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Abnormal grain growth in thin films not caused by decreased energy of their free surface
Materials Letters 65 (2011) 2618–2620
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Materials Letters 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 / m a t l e t
Abnormal grain growth in thin films not caused by decreased energy of their free surface Vladimir Yu. Novikov ⁎ Moscow Institute of Steel and Alloys, Moscow, Russian Federation
a r t i c l e
i n f o
Article history: Received 24 May 2011 Accepted 24 May 2011 Available online 1 June 2011 Keywords: Thin films Microstructure Abnormal grain growth Secondary recrystallization
a b s t r a c t We modeled the grain growth process in thin films on substrate. The only driving force for grain growth was a decrease in the total grain boundary energy; possible difference in the energies of the free surface of neighboring grains was not taken into account. The main features of capillarity-driven microstructure evolution qualitatively agree with those observed experimentally. This leads to the conclusion that abnormal grain growth in thin films can develop without assistance of decreased energy of the free film surface. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The properties and relevance of thin films are controlled, besides their thickness and phase composition, by film microstructure. Often it becomes very non-homogenous (see e.g. [1]) which is deleterious for the film properties. The non-homogeneity mainly results from the development of abnormal grain growth (AG) also known as secondary recrystallization. In this case, the microstructure is formed by columnar grains of diameter slightly larger than the film thickness δ and very big crystallites of size dozen(s) of times larger than δ. The AG evolution itself indicates that normal grain growth is inhibited [2]. Since AG commences at the stage where the mean diameter of columnar grains reaches some limit commensurable with δ [3] and ceases to increase further, it can be thought that the growth process is inhibited by thermal grooves on the film surface [4]. In thin films, some grains are able to overcome the growth inhibition under the influence of the following driving forces: 1) surface energy driving force (a decrease in the energy of the film free surface), 2) capillarity driving force (a reduction in the total grain boundary energy), and 3) strain energy driving force (a decrease in thermal or mismatch stresses). It is commonly believed that in the course of AG in thin films, those grains grow whose energy of the free surface is the lowest [5–7]. The basis for this explanation is given in Ref. [4] according to which boundaries of such grains are able to overcome the retarding force from thermal grooves. One of the main arguments for such an explanation is the observation [6,7] that the AG texture in films corresponds to the position of the low-energy lattice plane in the film free surface. Another
⁎ Treptower Str. 74 d, 22147 Hamburg, Germany. E-mail address: [email protected]. 0167-577X/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.matlet.2011.05.096
one is an increase in the growth rate of abnormal grains with a decrease in the film thickness [3], apparently, because of an increased contribution of the surface energy to the driving force for grain growth. However, there are experimental observations that do not agree with this explanation. For instance, crystallites occurring in the course of AG can have an orientation not corresponding to the minimum surface energy (this can be seen e.g. in Fig. 4 [9]). Besides, such a texture can evolve under the influence of the capillarity driving force in the case that crystallites growing in the course of AG are the largest in the initial microstructure [8]; numerical simulations [10] have proved that this is possible. In these cases the only driving force for AG is a decrease in the total grain boundary energy. At last, grain growth can lead to a decrease in the strain energy, owing to which the fiber texture b111N||ND observed in deposited Cu films changes as a result of AG into b100N||ND [11]. So, irrespective of several contradictory experimental observations (see above), a decrease in the energy of the free surface has remained a predominant explanation of AG in films. As to a reduction in the total grain boundary energy, it has virtually not been taken into account, although this driving force is the main one in any case. Our aim is to fill this gap. The possible effect of the strain energy was not considered. 2. Simulation details We studied the grain growth process in thin films on substrate by means of numerical simulation. The films were supposed to have columnar structure; in all films the initial mean grain diameter D0 was 345 nm. The initial grain size distribution was nearly log-normal and was characterized by the ratio Dmax/D0 = 3.0 where Dmax is the maximum grain diameter. The film thickness δ was varied from 100 to 1000 nm.
