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Residual stresses and ion implantation effects in Cr thin films
Nuclear Instruments and Methods in Physics Research B 148 (1999) 211±215
Residual stresses and ion implantation eects in Cr thin ®lms A. Misra *, S. Fayeulle 1, H. Kung, T.E. Mitchell, M. Nastasi Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Abstract The evolution of intrinsic residual stresses in sputtered Cr thin ®lms with substrate bias and post-deposition ion irradiation is investigated. The relaxation of tensile stresses and build up of compressive stresses with increasing ion irradiation dose is studied using ions of dierent masses and energies such as 110 keV Ar, 33 keV C and 330 keV Xe. The stress evolution is related to the corresponding microstructural changes in the ®lms. The changes in the residual stress during ion irradiation are explained by considering the manner in which the interatomic distances and forces change during irradiation, and the generation of defects during irradiation. Ó 1999 Elsevier Science B.V. All rights reserved. PACS: 61.80.Jh; 61.82.Rx; 81.15.Jj Keywords: Residual stress; Cr thin ®lms; Ion irradiation
1. Introduction Some general trends in the evolution of intrinsic residual stresses in thin ®lms are well established [1±4]. As an example, most materials show a transition from tensile to compressive stresses with decreasing working pressure and increasing substrate bias during ®lm growth [1,3]. Post-deposition irradiation also shows similar trends: tensile stresses are relaxed [5±7] and compressive stresses imposed [5±7] with increasing ion dose. In some
*
Corresponding author. Tel.: +1 505 667 9860; fax: +1 505 665 2992; e-mail: [email protected] 1 On leave from Laboratoire Materiaux-Mecanique Physique, UMR CNRS 5621 Ecole Centrale de Lyon, 69131 Ecully, France.
cases, compressive stresses were found to relax as a result of ion irradiation [7]. However, the detailed physical mechanisms involved are not well understood. For example, several dierent mechanisms have been proposed to explain the relaxation of tensile stress by ion irradiation such as: (i) eects of beam-induced Newtonian viscous ¯ow [5], (ii) generation of interstitial loops on planes normal to the tensile stress direction during irradiation, with the total volume being constant [6], and (iii) coalescence of vacancies to form voids resulting in an increase in the total volume of the deposited system [7]. In most cases, these hypotheses were not supported by detailed structural characterization using transmission electron microscopy (TEM). The build up of compressive stresses is usually attributed to an ``atomic-peening'' mechanism which could be energy or momentum driven [1]
0168-583X/98/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 8 ) 0 0 7 8 0 - 0
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A. Misra et al. / Nucl. Instr. and Meth. in Phys. Res. B 148 (1999) 211±215
and may result in incorporation of implanting species in the ®lm [3]. Preliminary experiments from our group showed that ion-irradiation of sputtered Cr ®lms resulted in relaxation of tensile stress and build up of compressive stress [8]. While the Cr ®lms with tensile stress showed columnar porosity, the ionirradiated, compressively stressed ®lms had dense microstructure with no porosity [8]. In the present investigation, Cr ®lms were irradiated with ions of dierent masses and energies to understand the evolution of stress and its relation to the microstructure during ion irradiation. The ion mass and energy were selected so that the penetration depth of ions was less than the ®lm thickness. The eect of initial stress state on the stress evolution under ion irradiation was also examined.
2. Experimental procedures Cr ®lms were DC sputter deposited on {1 0 0} Si wafers cleaned by etching with HF. The substrate was held at room temperature during deposition and sputtering was carried out under Ar partial pressure with 300 W power to the target. Substrate bias in the range of 0±600 V was used during deposition. The residual stresses were calculated using the Stoney equation [9], with the substrate curvature measured before and after deposition by a laser de¯ection apparatus. In a dierent type of experiment, 150 nm thick Cr ®lms were subjected to post-deposition irradiation to a dose of 5 ´ 1015 ions/cm2 with in situ monitoring of the de¯ection of the cantilever beam sample as a function of dose. The beam de¯ection data was used to calculate the stress following the approach used by Van Sambeek and Averback [10]. Dierent combinations of ion mass and energy (C 33 keV, Ar 110 keV and Xe 330 keV) were used to give approximately the same depth of penetration of 90 nm. Transmission electron microscopy (TEM) was performed on a Philips CM30 microscope operating at 300 kV. 3. Results
Fig. 1. The variation of residual stress in sputtered 150 nm thick Cr ®lms with (a) Ar working pressure (no substrate bias used), and (b) substrate bias voltage at constant Ar pressure of 1.1 mtorr. Positive values indicate tensile stresses and negative values indicate compressive stress.
