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Electromigration-induced stress interaction between vias and polygranular clusters
Scripta mater. 44 (2001) 2497–2501 www.elsevier.com/locate/scriptamat
ELECTROMIGRATION-INDUCED STRESS INTERACTION BETWEEN VIAS AND POLYGRANULAR CLUSTERS Young-Joon Park1 and Young-Chang Joo2 1
Thin Film Technology Research Center, Korea Institute of Science and Technology, Seoul 130650, Korea 2Seoul National University, School of Materials Science and Engineering, Seoul 151742, Korea (Received March 24, 2000) (Accepted in revised form June 5, 2000) Keywords: Electromigration; Computer simulation; Interconnects; Aluminum
Introduction Electromigration is atomic diffusion driven by a momentum transfer from conducting electrons. With every new generation of integrated circuits, interconnect linewidths have been reduced and the current densities in the interconnects have become higher. This will lead to an increase in the threat to interconnect reliability due to electromigration (1). Electromigration-induced failures occur at the site of flux divergences; i.e. the site where incoming flux is different from outgoing flux. For example, a void is nucleated when incoming flux is smaller than outgoing flux, and a hillock is formed the other way around. As electromigration occurs, compressive or tensile stress evolves along the length of interconnects at the location of material accumulation or depletion due to flux divergences. Electromigration-induced damage (voids or hillocks) occurs when the maximum stress reaches a critical value for void or hillock formation. In order to make highly reliable integrated circuits, understanding of the detailed mechanism is necessary. Considering the technical difficulties in measuring electromigrationinduced stress directly, computer simulation may be an alternative to understanding the inside of interconnects during electromigration conceptually. Many attempts have been made for computer simulation of electromigration, and the electromigration-induced stress as well as its impact on the kinetics of diffusion was reported (2–10). In interconnects, the two most important sites of flux divergences are the via and the (polygranular) cluster. The end of the line connected with the via should have large flux divergence. Because the via is made of tungsten or there is a diffusion barrier between the line and the via, the electromigration flux is discontinuous at the end of the line. Local variations of the grain structures are another important cause for the flux divergences. A grain boundary is a faster diffusion path than the bulk or interfaces. So, if a grain boundary is discontinuous along the line, flux divergence occurs. In near-bamboo lines, which have both connected grain boundary paths (the cluster) and bamboo grains which span the whole line width, flux divergence occurs at the intersection between the bamboo grain and the cluster (2,3,11). Usually, the effect of the via and the cluster have been investigated separately, and there is little study on the interaction of these two important flux divergence sources. If we only consider the diffusivity, the via should evolve the highest stress earliest and have the worst lifetime when the cluster is just under (or above) the via. This is because electromigration diffusion is faster in the cluster than in the bamboo grain. However, there is an important factor in electromigration to consider. That is the 1359-6462/01/$–see front matter. © 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S1359-6462(01)00674-1
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Figure 1. The schematic line structure which was used in this simulation. The total length of the line was 100m and the cluster length, l, was 20m. The distance of the cluster from the via, d, varied from 0 to 70 m.
stress field effect. The stress field inhibits or helps electromigration diffusion. For example, the stress gradient formed inside the cluster retards electromigration. This stress gradient reduces electromigration and when the two forces balance, no further electromigration occurs (12). This can explain the critical length effect of polycystalline segments for failures. However, if the stress gradient is opposite to that in the cluster, it should assist electromigration. This occurs in the bamboo grain between two closely-located cluster pairs or in the bamboo grain outside the cluster (3). The stress field effect should be considered in stress evolution at the end of the line (i.e., at the via). If the via is not directly over (or under) the cluster and is located over a bamboo grain, the stress field developed at the cluster may affect the stress evolution at the line end through the bamboo grain. When the via and the cluster are located close to each other, this interaction occurs within reasonable time, and it assists the pile-up of electromigration-induced stress at the end of the line. In this study we simulate the stress interaction between the via and the cluster by changing the distance between them to find the worst case (the fastest stress pile-up). Simulation Conditions Using 1-dimensional computer simulation, the evolution of mechanical stress resulting from electromigration in a near-bamboo A1 interconnects was investigated. The simulation was based on the model of Korhonen et al. (13). The stress was assumed hydrostatic and uniform over a finite element. A positive sign represents a tensile component. Figure 1 shows the schematic line structure which was used in this simulation. The total length of the line was 100m and the cluster length, l, was 20m. The distance of the cluster from the via, d, varied from 0 to 70m. Current density was 1 ⫻ 106 A/cm2 and temperature was 473K. The atomic diffusivity in a polygranular cluster was assumed 200 times larger than that in bamboo grains (4,5). Details of the simulation conditions are described elsewhere (4,5). Results and Discussion Figure 2 shows the stress profile along a 100-m-long line with a 20-m-long cluster located 10m apart from the cathode end of the line, for four different simulation times. The stress evolution with simulation time at the cathode end of the line, the cathode end of the cluster, and the anode end of the cluster is shown in Fig. 3. After 5556 hours, the stress is independent of the microstructure (the location of the cluster) and does not change further (i.e., it reaches a steady state). At the beginning of the test,
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Figure 2. The stress profile along a 100-m-long line with a 20-m-long cluster located 10m apart from the cathode end of the line, for four different simulation times, 3, 28, 278, and 5556 hours. Current density is 1 ⫻ 106 A/cm2 and temperature is 473K.
