Interaction of a void and a grain boundary under a high electric current stress employing three-dimensional molecular dynamics simulation

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applied surface science ELSEVIER

Applied Surface Science 91 (1995) 220-226

Interaction of a void and a grain boundary under a high electric current stress employing three-dimensional molecular dynamics simulation Shoso Shingubara *, Isao Utsunomiya, Takayuki Takahagi Department of Electrical Engineering, Hiroshima University, Kagamiyama 1-4-1, Higashi-Hiroshima 724, Japan Received 19 March 1995; accepted for publication 2 May 1995

Abstract

Molecular dynamics simulation of the behavior of a void in an A1 interconnect with a bamboo grain boundary under a high DC current stress has been accomplished. It is shown that when the current density is higher than some threshold value, a void can move across the grain boundary transversely without being trapped in it, and a disordered region is formed between a void and a grain boundary after the transverse process. Annihilation and reformation of the void is also simulated when the void comes close to the grain boundary, which was experimentally observed before. It should be noted that a backflow of a void is simulated after the current is turned-off at this situation. Analysis using local stress distribution reveals that a large compressive stress is built up near the grain boundary, and an enormous stress gradient is formed between the grain boundary and the void., and it is strongly suggested that this stress gradient is the driving force of the backflow of the void. The present computational work strongly suggests an existence of the backflow of a void, which has not yet been observed experimentally.

1. I n t r o d u c t i o n

Open circuit failures due to electromigration have been serious reliability problems in submicron A1based interconnections. Alloying with Cu, Sc, etc. [1,2], multilayering with refractory metals [3], and control o f polycrystalline grain structures [4] are proposed for improving the interconnection lifetime against electromigration. However, it is very difficult to obtain guiding principles, since the mechanisms o f

* Corresponding author. Tel.: + 81 824 24 7645; Fax: + 81 824 22 7195; E-marl: [email protected].

the failures have been little understood, owing to complexity arising from the polycrystalline nature. For an understanding of the electromigration-induced failure mechanisms, the most standard way is to investigate nucleation and growth of a void, and there have been numerous works for this purpose [5]. However, there are few models that treat the void movement process, which was recently found by in-situ S E M observation [6,7]. Molecular dynamics simulation is capable to treat dynamical behavior o f a void [8,9], since it can directly calculate migration o f atoms. It is well known that most o f the grain structures o f the submicron A1 interconnections are bamboo-like

0169-4332/95/$09.50 © 1995 Elsevier Science B.V. All fights reserved SSDI 0169-4332(95)00122-0

S. Shingubara et aL /Applied Surface Science 91 (1995) 220-226 fixed boundary

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[10], and there is a fundamental question of how a void interacts with a bamboo grain boundary. We have investigated an interaction of a void and a grain boundary under a high current stress by the molecular dynamic simulation using the empirical two body potential and Huntington-Grone ballistic model [11] for electron wind force. 1.1. Computational method A schematic diagram of the cell which is used for the present computational simulation is shown in Fig. 1. There are two A1 grains of the same size

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which face each other by a (111) tilt grain boundary. The number of the coincident site lattice ~ is 7, and the tilt angle is 38.21 °. There are 6 atomic layers in the z-direction, and (111) is taken as the x - y plane. There are periodic boundaries at the z- and x-directions, and the fixed boundaries at the y-direction. The grain boundary is perpendicular to the x-direction, and the periodic boundary at y-direction also constitutes the same grain boundary structure of (111), ~ ; = 7. Thus, this model well represents a typical bamboo-like interconnection. The number of free atoms is 1302, and the number of atoms which constitute the fixed boundaries is 584. Aluminum atoms interact with each other by the empirical Morse potentials [12], and the cut-off length r 0 of atomic interactions is 2.5d 0, where d o is the nearest-neighbor atomic distance. The semi-classical ballistic model of Huntington and Grone [11] of the electron wind force is used. Effective valence number Z* is chosen such that Z* = Z(1 - K p ) where K is the empirically obtained value of 45 [13], Z is 1, and p is the electrical resistivity of A1. Temperature is fixed constant during one run of the computer calculation. The temperature used for the present simulation is 700 K, the time step of the one iteration of simulation is 2 fs, and an equidirectional strain of 2% tensile is introduced by the fixed boundaries. Fluctuations in the current density distribution are ignored for simplicity. A very high current density stress of the order of 101° A / c m 2 is used for simula-

