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85034202119
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note
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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.
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16
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0038035318
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M. A. Korhonen, P. A. Börgesen, K. N. Tu, and C.-Y. Li, J. Appl. Phys. 73, 3790 (1993).
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Korhonen, M.A.1
Börgesen, P.A.2
Tu, K.N.3
Li, C.-Y.4
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18
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85034162433
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note
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N.
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20
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85034165350
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note
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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.
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21
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0022777623
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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).
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Koleshko, V.M.1
Belitsky, V.F.2
Kiryushin, I.V.3
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22
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0025522710
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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).
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Koleshko, V.M.1
Kiryushin, I.V.2
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25
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85034191588
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note
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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.
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26
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85034191579
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note
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jj, but this complication is not necessary to the argument.
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28
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0000802610
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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).
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, vol.74
, pp. 3855
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Bower, A.F.1
Freund, L.B.2
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29
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0000802610
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edited by J. M. Poate, K. N. Tu, and J. W. Mayer (Wiley, New York)
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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).
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(1978)
Thin Films - Interdiffusion and Reactions
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D'Heurle, F.M.1
Ho, P.S.2
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30
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0028524490
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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).
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(1994)
J. Phys. Chem. Solids
, vol.55
, pp. 907
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Hehenkamp, T.1
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31
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85034167907
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note
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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.
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32
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85034174742
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note
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GB is chosen from earlier measurements in different films than the ones used in Ref. 4.
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33
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85034193955
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note
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zz ≠ 0 stress term supported by the passivation.
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35
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0010279984
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M. A. Korhonen, P. Börgesen, D. D. Brown, and C.-Y. Li, J. Appl. Phys. 74, 4995 (1993).
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Korhonen, M.A.1
Börgesen, P.2
Brown, D.D.3
Li, C.-Y.4
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