In the absence of substrate bias, the residual stresses in Cr ®lms were large and tensile. Decreasing the Ar partial pressure during sputtering increased the residual tensile stress to a maximum of 1.7 GPa for a pressure of 3.5 mtorr (Fig. 1(a)). Further decrease in Ar partial pressure from 3.5 mtorr to 1 mtorr, resulted in a sharp decrease in the magnitude of residual stress, although a transition to compressive stress was not observed. Deposition under substrate bias conditions using Ar partial pressure of 1 mtorr resulted in a transition from tensile to compressive stress (Fig. 1(b)). Further increase in bias voltage during deposition caused a rapid build up of compressive stress which tended to saturate at 2 GPa, slightly higher than the maximum value of tensile stress observed. The conditions of decreasing Ar partial pressure and increasing substrate bias are analogous to increasing ion-irradiation during
A. Misra et al. / Nucl. Instr. and Meth. in Phys. Res. B 148 (1999) 211±215
deposition. Thus, deposition under conditions of increasing irradiation tends to ®rst increase the tensile stress to a maximum, then relax the tensile stress and cause a build up of compressive stress that eventually saturates. The results of post-deposition irradiation are shown in Fig. 2. Cr ®lms with initial residual tensile stress of 900 MPa, when irradiated with C 33 keV, Ar 110 keV and Xe 330 keV ions, show different behaviors in stress evolution. Irradiation with C ions had little eect on the stress. Irradiation with Ar and Xe caused a signi®cant modi®cation of the residual stress in the Cr ®lms, with the rate of change of stress with ion dose being higher for Xe. The cyclic ``noise'' in the Xe irradiation data at high doses may have resulted from ¯uctuations in the ion source or other mechanical vibrations in the set-up. After the total dose of 5 ´ 1015 ions cmÿ2 , ®lms irradiated with Xe had higher compressive stress than ®lms irradiated with Ar. Using the same ions, Ar, to irradiate Cr ®lms of dierent initial stress, similar behavior was found if the initial stress was tensile. Irradiation of ®lms that had initial compressive stress resulted in a slower rate of change of stress with ion dose. Since the depth of ion penetration was less than the ®lm thickness in these experiments, the irradiated region shows a stress change while the unirradiated region is expected to maintain its stress state leading to non-uniform stress distribution as
Fig. 2. The evolution of stress during ion irradiation with 110 keV Ar, 33 keV C and 330 keV Xe ions, and with 110 keV Ar for dierent initial residual stress. Note the slower rate of change of stress with dose when the ®lms have an initial compressive stress.
213
a function of ®lm thickness. In previous experiments [8], 300 keV Ar ions were used where the depth of ion penetration was greater than the ®lm thickness. Both experiments gave identical results indicating that factors such as modi®cation of interface stress and the non-uniform stress due to radiation of only a fraction of the ®lm thickness have little eect on the observed stress evolution. The microstructure of a 150 nm Cr ®lm deposited using a negative substrate bias of 100 V is shown in Fig. 3. In general, ®lms with high residual tensile stress showed columnar porosity, whereas irradiated ®lms with compressive residual stress had no columnar porosity [8]. 4. Discussion Ion irradiation of thin sputtered Cr ®lms, either during deposition by applying bias to the substrate or after deposition, has a pronounced eect on the residual stresses. For Cr ®lms with large tensile residual stresses, the general stress evolution trend with increasing ion dose is as follows: increase of tensile stress to a maximum, relaxation of tensile stress, transition from tensile to compressive stress, and build up of compressive stress which eventually tends to saturate. This trend is qualitatively similar to the manner in which interatomic forces vary with decreasing interatomic distances. Thus, stress evolution during irradiation is related to the
Fig. 3. TEM micrograph showing the cross-section view of the microstructure of a Cr ®lm sputtered at 100 V substrate bias. No columnar porosity was observed in ®lms having residual compressive stresses.
