Fast diffuser electromigration

A variety of solutes in the rare earth metals present a partly or total interstitial character. These solutes include beside the metalloid classical interstitials also some metallic elements, the so-called fast-diffusers, discussed in section 4. In general the study of electromigration of interstitials offers two advantages as compared to that of substitutional solutes. From the experimental point of view, the relatively high mobilities of the interstitial solutes increases the electrotransport effects often allowing to achieve steady state conditions within... 

Pb-Sn alloy (2) the electromigration of minor constituents such as fast diffusers, e.g., Cu or Ni. Both of these can be important. In the first case, electromigration of a major constituent can lead to voids or extrusions that can increase electrical resistance and produce open or short circuits [11-14]. When fast diffusing species are incorporated in the under bump metallurgy (UBM), fast diffusion can lead to the dissolution of the UBM materials, and the formation of interfacial intermetallic compounds layers that can lead to interfacial fracture, and ultimately, circuit failure [15]. Both of these failure modes have been observed. 

Electromigration of the fast diffusers exhibit interesting and varied effects. The measured Z of the impurities is often found to be strongly dependent, not only on temperature but on composition, varying with increased solute content or the presence of a second component (such as Sn in Pb-Sn alloys). In some cases, neither temperature nor composition was found to ha ve an effect on electromigration behavior, while in others the temperature effect is sufficient to reverse the sign of Z changing the direction of atomic flow of the solute from the anode to the cathode. 

Although electromigration data related to Pb-free solders is sparse in the published hterature, it is well known that Sn acts very much like Pb as a host for fast diffusers. The same metals that diffuse rapidly in Pb alloys also diffuse rapidly in Sn, and exhibit many of the same types of behavior. The differences are important, and they reside in the details. One important difference is that unlike Pb, Sn does not possess a cubic crystal structure so the important material properties are anisotropic. Metallic Sn is body centered tetragonal (BCT), whereas Pb is face centered cubic (FCC). For example, in Pb the diffusion coefficient is independent of the orientation, but in Sn there are marked diffusion rate differences parallel and perpendicular to the basal plane. This is true for self-diffusion as well, but nowhere is it more evident than in fast diffuser behavior where the ratio of the diffusion coefficient typically varies by a factor of 30-40 at 200°C. 

An important assumption in this modeling approach is that ion transport from macropore to micropore is sufficiently fast to be at equilibrium, that is, transport resistances are due to ion diffusion and electromigration across the thickness of the electrode. An extended model accounting for such a local transport resistance can be based on describing the individual ion adsorption fluxes into the carbon micropores y, by y, = exp( j a A( )d) S c i, exp(zj (1 - a) A( ), where... 

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