, i.e. a~ - a o .

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What follows from the above is that it should be possible to determine the XECs for a thin film by measuring the slope and intercept lattice parameter values of a series of SSPPs for different (hkl). The definitions o f s l and ½s2 (eqns. (4) and (5)) and the SSPP itself (eqns (1) and (3)) define the connection between the XECs and the results obtained in X R D stress measurements. Two further considerations need to be noted here. First, it is assumed that the level of stress is such that no plastic deformation (flow) has occurred on any crystal plane being studied. Second, it is assumed that the stress state is only simple

204

A . J . PERRY, M. JAGNER

compressive in the plane of the film and that no stress gradient occurs through the film perpendicular to its surface. The latter affects the results very easily because the depth of penetration of the incident X-ray beam (the amount of material sampled) depends on the 20 value of the particular plane. This can be demonstrated by calculating 34'3s the depth Xe of film at which the intensity has fallen to 1/e of its incident value as a function of the crystal plane being used for the study: .v~ 1 =/~ sin(0+~9)-~ sin((J-~p)

(7)

with p the atomic absorption coefficient (Sprauel e t a l . 34 give equations for f* and goniometers, both of which reduce to our eqn. (7)). The result is shown in Fig. 5 where account is also taken of the effect of the ~ range selected in the present study for the stress measurements, as this reduces the depth of penetration for both positive and negative angles ~. The maximum ~ values used were 12', 15 ~, 24 ~, 30', 3 2 and 36' for ( 111 ), (200), (220), (311), (222) and (400). The remaining planes were studied with a maximum angle ~ of 40 in each case. Brogg half-angle 8 (degrees) 20

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If a stress profile is present in a given sample then it is possible to deconvolut~ the intensity profile through the film. In the present work no deconvolution has beer carried out and the apparent stress on each plane, plotted as a function of the deptt x e, is used simply to confirm the presence or absence of such a stress profile. It shoulc be noted in this context that the competitive growth of the grains of differen~ orientation 36'37, leading to textured films under type (iii) conditions, has to lead to stress profile through the film 13 4. RESULTS AND DISCUSSION

A standard SSPP study was carried out for all four films in the as-receivec condition and after vacuum heat treatment, using the (422) family of planes. Thes( showed curvature plus ~0 splitting and linear plots respectively (Fig. 6(a)). The dat~ sets for all four films in the as-received and heat-treated conditions were evaluatec assuming linear behavior, which is not strictly valid for the as-received films becaus~

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206

A .J . PERRY, M. JAGNER

of the 0 splitting, then interpreted using the bulk constants given above and which resulted in the stress values which are included in Fig. 4. The data from the heattreated films fall close to the Rickerby plot for ZrN (eqn. (6)) which has to be the case because, as discussed above, it is an alternative interpretation of eqns. (1) and (3). In contrast, the as-received films do not follow the simple curve: the 0 splitting for example is indicative of shear stresses and hence a deviation from a state of simple compressive stress. This also makes these as-received films unsuitable for a study of the XECs, the original objective of the present study. To be sure of the reliabililty of the database, the X R D work was continued in a series of steps. In the next, the SSPPs from the (422) planes were studied as a function of sample rotation to confirm the stress homogeneity. In the as-received condition ~ splitting was again found in all cases. The series of SSPPs from the heattreated film were all linear (Fig. 6(a)) with intercept and slope values of 0.460811_+0.000090nm and 0.007791 +0.000085 respectively based on six measurements at different rotations with some replicates. The error bars indicate the good reproducibility of the data. Extending the study further to the other (hkl) planes again confirmed deviants in the behavior of the as-received sample but more importantly the general linearity of all the plots from the annealed film (Fig. 6(b)). Exceptions are (400) and (222) as discussed below, both of which showed ~ splitting. The observations as a whole validate the preliminary requirement that the heat treatment brings the films nearer to a condition where elastic behavior could be expected.

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RESIDUAL STRESS IN PVD FILMS

207

The stress experiments were then completed by making some replicate studies of both the slope and the intercept lattice parameter of all the (hkl) planes of the heat-treated film to confirm the behavior of the different planes. In addition, a standard X R D pattern was taken from the samples. This gave the subsidiary set of lattice parameters shown in Fig. 3(a) (i.e. identical to the ~b = 0 extrapolated condition) which could themselves have been used as an indication of the stress level in the facile way discussed elsewhere 14. Further, the half-widths of the X R D peaks were measured with the instrumental broadening being subtracted to allow Williamson-Hall plots to be drawn, following Rickerby et al. T M This was also repeated for both films in a free-standing condition after the stainless steel substrate had been dissolved away. The data are given in Fig. 7.

