PROCEEDINGS LETTERS 833 which is (12) of my letter. Note that C=O when Q = f in ( f ) and that C is or less than n for all Q greater than f . When C is less than x. it must be emphasized again that the dominant complex pole pair is in the left-half R = AjC(T) plane. where A incorporates all the constants in (5). The resulting expression for R The equations which sah PreSnts as ''corrections" apply only to Tight-gives a linear dependence of R on j , which agrees with the theories presented half plane poles since in [2]-[4] and t2) It is conceded by the author in [l] that the experimental determination of the power ofj, which yields 2 and appears to support his theoretical R,C, fi = uR,C, = C 2 -x 2 when u is greater than zero. However, by convention, a discussion of Q is restricted to a complex pole pair in the left-half plane. Hence, his numerical results must be different since the Q he refers to is applicable only to right-half plane (unstable) poles.DEXIS I. H o w Moore School of Elec. Engrg.Abstract-Comments are made on a recently publicized theory on electromigration in thin films. It is shown that the rate of electromigration is a linear function of the current density and not a quadratic function as proposed by Black.In a recent paper [l], a theory on electromigration in metals was presented, resulting in a quadratic dependence of the rate of electromigration on current density.Several theoretical treatments, namely, those by Fiks [2], Huntington and Grone [3]. and Bosvieux and Friedel [4] (all based on the electron drag model, as is the presently discussed paper), result in a linear relation between the rate of electromigration and current density.1) Adopting the proposition of a "simple theory," and neglecting such phenomena as the Coulomb force on the metal ions and the size effect in thin films, we obtain an expression different from that presented in [ l ] for the electromigration rate, and a linear relationship between electromigration rate and current density. Using the same notations as in [ I 1. we have R = F x (average change in momentum due to E per electron, (dpi I x (number of conduction electrons colliding with the metal x (effective ion target cross section for electrons) x (number of activated aluminum ions per unit volume)where R is the rate of mass transport and F is a constant. The average change in momentum for any conduction electron due to the applied field E is ions per unit volume per second)(1)The number of electrons colliding with the metal ions per unit volume per second is given bywhere n, is the conduction electron density and z is a proportionality constant.Now if C ( T ) is the number of activated aluminum ions and b i the effective target cross section, we then havederivation, may be inaccurate because of errors in the film temperature measurements. However, no indication is given as to how large the error could be. We believe that a change in current density whether achieved by increasing the current or decreasing the film cross section may result in differences in failure...
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