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Grain resolved orientation changes and texture evolution in a thermally strained Al film on Si substrate
Surface & Coatings Technology 206 (2011) 1850–1854
Contents lists available at ScienceDirect
Surface & Coatings Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s u r f c o a t
Grain resolved orientation changes and texture evolution in a thermally strained Al film on Si substrate W. Heinz a,⁎, G. Dehm a, b a b
Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, Jahnstr. 12, 8700 Leoben, Austria Department Materials Physics, Montanuniversität Leoben, Jahnstr. 12, 8700 Leoben, Austria
a r t i c l e
i n f o
Available online 7 August 2011 Keywords: Thermal fatigue Thin film Dislocation plasticity EBSD Electron microscopy
a b s t r a c t Temperature changes induce thermal stresses in thin films on substrates due to differences in the thermal expansion coefficients. Repeated thermal cycling may finally lead to severe surface roughening and a change in film texture. In this study we investigate the orientation changes for a 600 nm thick Al film during subsequent thermal cycles between 25 °C and 450 °C by analyzing individual grains. The results reveal orientation changes by up to 3° after one thermal cycles and unexpected large orientation gradients within individual grains. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Fatigue failure of metallization in microelectronic devices is limiting their lifetime and reliability. In order to provide strategies to overcome these limitations in future, a thorough understanding of the underlying mechanisms is required. Fatigue failure in metal films can be caused by cyclic thermal stresses, which eventually lead to damage accumulation in the form of surface roughening and void formation [1]. The main course for cyclic thermal straining accompanied by damage accumulation is Joule heating [1–9] during electrical service of a device or external temperature changes [10–13]. As a consequence of the difference in thermal expansion coefficients between the metallic film and the substrate material stresses evolve in the film. In the case of Al films on Si substrates a temperature change of 10 °C can induce biaxial film stresses of up to ~20 MPa according to: σ = Δα⋅ΔT⋅M;
ð1Þ
where Δα is the difference in thermal expansion coefficients between film and substrate (Δα = 19.5 ∙ 10 −6 for Al on Si [14,15]) and M the biaxial modulus of the film (M = 109.4 GPa for polycrystalline (111) oriented Al [15]). Several studies have shown that fatigue of Al and Cu films due to repeated Joule heating [2–9] and/or repeated thermal cycling [10–13] depends on film thickness, grain size and texture. Usually, thinner films with small grains are less prone to damage evolution since there flow stress can become extremely high by constraining dislocation plasticity in small dimensions [16], thus retarding microstructural changes. ⁎ Corresponding author. E-mail address: [email protected] (W. Heinz). 0257-8972/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2011.07.046
Always under debate is the contribution of diffusion and dislocation glide to the microstructure evolution occurring in thin metallic films. While for cyclic loading experiments performed at room temperature G.P. Zhang et al. [17] resolved that dislocation cell structures vanish below a film thickness of ~1 μm in polycrystalline Cu films, are the mechanisms causing damage accumulation at elevated temperatures or during thermal cycling not yet clear. In a recent study of thermally cycled Al films up to 10.000 thermal cycles with an initial (111) texture [12] we observed that the fatigued samples do not only possess an extremely rough surface with roughness values in the regime of the initial film thickness, but also a change in texture toward (112). This indicates that the main reason for surface roughening stems from dislocation plasticity. In order to analyze the influence of dislocation plasticity on the fatigue behavior we choose a 600 nm thick polycrystalline Al film on (100) Si and followed the orientation changes of individual grains over a period of 35 thermal cycles by electron backscattered diffraction (EBSD) in the scanning electron microscope (SEM). This should reveal the contribution of dislocation plasticity to orientation changes as well as surface roughening. 2. Experimental 600 nm thick Al films were grown at nominally room temperature by magnetron sputtering on 280 μm thick oxidized (100) Si substrates. Prior to deposition the substrate was Ar-sputter cleaned for ~3 min at −200 eV. The base pressure of the sputter chamber is ~2 ∙ 10−9 mbar. Sputtering was performed at a power of 200 W from a high purity Al target (99,999% Al). Directly after film deposition, the film was annealed for 15 min at 450 °C without breaking the vacuum of the system. The microstructure was investigated with SEM and EBSD using a SEM Leo 1525. The grain size was determined using EBSD by measuring the