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A. Misra et al. / Nucl. Instr. and Meth. in Phys. Res. B 148 (1999) 211±215
decreasing interatomic distances with increasing irradiation dose [8]. This hypothesis is consistent with 2-d molecular dynamics (MD) simulations on ion-beam assisted deposition of Ni ®lms [11] and with the microstructure evolution of Cr ®lms with irradiation where columnar porosity is observed in ®lms with large tensile stress and a dense microstructure with no porosity is observed in ®lms having compressive stress. In other work where no obvious microstructural changes could be discerned by TEM, the stress evolution was explained using the concept of ion-induced viscous ¯ow [5]. In the present case, stress evolution can be explained by microstructural changes and the formation of defects during irradiation. The role of viscous ¯ow on the stress evolution in ion irradiated Cr is unknown at this time. The eective interatomic distance may decrease during irradiation through the formation of defect clusters. It is well established that self-interstitial atoms can form clusters during the cascade process itself [12] and that in the presence of a tensile stress, these disk-shaped clusters (or loops) will preferentially align normal to the tensile axis [13]. Thus, the relaxation of tensile stress and the eventual build up of compressive stress may be interpreted by considering the strain imposed by the interstitial loops aligned normal to the plane of the ®lm. This imposed strain, De, after subtracting the strain due to vacancy loops is given as [6]: De p=3fNr2 b 1 ÿ t;
the corresponding dpa can be calculated and hence, for each ion, Dr can be plotted as a function of dpa. Dr is obtained from Fig. 2 as the magnitude of the dierence between the initial stress and the stress at a given dose. Only the data for the highest initial stress (tensile, 900 MPa) from Fig. 2, are analyzed here. For simplicity, the initial stress is taken as the peak value of tensile stress that was achieved at very low dose before the relaxation of tensile stress begins. This peak value was roughly the same for all samples. The Dr vs dpa plots are shown in Fig. 4 for each of the three ions used along with the ®t using Eq. (3). The value of N which gives the best ®t is 5 ´ 1016 /cm3 , a reasonable estimate for interstitial loop density in Cr for near ambient temperature ion irradiation [6]. Note from Fig. 4 that at the same dpa level, all three ions cause the same stress change. The variation of Dr as (dpa)2=3 is evident for Xe data where irradiation was carried out to high dpa. The data for Ar and C irradiation also fall on the same curve but irradiation to much higher dose is needed to clearly verify whether the variation of Dr as (dpa)2=3 is still valid. This approximate calculation indicates that the strain imposed by defect clusters formed during irradiation can be used to model the stress evolution. The incorporated Ar (or other irradiating ions) would also tend to introduce compressive stresses similar to the eect of Cr self-interstitials. The amount of Ar
1
where f is the fraction of interstitial loops aligned normal to the plane of the ®lm and is 0.5 for an initial stress approaching 1 GPa [13], N is the loop density, b is the Burgers vector, t is PoissonÕs ratio and r is the radius of the loop given as [6], 1=3
r dpa=pN
;
2
where dpa is displacement per atom. Using the biaxial modulus E/(1 ) t), where E is YoungÕs modulus, the stress change at a given dpa may be obtained from (1) and (2) as follows: Dr 1=3E pN
1=3
fb dpa
2=3
:
3
It is assumed that N is constant during irradiation and only r increases with dose. For a given dose,
Fig. 4. The magnitude of change in residual stress as a function of dpa for irradiation with 110 keV Ar, 33 keV C and 330 keV Xe ions. The initial tensile stress was 0.9 GPa. The model ®t using Eq. (3) is also shown.
