Numerical simulation of nucleation and migration voids in interconnects of electrical circuits
Matematičeskoe modelirovanie, Tome 19 (2007) no. 10, pp. 29-43.

Voir la notice de l'article provenant de la source Math-Net.Ru

Problems of modeling of voids nucleation and migration in electrical circuits interconnects are considered. There is suggested a mathematical model of the processes based upon drift-diffuse approach. For the case of rectangular interconnection shape there are constructed monotone conservative numerical finite-difference schemes and developed implementation algorithms for PC and multiprocessor systems. Established approach is applied to the test problem. Numerical experiments show that constructed model adequately reflects all the physical processes and can be used for development of new chips.
@article{MM_2007_19_10_a2,
     author = {Yu. N. Karamzin and S. V. Polyakov and I. V. Popov and G. M. Kobel'kov and S. G. Kobel'kov and Jun Ho Choy},
     title = {Numerical simulation of nucleation and migration voids in interconnects of electrical circuits},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {29--43},
     publisher = {mathdoc},
     volume = {19},
     number = {10},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2007_19_10_a2/}
}
TY  - JOUR
AU  - Yu. N. Karamzin
AU  - S. V. Polyakov
AU  - I. V. Popov
AU  - G. M. Kobel'kov
AU  - S. G. Kobel'kov
AU  - Jun Ho Choy
TI  - Numerical simulation of nucleation and migration voids in interconnects of electrical circuits
JO  - Matematičeskoe modelirovanie
PY  - 2007
SP  - 29
EP  - 43
VL  - 19
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2007_19_10_a2/
LA  - ru
ID  - MM_2007_19_10_a2
ER  - 
%0 Journal Article
%A Yu. N. Karamzin
%A S. V. Polyakov
%A I. V. Popov
%A G. M. Kobel'kov
%A S. G. Kobel'kov
%A Jun Ho Choy
%T Numerical simulation of nucleation and migration voids in interconnects of electrical circuits
%J Matematičeskoe modelirovanie
%D 2007
%P 29-43
%V 19
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2007_19_10_a2/
%G ru
%F MM_2007_19_10_a2
Yu. N. Karamzin; S. V. Polyakov; I. V. Popov; G. M. Kobel'kov; S. G. Kobel'kov; Jun Ho Choy. Numerical simulation of nucleation and migration voids in interconnects of electrical circuits. Matematičeskoe modelirovanie, Tome 19 (2007) no. 10, pp. 29-43. http://geodesic.mathdoc.fr/item/MM_2007_19_10_a2/

[1] J. R. Lloyd, “Electromigration in integrated circuits conductors”, J. Phys. D: Appl. Phys., 32 (1999), R109–R118 | DOI | MR

[2] J. R. Lloyd, J. Clemens, R. Snede, “Copper metallization reliability”, Microelectronics reliability, 39 (1999), 1595–1602 | DOI

[3] J. W. Cahn, J. E. Hilliard, “Free Energy of a Nonuniform System. I. Interfacial Free Energy”, J. Chemical Physics, 28:2 (1958), 258–267 | DOI

[4] J. W. Barrett, J. F. Blowey, “Finite Element Approximation of an Allen-Cahn/Cahn-Hilliard System”, J. Numer. Anal., 22:1 (2002), 11–71 | DOI | MR | Zbl

[5] D. N. Bhate, A. Kumar, A. F. Bower, “Diffuse interface model for electromigration and stress voiding”, J. Applied Physics, 87:4 (2000), 1712–1721 | DOI

[6] J. A. Sethian, Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Cambridge University Press, 1999 | MR | Zbl

[7] V. Sukharev, “Physically-Based Simulation of Electromigration Induced Failures in Copper Dual-Damascene Interconnect”, 5th International Symposium on Quality Electronic Design (ISQED'04), 2004, 225–231, special issue 2f

[8] V. Sukharev, “Physically based simulation of electromigration-induced degradation mechanisms in dual-inlaid copper interconnects”, IEEE Trans. On CAD of Integrated Circuits and Systems, 24:9 (2005), 1326–1335 | DOI

[9] V. Sukharev, “Simulation of Microstructure Influence on EM-Induced Degradation In Cu Interconnects”, 8th International Stress-Induced Phenomena in Metallization (12–14 September 2005, Dresden, Germany), AIP Conference Proceedings, 817, eds. Ehrenfried Zschech, Karen Maex, Paul S. Ho, Tomoji Nakamura, American Institute of Physics, Melville, NY, 2006, 244–253

[10] Ch. Kittel, Vvedenie v fiziku tverdogo tela, Nauka, M., 1978

[11] S. Z. Bokshtein, Diffuziya i struktura metallov, Metallurgiya, M., 1973

[12] Ya. E. Geguzin, Diffuzionnaya zona, Nauka, M., 1979

[13] V. N. Chebotin, Yavleniya perenosa v ionnykh kristallakh, Nauka, M., 1968

[14] V. N. Chebotin, Khimicheskaya diffuziya v tverdykh telakh, Nauka, M., 1989

[15] A. A. Samarskii, Teoriya raznostnykh skhem, Nauka, M., 1989 | MR

[16] V. I. Lebedev, “Extremal polynomials and methods of optimization of numerical algorithms”, Sb. Math., 195:10 (2004), 1413–1459 | DOI | MR | Zbl

[17] O. Yu. Milyukova, Parallelnye iteratsionnye metody s faktorizovannoi matritsei predobuslovlivaniya dlya resheniya ellipticheskikh uravnenii, Dissertatsiya na soiskanie uchenoi stepeni doktora fiziko-matematicheskikh nauk, IMM RAN, M., 2004

[18] A. A. Samarskii, E. S. Nikolaev, Metody resheniya setochnykh uravnenii, Nauka, M., 1978 | MR | Zbl