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222

S. Shingubara et al. /Applied Surface Science 91 (1995) 220-226

tion of electromigration. In actual systems, A1 interconnects melt and evaporate rapidly in such high current stresses; however, the Joule heating effect is completely suppressed by keeping temperature constant in the present molecular dynamics simulation. These conditions assure stability of the void and are adequate to realize void movement phenomena within a realistic computational time of a few weeks by DEC a-AXP workstation [8,9]. A void is given by the initial condition at the center of the right grain as shown in Fig. 1. The void penetrates to the z-direction since this model has only 6 atomic layers in the z-direction, and this situation is preserved after runs of computation. The size of a void is carefully chosen so that a void is not influenced by the fixed boundaries and kept stable, since it breaks up into vacancies if it is too small. When there is no current stress, a void is stable and never moves when it is distant from the grain boundary. On the other hand, a void moves into the grain boundary and stabilizes when the distance between the void and the grain boundary is smaller than the critical value of about 3 r 0.

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At first, the configuration of the initial atoms at the grain boundary is investigated. Fig. 2 shows three types of the initial atom configurations. The initially given void is stable for type A and B, but it is unstable for type C. The grain boundary energy of type A is larger than that of type B; however, a time needed for the relaxation of the cell is shorter for the case of type A. Generally, a void is more stable when a grain boundary energy is larger. From these reasons, we adopted type A for the initial grain boundary atoms configuration. Then, the behavior of a void under a high current density of J = 4 X 101° A / c m 2 is investigated, at which a void movement toward the cathode was clearly simulated for the case with no grain boundary [9]. Fig. 3 shows the behavior of a void at different time steps at 700 K, and J = 4 × 10 l° A / c m 2. The void gradually moved toward the cathode direction (Fig. 3a; 240 ps), it suddenly annihilated (Fig. 3b), shortly after the void was reformed at the grain boundary (Fig. 3c; 300 ps), and it gradually moved

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toward the cathode direction (Fig. 3d; 1000 ps). Fig. 4 shows the position of the void center as a function of time. It is clearly shown that the drift velocity of the void is almost a constant value of 2.4 m / s , while the movement of the void center is very fast when it was annihilated as shown by the dotted line. The void was broken up into the cluster of vacancies, and then the vacancies gathered together to form a void again at the grain boundary, and a large diffusion flux took place accompanied by the large number of vacancies. Similar phenomena have been experimentally observed by in-situ SEM observations, which were accompanied with a large resistance change [6]. A potential energy per atom is shown as a func-

S. Shingubara et al. // Applied Surface Science 91 (1995) 220-226

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fion of time in Fig. 5. Sudden increase and decrease of the potential energy were observed when the void was annihilated, and a gradual increase was observed after the void moved further from the grain boundary. This corresponds to the formation of the disordered region between the void and the grain boundary. Fig. 6 shows trajectories of each atom between 940 and 960 ps, and active diffusion in the disordered region is clearly observed. When the current density was 2 × 1 0 1 ° A / c m 2, a void was stabilized at the grain boundary and it never went away from the grain boundary transversely. It should be noted that the backflow of the void is simulated after turning off the current at 1000 ps. After turning off the current, a void slightly moved towards the anode, then it disappeared at 1140 ps, Temperature : 700K J : 4.32 x 10]° A/cm2 Strain : 2% Tensile -0.72 . . . . Void

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and it was formed again at the grain boundary and stayed there, as shown in Fig. 4. Fig. 7 shows the atom configuration at several time steps after stopping the current. Atoms which have a number of nearest-neighbor atoms of less than 10 are designated as dark circles, and other atoms which have more nearest-neighbor atoms are designated as open circles. The periphery of the void, the grain boundary, and the vacancies in a lattice are clearly depicted by the dark atoms. The void was situated in the middle of the left crystal, and there were several vacancies between the void and the grain boundary (Fig. 7a) when it was just before turning off the current. There was a little change in the atom configuration when 2 ps passed after turning off the current (Fig. 7b), and soon after, the void disappeared when 160 ps passed and a lot of vacancies were formed (Fig. 7c). This cluster of vacancies backflowed to the anode, and reached the grain boundary. Then, the void was formed again at the grain boundary when 240 ps passed (Fig. 7d), and the backflow of the void actually occurred. In order to analyze the mechanism of the backflow of the void, we have investigated the distribution of local stresses at each time step. The local stress Xi of the ith atom is calculated as follows

[14]. Xi = (1/AtVi) f ( ~ F u r , 2 ) dt. (1) FU and rij is a force and a distance between two adjacent atoms, respectively. The sum is taken over

S. Shingubara et al. /Applied Surface Science 91 (1995) 220-226

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S. Shingubara et al. / Applied Surface Science 91 (1995) 220-226