V.Y. Novikov / Materials Letters 65 (2011) 2618–2620
2619
In this study we used our statistical model [12,13] that delivers changes in the grain size distribution with time. The growth of all grains was supposed to be inhibited by the drag force ΔFG from thermal grooves. Since the groove formation on the substrate/film surface is not energetically possible, we considered the drag from the grooves on the free film surface only. Owing to this, the magnitude of ΔFG was two times smaller than that proposed in Ref. [4]: ΔFG = γ=6δ
ð1Þ
where γ is the grain boundary energy. The net driving force, ΔFij, for growth of some grain of size Di at the expense of its immediate neighbor of size Dj was described as ΔFij = kγ 1=Dj −1=Di −ΔFG
ð2Þ
where k ≅ 1. The first term in the right-hand part of Eq. (2) describes the capillarity driving force. The grain of size Di can grow if ΔFij N 0. The displacements of grain boundaries Δdij = MΔFij (where M is the grain boundary mobility) were used to find the size increments of growing grains and size decrements of consumed grains. These size alterations, in turn, were employed for deriving the corresponding changes in the grain size distribution under the condition of volume preservation. Magnitudes of γ = 0.5·10 − 4 J cm − 2 and M = 2·10 − 4 cm 4 J − 1 s − 1, taken from Ref. [14] for Al at T = 673 K, were identical for all grain boundaries and independent of time. The average grain diameter D and the maximum grain diameter Dmax were found from the grain size distribution. The character of the growth process was determined from the scatter of grain sizes defined by the ratio Dmax/D. Namely, normal grain growth was assumed to proceed at Dmax/D ≤ 5 and AG at Dmax/D N 5. The time of the AG commencement was defined as the point where Dmax/D becomes larger than 5 and steadily increases further. The maximum grain size reached by this time was taken as the minimum size of abnormal grains. This made it possible to find their number and volume fraction VA. 3. Results and discussion Fig. 1a shows the growth kinetics in films of different thicknesses. It is clearly seen that a decrease in δ leads to the growth retardation, which results from an increase in the groove drag ΔFG. Especially noticeable retardation is observed at δ = 100 and 200 nm, i.e. at D0 higher than the film thickness. In this case the magnitude of D rapidly becomes constant. On the contrary, at D0 smaller than the film thickness (δ = 700 and
Fig. 1. (a) Growth kinetics in films of thickness (solid squares) 100, (open squares) 200, (open triangles) 300, (solid triangles) 700, and (open circles) 1000 nm. (b) The same in co-ordinates D/δ − t.
Fig. 2. Volume fraction of abnormal grains reached by t = 180 s vs. time.
1000 nm), the time dependence of D is close to a parabolic one D = ktn with n ≈ 0.2. As Fig. 1b suggests, in all cases D tends to ~3.5δ, which agrees with 2δ, ~2.5δ and ~6δ found experimentally in thin films of Al [15], Ge [5] and Ni–Fe [16], respectively. Study of grain size distributions shows that the cessation of grain growth in films of δ = 100 and 200 nm is not connected with the absence of grains that could be able to grow. On the contrary, it results from the almost complete disappearance of small grains that must be consumed by growing crystallites. AG was observed in all films investigated, even in those of δ=00 and 200 nm where the growth process apparently comes to a stop. The latter contradicts the simulation data [17], according to which the capillaritydriven grain growth completely ceases under the influence of groove drag. This contradiction can be resolved as follows. At the stage where the mean grain size stops to increase, the total grain number in Ref. [17] was ~103. According to our simulations, the relative number of grains able to grow at the commencement of AG was ~10− 9 and 3·10− 6 in films of thicknesses 100 and 200 nm, respectively. This shows that the size of the grain ensemble studied in Ref. [17] was insufficient for revealing abnormal grain growth. It is worth mentioning that AG in our numerical simulations was incomplete. Fig. 2 shows that the dependence of the volume fraction of abnormal grains VA on the film thickness is described by a peaked curve.