W. Heinz, G. Dehm / Surface & Coatings Technology 206 (2011) 1850–1854
grain area from which an equivalent circular grain diameter is obtained. The 600 nm thick film reveals an average grain size of 4.19 μm ±0.39 and a (111) fiber texture. Microstructural changes due to repeated thermal excursion were monitored by SEM/EBSD. EBSD scan was performed with a step size of 0.25 μm at areas of 75 μm × 75 μm on the sample surface. Identical surface areas were examined after several thermal cycles in order to monitor grain size and orientation changes. Up to 35 thermal cycles of the Al film on Si substrate were performed between room temperature and 450 °C in a nitrogen flooded tube. A heating rate of 30 °C/s was applied while for cooling a slower rate of 10 °C/s was accomplished. A temperature change by ΔT = 425 °C, as experienced during heating or cooling cycle, induces a thermal strain by 0.83% for the Al film on Si substrate. Thermal strain εth = Δα ∙ ΔT is calculated with thermal expansion coefficients αAl = 23× 10 −6 [14] and αSi = 3.5 × 10−6 [15]. After each thermal cycle the sample was transferred within less than 15 min to the SEM and identical surface areas were analyzed by EBSD. Subsequently, the sample was again subjected to thermal cycling. 3. Results The initial microstructure prior to thermal cycling permits to resolve individual grains due to some thermal grooving at the grain boundaries by the annealing at 450 °C for 15 min (see Fig. 1). The EBSD scans reveal a typically (111) fiber texture with a maximum deviation of about 7° from the exact (111) orientation as indicated in the inverse pole figure shown in Fig. 1b. In Fig. 2 several grains are identified and followed in their orientation change over a total of 35 cycles. It is interesting to note that all grains reveal a change in orientation. The orientation changes from initial to final orientation after 35 cycles range between 1° and 14° with larger changes occurring for grains with an initial orientation further away from the exact (111) pole or the (100)–(111) connecting line. Between individual thermal cycles grains reorient by up to 3°. For large grains, such as grain 1 in Fig. 2, orientation differences of ~ 1° exist in the initial stage. Upon cycling the orientation gradient in the grain increases (see Fig. 3). In this case a continuous gradient in orientation evolves with a maximum deviation of ~4° after 25 thermal cycles. SEM investigations reveal no well-defined sub-grain formation within this grain. The grain reorients toward the (112) pole of the (100)–(111) connecting line. 4. Discussion The SEM/EBSD studies reveal orientation changes in all 7 grains studied with values up to 3° between individual cycles and orientation gradients in larger grains, most prominent in grain 1 (Fig. 3). This
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raises the question whether dislocation plasticity is capable of explaining the observed orientation changes and gradients. To cause lattice rotations in a grain (geometrically necessary) dislocations must be stored. Fig. 4 presents a simple model permitting to estimate the required dislocation density to induce an orientation gradient of 4° over a distance of ~ 20 μm. For simplification, we suppose that the orientation of the surface of the grains corresponds to the grain cross-sections. Assuming that an edge dislocation with b = 0.286 nm is stored near the film/substrate interface, an orientation change of: tan α ≈ b = h
ð2Þ