4.1. The lattice parameters The lattice parameters are given in Figs. 3(a)-3(c) plotted as functions of the N R function, the depth x e of X-ray penetration and the 3F crystal orientation factor respectively. As is apparent from the above discussions, the presence of a stress gradient affects both the N R and the 3F plots, the former in its slope (which is of opposite sign to that in an xe plot because the 0 dependence is reversed) and the latter in terms of a difference in lattice parameter for any given family of planes such as (h00), or planes of the same 3F value such as (422) and the (220), i.e. data measured at different depths of penetration (Fig. 5). Similarly, deviations from classical elastic behavior can increase the apparent scatter in both N R and x~ plots. The three plots thus need to be considered together, bearing in mind that the preliminary studies, referred to above, indicate that no instrumental effects should be present. The data are taken to indicate that there is a stress gradient through the film (Fig. 3(b)) and also that strong differences in the XECs of the different planes (Fig. 3(c)) exist. These taken together lead to the slope and scatter respectively in the N R plot (Fig. 3(a)). The obvious deviant features in the annealed film are the lower lattice parameter values of (h00) in Fig. 3(a) and of (hhh) in Fig. 3(c). Both are associated with ff splitting in the SSPP (Fig. 6(b)).

4.2. The slope of the sin2~k plots The results from the annealed film are given in Fig. 3(d) as a function of the crystallographic function 3F. In the case of (222) and (400) which showed ~k splitting, the average values are indicated in parentheses because this is known to be an incorrect interpretation. The behavior of the data is clearly non-linear with 3F, as was found with the lattice parameters and in contrast to the theory given above, taking the experimental error for the (422) planes given above as being typical of all measurements.

4.3. Williamson-Hall plots The results for the as-received and the heat-treated films, both before and after their removal from the substrate (i.e. as a substrate-bound film and as a freestanding entity respectively) are given in Fig. 7. Before and after removal, the

208

A.J. PERRY, M. JAGNER

annealed film shows linear behavior with a strain distribution of 0.27~o. The difference in the ordinate values is believed to be the result of using different instrumentation, i.e. different instrument broadening. In contrast, the as-received film before substrate removal shows great scatter in the data with a negative intercept on the ordinate of the Williamson Hall plot. The analysis assumes ~5 a gaussian form to the diffraction peaks. This was studied for the (111), (200), (220) and (311) planes for both as-received and heat-treated samples. The results for (111) are given in Fig. 8 and are quite typical. Before heat treatment non-gaussian behavior is found (which is corrected by the heat treatment), which leads to the type of behavior shown in Fig. 7 where a negative ordinate intercept is f o u n d 15.

These data are interpreted as follows. In the as-received condition the strained condition is due to both a differential thermal contraction (type (i) extrinsic macrostrain) and an intrinsic microstrain resulting from the growth process. The extrinsic contribution is removed when the substrate is dissolved away and the strain distribution factor ~ falls from 1.76~o to 1.03~o. The intrinsic component is

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209

RESIDUAL STRESS IN PVD FILMS

removed by the heat treatment so that the remnant 0.27~o in the film and freestanding condition is assumed to be due to differential thermal contraction induced deformation in the film after the heat treatment step. This is confirmed by the fall in the lattice parameter of the heat-treated film when in the free-standing condition. It is interesting to note that the N R plot (and hence the 3F plot) is now flat with an extrapolated lattice parameter of 0.4574 mn (compare with the datum in Section 2) and consistent with the foregoing discussion. It is concluded that the present ZrN films are quite typical of samples made under PVD conditions and are type (iii) in the Rickerby classification ~1,12. Further, that the heat treatment does indeed bring the film near to an equilibrium condition. 4.4. The stress state in the substrate

Many studies have shown 5-s that the very high stress in the films finds no counterpart in the substrates; their residual stresses tend to be low. In view of the deviant behavior found in the low index planes of the film, i.e. in (h00) and (hhh), a similar set of experiments was made with the substrate. Unfortunately, the (222) peak could not be studied, as mentioned above. The SSPPs (Fig. 9) were linear in nearly all cases (including the (331) peak used previously) with low residual compressive stress. In contrast, the condition found on the (200) planes (and possibly on the (220) planes also) was ~bsplitting with a positive slope to the SSPP of the former in the as-received condition which is indicative of a tensile stress and a marked shear stress condition. This ~Osplitting and shear stress on the (200) are also

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210

A.J.