Fig. 3. Dmax/D reached by t = 180 s vs. time.
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V.Y. Novikov / Materials Letters 65 (2011) 2618–2620
This results from a decrease in the drag force δFG with an increase in δ. Namely, a large ΔFG at relatively low δ favors the AG development but, at greaterδ, ΔFG becomes more and more insufficient to retard the growth of the majority of grains. This tendency is also illustrated by the following simulation results: the number of abnormal grains at the start of AG first increases with δ and then drastically decreases after reaching a maximum at δ = 400 nm. The picture of the AG evolution in the course of grain growth in films is supplemented by the data in Fig. 3. First of all, the ratio Dmax/D is noticeably larger than 5, i.e. there evolves a grain size non-homogeneity that exceeds the value characteristic of normal grain growth. As seen in the figure, Dmax/D depends on the film thickness, strongly increasing at low δ. Such behavior of Dmax/D indicates that the growth rate of large crystallites increases with a decrease in δ, which agrees with the experimental data [3]. Moreover, the graph of the dependence Dmax/D on δ qualitatively agrees with the experimental data for Si films [5]. In summary, the capillarity driving force can cause the AG process in thin films on substrate. The simulation results are in a good agreement with almost all available experimental data. It seems rather possible that, in the absence of strain energy, annealing texture in films could also evolve under the influence of the capillarity driving force. Thus, AG in thin films can be a capillarity-driven process. References [1] Dannenberg R, Stach EA, Groza JR, Dresser BJ. In-situ TEM observations of abnormal grain growth, coarsening and substrate de-wetting in nanocrystalline Ag thin films. Thin Solid Films 2000;370:54–62.
[2] Novikov V. Grain Growth and Control of Microstructure and Texture in Polycrystalline Materials. Boca Raton (USA): CRC Press; 1996. [3] Palmer JE, Thompson CV, Smith HI. Grain growth and grain size distributions in thin germanium films. J Appl Phys 1987;62:2492–7. [4] Mullins WW. The effect of thermal grooving on grain boundary motion. Acta Metall 1958;6:414–27. [5] Gangulee A. Structure of electroplated and vapor-deposited copper films. III. Recrystallization and grain growth. J Appl Phys 1974;45:3749–56. [6] Thompson CV, Smith HI. Surface-energy-driven secondary grain growth in ultrathin (b 100 nm) films of silicon. Appl Phys Lett 1984;44:603–5. [7] Thompson CV, Carel R. Grain growth and texture evolution in thin films. Mat Sci Forum 1996;204–206:83–98. [8] Fisher IM, Smith DA. Grain boundary migration and the texture of films. Text Microstruct 1991;13:91–9. [9] Huang M, Wang Y, Chang YA. Grain growth in sputtered nanoscale PdIn thin films. Thin Solid Films 2004;449:113–9. [10] Novikov VY. Simulation of grain growth in thin films with columnar microstructure. Acta Mater 1999;47:4507–14. [11] Park NJ, Field DP, Nowell MM, Besser PR. Effect of film thickness on the evolution of annealing texture in sputtered copper films. J Electronic Mat 2005;34:1500–8. [12] Novikov VY. Computer simulation of normal grain growth. Acta Metall 1978;26: 1739–44. [13] Novikov VY. On abnormal grain growth in nanocrystalline materials induced by small particles. Int J Mat Res 2011;102:446–51. [14] Gottstein G, Shvindlerman LS. Grain Boundary Migration in Metals: Thermodynamics, Kinetics, Applications. Boca Raton (USA): CRC Press; 2010. [15] Barmak K, Kim J, Kim CS, Archibald WE, Rohrer GS, Rollett AD, et al. Scr Mater 2006;54:1059–63. [16] Gangulee A, Krongelb AS. Grain growth in Fe–Ni thin films. Thin Solid Films 1974;24: 273–7. [17] Frost HJ, Thompson CV, Walton DT. Simulation of thin film grain structures — I. Grain growth stagnation. Acta Metall Mater 1990;38:1445–62.