of α ≈ 0.027° is induced in the 600 nm thick Al film. This estimate is an upper limit as the glide system is inclined with respect to the film surface. In the present case assuming an angle of 70° between glide plane and film surface only a ~1/3 of the dislocation's Burgers vector would contribute as a lower limit to the sketched orientation change of the sample surface. This means that in order to achieve an orientation gradient of 4° over a distance of ~20 μm as in grain 1 (Fig. 3) about ~ 150 to ~ 450 dislocations must be stored. That would translate in an average dislocation distance l of ~ 150 nm to ~ 50 nm, or by using the relationship, l = p1ffiffiρ, a stored dislocation density ρ of ~ 4 ∙ 10 13 m −2 to 5 ∙ 10 14 m −2 is obtained. Using the relationship εpl = N⋅b the amount of dislocations, N, compensating the plastic d strain, εpl, in a grain of size, d, can be estimated. In the present case the width of the stress-temperature curve (Fig. 5) indicates a plastic strain of ~ 0.4%. Assuming again a grain size of ~20 μm and a 1/3 of the Burgers vector contributing to the plastic deformation, ~ 850 mobile dislocations are required to fully compensate the plastic strain. However, a dislocation density cannot be calculated based on that number since many mobile dislocations escape at the surface (and interface [e.g. 18]). To obtain an estimate of the dislocation density compensating the plastic strain one can use the Taylor–Orowan equation, εpl = ρ ⋅ b ⋅ λ, where λ is the mean free path dislocations glide during plastic deformation. Considering again a plastic strain of ~0.4%, a 1/3 of the Burgers vector contributing to the plastic strain compensation and a mean free path distance of ~ 630 nm on the inclined {111} glide plane a dislocation density of ρ of ~ 7 ∙ 10 13 m −2 is calculated. This is a lower bound as other dislocations may obstruct the mean free path dislocations glide. Considering a mean free path value of ~ 85 nm as deduced from a value of ~ 70 for a thermally strained 500 nm thick Cu film on Si nm as found by a transmission electron microscopy study [18] a value of ~5 ∙ 10 14 m −2 is obtained for the 600 nm thick Al film in the present case. This value may be considered as an upper bound. Note that for these calculations it is assumed that plastic deformation is done solely by dislocation glide, which may not be the case as also
Fig. 1. a) SEM image of the 600 nm Al film on Si (100) reveals a smooth surface with no hillocks. b) Inverse pole figure obtained by EBSD scans revealing the typical (111) fiber texture with a maximum out of plane misorientation of ~ 7°.
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W. Heinz, G. Dehm / Surface & Coatings Technology 206 (2011) 1850–1854
Fig. 2. a) Overview of the investigated area and b) the corresponding pole figures after 35 thermal cycles for grains 2–7. The green marker shows the initial orientation before thermal cycling and the red marker shows the orientation after 35 thermal loads.
diffusional processes such as grain boundary diffusion can contribute to strain compensation. These simple dislocation density estimates agree with measured dislocation densities of 1013 m−2 to 1014 m−2 reported in literature by transmission electron microscopy studies for similar film systems [18–20]. The present observations and interpretations also agree with classical dislocation plasticity. It is well known since Schmid and Boas [21] that under uniaxial loading of tensile specimens a change in orientation occurs due to plastic deformation by dislocation glide. In face centered cubic single crystals this behavior leads to a crystal axis rotation toward (112), while for compression a rotation toward (110) is expected [21,22]. Orientation changes during cycling loading are shown in [23]. Now, in the present case thermal cycling leads to
biaxial compressive stresses during heating and biaxial tensile stresses during cooling. This should cause crystal rotations toward the (112) pole and subsequently backwards toward the (110) pole for alternating heating and cooling cycles. Note that a biaxial compressive in-plane film stress corresponds with respect to the orientation changes to a uniaxial tensile stress perpendicular to the film surface. As observed and discussed earlier [12], the stresses evolving in compression are smaller than in tension (Fig. 5), indicating a stronger plastic deformation during the heating cycle compared to the cooling cycle, i.e. a larger orientation change can occur during heating compared to cooling. This finally gives rise to a global orientation change toward (112). The stochastic nature of dislocation plasticity in small dimensions [24,25] and the constraints by neighboring grains
W. Heinz, G. Dehm / Surface & Coatings Technology 206 (2011) 1850–1854
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Fig. 3. Orientation gradients in a grain (grain 1 in Fig. 2) after 25 thermal cycles. a) Initial state with a maximum orientation deviation of ~ 1° within the grain. b) A continuous orientation gradient of ~ 4° evolves during the 25 thermal cycles. Insets reveal the orientation in the inverse pole figures.