A. Misra et al. / Nucl. Instr. and Meth. in Phys. Res. B 148 (1999) 211±215
incorporated during irradiation with 300 keV ions was estimated to be 0.4 at.% after a dose of 5 ´ 1015 ions/cm2 [8] using TRIM simulations [14]. Experimental determination of Ar incorporation in Cr ®lms deposited using substrate bias revealed that TRIM simulations may overestimate the amount of Ar incorporated [15]. In fact for Cr it was found that the concentration of Ar decreased with increasing ion ¯ux, possibly due to the diusion of Ar to the ®lm surface assisted by grain boundaries and vacancies produced by ion bombardment [15]. Thus, the observed stress changes cannot be attributed entirely to Ar incorporation. The maximum value of residual stress observed is higher in compression than in tension. Assuming that residual stresses are limited by ®lm yield stress, this indicates irradiation hardening since compressive stresses were observed at high irradiation doses. The hardening may be interpreted primarily due to pinning of dislocations by defect clusters, and saturation in yield stress with increasing dose may be reached when the defect density saturates. Indeed, TEM observations of cluster densities in ion irradiated metals at room temperature has indicated that a saturation is reached 1017 ±1018 /cm3 [16].
5. Summary The large tensile residual stresses in sputtered Cr ®lms were relaxed and compressive stresses imposed by both deposition under negative substrate bias and post-deposition irradiation. Microstructure observations indicate that tensile stresses are associated with ®lms having columnar porosity while dense ®lms with a high density of defect clusters are observed in irradiated ®lms having compressive stresses. The evolution of stress with irradiation dpa is interpreted using a
215
model that calculates the stress imposed by defect clusters. Acknowledgements This research was funded in part by DOE, Of®ce of Basic Energy Sciences and in part by Los Alamos National Laboratory. References [1] H. Windischmann, Crit. Rev. Sol. St. Mat. Sci. 17 (1992) 547. [2] M.F. Doerner, W.D. Nix, Crit. Rev. Sol. St. Mat. Sci. 14 (1988) 25. [3] J.A. Thornton, D.W. Homan, Thin Solid Films 171 (1989) 5. [4] M. Nastasi, J.W. Mayer, J.K. Hirvonen, Ion-Solid Interactions: Fundamentals and Applications, Cambridge Solid State Science Series, Cambridge University Press, Cambridge, 1996. [5] E. Snoeks, K.S. Boutros, J. Barone, Appl. Phys. Lett. 71 (1997) 267. [6] A. Jain, S. Loganathan, U. Jain, Nucl. Instr.and Meth. B 127/128 (1997) 43. [7] L. Pranevicius, K.-F. Badawi, N. Durand, J. Delaford, Ph. Goudeau, Surf. and Coatings Technol. 71 (1995) 254. [8] A. Misra, S. Fayeulle, H. Kung, T.E. Mitchell, M. Nastasi, Appl. Phys. Lett. 73 (1998) 891. [9] G.G. Stoney, Proc. Roy. Soc. London Ser. A 82 (1909) 172. [10] A.I. Van Sambeek, R.S. Averback, Mat. Res. Soc. Symp. Proc. 396 (1996) 137. [11] K.H. Muller, J. Appl. Phys. 51 (1987) 1799. [12] D.J. Bacon, A.F. Calder, F. Cao, Radiation Eects and Defects in Solids 141 (1997) 283. [13] A.B. Lidiard, R. Perrin, Phil. Mag. 14 (1973) 49. [14] TRIM, in: J.F. Ziegler, J.P. Biersack, U. Littmark (Eds.), The stopping and range of ions in solids, Pergamon Press, New York, 1985. [15] B. Window, G.L. Harding, J. Vac. Sci. Tech. A 11 (1993) 1447. [16] S.J. Zinkle, A. Horsewell, B.N. Singh, W.F. Sommer, J. Nucl. Mat. 212±215 (1994) 132.