PERRY. M. JAGNER

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10

3P

Fig. 10. Plots of (a) the negative slope and (b) the intercept lattice parameter of the SSPP from the stainless steel substrate as a function of the 3F crystallographic parameter. Additional lattice parameter data are included in (b) from a standard X R D experiment. The data given in (a) in parentheses correspond to the median slopes o f ~ split SSPPs.

by the SSPP, a general state of compressive stress is indicated by the increased lattice parameters relative to those in the heat-treated condition (Fig. 2(a)), and shear stresses are found associated with the (200) slip plane. The heat treatment of 1 h at 900 °C is efficacious in removing the steel sheet production-related cold-work effects. It is to be anticipated that the condition after such a heat treatment should allow the effect of the residual stress in the film to be detected. The stress resulting from differential thermal expansion is expected to bring the substrate, at least in the immediate neighborhood of the film, beyond its elastic limit 8. The resultant residual stress is indeed nearly zero (Fig. 10(a)) on the high index planes (as confirmed by the lower lattice parameters (Fig. 2(a))) but compressive, with shear on the (200) planes. It would seem that the stress imposed on the substrate by the film is absorbed by shear stresses (and probably plastic deformation) on the low index planes of the stainless steel. This condition does not affect the low residual stress condition on the high index planes which are those normally studied in residual stress measurements. A further observation is that the N R plots have a negative slope both before and after heat treatment (Fig. 2(a)). Assuming again that this is not due to the instrumentation, then it could be argued that there is also a stress profile present with the stress decreasing towards the film-substrate interface. This profile is

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apparently not great enough to be visible to the normal stress measurements, and causes no curvature in the SSPP. Finally, the slope of the data as referred to the 3F parameter (Fig. 10(b)) is of opposite sign to that of the film. This is the normal situation for metallic materials33. It is worth noting that the lattice parameters of the (200) diffraction peaks are below what would be extrapolated from the trend indicated by the remaining data, both before and after the heat treatment cycle. This effect was also found in the ZrN films and again with @split SSPPs. It is possible that the explanation is the same, namely a deviation from simple biaxial residual stress behavior leads to deviant behavior in the lattice parameters. 5. GENERAL DISCUSSION

One of the most significant observations made in the present work is the differences in the stress field indicated by the X R D studies as existing on the different planes of both film and substrate. The peaks which would be studied traditionally, such as the (422) in ZrN, show classical linear SSPP behavior. Only the study of other ZrN planes such as (400) and (222) shows indications of deviant behavior in the form of ~b splitting due to the presence of shear stresses. This is true also of the stainless steel substrate: the traditional (33 l) peak shows linear behavior and a low compressive stress, whereas the (200) peak shows high compressive stress with a large shear component. It is unfortunate that the (222) peak was not available for study as { 111} is the principal slip plane. It is clear from the foregoing discussion that these effects are not instrumental and that they cannot be explained by the existence of the slight stress profile through the film. However, their presence means that the XECs cannot be measured because the residual stress condition is not simple biaxial compressive. It is generally tacitly assumed s that linear SSPP behavior on a high 20 peak (as normally selected for experimental convenience) will return slope and intercept values which can be interpreted directly to give a reliable measure of the residual stress. The present work does not argue this point, but shows that an X R D stress measurement study of several peaks is needed to confirm whether the residual stress condition on all {hkl} is only one of simple compression in the plane of the film, or not. In the present work this appears not to be the case, neither in the film nor in the substrate even after a heat treatment. The complex stress pattern, with strain values near to 1~o of the shear modulus of the film, has often been reported before 4,8,11,12 The shear stresses are extensively removed by the heat treatment, but the final stress pattern is still not simple elastic. Some general observations can be made about measurements carried out on PVD films under high compressive residual stress and related to the type (iii) pseudomacrostrains. The stress situation seen in the present ZrN films is less complex than was found in TiN films 14 which were made by reactive sputtering in the same PVD unit but at higher target input power (10 kW). This seems to be in accord with the view that the amount of built-in damage increases with the energy input into the coating during its growth. There is a lot of evidence for defects in such films38: in ion-plated films, it has been found that reducing the rate of growth