Contents lists available at ScienceDirect
Materials Letters 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 / m a t l e t
Abnormal grain growth in thin films not caused by decreased energy of their free surface Vladimir Yu. Novikov ⁎ Moscow Institute of Steel and Alloys, Moscow, Russian Federation
a r t i c l e
i n f o
Article history: Received 24 May 2011 Accepted 24 May 2011 Available online 1 June 2011 Keywords: Thin films Microstructure Abnormal grain growth Secondary recrystallization
a b s t r a c t We modeled the grain growth process in thin films on substrate. The only driving force for grain growth was a decrease in the total grain boundary energy; possible difference in the energies of the free surface of neighboring grains was not taken into account. The main features of capillarity-driven microstructure evolution qualitatively agree with those observed experimentally. This leads to the conclusion that abnormal grain growth in thin films can develop without assistance of decreased energy of the free film surface. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The properties and relevance of thin films are controlled, besides their thickness and phase composition, by film microstructure. Often it becomes very non-homogenous (see e.g. [1]) which is deleterious for the film properties. The non-homogeneity mainly results from the development of abnormal grain growth (AG) also known as secondary recrystallization. In this case, the microstructure is formed by columnar grains of diameter slightly larger than the film thickness δ and very big crystallites of size dozen(s) of times larger than δ. The AG evolution itself indicates that normal grain growth is inhibited [2]. Since AG commences at the stage where the mean diameter of columnar grains reaches some limit commensurable with δ [3] and ceases to increase further, it can be thought that the growth process is inhibited by thermal grooves on the film surface [4]. In thin films, some grains are able to overcome the growth inhibition under the influence of the following driving forces: 1) surface energy driving force (a decrease in the energy of the film free surface), 2) capillarity driving force (a reduction in the total grain boundary energy), and 3) strain energy driving force (a decrease in thermal or mismatch stresses). It is commonly believed that in the course of AG in thin films, those grains grow whose energy of the free surface is the lowest [5–7]. The basis for this explanation is given in Ref. [4] according to which boundaries of such grains are able to overcome the retarding force from thermal grooves. One of the main arguments for such an explanation is the observation [6,7] that the AG texture in films corresponds to the position of the low-energy lattice plane in the film free surface. Another
⁎ Treptower Str. 74 d, 22147 Hamburg, Germany. E-mail address: [email protected]. 0167-577X/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.matlet.2011.05.096
one is an increase in the growth rate of abnormal grains with a decrease in the film thickness [3], apparently, because of an increased contribution of the surface energy to the driving force for grain growth. However, there are experimental observations that do not agree with this explanation. For instance, crystallites occurring in the course of AG can have an orientation not corresponding to the minimum surface energy (this can be seen e.g. in Fig. 4 [9]). Besides, such a texture can evolve under the influence of the capillarity driving force in the case that crystallites growing in the course of AG are the largest in the initial microstructure [8]; numerical simulations [10] have proved that this is possible. In these cases the only driving force for AG is a decrease in the total grain boundary energy. At last, grain growth can lead to a decrease in the strain energy, owing to which the fiber texture b111N||ND observed in deposited Cu films changes as a result of AG into b100N||ND [11]. So, irrespective of several contradictory experimental observations (see above), a decrease in the energy of the free surface has remained a predominant explanation of AG in films. As to a reduction in the total grain boundary energy, it has virtually not been taken into account, although this driving force is the main one in any case. Our aim is to fill this gap. The possible effect of the strain energy was not considered. 2. Simulation details We studied the grain growth process in thin films on substrate by means of numerical simulation. The films were supposed to have columnar structure; in all films the initial mean grain diameter D0 was 345 nm. The initial grain size distribution was nearly log-normal and was characterized by the ratio Dmax/D0 = 3.0 where Dmax is the maximum grain diameter. The film thickness δ was varied from 100 to 1000 nm.
