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Volumn 85, Issue 12, 1999, Pages 8145-8154

Threshold stress behavior in thin film electromigration

Author keywords

[No Author keywords available]

Indexed keywords

CONDUCTIVE FILMS; CRYSTAL MICROSTRUCTURE; GRAIN BOUNDARIES; INTEGRATED CIRCUITS; MATHEMATICAL MODELS; PLASTIC DEFORMATION; POINT DEFECTS; STRAIN; STRESS ANALYSIS; STRESS CONCENTRATION; TEXTURES; THIN FILMS;

EID: 0032622015     PISSN: 00218979     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.370653     Document Type: Article
Times cited : (6)

References (37)
  • 1
    • 36749115512 scopus 로고    scopus 로고
    • I. A. Blech and C. Herring, Appl. Phys. Lett. 29, 131 (1976); I. A. Blech, J. Appl. Phys. 47, 1203 (1976); 48, 2648 (1997); I. A. Blech and K. L. Tai, Appl. Phys. Lett. 30, 387 (1977).
    • (1976) Appl. Phys. Lett. , vol.29 , pp. 131
    • Blech, I.A.1    Herring, C.2
  • 2
    • 0016940795 scopus 로고
    • I. A. Blech and C. Herring, Appl. Phys. Lett. 29, 131 (1976); I. A. Blech, J. Appl. Phys. 47, 1203 (1976); 48, 2648 (1997); I. A. Blech and K. L. Tai, Appl. Phys. Lett. 30, 387 (1977).
    • (1976) J. Appl. Phys. , vol.47 , pp. 1203
    • Blech, I.A.1
  • 3
    • 36749115512 scopus 로고    scopus 로고
    • I. A. Blech and C. Herring, Appl. Phys. Lett. 29, 131 (1976); I. A. Blech, J. Appl. Phys. 47, 1203 (1976); 48, 2648 (1997); I. A. Blech and K. L. Tai, Appl. Phys. Lett. 30, 387 (1977).
    • (1997) J. Appl. Phys. , vol.48 , pp. 2648
  • 4
    • 0000654704 scopus 로고
    • I. A. Blech and C. Herring, Appl. Phys. Lett. 29, 131 (1976); I. A. Blech, J. Appl. Phys. 47, 1203 (1976); 48, 2648 (1997); I. A. Blech and K. L. Tai, Appl. Phys. Lett. 30, 387 (1977).
    • (1977) Appl. Phys. Lett. , vol.30 , pp. 387
    • Blech, I.A.1    Tai, K.L.2
  • 15
    • 85034202119 scopus 로고    scopus 로고
    • note
    • The analogy falls short of quantitative accuracy because the capacitor charge is proportional to voltage, while the true vacancy concentration is exponential in the local chemical potential. The pictorial analogy is, therefore, only correct to linear order.
  • 18
    • 85034162433 scopus 로고    scopus 로고
    • note
    • N.
  • 20
    • 85034165350 scopus 로고    scopus 로고
    • note
    • Note that the linear circuit analogy is even more imprecise in Fig. 3(b) because the equilibrium vacancy concentration now depends on the local stress field, σ. This nonlinear dependence is expressed graphically by a variable capacitor.
  • 22
    • 0025522710 scopus 로고
    • V. M. Koleshko, V. F. Belitsky, and I. V. Kiryushin, Thin Solid Films 142, 199 (1986); V. M. Koleshko and I. V. Kiryushin, ibid. 192, 181 (1990).
    • (1990) Thin Solid Films , vol.192 , pp. 181
    • Koleshko, V.M.1    Kiryushin, I.V.2
  • 25
    • 85034191588 scopus 로고    scopus 로고
    • note
    • zz) is given for a hydrostatic pressure in Eq. (8). The final result is the same as would be derived in the general case. It is also equivalent to the common approximation of entirely neglecting the vacancy relaxation volume.
  • 26
    • 85034191579 scopus 로고    scopus 로고
    • note
    • jj, but this complication is not necessary to the argument.
  • 28
    • 0000802610 scopus 로고
    • 3/s in Fig. 8.6; F. M. d'Heurle and P. S. Ho, Thin Films - Interdiffusion and Reactions, edited by J. M. Poate, K. N. Tu, and J. W. Mayer (Wiley, New York, 1978), and Z* = -10. The vacancy relaxation volume, fΩ, is 0.3Ω (see Ref. 11; vacancy concentrations are taken from Ref. 23 of T. Hehenkamp, J. Phys. Chem. Solids 55, 907 (1994). The film thickness and grain sizes are 100 nm, and the resistivity is 3.3 μΩ cm (see Ref. 4).
    • (1993) J. Appl. Phys. , vol.74 , pp. 3855
    • Bower, A.F.1    Freund, L.B.2
  • 29
    • 0000802610 scopus 로고
    • edited by J. M. Poate, K. N. Tu, and J. W. Mayer (Wiley, New York)
    • 3/s in Fig. 8.6; F. M. d'Heurle and P. S. Ho, Thin Films - Interdiffusion and Reactions, edited by J. M. Poate, K. N. Tu, and J. W. Mayer (Wiley, New York, 1978), and Z* = -10. The vacancy relaxation volume, fΩ, is 0.3Ω (see Ref. 11; vacancy concentrations are taken from Ref. 23 of T. Hehenkamp, J. Phys. Chem. Solids 55, 907 (1994). The film thickness and grain sizes are 100 nm, and the resistivity is 3.3 μΩ cm (see Ref. 4).
    • (1978) Thin Films - Interdiffusion and Reactions
    • D'Heurle, F.M.1    Ho, P.S.2
  • 30
    • 0028524490 scopus 로고
    • 3/s in Fig. 8.6; F. M. d'Heurle and P. S. Ho, Thin Films - Interdiffusion and Reactions, edited by J. M. Poate, K. N. Tu, and J. W. Mayer (Wiley, New York, 1978), and Z* = -10. The vacancy relaxation volume, fΩ, is 0.3Ω (see Ref. 11; vacancy concentrations are taken from Ref. 23 of T. Hehenkamp, J. Phys. Chem. Solids 55, 907 (1994). The film thickness and grain sizes are 100 nm, and the resistivity is 3.3 μΩ cm (see Ref. 4).
    • (1994) J. Phys. Chem. Solids , vol.55 , pp. 907
    • Hehenkamp, T.1
  • 31
    • 85034167907 scopus 로고    scopus 로고
    • note
    • 3/s. with Z* = -5.2. A large value of Z* approximately -10 would imply twofold slower grain boundary diffusion and transient decay which gives better agreement for the inhomogeneous stress simulations.
  • 32
    • 85034174742 scopus 로고    scopus 로고
    • note
    • GB is chosen from earlier measurements in different films than the ones used in Ref. 4.
  • 33
    • 85034193955 scopus 로고    scopus 로고
    • note
    • zz ≠ 0 stress term supported by the passivation.


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