212

A . J . PERRY, M. JAGNER

changes the type of defects from vacancies to interstitials with trapped argon 2s, while the dislocation loop density increases with substrate bias during the growth of TiN single-crystal films by a sputtering process 39. Further, the microstrain found in TiN films depends on the bias applied during deposition as well as on the nature of the substrate 11,12. The very high stress levels in the present ZrN film appear to have caused a nonclassical situation where the lattice parameters and behavior of the SSPP show deviant effects. Neither the (200) nor the (111) planes are under the same condition of simple compressive stress which is indicated by the remaining diffraction planes. Departures from linear 3F behavior have been reported in other studies: both TiN and Ti(CN) films made by PVD methods 11,13,4o have shown a type of deviant behavior which is different from that found in the present case: they had higher stress and lattice parameter values on the (111 ) planes than would be expected from the 3F plots. In contrast, other TiN films ~4 have behaved like the present Z r N films and shown a relative fall in the (111) lattice parameters and may also have had a lower value on (200) (although this aspect was not discussed in that earlier work which dealt only with the general behavior of the lattice parameters). It thus appears that there are two distinct types of deviant 3F behavior associated with the ( 111 ) and (200) planes in these highly stressed films, although the actual stress levels recorded on the high 20 peaks are about the same in all cases. The behavior can be summarized as follows. It appears that the increase in lattice parameter on (111) relative to the 3F plot increases with substrate bias under otherwise constant deposition conditions 13. The fall of the (111) lattice parameter and concurrent fall of the (200) lattice parameter are only observed at still higher deposition energy conditions (i.e. the present 8 kW sputter target energy) and this is followed by a Voigt type of behavior 14 at very high sputter target energy (i.e. 10 kW) with a state of constant high strain across all planes. Studies by transmission electron microscopy have shown ~7'~8 that ultrafine cracking can be found at the grain boundaries and also on the (200) and (220) planes in N b N and TiN films respectively in a high residual compressive stress condition. It is tempting to correlate the various observations in the following phenomenological way. As the residual strain (input energy) in the films is increased (by altering the deposition conditions), a condition is reached where plastic deformation can occur on the (111) family of planes, which is the primary slip plane in TiC at elevated temperatures 41, and a shear stress condition develops on them. A further increase in the energy input to the film during growth leads to microcracking on (200), which is then a secondary slip system, relieving the shear stress built up on (111 ). Ultimately grain boundary cracking occurs, leading to a Voigt condition with constant high lattice parameters in the 3F plot and a constant strain across all planes. For this type of argument to be true, the initial increase and subsequent fall of the (111) lattice parameter with input strain energy need to be clarified. The Rickerby plot in Fig. 4 has first to be examined. As discussed above, in a state of simple biaxial residual stress the intercept lattice parameter and slope of the SSPP have to correlate with the Rickerby plot. It follows that a deviation from a simple stress condition causes non-identity of the data with the Rickerby plot. In extreme cases of shear stress, the median curve drawn through a split SSPP

RESIDUAL STRESS IN PVD FILMS

213

incorrectly estimates the residual stress, and the intercept lattice parameter is high (Fig. 4) relative to this apparent residual stress 29. If it is now assumed to be a general result that the presence of a shear stress on a lattice plane causes the intercept lattice parameter of the SSPP to be too high, then the increase in the (111) lattice parameters with increasing bias can be understood: plastic deformation on these planes, which are the primary slip system and high elastic modulus direction (Figs 3(c) and 3(d)), creates a shear stress situation with the stress itself increasing (and hence the lattice parameter) with substrate bias. If the amount of energy absorbed by the film during growth increases further (as a result of growth rate or further bias increase, for example) then this can be absorbed by the development of the experimentally observed microcrackingl 7.18 on the (200) family of planes, which are the secondary slip system and also the direction of lowest elastic modulus. The cracking relieves their residual stress so that this falls together with the intercept lattice parameter. It is possible that this stress relief on (200) also reduces the stress on the (111) family of planes so that both this and the intercept lattice parameter fall below the values expected from the 3F plots. Finally, a further increase in strain energy in the films leads to grain boundary cracking, a concurrent condition of uniform strain can then prevail on all planes and Voigt-type residual stress behavior is found. It should be added that the onset of a positive deviation of the (111) planes in 3F plots indicates that the local elastic limit has been exceeded. This is possibly why so many residual stress studies have returned approximately the same residual stress values as measured on high index planes such as (422). It should follow that an intermediate condition could be observed in the sequence discussed above, where plastic deformation on both (111) and (200) is found (the primary and secondary slip systems) such that positive departures of both these planes from the linear 3F behavior should occur, before cracking on the (200) causes the drop in both the (200) and (111) lattice parameters as discussed above. A detailed study of such a behavioral sequence, coupled with the analysis of ~, split SSPPs as carried out for example by Rickerby et al. 29, could allow the elastic limit of such films on the (111) and (200) crystal planes to be analyzed quantitatively. The foregoing discussion needs to be related to the deformation behavior of the nitride phases themselves. As far as we are aware, no work has been done on these. The situation for the carbide phases is well established, however. The group IVB carbides TiC, ZrC and HfC all slip on the (110) planes at low temperatures 4z and on (111) planes at elevated temperatures (800-1200 °C for TIC43). Some limited slip on (110) phases is possible on ZrC at elevated temperatures 44. In contrast, the group VB carbides are different in the sense that VC behaves like TiC but TaC only slips on (111) planes at all temperatures 42. No data are known to us on NbC. It would have been expected that slip would only occur on (111) planes as these are the planes of the closest atom density in the NaC! structure, as in an f.c.c, lattice. It is not immediately obvious therefore what the principal slip plane should be in ZrN. In the foregoing discussion it was assumed to be the (111) plane. Similarly, it is not clear whether (110) would be the secondary in ZrN, as is the case in f.c.c. metals.