V.Y. Novikov / Materials Letters 65 (2011) 2618–2620
2619
In this study we used our statistical model [12,13] that delivers changes in the grain size distribution with time. The growth of all grains was supposed to be inhibited by the drag force ΔFG from thermal grooves. Since the groove formation on the substrate/film surface is not energetically possible, we considered the drag from the grooves on the free film surface only. Owing to this, the magnitude of ΔFG was two times smaller than that proposed in Ref. [4]: ΔFG = γ=6δ
ð1Þ
where γ is the grain boundary energy. The net driving force, ΔFij, for growth of some grain of size Di at the expense of its immediate neighbor of size Dj was described as ΔFij = kγ 1=Dj −1=Di −ΔFG
ð2Þ
where k ≅ 1. The first term in the right-hand part of Eq. (2) describes the capillarity driving force. The grain of size Di can grow if ΔFij N 0. The displacements of grain boundaries Δdij = MΔFij (where M is the grain boundary mobility) were used to find the size increments of growing grains and size decrements of consumed grains. These size alterations, in turn, were employed for deriving the corresponding changes in the grain size distribution under the condition of volume preservation. Magnitudes of γ = 0.5·10 − 4 J cm − 2 and M = 2·10 − 4 cm 4 J − 1 s − 1, taken from Ref. [14] for Al at T = 673 K, were identical for all grain boundaries and independent of time. The average grain diameter D and the maximum grain diameter Dmax were found from the grain size distribution. The character of the growth process was determined from the scatter of grain sizes defined by the ratio Dmax/D. Namely, normal grain growth was assumed to proceed at Dmax/D ≤ 5 and AG at Dmax/D N 5. The time of the AG commencement was defined as the point where Dmax/D becomes larger than 5 and steadily increases further. The maximum grain size reached by this time was taken as the minimum size of abnormal grains. This made it possible to find their number and volume fraction VA. 3. Results and discussion Fig. 1a shows the growth kinetics in films of different thicknesses. It is clearly seen that a decrease in δ leads to the growth retardation, which results from an increase in the groove drag ΔFG. Especially noticeable retardation is observed at δ = 100 and 200 nm, i.e. at D0 higher than the film thickness. In this case the magnitude of D rapidly becomes constant. On the contrary, at D0 smaller than the film thickness (δ = 700 and
Fig. 1. (a) Growth kinetics in films of thickness (solid squares) 100, (open squares) 200, (open triangles) 300, (solid triangles) 700, and (open circles) 1000 nm. (b) The same in co-ordinates D/δ − t.
Fig. 2. Volume fraction of abnormal grains reached by t = 180 s vs. time.
1000 nm), the time dependence of D is close to a parabolic one D = ktn with n ≈ 0.2. As Fig. 1b suggests, in all cases D tends to ~3.5δ, which agrees with 2δ, ~2.5δ and ~6δ found experimentally in thin films of Al [15], Ge [5] and Ni–Fe [16], respectively. Study of grain size distributions shows that the cessation of grain growth in films of δ = 100 and 200 nm is not connected with the absence of grains that could be able to grow. On the contrary, it results from the almost complete disappearance of small grains that must be consumed by growing crystallites. AG was observed in all films investigated, even in those of δ=00 and 200 nm where the growth process apparently comes to a stop. The latter contradicts the simulation data [17], according to which the capillaritydriven grain growth completely ceases under the influence of groove drag. This contradiction can be resolved as follows. At the stage where the mean grain size stops to increase, the total grain number in Ref. [17] was ~103. According to our simulations, the relative number of grains able to grow at the commencement of AG was ~10− 9 and 3·10− 6 in films of thicknesses 100 and 200 nm, respectively. This shows that the size of the grain ensemble studied in Ref. [17] was insufficient for revealing abnormal grain growth. It is worth mentioning that AG in our numerical simulations was incomplete. Fig. 2 shows that the dependence of the volume fraction of abnormal grains VA on the film thickness is described by a peaked curve.
Fig. 3. Dmax/D reached by t = 180 s vs. time.
