Theory of Electromigration

Solid State Physics - Advances in Research and Applications

Volumn 51, Issue C, 1998, Pages 159-231

  Sorbello, Richard S ^a  

^a UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77956662474     PISSN: 00811947     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0081-1947(08)60191-5     Document Type: Chapter

References (132)

1. Huntington H.B. In: Nowick A.S., and Burton J.J. (Eds). Diffusion in Solids (1975), Academic Press, New York 303
2. Verbruggen A.H. IBM J. Res. Dev. 52 (1988) 93
3. Ho P.S., and Kwok T. Rep. Prog. Phys. 52 (1989) 301
4. Kwok T., and Ho P.S. In: Gupta D., and Ho P.S. (Eds). Diffusion Phenomena in Thin Films and Microelectronic Materials (1988), Noyes Publications, Park Ridge, NJ 369
5. R.S. Sorbello Materials Reliability Issues in Microelectronics ed. J.R. Lloyd, P.S. Ho, C.T. Sah, F. Yost MRS Symposia Proceedings 225, Materials Research Society, Pittsburgh, PA (1991), p. 3.
6. Fiks V.B. Fiz. Tverd. Tela (Leningrad) 1 (1959) 16
7. Sov. Phys. Solid State 1 (1959) 14
8. Huntington H.B., and Grone A.R. J. Phys. Chem. Solids 20 (1961) 76
9. Bosvieux C., and Friedel J. J. Phys. Chem. Solids 23 (1962) 123
10. Landauer R., and Woo J.W.F. Phys. Rev. B 10 (1974) 1266
11. Landauer R. J. Phys. C 8 (1975) L389
12. Landauer R. Phys. Rev. B 14 (1976) 1474
13. Das A.K., and Peierls R. J. Phys. C 6 (1973) 2811
14. Das A.K., and Peierls R. J. Phys. C 8 (1975) 3348
15. Sorbello R.S., and Dasgupta B. Phys. Rev. B 16 (1977) 5193
16. Dasgupta B.B., and Sorbello R.S. Phys. Rev. B 21 (1980) 4196
17. Schaich W.L. Phys. Rev. B 19 (1979) 620
18. Kumar P., and Sorbello R.S. Thin Solid Films 25 (1975) 25
19. Kubo R. J. Phys. Soc. Jpn. 12 (1957) 570
20. Sham L.J. Phys. Rev. B 12 (1975) 3142
21. Rimbey P.R., and Sorbello R.S. Phys. Rev. B 21 (1980) 2150
22. Sorbello R.S. Phys. Rev. B 31 (1985) 798
23. Schaich W.L. Phys. Rev. B 13 (1976) 3350 3360(1976).
24. Lodder A. Physica A 158 (1989) 723
25. van Ek J., and Lodder A. Defect Diffus. Forum 115/116 (1994) 1
26. Turban L., Noziéres P., and Gerl M. J. Phys. (Paris) 37 (1976) 159
27. Bly D.N., and Rous P.J. Phys. Rev. B 53 (1996) 13909
28. Sorbello R.S. Solid State Commun. 76 (1990) 747
29. Landauer R. IBM J. Res. Dev. 1 (1957) 223
30. see also. Landauer R. Z. Phys. B 21 (1975) 247
31. Eigler D.M., Lutz C.P., and Rudge W.E. Nature 352 (1991) 600
32. Yasunga H., and Natori A. Surf. Sci. Rep. 15 (1992) 208
33. van Ek J., Dekker J.P., and Lodder A. Phys. Rev. B 52 (1995) 8794
34. R.S. Sorbello Advanced Metallization for Future ULSI ed, K.N. Tu, J.W. Mayer, J.M. Poate, L.J. Chen MRS Symposia Proceedings 427, Materials Research Society, Pittsburgh, PA (1996).
35. Sorbello R.S. Phys. Rev. Lett. 63 (1989) 1815
36. Howard R.E., and Lidiard A.B. Rep. Prog. Phys. 27 (1964) 161
37. Flynn C.P. Point Defects and Diffusion (1972), Oxford University Press, London
38. In the usual display of the phenomenological equations, as in Refs. 1 and 35, a factor of 1/T, where T is the absolute temperature, would appear with each L-coefficient in Eqs. (1.1) and (1.2). Because we shall be dealing with systems at constant temperature, it is permissible to absorb the 1/T factors into our L-coefficients.
39. Mahan G.D. Many-Particle Physics (1981), Plenum Press, New York
40. Routbort J.L. Phys. Rev. 176 (1968) 796