214

A.J. PERRY, M. JAGNER

A further aspect needs to be considered. The nitride films made by PVD methods contain a variety of defects ranging from trapped argon 3s to grain boundary voids 36'43'45 which depend on deposition method and conditions. Twins, stacking faults and low angle grain boundaries have been observed on (111) planes of TiN made by the PVD method 39. Consequently it cannot be assumed that the slip systems operative under equilibrium conditions necessarily apply in PVD films. 6. CONCLUSIONS

A state of residual stress in a series of ZrN films made by reactive magnetron sputtering on stainless steel substrates has been studied using the standard XRD SSPP method. Preliminary work was carried out to confirm the avoidance of instrumental effects and also the typicity of the data recorded. A detailed study of one of the films, both in the as-received condition as well as after a vacuum heat treatment of 1 h at 900 °C, was carried through on all ZrN peaks from (111 ) to (440) as well as on the stainless steel substrate in the as-received and heat-treated conditions from (! 11) to (420). The SSPP from the stainless steel indicated a state of low stress, as reported before from high 20 studies, in spite of the high compressive residual stress in the films. The exception is (200) which indicates a state of high compressive stress with large shear components. It appears that this is the mechanism by which the substrate absorbs the stress imposed by the film: plastic deformation on (200). It was unfortunate in the present study that the condition of the { 111 } primary slip plane could not be investigated: the (222) diffraction peak could not be used for residual stress measurements. The SSPPs of the film in the as-received condition indicate a complexity of stresses. After heat treatment, linear SSPPs were found on all high 20 plots, but deviant behavior was found on both (200) and (111) planes where splitting due to shear stresses and low intercept lattice parameters (from the 3 F a n d N R plots) were recorded. As a consequence, it was not possible to derive the XECs because the 3F spectrum available was thus reduced to too narrow a range. A model is proposed for the deviant behavior often found in films made by plasma-enhanced PVD methods by referencing existing data in the scientific literature. It is suggested that the behavior changes as the energy input during film growth is increased. The first deviation from a linear 3F plot is found e:~ the primary (111) slip plane where flow and hence shear stresses are generated. The SSPPs show splitting and an intercept lattice parameter which is higher than the value expected from the 3F and Rickerby plots. As the input energy is increased further, slip could be found on the (200) secondary slip system and then microcracking should occur. The latter allows stress relief on (200) and also on (111), causing a fall in the intercept lattice parameters and ~bsplitting in the SSPP. Ultimately, grain boundary cracking occurs and Voigt-type flat 3F plots are found, reflecting a condition of constant strain across all grains.

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ACKNOWLEDGMENTS

Research work and new ideas are often triggered by discussions with colleagues. This is also the case here. The samples used in this work had been made by Dr. William D. Sproul of BIRL Northwestern University as part of a collaborative study of some properties of nitride coatings. Discussions during this study had directed our thoughts more intensively to consider the question of defects in PVD films and their effect on mechanical properties such as the residual stress. In the present work, as in previous studies on residual stress, our basic considerations have been very much affected by discussions with Dr. Lucien Chollet of CSEM, Neuchfitel, and with Dr. David S. ~ickerby of AERE, Harwell. It is a pleasure for us to thank these three friends and :olleagues for their interest, discussion and availability of unpublished work. The analysis of the free-standing films from sample 74 was carried out at AERE, -Iarwell, by Dr. B. A. Bellamy and Mr. A. M. Jones, to whom the authors wish to :xpress their thanks. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

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