leads, however, to quite complex local orientation changes as seen in the inverse pole figures in Fig. 2. The (112) pole is approached by a random walk like behavior. Analyzing the film/substrate interface to search for the stored dislocations is prevented by vanishing strain contrast of the dislocations at the interface between the Al film and the amorphous SiO layer covering the Si substrate. This was interpreted as dislocation core spreading, a diffusional delocalization of the dislocation core possibly by atom migration at the interface [26–29]. The strain contrast of the dislocations incorporated into the interface vanishes especially at elevated temperatures. However, the dislocation core spreading prevents a backward motion of dislocations stored at the interface during the heating cycle in the subsequent cooling cycle. Thus, it can be speculated that new dislocation sources must be activated to compensate the biaxial tensile stress by dislocation
motion during the cooling cycle, which gets increasingly difficult with decreasing temperature. Thus, we conclude that the interplay of dislocation glide and diffusion-induced interfacial dislocation core spreading causes the final orientation changes toward (112) accompanied by surface steps created by each glide dislocation channeling through the film and emerging at the film surface (see Fig. 4). If grain boundary and surface diffusion would cause the orientation change from (111) toward (112) this should also occur for thinner Al films with their smaller grain sizes and shorter diffusion distances. However, films with 400 nm thickness and below did not reveal a change in orientation but maintained their initial (111) fiber texture within the analyzed 10.000 thermal cycles as reported in [12]. Note, that this observation does not exclude that diffusional processes contribute to strain compensation during each thermal cycle in addition to dislocation glide. However, all observations strongly imply that the texture evolution is driven by dislocation glide and diffusioninduced interfacial dislocation core spreading as described above.
5. Conclusion Repeated thermal cycling of a 600 nm thick polycrystalline Al film on a (100) Si substrate reveals orientation changes between subsequent thermal cycles between 25 °C and 450 °C. The basic findings can be explained by classical dislocation plasticity [21]. The results reveal that: • Orientation gradients within grains can be explained by stored dislocations with calculated dislocation densities of 4 ∙ 10 13 cm −2 to 5 ∙ 10 14 cm −2 in agreement with measured dislocation densities in such films. • Reorientation of grains in the Al film toward (112) can be explained by classical slip induced lattice rotation. • Grain–grain interactions and localized plasticity prevent a continuous orientation change toward (112). The (112) pole is approached by a random walk like behavior during thermal cycling.
Acknowledgment Fig. 4. Comparison of (a) free dislocation glide on an inclined (111) plane causing no orientation change and (b) the constraining effect of a substrate, leading to an orientation change for the slipped portion due to the stiff substrate by storing the dislocation at the interface. (c) Orientation changes α caused by a dislocation with Burgers vector b in a material of thickness h.
The authors are grateful to the Max-Planck Institute for Metals Research, Stuttgart, for providing polycrystalline Al films in the thin film deposition group headed by Dr. Gunter Richter.
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Fig. 5. Stress-temperature cycle of a 600 nm thick Al film on Si (100) substrate.
References [1] [2] [3] [4] [5] [6]
R. Schwaiger, O. Kraft, Acta Materialia 51 (a) (2003) 195. F.M. d'Heurle, R. Rosenberg, Physics of Thin Films, 7, Academic Press, 1973, p. 257. R. Mönig, R.R. Keller, C.A. Volkert, Rev. Sci. Instrum. 75 (11) (2004) 4997. Y.-B. Park, R. Mönig, C.A. Volkert, Thin Solid Films 504 (1–2) (2006) 321. Y.-B. Park, R. Mönig, C.A. Volkert, Thin Solid Films 515 (6) (2007) 3253. R.R. Keller, R. Mönig, C.A. Volkert, E. Arzt, R. Schwaiger, O. Kraft, Stress-Induced Phenomena in Metallizations: 6th Int. Workshop (2002) 119. [7] R.R. Keller, R.H. Geiss, N. Barbosa, A.J. Slifka, D.T. Read, Metall. Mater. Trans. A: Phys. Metall. Mater. Sci. 38A (13) (2007) 2263.
