Part XII – December 1969 – Papers - Current Basic Problems in Electromigration in Metals

Some of the basic problems in understanding elec-tromigration in metals are discussed, along with the attempts that are being made to handle them. One such problem is the effect of the electrostatic forces. It is now acknowledged that the momentum exchange with charge carriers plays generally a dominant role in the driving force but the question remains to what extent the electrostatic force may still be effective. The electromigration of interstitial impurities is also an area which presents some intriguing questions. For the substitutional impurity, moving by the vacancy mechanism under the influence of an electric field, the correlation considerations are somewhat more complex than have been previously recognized. Another problem of basic importance in the calculution from first principles is the strength of the "electron friction" force, say for a simple one-band metal. A related problem growing out of the preceding is the prediction of the direction of the "electron wind" force for metals with band structure involving both holes and electrons. THE term electromigration has come to be used to describe the flow of matter in condensed phases carrying high electronic currents such as metals and alloys, whereas one usually reserves the term electrolysis for situations where the current is largely ionic, particularly in the liquid state such as molten salts. It follows that the mass transport number in electromigration is always very small, of the order of 10-7. Studies of electromigration date back some 30 years but the modern period would appear to date from the work of Seith and Wever1 who in the mid 1950's first incorporated markers to display mass motion relative to the lattice and first suggested that the direction of the mass flow was primarily determined by the sign of the charge carriers. Since that time interest in the field has grown steadily and more rapidly recently as certain technological applications became apparent. Chief of these is certainly the deleterious effects that electromigration can cause, even at relatively low temperature, to current-carrying elements in integrated circuitry.2 These phenomena have been the subject of intense study and considerable ingenuity. On the constructive side electromigration has proved a useful tool in the purification of certain metals.3 The interest of this paper is, however, centered more on the basic aspects of the subject than on its technological applications. That high electric currents should give rise to mass flow in metals and that the driving force should be more directly associated with momentum exchange with the charge carriers than with the electrostatic field are ideas that no longer cause surprise or particular interest. The field has matured to the point where the general concepts are widely accepted and continued progress in basic understanding rests on more detailed and quantitative exploration. It is the purpose of this paper to point out what are some of the current problems. As a result, we expect to raise more questions than we answer. The first of these will be the role of electrostatic forces, if any, in electromigration. A second section will deal with the electromigration of interstitials. A third and final section treats with electromigration of substitutional impurities or of the matrix atoms themselves. ELECTROSTATIC DRIVING FORCE In the conceptual treatments of electromigration it has been customary to write the driving force in terms of an effective charge number Z* and to divide it into two terms F = e£Z* = e£[Zel- z(pd/Nd)(N/p)(m*\m*\)] [1] The first of these represents the electrostatic force under immediate consideration in this section and the second and usually dominating term for metals arises from momentum exchange with charge carriers, commonly called the "electron drag" term. As can be seen it is set proportional to the electrons per atom, z, and the ratio of the specific resistivity of the moving entity to the corresponding resistivity per matrix atom. The (m*/Im*I) factor takes into account the fact that the sign of the charge carrier determines the sign of the driving force. The specific resistivity of the moving entity is averaged over its path. In the case of motion of the matrix atoms by vacancies this gives rise to approximately one-half the resistivity at the saddle point since the scattering power of the atom at its equilibrium position bordering the vacancy differs only slightly from that of a normal matrix atom. Although the formulation of the "electron drag" term in Eq. [I] is based on a highly simplified model for electron defect scattering, the essential features implicit in the expression are common to all the theoretical approaches that have so far appeared in the literature.4-6 As for Zel, most treatments of electromigration have included the quantity as the parameter which measures the direct interaction of the electrostatic field with the ion and equated it to the nominal valence of the latter. However, there has been considerable discussion whether this interaction may not be 0 in many cases.6 If the moving ion is always enveloped by the same distribution of shielding charge, then clearly its motion will not involve any work done by the electric field and one can expect there will be no electrostatic force exerted on such a neutral composite. From this point of view the shielding charge around the ion would be said to be complete and hence the entity within the Debye shielding sphere would be unaffected by the electrostatic field per se. There is, however, the prospect that, as the moving ion progresses, new charge comes in to participate in the shielding action