41. Alexander W.B. Z. Naturforsch. 26a (1971) 18
42. Wohlgemuth J. J. Phys. Chem. Solids 36 (1975) 1025
43. Lou L., Schaich W.L., and Swihart J.C. Phys. Rev. B 33 (1986) 2170
44. Genoni T.C., and Huntington H.B. Phys. Rev. B16 (1977) 1344
45. Huntington H.B., Alexander W.B., Feit M.D., and Routbort J.L. In: Lodding A., and Lagerwall T. (Eds). Atomic Transport in Solids and Liquids (1971), Verlag der Zeitschrift fur Naturforschung, Tübingen, Germany 91
46. Verbruggen A.H., and Griessen R. Phys. Rev. B32 (1985) 1426
47. see also. Verbruggen A.H., Griessen R., and de Groot D.G. J. Phys. F16 (1986) 557
48. See also. Wipf H. In: Alefield G., and Völkl J. (Eds). Topics in Applied Physics 29 (1978), Springer-Verlag, Berlin 273 Hydrogen in Metals II
49. Sorbello R.S. J. Phys. Chem. Solids 34 (1973) 937
50. Rorschach H.E. Ann. Phys. (N.Y.) 98 (1976) 70
51. Hesketh R.V. Phys. Rev. B18 (1978) 596
52. Frohberg G. In: Lodding A., and Lagerwall T. (Eds). Atomic Transport in Solids and Liquids (1971), Verlag der Zeitschrift für Naturforschung, Tübingen, Germany 19
53. Born M., and Oppenheimer J.R. Ann. Phys. 84 (1927) 457
54. Seitz F. The Modern Theory of Solids (1940), McGraw-Hill, New York
55. R.S. Sorbello, Ph.D. thesis, Stanford University (1970).
56. Sorbello R.S. J. Phys. Chem. Solids 42 (1981) 309
57. Stoneham A.M., and Flynn C.P. J. Phys. F3 (1953) 505
58. Flynn C.P., and Stoneham A.M. Phys. Rev. B1 (1970) 3966
59. Feynman R.P. Phys. Rev. 56 (1939) 340
60. Hellmann H. Einführung in die Quantenchemie (1937), Deuticke, Vienna
61. Deb B.M. Rev. Mod. Phys. 45 (1973) 22
62. Sorbello R.S., and Dasgupta B. Phys. Rev. B21 (1980) 2196
63. Messiah A. Quantum Mechanics (1962), Wiley, New York
64. Fiks V.B. Sov. Phys. Solid State 6 (1964) 1251
65. Kaganov M.I., Lofshits I.M., and Fiks V.B. Sov. Phys. Solid State 6 (1965) 2167
66. Pines D. Elementary Excitations in Solids (1963), Benjamin, New York
67. Das A.K. Helv. Phys. Acta 49 (1976) 829
68. Pines D., and Noziéres P. The Theory of Quantum Liquids I (1966), W. A. Benjamin, New York
69. Ehrenreich H., and Cohen M.H. Phys. Rev. 115 (1959) 786
70. Harrison W.A. Pseudopotentials in the Theory of Metals (1966), W. A. Benjamin, New York
71. See, for example. In: Ehrenreich H., Seitz F., and Turnbull D. (Eds). Solid State Physics 24 (1970), Academic Press, New York
72. We have chosen w(q), like v(q), to be independent of normalization volume, unlike the choice made in Refs.44: 51, and 65, where the atomic volume enters into the definition of the form factor.
73. Sorbello R.S. Phys. Status Solidi B 86 (1978) 671
74. Faber T.E. Theory of Liquid Metals (1970), Cambridge University Press, Cambridge
75. Stroud D. Phys. Rev. B13 (1976) 4221
76. Blough J.L., Olson D.L., and Rigney D.A. J. Appl. Phys. 43 (1972) 2476
77. see also. Epstein S.G., and Dickey J.M. Phys. Rev. B1 (1970) 2442
78. Sorbello R.S. Phys. Rev. B 23 (1981) 5119
79. Sorbello R.S., and Chu C.S. IBM J. Res. Dev. 32 (1988) 58
80. Chu C.S., and Sorbello R.S. Phys. Rev. B38 (1988) 7260
81. Sorbello R.S. Phys. Rev. B 39 (1989) 4984
82. Knäbchen A. J. Phys. Condens. Matter 3 (1991) 6989
83. Lenk R. Z. Phys. B 96 (1994) 121
84. Kunze C. J. Phys. Condens. Matter 6 (1994) 10011
85. Phys. Rev. B 51 (1995) 6979
86. Landauer R. Phys. Rev. B 52 (1995) 11225