[8] R.R. Keller, R.H. Geiss, Y.-W. Cheng, D.T. Read, Mater. Res. Soc. Proc. 863 (2005) 295. [9] G.P. Zhang, C.A. Volkert, R. Schwaiger, R. Mönig, O. Kraft, Microelectron. Reliab. 47 (2007) 2007. [10] A.K. Sinha, T.T. Sheng, Thin Solid Films 48 (1978) 117. [11] M. Legros, K.J. Hemker, A. Gouldstone, S. Suresh, R.M. Keller-Flaig, E. Arzt, Acta Materialia 50 (2002) 3435. [12] W. Heinz, R. Pippan, G. Dehm, Materials Science and Engineering A 527 (2010) 7757. [13] W. Heinz, PHD thesis (2010), University of Leoben. [14] G. Dehm, B.J. Inkson, T. Wagner, Acta Mater. 50 (2002) 5021. [15] L.B. Freund, S. Suresh, Thin Film Materials, Cambridge University Press, Cambridge, 2003. [16] W.D. Nix, Metallurgical and Materials Transaction A 20 (1989) 2217. [17] G.P. Zhang, R. Schwaiger, C.A. Volkert, O. Kraft, Philos. Mag. Lett. 83 (8) (2003) 477. [18] G. Dehm, D. Weiss, E. Arzt, Mater. Sci. Eng. A 309–310 (2001) 468. [19] E. Eiper, J. Keckes, K.J. Martinschitz, I. Zizak, M. Cabié, G. Dehm, Acta Materialia 55 (2007) 1941. [20] M. Legros, G. Dehm, R.M. Keller-Flaig, E. Arzt, K.J. Hemker, S. Suresh, Mater. Sci. Eng. A 309–310 (2001) 463. [21] E. Schmid, W. Boas, Kristallplastizität, mit besonderer Berücksichtigung der Metalle, Springer, Berlin, 1935. [22] W. Hosford, The Mechanics of Crystals and Textured Polycrystals, Oxford University Press, Oxford, 1993. [23] S.X. Li, X.W. Li, Z.F. Zhang, Z.G. Wang, K. Lu, Philosophical Magazine A 82 (16) (2002) 3129. [24] M.D. Uchic, D.M. Dimiduk, J.N. Florando, W.D. Nix, Science 305 (5686) (2004) 986. [25] F.F. Csikor, C. Motz, D. Weygand, M. Zaiser, S. Zapperi, Science 318 (5848) (2007) 251. [26] P. Müllner, E. Arzt, Mater. Res. Soc. Symp. Proc. 505 (1998) 149. [27] G. Dehm, E. Arzt, Appl. Phys. Lett. 77 (2000) 1126. [28] H. Gao, L. Zhang, S.P. Baker, J. Mech. Phys. of Solids 50 (2002) 2169. [29] G. Dehm, T. Balk, H. Edongue, E. Arzt, Microelectron. Eng. 70 (2003) 412.
Contents lists available at ScienceDirect
Surface & Coatings Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s u r f c o a t
Grain resolved orientation changes and texture evolution in a thermally strained Al film on Si substrate W. Heinz a,⁎, G. Dehm a, b a b
Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, Jahnstr. 12, 8700 Leoben, Austria Department Materials Physics, Montanuniversität Leoben, Jahnstr. 12, 8700 Leoben, Austria
a r t i c l e
i n f o
Available online 7 August 2011 Keywords: Thermal fatigue Thin film Dislocation plasticity EBSD Electron microscopy
a b s t r a c t Temperature changes induce thermal stresses in thin films on substrates due to differences in the thermal expansion coefficients. Repeated thermal cycling may finally lead to severe surface roughening and a change in film texture. In this study we investigate the orientation changes for a 600 nm thick Al film during subsequent thermal cycles between 25 °C and 450 °C by analyzing individual grains. The results reveal orientation changes by up to 3° after one thermal cycles and unexpected large orientation gradients within individual grains. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Fatigue failure of metallization in microelectronic devices is limiting their lifetime and reliability. In order to provide strategies to overcome these limitations in future, a thorough understanding of the underlying mechanisms is required. Fatigue failure in metal films can be caused by cyclic thermal stresses, which eventually lead to damage accumulation in the form of surface roughening and void formation [1]. The main course for cyclic thermal straining accompanied by damage accumulation is Joule heating [1–9] during electrical service of a device or external temperature changes [10–13]. As a consequence of the difference in thermal expansion coefficients between the metallic film and the substrate material stresses evolve in the film. In the case of Al films on Si substrates a temperature change of 10 °C can induce biaxial film stresses of up to ~20 MPa according to: σ = Δα⋅ΔT⋅M;
ð1Þ