the fastest stress pile-up is located at the cathode end of the cluster not at the cathode end of the line (the via end) (Fig. 2 and Fig. 3). This is because the flux divergence is bigger at the end of the cluster than at the end of the line. The flux divergences at the cathode end of the line and the cathode end of the cluster are ⌬Jvia ⫽ Jbulk ⫺ 0 and ⌬Jcluster ⫽ Jgb ⫺ Jbulk, respectively. Therefore, if Jgb is more than 2 times larger than Jbulk, the flux divergence at the cluster end is larger than that at the line end. In most cases, the grain boundary diffusivity is more than an order of magnitude larger than that of bulk or interface diffusion. The stress at the cathode end of the cluster evolves to tensile stress (Fig. 2 and Fig. 3) as the test goes on. After a certain time, the stress at the cathode end of the line starts to increase at a faster rate than before, while that at cluster ends reaches the local plateau (Fig. 3). The plateau stress at the cluster end is a function of the cluster length. After the cluster reaches a local steady state, the stress at the cathode end of the line starts to increase. Eventually, the stress at the cathode end of the line exceeds that at the cathode end of the cluster around 200MPa. The fast increase in the tensile stress at the line end occurs when the stress field from the cluster starts to interact with the line end. While the initial stress gradient
Figure 3. The stress evolution with simulation time at the cathode end of the line, the cathode end of the cluster, and the anode end of the cluster. Current density is 1 ⫻ 106 A/cm2 and temperature is 473K. The cluster is located 10m apart from the cathode end.
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Figure 4. The stress evolution at the cathode end of the line for different locations of the clusters with respect to via, (a) 0, (b) 10, (c) 20, and (d) 70m. Current density is 1 ⫻ 106A/cm2 and temperature is 473K.
near the cathode end of the line is against electromigration, the stress gradient outside the cluster acts to help electromigration. Depending on the critical stress, the failure site and time are determined. For example, if the critical stress is below 200MPa, failure occurs at the cluster under these conditions. If it exceeds 200MPa, the failure location should be at the end of line. It should be also noted that the critical stress of failure may be different at failure sites. The via has different interface property from that of the grain boundary. So does the critical stress. Beyond a certain stress (for example, about 200MPa in these simulation conditions), the via end always has the largest maximum tensile stress after certain time in this geometry. Figure 4 shows the stress evolution at the cathode end of the line for different locations of the clusters with respect to the via. Curve (a) shows the stress profile when the cluster is located just below the via and curves (b) to (d) show the stress profile when the cluster is located 10, 20, and 70 m from the via, respectively. The initial tensile stress development is fastest when the cluster is just below the via. This is because the responsible diffusivity in this case is grain boundary diffusivity. Soon, it reaches a steady state, when stress distribution inside the cluster works against the electromigration flow. It starts to increase again, after the entire line sees the stress distribution through bamboo diffusion. When the cluster is apart from the via as in (b)–(d), the initial stress increase is slow, because the diffusion occurs slowly in bamboo grains. During this period, stress at the end of the cluster evolves rapidly as shown in Fig. 3. The stress pile-up at the cathode end of the cluster will help electromigration in the bamboo region. When the via end feels this stress field, the growth of tensile stress is very rapid. Later on, the stress may grow larger than when the cluster is just below the via. This result indicates that if critical stress is above a certain value (for example, about 250MPa when a cluster is 10m apart from the via under these conditions), failure occurs faster when the cluster is separated from the via. The conventional understanding is that early failure occurs when a cluster is located just below the via. This observation is contrary to that understanding. As the distance between the via and the cluster becomes larger, the incubation time increases. Accordingly the cross-over stress is also increasing. Conclusions The stress field assisting the electromigration flux can be created when the cluster is apart from the via, through the stress interaction between the via and the cluster. In that case, despite slower diffusion