Residual stresses and ion implantation eects in Cr thin ®lms A. Misra *, S. Fayeulle 1, H. Kung, T.E. Mitchell, M. Nastasi Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Abstract The evolution of intrinsic residual stresses in sputtered Cr thin ®lms with substrate bias and post-deposition ion irradiation is investigated. The relaxation of tensile stresses and build up of compressive stresses with increasing ion irradiation dose is studied using ions of dierent masses and energies such as 110 keV Ar, 33 keV C and 330 keV Xe. The stress evolution is related to the corresponding microstructural changes in the ®lms. The changes in the residual stress during ion irradiation are explained by considering the manner in which the interatomic distances and forces change during irradiation, and the generation of defects during irradiation. Ó 1999 Elsevier Science B.V. All rights reserved. PACS: 61.80.Jh; 61.82.Rx; 81.15.Jj Keywords: Residual stress; Cr thin ®lms; Ion irradiation
1. Introduction Some general trends in the evolution of intrinsic residual stresses in thin ®lms are well established [1±4]. As an example, most materials show a transition from tensile to compressive stresses with decreasing working pressure and increasing substrate bias during ®lm growth [1,3]. Post-deposition irradiation also shows similar trends: tensile stresses are relaxed [5±7] and compressive stresses imposed [5±7] with increasing ion dose. In some
*
Corresponding author. Tel.: +1 505 667 9860; fax: +1 505 665 2992; e-mail: [email protected] 1 On leave from Laboratoire Materiaux-Mecanique Physique, UMR CNRS 5621 Ecole Centrale de Lyon, 69131 Ecully, France.
cases, compressive stresses were found to relax as a result of ion irradiation [7]. However, the detailed physical mechanisms involved are not well understood. For example, several dierent mechanisms have been proposed to explain the relaxation of tensile stress by ion irradiation such as: (i) eects of beam-induced Newtonian viscous ¯ow [5], (ii) generation of interstitial loops on planes normal to the tensile stress direction during irradiation, with the total volume being constant [6], and (iii) coalescence of vacancies to form voids resulting in an increase in the total volume of the deposited system [7]. In most cases, these hypotheses were not supported by detailed structural characterization using transmission electron microscopy (TEM). The build up of compressive stresses is usually attributed to an ``atomic-peening'' mechanism which could be energy or momentum driven [1]
0168-583X/98/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 8 ) 0 0 7 8 0 - 0
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A. Misra et al. / Nucl. Instr. and Meth. in Phys. Res. B 148 (1999) 211±215
and may result in incorporation of implanting species in the ®lm [3]. Preliminary experiments from our group showed that ion-irradiation of sputtered Cr ®lms resulted in relaxation of tensile stress and build up of compressive stress [8]. While the Cr ®lms with tensile stress showed columnar porosity, the ionirradiated, compressively stressed ®lms had dense microstructure with no porosity [8]. In the present investigation, Cr ®lms were irradiated with ions of dierent masses and energies to understand the evolution of stress and its relation to the microstructure during ion irradiation. The ion mass and energy were selected so that the penetration depth of ions was less than the ®lm thickness. The eect of initial stress state on the stress evolution under ion irradiation was also examined.
2. Experimental procedures Cr ®lms were DC sputter deposited on {1 0 0} Si wafers cleaned by etching with HF. The substrate was held at room temperature during deposition and sputtering was carried out under Ar partial pressure with 300 W power to the target. Substrate bias in the range of 0±600 V was used during deposition. The residual stresses were calculated using the Stoney equation [9], with the substrate curvature measured before and after deposition by a laser de¯ection apparatus. In a dierent type of experiment, 150 nm thick Cr ®lms were subjected to post-deposition irradiation to a dose of 5 ´ 1015 ions/cm2 with in situ monitoring of the de¯ection of the cantilever beam sample as a function of dose. The beam de¯ection data was used to calculate the stress following the approach used by Van Sambeek and Averback [10]. Dierent combinations of ion mass and energy (C 33 keV, Ar 110 keV and Xe 330 keV) were used to give approximately the same depth of penetration of 90 nm. Transmission electron microscopy (TEM) was performed on a Philips CM30 microscope operating at 300 kV. 3. Results
Fig. 1. The variation of residual stress in sputtered 150 nm thick Cr ®lms with (a) Ar working pressure (no substrate bias used), and (b) substrate bias voltage at constant Ar pressure of 1.1 mtorr. Positive values indicate tensile stresses and negative values indicate compressive stress.