where Δα is the difference in thermal expansion coefficients between film and substrate (Δα = 19.5 ∙ 10 −6 for Al on Si [14,15]) and M the biaxial modulus of the film (M = 109.4 GPa for polycrystalline (111) oriented Al [15]). Several studies have shown that fatigue of Al and Cu films due to repeated Joule heating [2–9] and/or repeated thermal cycling [10–13] depends on film thickness, grain size and texture. Usually, thinner films with small grains are less prone to damage evolution since there flow stress can become extremely high by constraining dislocation plasticity in small dimensions [16], thus retarding microstructural changes. ⁎ Corresponding author. E-mail address: [email protected] (W. Heinz). 0257-8972/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2011.07.046
Always under debate is the contribution of diffusion and dislocation glide to the microstructure evolution occurring in thin metallic films. While for cyclic loading experiments performed at room temperature G.P. Zhang et al. [17] resolved that dislocation cell structures vanish below a film thickness of ~1 μm in polycrystalline Cu films, are the mechanisms causing damage accumulation at elevated temperatures or during thermal cycling not yet clear. In a recent study of thermally cycled Al films up to 10.000 thermal cycles with an initial (111) texture [12] we observed that the fatigued samples do not only possess an extremely rough surface with roughness values in the regime of the initial film thickness, but also a change in texture toward (112). This indicates that the main reason for surface roughening stems from dislocation plasticity. In order to analyze the influence of dislocation plasticity on the fatigue behavior we choose a 600 nm thick polycrystalline Al film on (100) Si and followed the orientation changes of individual grains over a period of 35 thermal cycles by electron backscattered diffraction (EBSD) in the scanning electron microscope (SEM). This should reveal the contribution of dislocation plasticity to orientation changes as well as surface roughening. 2. Experimental 600 nm thick Al films were grown at nominally room temperature by magnetron sputtering on 280 μm thick oxidized (100) Si substrates. Prior to deposition the substrate was Ar-sputter cleaned for ~3 min at −200 eV. The base pressure of the sputter chamber is ~2 ∙ 10−9 mbar. Sputtering was performed at a power of 200 W from a high purity Al target (99,999% Al). Directly after film deposition, the film was annealed for 15 min at 450 °C without breaking the vacuum of the system. The microstructure was investigated with SEM and EBSD using a SEM Leo 1525. The grain size was determined using EBSD by measuring the
W. Heinz, G. Dehm / Surface & Coatings Technology 206 (2011) 1850–1854
grain area from which an equivalent circular grain diameter is obtained. The 600 nm thick film reveals an average grain size of 4.19 μm ±0.39 and a (111) fiber texture. Microstructural changes due to repeated thermal excursion were monitored by SEM/EBSD. EBSD scan was performed with a step size of 0.25 μm at areas of 75 μm × 75 μm on the sample surface. Identical surface areas were examined after several thermal cycles in order to monitor grain size and orientation changes. Up to 35 thermal cycles of the Al film on Si substrate were performed between room temperature and 450 °C in a nitrogen flooded tube. A heating rate of 30 °C/s was applied while for cooling a slower rate of 10 °C/s was accomplished. A temperature change by ΔT = 425 °C, as experienced during heating or cooling cycle, induces a thermal strain by 0.83% for the Al film on Si substrate. Thermal strain εth = Δα ∙ ΔT is calculated with thermal expansion coefficients αAl = 23× 10 −6 [14] and αSi = 3.5 × 10−6 [15]. After each thermal cycle the sample was transferred within less than 15 min to the SEM and identical surface areas were analyzed by EBSD. Subsequently, the sample was again subjected to thermal cycling. 3. Results The initial microstructure prior to thermal cycling permits to resolve individual grains due to some thermal grooving at the grain boundaries by the annealing at 450 °C for 15 min (see Fig. 1). The EBSD scans reveal a typically (111) fiber texture with a maximum deviation of about 7° from the exact (111) orientation as indicated in the inverse pole figure shown in Fig. 1b. In Fig. 2 several grains are identified and followed in their orientation change over a total of 35 cycles. It is interesting to note that all grains reveal a change in orientation. The orientation changes from initial to final orientation after 35 cycles range between 1° and 14° with larger changes occurring for grains with an initial orientation further away from the exact (111) pole or the (100)–(111) connecting line. Between individual