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kinetics in bamboo grains, the electromigration flux divergences at the via end will be larger than when the cluster is just below the via. This means that the line may fail faster when the via is not over the cluster than when the via is over the cluster. The incubation time before the interaction between the via and the cluster strongly depends on the distance between them. Thus the distribution of distances of clusters from the via may cause scattered time to failures at via ends. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
J. R. Lloyd, J. Phys. D Appl. Phys. 32, R109 (1999). D. Brown, J. E. Sanchez, M. A. Korhonen, and C. Y. Li, Appl. Phys. Lett. 67, 439 (1995). B. D. Knowlton, J. J. Clement, and C. V. Thompson, J. Appl. Phys. 81, 6073 (1997). Y. J. Park and C. V. Thompson, J. Appl. Phys. 82, 4277 (1997). Y. J. Park, V. K. Andleigh, and C. V. Thompson, J. Appl. Phys. 85, 3546 (1999). V. K. Andleigh, V. T. Srikar, Y. J. Park, and C. V. Thompson, J. Appl. Phys. 86, 6737 (1999). B. D. Knowlton and C. V. Thompson, J. Mater. Res. 13, 1164 (1998). Q. F. Duan and Y. L. Shen, J. Appl. Phys. 87, 4039 (2000). Y. K. Liu and R. J. Diefendorf, Appl. Phys. Lett. 71, 3171 (1997). Y. K. Liu, C. L. Cox, and R. J. Diefendorf, J. Appl. Phys. 83, 3600 (1998). E. Kinsbron, Appl. Phys. Lett. 36, 968 (1980). I. A. Blech, J. Appl. Phys. 47, 1203 (1976). M. A. Korhonen, P. Børgesen, K. A. Tu, and C. Y. Li, J. Appl. Phys. 73, 3790 (1993).
ELECTROMIGRATION-INDUCED STRESS INTERACTION BETWEEN VIAS AND POLYGRANULAR CLUSTERS Young-Joon Park1 and Young-Chang Joo2 1
Thin Film Technology Research Center, Korea Institute of Science and Technology, Seoul 130650, Korea 2Seoul National University, School of Materials Science and Engineering, Seoul 151742, Korea (Received March 24, 2000) (Accepted in revised form June 5, 2000) Keywords: Electromigration; Computer simulation; Interconnects; Aluminum
Introduction Electromigration is atomic diffusion driven by a momentum transfer from conducting electrons. With every new generation of integrated circuits, interconnect linewidths have been reduced and the current densities in the interconnects have become higher. This will lead to an increase in the threat to interconnect reliability due to electromigration (1). Electromigration-induced failures occur at the site of flux divergences; i.e. the site where incoming flux is different from outgoing flux. For example, a void is nucleated when incoming flux is smaller than outgoing flux, and a hillock is formed the other way around. As electromigration occurs, compressive or tensile stress evolves along the length of interconnects at the location of material accumulation or depletion due to flux divergences. Electromigration-induced damage (voids or hillocks) occurs when the maximum stress reaches a critical value for void or hillock formation. In order to make highly reliable integrated circuits, understanding of the detailed mechanism is necessary. Considering the technical difficulties in measuring electromigrationinduced stress directly, computer simulation may be an alternative to understanding the inside of interconnects during electromigration conceptually. Many attempts have been made for computer simulation of electromigration, and the electromigration-induced stress as well as its impact on the kinetics of diffusion was reported (2–10). In interconnects, the two most important sites of flux divergences are the via and the (polygranular) cluster. The end of the line connected with the via should have large flux divergence. Because the via is made of tungsten or there is a diffusion barrier between the line and the via, the electromigration flux is discontinuous at the end of the line. Local variations of the grain structures are another important cause for the flux divergences. A grain boundary is a faster diffusion path than the bulk or interfaces. So, if a grain boundary is discontinuous along the line, flux divergence occurs. In near-bamboo lines, which have both connected grain boundary paths (the cluster) and bamboo grains which span the whole line width, flux divergence occurs at the intersection between the bamboo grain and the cluster (2,3,11). Usually, the effect of the via and the cluster have been investigated separately, and there is little study on the interaction of these two important flux divergence sources. If we only consider the diffusivity, the via should evolve the highest stress earliest and have the worst lifetime when the cluster is just under (or above) the via. This is because electromigration diffusion is faster in the cluster than in the bamboo grain. However, there is an important factor in electromigration to consider. That is the 1359-6462/01/$–see front matter. © 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S1359-6462(01)00674-1
2498
ELECTROMIGRATION-INDUCED STRESS INTERACTION
Vol. 44, No. 10
Figure 1. The schematic line structure which was used in this simulation. The total length of the line was 100m and the cluster length, l, was 20m. The distance of the cluster from the via, d, varied from 0 to 70 m.