87. 0 and n. This is possible only because background scattering (due to phonons) is present, so that a finite transport current can be established in response to a macroscopic field when only one impurity is present.
88. Landauer R. IBM J. Res. Dev. 32 (1988) 306
89. Stone A.D., and Szafer A. IBM J. Res. Dev. 32 (1988) 384
90. Landauer R. J. Phys. C 8 (1975)
91. Peierls R. More Surprises in Theoretical Physics (1991), Princeton University Press, Princeton, NJ
92. McGraw R., and Schaich W.L. J. Phys. Chem. Solids 38 (1977) 193
93. Kohn W., and Luttinger J.M. Phys. Rev. 108 (1957) 590
94. Mermin N.D. Phys. Rev. B 1 (1970) 2362
95. Chu C.S., and Sorbello R.S. J. Phys. Chem. Solids 52 (1991) 501
96. Abrikosov A.A., Gorkov L.P., and Dzyoloshinski I.E. Methods of Quantum Field Theory in Statistical Physics (1963), Prentice Hall, Upper Saddle River, NJ
97. Turban L., and Gerl M. Phys. Rev. B 13 (1976) 939
98. R.S. Sorbello, unpublished result.
99. Gupta R.P. Phys. Rev. B 25 (1982) 5188
100. Gupta R.P., Seeuys Y., Brebec G., and Adda Y. Phys. Rev. B 27 (1983) 672
101. Sorbello R.S., Lodder A., and Hoving S.J. Phys. Rev. B 25 (1982) 6178
102. Lodder A., and Brand M.G.E. J. Phys. F14 (1984) 2955
103. van Ek J., and Lodder A. J. Phys. Condens. Matter 3 (1991) 7331
104. Lodder A. J. Phys. F 14 (1984) 2943
105. Erckmann V., and Wipf H. Phys. Rev. Lett. 37 (1976) 341
106. Pendry J.B. Low Energy Electron Diffraction (1974), Academic Press, New York
107. Duryea T.W., and Huntington H.B. Surf. Sci. 199 (1988) 261
108. Ishida H. Phys. Rev. B 51 (1995) 10345
109. Zangwill A., and Soven P. Phys. Rev. A21 (1980) 1561
110. Ishida H. Phys. Rev. B 49 (1994) 14610
111. At higher temperatures, where lattice atoms perform significant vibrations about their equilibrium positions, it is permissible to use a Debye-Waller factor to specify their locations. This procedure, used by Lou et al. (Ref. 39), provides a way of averaging over the positions of all atoms other than the migrating one.
112. Ralls K.S., Ralph D.C., and Buhrman R.A. Phys. Rev. B 40 (1989) 11561
113. Chen Z., and Sorbello R.S. Phys. Rev. B 47 (1993) 13527
114. Walkup R.E., Newns D.M., and Avouris P. Phys. Rev. B 48 (1993) 1858
115. Itskovich I.F., and Sorbello R.S. Phys. Rev. B 45 (1992) 718
116. Emin D., Baskes M.I., and Wilson W.D. Phys. Rev. Lett. 42 (1979) 791
117. Teichler H., and Klamt A. Phys. Lett. A 108 (1985) 281
118. Fukai Y., and Sugimoto H. Adv. Phys. 34 (1985) 263
119. McCaskill J.S., and March N.H. J. Phys. Chem. Solids 45 (1984) 215
120. Lodder A. Solid State Commun. 71 (1991) 259 79: 143 (1989).
121. Landauer R. Solid State Commun. 72 (1989) 867
122. Lang N.D., Yacoby A., and Imry Y. Phys. Rev. Lett. 63 (1989) 1499
123. Lang N.D. Phys. Rev. B 45 (1992) 13599 49: 2067(1994).
124. Hirose K., and Tsukada M. Phys. Rev. B 51 (1995) 5278
125. Kobayashi N., Hirose K., and Tsukada M. Surf. Sci. 345 (1966) 299
126. See. Stoyanov S. Jpn. J. Appl. Phys. 30 (1991) 1
127. Latyshev A.V., Krasilnikov A.B., and Aseev A.L. Surf. Sci. 311 (1994) 395
128. Williams E.D., Fu E., Yang Y.-N., Kandel D., and Weeks J.D. Surf. Sci. 336 (1995) L746
129. See. Natori A. Jpn. J. Appl. Phys. 33 (1994) 3538
130. Kandel D., and Kaxiras E. Phys. Rev. Lett. 76 (1996) 1114
131. Car R., and Parinello M. Phys. Rev. Lett. 55 (1985) 2471
132. See. Li Y., and Wahnström G. Phys. Rev. B 46 (1992) 14528