thermal cycles grains reorient by up to 3°. For large grains, such as grain 1 in Fig. 2, orientation differences of ~ 1° exist in the initial stage. Upon cycling the orientation gradient in the grain increases (see Fig. 3). In this case a continuous gradient in orientation evolves with a maximum deviation of ~4° after 25 thermal cycles. SEM investigations reveal no well-defined sub-grain formation within this grain. The grain reorients toward the (112) pole of the (100)–(111) connecting line. 4. Discussion The SEM/EBSD studies reveal orientation changes in all 7 grains studied with values up to 3° between individual cycles and orientation gradients in larger grains, most prominent in grain 1 (Fig. 3). This
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raises the question whether dislocation plasticity is capable of explaining the observed orientation changes and gradients. To cause lattice rotations in a grain (geometrically necessary) dislocations must be stored. Fig. 4 presents a simple model permitting to estimate the required dislocation density to induce an orientation gradient of 4° over a distance of ~ 20 μm. For simplification, we suppose that the orientation of the surface of the grains corresponds to the grain cross-sections. Assuming that an edge dislocation with b = 0.286 nm is stored near the film/substrate interface, an orientation change of: tan α ≈ b = h
ð2Þ
of α ≈ 0.027° is induced in the 600 nm thick Al film. This estimate is an upper limit as the glide system is inclined with respect to the film surface. In the present case assuming an angle of 70° between glide plane and film surface only a ~1/3 of the dislocation's Burgers vector would contribute as a lower limit to the sketched orientation change of the sample surface. This means that in order to achieve an orientation gradient of 4° over a distance of ~20 μm as in grain 1 (Fig. 3) about ~ 150 to ~ 450 dislocations must be stored. That would translate in an average dislocation distance l of ~ 150 nm to ~ 50 nm, or by using the relationship, l = p1ffiffiρ, a stored dislocation density ρ of ~ 4 ∙ 10 13 m −2 to 5 ∙ 10 14 m −2 is obtained. Using the relationship εpl = N⋅b the amount of dislocations, N, compensating the plastic d strain, εpl, in a grain of size, d, can be estimated. In the present case the width of the stress-temperature curve (Fig. 5) indicates a plastic strain of ~ 0.4%. Assuming again a grain size of ~20 μm and a 1/3 of the Burgers vector contributing to the plastic deformation, ~ 850 mobile dislocations are required to fully compensate the plastic strain. However, a dislocation density cannot be calculated based on that number since many mobile dislocations escape at the surface (and interface [e.g. 18]). To obtain an estimate of the dislocation density compensating the plastic strain one can use the Taylor–Orowan equation, εpl = ρ ⋅ b ⋅ λ, where λ is the mean free path dislocations glide during plastic deformation. Considering again a plastic strain of ~0.4%, a 1/3 of the Burgers vector contributing to the plastic strain compensation and a mean free path distance of ~ 630 nm on the inclined {111} glide plane a dislocation density of ρ of ~ 7 ∙ 10 13 m −2 is calculated. This is a lower bound as other dislocations may obstruct the mean free path dislocations glide. Considering a mean free path value of ~ 85 nm as deduced from a value of ~ 70 for a thermally strained 500 nm thick Cu film on Si nm as found by a transmission electron microscopy study [18] a value of ~5 ∙ 10 14 m −2 is obtained for the 600 nm thick Al film in the present case. This value may be considered as an upper bound. Note that for these calculations it is assumed that plastic deformation is done solely by dislocation glide, which may not be the case as also
Fig. 1. a) SEM image of the 600 nm Al film on Si (100) reveals a smooth surface with no hillocks. b) Inverse pole figure obtained by EBSD scans revealing the typical (111) fiber texture with a maximum out of plane misorientation of ~ 7°.
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W. Heinz, G. Dehm / Surface & Coatings Technology 206 (2011) 1850–1854
Fig. 2. a) Overview of the investigated area and b) the corresponding pole figures after 35 thermal cycles for grains 2–7. The green marker shows the initial orientation before thermal cycling and the red marker shows the orientation after 35 thermal loads.