In the absence of substrate bias, the residual stresses in Cr ®lms were large and tensile. Decreasing the Ar partial pressure during sputtering increased the residual tensile stress to a maximum of 1.7 GPa for a pressure of 3.5 mtorr (Fig. 1(a)). Further decrease in Ar partial pressure from 3.5 mtorr to 1 mtorr, resulted in a sharp decrease in the magnitude of residual stress, although a transition to compressive stress was not observed. Deposition under substrate bias conditions using Ar partial pressure of 1 mtorr resulted in a transition from tensile to compressive stress (Fig. 1(b)). Further increase in bias voltage during deposition caused a rapid build up of compressive stress which tended to saturate at 2 GPa, slightly higher than the maximum value of tensile stress observed. The conditions of decreasing Ar partial pressure and increasing substrate bias are analogous to increasing ion-irradiation during
A. Misra et al. / Nucl. Instr. and Meth. in Phys. Res. B 148 (1999) 211±215
deposition. Thus, deposition under conditions of increasing irradiation tends to ®rst increase the tensile stress to a maximum, then relax the tensile stress and cause a build up of compressive stress that eventually saturates. The results of post-deposition irradiation are shown in Fig. 2. Cr ®lms with initial residual tensile stress of 900 MPa, when irradiated with C 33 keV, Ar 110 keV and Xe 330 keV ions, show different behaviors in stress evolution. Irradiation with C ions had little eect on the stress. Irradiation with Ar and Xe caused a signi®cant modi®cation of the residual stress in the Cr ®lms, with the rate of change of stress with ion dose being higher for Xe. The cyclic ``noise'' in the Xe irradiation data at high doses may have resulted from ¯uctuations in the ion source or other mechanical vibrations in the set-up. After the total dose of 5 ´ 1015 ions cmÿ2 , ®lms irradiated with Xe had higher compressive stress than ®lms irradiated with Ar. Using the same ions, Ar, to irradiate Cr ®lms of dierent initial stress, similar behavior was found if the initial stress was tensile. Irradiation of ®lms that had initial compressive stress resulted in a slower rate of change of stress with ion dose. Since the depth of ion penetration was less than the ®lm thickness in these experiments, the irradiated region shows a stress change while the unirradiated region is expected to maintain its stress state leading to non-uniform stress distribution as
Fig. 2. The evolution of stress during ion irradiation with 110 keV Ar, 33 keV C and 330 keV Xe ions, and with 110 keV Ar for dierent initial residual stress. Note the slower rate of change of stress with dose when the ®lms have an initial compressive stress.
213
a function of ®lm thickness. In previous experiments [8], 300 keV Ar ions were used where the depth of ion penetration was greater than the ®lm thickness. Both experiments gave identical results indicating that factors such as modi®cation of interface stress and the non-uniform stress due to radiation of only a fraction of the ®lm thickness have little eect on the observed stress evolution. The microstructure of a 150 nm Cr ®lm deposited using a negative substrate bias of 100 V is shown in Fig. 3. In general, ®lms with high residual tensile stress showed columnar porosity, whereas irradiated ®lms with compressive residual stress had no columnar porosity [8]. 4. Discussion Ion irradiation of thin sputtered Cr ®lms, either during deposition by applying bias to the substrate or after deposition, has a pronounced eect on the residual stresses. For Cr ®lms with large tensile residual stresses, the general stress evolution trend with increasing ion dose is as follows: increase of tensile stress to a maximum, relaxation of tensile stress, transition from tensile to compressive stress, and build up of compressive stress which eventually tends to saturate. This trend is qualitatively similar to the manner in which interatomic forces vary with decreasing interatomic distances. Thus, stress evolution during irradiation is related to the
Fig. 3. TEM micrograph showing the cross-section view of the microstructure of a Cr ®lm sputtered at 100 V substrate bias. No columnar porosity was observed in ®lms having residual compressive stresses.
