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Electromigration AimsBefore you startIntroductionThe theory of electromigrationElectromigration damageFlux divergence (I)Flux divergence (II)Avoiding electromigration problemsAlternatives to aluminium metallizationSummaryQuestionsGoing further
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Data from Smithells Metals Reference Book

The relationship D =D0 exp(-Q/RT) is used to obtain the self diffusion of Al in Al and W in W.

 

D0 / m2 s-1

Q / kJ mol-1

W*

D1 = 0.04 × 10-4
D2 = 46 × 10-4

Q1 = 526 ± 50
Q2 = 666 ± 59

Al

1.71 × 10-4

142 ± 1

* The measured diffusivity of tungsten when plotted as lnD vs 1/T is curved and can be fitted by a sum of two terms: D = D1exp(Q1/RT) + D2exp(Q2/RT).

To obtain values for grain-boundary diffusion at 300 K, measured data have been extrapolated to give a relationship with the melting temperature, Tm, for:

FCC metals:
Dgb = 0.3 × 10-4 exp (-8.9 Tm/T) m2 s-1
Tm,Al = 933 K
Dgb,Al = 2.86 × 10-17 m2 s-1

BCC metals:
Dgb = 1.84 × 10-5 exp (-10.4 Tm/T)
Tm,W = 3695 K
Dgb = 4.31 × 10-61 m2 s-1

Note how W, having a much higher melting point, has a lower diffusivity than Al at a given temperature (in this case 300 K).

Equations obtained from ‘Fundamentals of Grain and Interphase Boundary Diffusion Third Edition’ by I. Kaur, Y. Mishin and W. Gus; Wiley, Chichester, 1995.

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