diffusional processes such as grain boundary diffusion can contribute to strain compensation. These simple dislocation density estimates agree with measured dislocation densities of 1013 m−2 to 1014 m−2 reported in literature by transmission electron microscopy studies for similar film systems [18–20]. The present observations and interpretations also agree with classical dislocation plasticity. It is well known since Schmid and Boas [21] that under uniaxial loading of tensile specimens a change in orientation occurs due to plastic deformation by dislocation glide. In face centered cubic single crystals this behavior leads to a crystal axis rotation toward (112), while for compression a rotation toward (110) is expected [21,22]. Orientation changes during cycling loading are shown in [23]. Now, in the present case thermal cycling leads to
biaxial compressive stresses during heating and biaxial tensile stresses during cooling. This should cause crystal rotations toward the (112) pole and subsequently backwards toward the (110) pole for alternating heating and cooling cycles. Note that a biaxial compressive in-plane film stress corresponds with respect to the orientation changes to a uniaxial tensile stress perpendicular to the film surface. As observed and discussed earlier [12], the stresses evolving in compression are smaller than in tension (Fig. 5), indicating a stronger plastic deformation during the heating cycle compared to the cooling cycle, i.e. a larger orientation change can occur during heating compared to cooling. This finally gives rise to a global orientation change toward (112). The stochastic nature of dislocation plasticity in small dimensions [24,25] and the constraints by neighboring grains
W. Heinz, G. Dehm / Surface & Coatings Technology 206 (2011) 1850–1854
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Fig. 3. Orientation gradients in a grain (grain 1 in Fig. 2) after 25 thermal cycles. a) Initial state with a maximum orientation deviation of ~ 1° within the grain. b) A continuous orientation gradient of ~ 4° evolves during the 25 thermal cycles. Insets reveal the orientation in the inverse pole figures.
leads, however, to quite complex local orientation changes as seen in the inverse pole figures in Fig. 2. The (112) pole is approached by a random walk like behavior. Analyzing the film/substrate interface to search for the stored dislocations is prevented by vanishing strain contrast of the dislocations at the interface between the Al film and the amorphous SiO layer covering the Si substrate. This was interpreted as dislocation core spreading, a diffusional delocalization of the dislocation core possibly by atom migration at the interface [26–29]. The strain contrast of the dislocations incorporated into the interface vanishes especially at elevated temperatures. However, the dislocation core spreading prevents a backward motion of dislocations stored at the interface during the heating cycle in the subsequent cooling cycle. Thus, it can be speculated that new dislocation sources must be activated to compensate the biaxial tensile stress by dislocation
motion during the cooling cycle, which gets increasingly difficult with decreasing temperature. Thus, we conclude that the interplay of dislocation glide and diffusion-induced interfacial dislocation core spreading causes the final orientation changes toward (112) accompanied by surface steps created by each glide dislocation channeling through the film and emerging at the film surface (see Fig. 4). If grain boundary and surface diffusion would cause the orientation change from (111) toward (112) this should also occur for thinner Al films with their smaller grain sizes and shorter diffusion distances. However, films with 400 nm thickness and below did not reveal a change in orientation but maintained their initial (111) fiber texture within the analyzed 10.000 thermal cycles as reported in [12]. Note, that this observation does not exclude that diffusional processes contribute to strain compensation during each thermal cycle in addition to dislocation glide. However, all observations strongly imply that the texture evolution is driven by dislocation glide and diffusioninduced interfacial dislocation core spreading as described above.
5. Conclusion Repeated thermal cycling of a 600 nm thick polycrystalline Al film on a (100) Si substrate reveals orientation changes between subsequent thermal cycles between 25 °C and 450 °C. The basic findings can be explained by classical dislocation plasticity [21]. The results reveal that: • Orientation gradients within grains can be explained by stored dislocations with calculated dislocation densities of 4 ∙ 10 13 cm −2 to 5 ∙ 10 14 cm −2 in agreement with measured dislocation densities in such films. • Reorientation of grains in the Al film toward (112) can be explained by classical slip induced lattice rotation. • Grain–grain interactions and localized plasticity prevent a continuous orientation change toward (112). The (112) pole is approached by a random walk like behavior during thermal cycling.
Acknowledgment Fig. 4. Comparison of (a) free dislocation glide on an inclined (111) plane causing no orientation change and (b) the constraining effect of a substrate, leading to an orientation change for the slipped portion due to the stiff substrate by storing the dislocation at the interface. (c) Orientation changes α caused by a dislocation with Burgers vector b in a material of thickness h.
The authors are grateful to the Max-Planck Institute for Metals Research, Stuttgart, for providing polycrystalline Al films in the thin film deposition group headed by Dr. Gunter Richter.
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Fig. 5. Stress-temperature cycle of a 600 nm thick Al film on Si (100) substrate.
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