214
A. Misra et al. / Nucl. Instr. and Meth. in Phys. Res. B 148 (1999) 211±215
decreasing interatomic distances with increasing irradiation dose [8]. This hypothesis is consistent with 2-d molecular dynamics (MD) simulations on ion-beam assisted deposition of Ni ®lms [11] and with the microstructure evolution of Cr ®lms with irradiation where columnar porosity is observed in ®lms with large tensile stress and a dense microstructure with no porosity is observed in ®lms having compressive stress. In other work where no obvious microstructural changes could be discerned by TEM, the stress evolution was explained using the concept of ion-induced viscous ¯ow [5]. In the present case, stress evolution can be explained by microstructural changes and the formation of defects during irradiation. The role of viscous ¯ow on the stress evolution in ion irradiated Cr is unknown at this time. The eective interatomic distance may decrease during irradiation through the formation of defect clusters. It is well established that self-interstitial atoms can form clusters during the cascade process itself [12] and that in the presence of a tensile stress, these disk-shaped clusters (or loops) will preferentially align normal to the tensile axis [13]. Thus, the relaxation of tensile stress and the eventual build up of compressive stress may be interpreted by considering the strain imposed by the interstitial loops aligned normal to the plane of the ®lm. This imposed strain, De, after subtracting the strain due to vacancy loops is given as [6]: De p=3fNr2 b 1 ÿ t;
the corresponding dpa can be calculated and hence, for each ion, Dr can be plotted as a function of dpa. Dr is obtained from Fig. 2 as the magnitude of the dierence between the initial stress and the stress at a given dose. Only the data for the highest initial stress (tensile, 900 MPa) from Fig. 2, are analyzed here. For simplicity, the initial stress is taken as the peak value of tensile stress that was achieved at very low dose before the relaxation of tensile stress begins. This peak value was roughly the same for all samples. The Dr vs dpa plots are shown in Fig. 4 for each of the three ions used along with the ®t using Eq. (3). The value of N which gives the best ®t is 5 ´ 1016 /cm3 , a reasonable estimate for interstitial loop density in Cr for near ambient temperature ion irradiation [6]. Note from Fig. 4 that at the same dpa level, all three ions cause the same stress change. The variation of Dr as (dpa)2=3 is evident for Xe data where irradiation was carried out to high dpa. The data for Ar and C irradiation also fall on the same curve but irradiation to much higher dose is needed to clearly verify whether the variation of Dr as (dpa)2=3 is still valid. This approximate calculation indicates that the strain imposed by defect clusters formed during irradiation can be used to model the stress evolution. The incorporated Ar (or other irradiating ions) would also tend to introduce compressive stresses similar to the eect of Cr self-interstitials. The amount of Ar
1
where f is the fraction of interstitial loops aligned normal to the plane of the ®lm and is 0.5 for an initial stress approaching 1 GPa [13], N is the loop density, b is the Burgers vector, t is PoissonÕs ratio and r is the radius of the loop given as [6], 1=3
r dpa=pN
;
2
where dpa is displacement per atom. Using the biaxial modulus E/(1 ) t), where E is YoungÕs modulus, the stress change at a given dpa may be obtained from (1) and (2) as follows: Dr 1=3E pN
1=3
fb dpa
2=3
:
3
It is assumed that N is constant during irradiation and only r increases with dose. For a given dose,
Fig. 4. The magnitude of change in residual stress as a function of dpa for irradiation with 110 keV Ar, 33 keV C and 330 keV Xe ions. The initial tensile stress was 0.9 GPa. The model ®t using Eq. (3) is also shown.