stress field effect. The stress field inhibits or helps electromigration diffusion. For example, the stress gradient formed inside the cluster retards electromigration. This stress gradient reduces electromigration and when the two forces balance, no further electromigration occurs (12). This can explain the critical length effect of polycystalline segments for failures. However, if the stress gradient is opposite to that in the cluster, it should assist electromigration. This occurs in the bamboo grain between two closely-located cluster pairs or in the bamboo grain outside the cluster (3). The stress field effect should be considered in stress evolution at the end of the line (i.e., at the via). If the via is not directly over (or under) the cluster and is located over a bamboo grain, the stress field developed at the cluster may affect the stress evolution at the line end through the bamboo grain. When the via and the cluster are located close to each other, this interaction occurs within reasonable time, and it assists the pile-up of electromigration-induced stress at the end of the line. In this study we simulate the stress interaction between the via and the cluster by changing the distance between them to find the worst case (the fastest stress pile-up). Simulation Conditions Using 1-dimensional computer simulation, the evolution of mechanical stress resulting from electromigration in a near-bamboo A1 interconnects was investigated. The simulation was based on the model of Korhonen et al. (13). The stress was assumed hydrostatic and uniform over a finite element. A positive sign represents a tensile component. Figure 1 shows the schematic line structure which was used in this simulation. The total length of the line was 100m and the cluster length, l, was 20m. The distance of the cluster from the via, d, varied from 0 to 70m. Current density was 1 ⫻ 106 A/cm2 and temperature was 473K. The atomic diffusivity in a polygranular cluster was assumed 200 times larger than that in bamboo grains (4,5). Details of the simulation conditions are described elsewhere (4,5). Results and Discussion Figure 2 shows the stress profile along a 100-m-long line with a 20-m-long cluster located 10m apart from the cathode end of the line, for four different simulation times. The stress evolution with simulation time at the cathode end of the line, the cathode end of the cluster, and the anode end of the cluster is shown in Fig. 3. After 5556 hours, the stress is independent of the microstructure (the location of the cluster) and does not change further (i.e., it reaches a steady state). At the beginning of the test,
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Figure 2. The stress profile along a 100-m-long line with a 20-m-long cluster located 10m apart from the cathode end of the line, for four different simulation times, 3, 28, 278, and 5556 hours. Current density is 1 ⫻ 106 A/cm2 and temperature is 473K.
the fastest stress pile-up is located at the cathode end of the cluster not at the cathode end of the line (the via end) (Fig. 2 and Fig. 3). This is because the flux divergence is bigger at the end of the cluster than at the end of the line. The flux divergences at the cathode end of the line and the cathode end of the cluster are ⌬Jvia ⫽ Jbulk ⫺ 0 and ⌬Jcluster ⫽ Jgb ⫺ Jbulk, respectively. Therefore, if Jgb is more than 2 times larger than Jbulk, the flux divergence at the cluster end is larger than that at the line end. In most cases, the grain boundary diffusivity is more than an order of magnitude larger than that of bulk or interface diffusion. The stress at the cathode end of the cluster evolves to tensile stress (Fig. 2 and Fig. 3) as the test goes on. After a certain time, the stress at the cathode end of the line starts to increase at a faster rate than before, while that at cluster ends reaches the local plateau (Fig. 3). The plateau stress at the cluster end is a function of the cluster length. After the cluster reaches a local steady state, the stress at the cathode end of the line starts to increase. Eventually, the stress at the cathode end of the line exceeds that at the cathode end of the cluster around 200MPa. The fast increase in the tensile stress at the line end occurs when the stress field from the cluster starts to interact with the line end. While the initial stress gradient
Figure 3. The stress evolution with simulation time at the cathode end of the line, the cathode end of the cluster, and the anode end of the cluster. Current density is 1 ⫻ 106 A/cm2 and temperature is 473K. The cluster is located 10m apart from the cathode end.