225

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S. Shingubara et al. /Applied Surface Science 91 (1995) 220-226

butions at each time step which corresponds to Fig. 7. It should be noted that there is a large stress gradient between the grain boundary and the void just before turning off the current (Fig. 8a). A large compressive stress is built up near the grain boundary. This is presumably because the electromigration flux of atoms from the void area to the grain boundary is so large that an accumulation of atoms occurs near the grain boundary. When the current was turned off, this large compressive stress near the grain boundary soon relaxed (Fig. 8b), and a tensile stress region developed at the cathode site of the grain boundary (Fig. 8c). This is due to the annihilation of the void, which produced a large number of vacancies. When the void is formed again at the grain boundary (Fig. 8d), this tensile stress region disappeared, and the stress distribution became flattened. The present results strongly suggest that the stress gradient which was built up between the void and the grain boundary due to electromigration is a driving force of the backflow of the void after turning off the current. The force caused by this stress gradient shown in Fig. 8a is about 1.8 × 10 - 9 N / a t o m . This value is almost the same as the thermal fluctuation force of 2.2 × 10 - 9 N / a t o m at 700 K, and is much larger than the electron find force of 1.4 × 10 - t l N / a t o m . Thus, it is reasonable that the backflow of the void is faster than the drift velocity of the void due to electromigration. Backflow of a void has not been reported yet; however, the backflow of the AI stripe has been reported by Blech [15]. Thus, the present work strongly suggests the existence of the backflow of a void.

3. Conclusions

The present molecular dynamics simulation of electromigration under DC current stress shows the interesting interactions between the bamboo grain boundary and the void. Void annihilation and subsequent formation are caused by the effect of the grain boundary, and these may qualitatively explain the experimentally observed similar phenomena concerning the several hundred nanometer size void. Analysis using local stress distribution reveals that an enormous stress gradient between the grain boundary

and the void is formed when the void goes across the grain boundary, and it is strongly suggested that this stress gradient is the driving force of the backflow of the void. It should be noted that the stress distribution of nanometer resolution can only be obtained by the molecular dynamics simulation, and never can be obtained experimentally, even if one uses a high resolution transmission electron microscopy or X-ray diffractometer. Although the present simulation assumes an unusually high current density and is based on very simple empirical formulations of electromigration, the simulated results are well consistent with the experiments, and further they make predictions of void backflow phenomena. Thus, the molecular dynamics simulation is a powerful method for the analysis of electromigration related phenomena, and also an extension to a stress-induced migration would be investigated in the near future.

References [1] I. Ames, F.M. d'Heurle and R. Horstmann, IBM J. Res. Dev. 14 (1970) 461. [2] S. Ogawa and H. Nishimura, Tech. Dig. IEEE IEDM (IEEE, New York, 1991) 277. [3] H.H. Hoang, in: Proc. 26th Int. Reliability Physics Symp. (IEEE, New York, 1988) p. 173. [4] M. Hasunuma, H. Kaneko, A. Sawabe, T. Kawanoue, Y. Kohanawa, S. Komatsu and M. Miyanchi, Tech. Dig. IEEE IEDM (IEEE, New York, 1989) 677. [5] M.J. Attardo, R. Rutledge and R.C. Jack, J. Appl. Phys. 42 (1971) 4343. [6] S. Shingubara, M. Saitoh and H. Kaneko, J. Appl. Phys. 69 (1991) 207. [7] S. Shingubara, Y. Nakasaki and H. Kaneko, Extended Abstracts 22nd Conf. on Solid State Devices and Materials (1990), Business Center for Academic Society of Japan, p. 251. [8] S. Shingubara, T. Fujii and Y. Horiike, Extended Abstracts 22nd Conf. on Solid State Devices and Materials (1993), Business Center for Academic Society of Japan, p. 186. [9] S. Shingubara, I. Utsunomiya and Y. Horiike, in: Proc. VLSI Multilevel Interconnection Conf. (1994) p. 518. [10] S. Valdya, D.B. Fraser and A.K. Sinha, in: Proc. 18th Int. Reliability Physics Symp. (IEEE, New York, 1980) p. 165. [11] H.B. Huntington and A.R. Grone, J. Phys. Chem. Solids 20 (1961) 76. [12] M.J. Weins, Surf. Sci. 31 (1972) 138. [13] R.S. Sorbello, J. Phys. Chem. Solids 34 (1973) 937. [14] C.C. Fang, V. Prasad and F. Jones, J. Vac. Sci. Technol. A 11 (1993) 2778. [15] I.A. Blech, J. Appl. Phys. 47 (1976) 1203.