A. Misra et al. / Nucl. Instr. and Meth. in Phys. Res. B 148 (1999) 211±215
incorporated during irradiation with 300 keV ions was estimated to be 0.4 at.% after a dose of 5 ´ 1015 ions/cm2 [8] using TRIM simulations [14]. Experimental determination of Ar incorporation in Cr ®lms deposited using substrate bias revealed that TRIM simulations may overestimate the amount of Ar incorporated [15]. In fact for Cr it was found that the concentration of Ar decreased with increasing ion ¯ux, possibly due to the diusion of Ar to the ®lm surface assisted by grain boundaries and vacancies produced by ion bombardment [15]. Thus, the observed stress changes cannot be attributed entirely to Ar incorporation. The maximum value of residual stress observed is higher in compression than in tension. Assuming that residual stresses are limited by ®lm yield stress, this indicates irradiation hardening since compressive stresses were observed at high irradiation doses. The hardening may be interpreted primarily due to pinning of dislocations by defect clusters, and saturation in yield stress with increasing dose may be reached when the defect density saturates. Indeed, TEM observations of cluster densities in ion irradiated metals at room temperature has indicated that a saturation is reached 1017 ±1018 /cm3 [16].
5. Summary The large tensile residual stresses in sputtered Cr ®lms were relaxed and compressive stresses imposed by both deposition under negative substrate bias and post-deposition irradiation. Microstructure observations indicate that tensile stresses are associated with ®lms having columnar porosity while dense ®lms with a high density of defect clusters are observed in irradiated ®lms having compressive stresses. The evolution of stress with irradiation dpa is interpreted using a
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model that calculates the stress imposed by defect clusters. Acknowledgements This research was funded in part by DOE, Of®ce of Basic Energy Sciences and in part by Los Alamos National Laboratory. References [1] H. Windischmann, Crit. Rev. Sol. St. Mat. Sci. 17 (1992) 547. [2] M.F. Doerner, W.D. Nix, Crit. Rev. Sol. St. Mat. Sci. 14 (1988) 25. [3] J.A. Thornton, D.W. Homan, Thin Solid Films 171 (1989) 5. [4] M. Nastasi, J.W. Mayer, J.K. Hirvonen, Ion-Solid Interactions: Fundamentals and Applications, Cambridge Solid State Science Series, Cambridge University Press, Cambridge, 1996. [5] E. Snoeks, K.S. Boutros, J. Barone, Appl. Phys. Lett. 71 (1997) 267. [6] A. Jain, S. Loganathan, U. Jain, Nucl. Instr.and Meth. B 127/128 (1997) 43. [7] L. Pranevicius, K.-F. Badawi, N. Durand, J. Delaford, Ph. Goudeau, Surf. and Coatings Technol. 71 (1995) 254. [8] A. Misra, S. Fayeulle, H. Kung, T.E. Mitchell, M. Nastasi, Appl. Phys. Lett. 73 (1998) 891. [9] G.G. Stoney, Proc. Roy. Soc. London Ser. A 82 (1909) 172. [10] A.I. Van Sambeek, R.S. Averback, Mat. Res. Soc. Symp. Proc. 396 (1996) 137. [11] K.H. Muller, J. Appl. Phys. 51 (1987) 1799. [12] D.J. Bacon, A.F. Calder, F. Cao, Radiation Eects and Defects in Solids 141 (1997) 283. [13] A.B. Lidiard, R. Perrin, Phil. Mag. 14 (1973) 49. [14] TRIM, in: J.F. Ziegler, J.P. Biersack, U. Littmark (Eds.), The stopping and range of ions in solids, Pergamon Press, New York, 1985. [15] B. Window, G.L. Harding, J. Vac. Sci. Tech. A 11 (1993) 1447. [16] S.J. Zinkle, A. Horsewell, B.N. Singh, W.F. Sommer, J. Nucl. Mat. 212±215 (1994) 132.