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Figure 4. The stress evolution at the cathode end of the line for different locations of the clusters with respect to via, (a) 0, (b) 10, (c) 20, and (d) 70m. Current density is 1 ⫻ 106A/cm2 and temperature is 473K.
near the cathode end of the line is against electromigration, the stress gradient outside the cluster acts to help electromigration. Depending on the critical stress, the failure site and time are determined. For example, if the critical stress is below 200MPa, failure occurs at the cluster under these conditions. If it exceeds 200MPa, the failure location should be at the end of line. It should be also noted that the critical stress of failure may be different at failure sites. The via has different interface property from that of the grain boundary. So does the critical stress. Beyond a certain stress (for example, about 200MPa in these simulation conditions), the via end always has the largest maximum tensile stress after certain time in this geometry. Figure 4 shows the stress evolution at the cathode end of the line for different locations of the clusters with respect to the via. Curve (a) shows the stress profile when the cluster is located just below the via and curves (b) to (d) show the stress profile when the cluster is located 10, 20, and 70 m from the via, respectively. The initial tensile stress development is fastest when the cluster is just below the via. This is because the responsible diffusivity in this case is grain boundary diffusivity. Soon, it reaches a steady state, when stress distribution inside the cluster works against the electromigration flow. It starts to increase again, after the entire line sees the stress distribution through bamboo diffusion. When the cluster is apart from the via as in (b)–(d), the initial stress increase is slow, because the diffusion occurs slowly in bamboo grains. During this period, stress at the end of the cluster evolves rapidly as shown in Fig. 3. The stress pile-up at the cathode end of the cluster will help electromigration in the bamboo region. When the via end feels this stress field, the growth of tensile stress is very rapid. Later on, the stress may grow larger than when the cluster is just below the via. This result indicates that if critical stress is above a certain value (for example, about 250MPa when a cluster is 10m apart from the via under these conditions), failure occurs faster when the cluster is separated from the via. The conventional understanding is that early failure occurs when a cluster is located just below the via. This observation is contrary to that understanding. As the distance between the via and the cluster becomes larger, the incubation time increases. Accordingly the cross-over stress is also increasing. Conclusions The stress field assisting the electromigration flux can be created when the cluster is apart from the via, through the stress interaction between the via and the cluster. In that case, despite slower diffusion
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kinetics in bamboo grains, the electromigration flux divergences at the via end will be larger than when the cluster is just below the via. This means that the line may fail faster when the via is not over the cluster than when the via is over the cluster. The incubation time before the interaction between the via and the cluster strongly depends on the distance between them. Thus the distribution of distances of clusters from the via may cause scattered time to failures at via ends. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
J. R. Lloyd, J. Phys. D Appl. Phys. 32, R109 (1999). D. Brown, J. E. Sanchez, M. A. Korhonen, and C. Y. Li, Appl. Phys. Lett. 67, 439 (1995). B. D. Knowlton, J. J. Clement, and C. V. Thompson, J. Appl. Phys. 81, 6073 (1997). Y. J. Park and C. V. Thompson, J. Appl. Phys. 82, 4277 (1997). Y. J. Park, V. K. Andleigh, and C. V. Thompson, J. Appl. Phys. 85, 3546 (1999). V. K. Andleigh, V. T. Srikar, Y. J. Park, and C. V. Thompson, J. Appl. Phys. 86, 6737 (1999). B. D. Knowlton and C. V. Thompson, J. Mater. Res. 13, 1164 (1998). Q. F. Duan and Y. L. Shen, J. Appl. Phys. 87, 4039 (2000). Y. K. Liu and R. J. Diefendorf, Appl. Phys. Lett. 71, 3171 (1997). Y. K. Liu, C. L. Cox, and R. J. Diefendorf, J. Appl. Phys. 83, 3600 (1998). E. Kinsbron, Appl. Phys. Lett. 36, 968 (1980). I. A. Blech, J. Appl. Phys. 47, 1203 (1976). M. A. Korhonen, P. Børgesen, K. A. Tu, and C. Y. Li, J. Appl. Phys. 73, 3790 (1993).