2620
V.Y. Novikov / Materials Letters 65 (2011) 2618–2620
This results from a decrease in the drag force δFG with an increase in δ. Namely, a large ΔFG at relatively low δ favors the AG development but, at greaterδ, ΔFG becomes more and more insufficient to retard the growth of the majority of grains. This tendency is also illustrated by the following simulation results: the number of abnormal grains at the start of AG first increases with δ and then drastically decreases after reaching a maximum at δ = 400 nm. The picture of the AG evolution in the course of grain growth in films is supplemented by the data in Fig. 3. First of all, the ratio Dmax/D is noticeably larger than 5, i.e. there evolves a grain size non-homogeneity that exceeds the value characteristic of normal grain growth. As seen in the figure, Dmax/D depends on the film thickness, strongly increasing at low δ. Such behavior of Dmax/D indicates that the growth rate of large crystallites increases with a decrease in δ, which agrees with the experimental data [3]. Moreover, the graph of the dependence Dmax/D on δ qualitatively agrees with the experimental data for Si films [5]. In summary, the capillarity driving force can cause the AG process in thin films on substrate. The simulation results are in a good agreement with almost all available experimental data. It seems rather possible that, in the absence of strain energy, annealing texture in films could also evolve under the influence of the capillarity driving force. Thus, AG in thin films can be a capillarity-driven process. References [1] Dannenberg R, Stach EA, Groza JR, Dresser BJ. In-situ TEM observations of abnormal grain growth, coarsening and substrate de-wetting in nanocrystalline Ag thin films. Thin Solid Films 2000;370:54–62.
[2] Novikov V. Grain Growth and Control of Microstructure and Texture in Polycrystalline Materials. Boca Raton (USA): CRC Press; 1996. [3] Palmer JE, Thompson CV, Smith HI. Grain growth and grain size distributions in thin germanium films. J Appl Phys 1987;62:2492–7. [4] Mullins WW. The effect of thermal grooving on grain boundary motion. Acta Metall 1958;6:414–27. [5] Gangulee A. Structure of electroplated and vapor-deposited copper films. III. Recrystallization and grain growth. J Appl Phys 1974;45:3749–56. [6] Thompson CV, Smith HI. Surface-energy-driven secondary grain growth in ultrathin (b 100 nm) films of silicon. Appl Phys Lett 1984;44:603–5. [7] Thompson CV, Carel R. Grain growth and texture evolution in thin films. Mat Sci Forum 1996;204–206:83–98. [8] Fisher IM, Smith DA. Grain boundary migration and the texture of films. Text Microstruct 1991;13:91–9. [9] Huang M, Wang Y, Chang YA. Grain growth in sputtered nanoscale PdIn thin films. Thin Solid Films 2004;449:113–9. [10] Novikov VY. Simulation of grain growth in thin films with columnar microstructure. Acta Mater 1999;47:4507–14. [11] Park NJ, Field DP, Nowell MM, Besser PR. Effect of film thickness on the evolution of annealing texture in sputtered copper films. J Electronic Mat 2005;34:1500–8. [12] Novikov VY. Computer simulation of normal grain growth. Acta Metall 1978;26: 1739–44. [13] Novikov VY. On abnormal grain growth in nanocrystalline materials induced by small particles. Int J Mat Res 2011;102:446–51. [14] Gottstein G, Shvindlerman LS. Grain Boundary Migration in Metals: Thermodynamics, Kinetics, Applications. Boca Raton (USA): CRC Press; 2010. [15] Barmak K, Kim J, Kim CS, Archibald WE, Rohrer GS, Rollett AD, et al. Scr Mater 2006;54:1059–63. [16] Gangulee A, Krongelb AS. Grain growth in Fe–Ni thin films. Thin Solid Films 1974;24: 273–7. [17] Frost HJ, Thompson CV, Walton DT. Simulation of thin film grain structures — I. Grain growth stagnation. Acta Metall Mater 1990;38:1445–62.