Home Page of A. Lodder
Global description of the subject of Electromigration
The driving force on an atom in a metal due to an applied electric field
has been the subject on a long lasting controversy. It is most simple
to formulate this controversy for an interstitial atom, let us say a
hydrogen atom, so effectively a proton, occupying some position in between
the metal atoms occupying lattice sites. Such a position is called an
interstitial position. The driving force is commonly understood as being
built up out of two contributions, a direct force and the wind force.
The direct force is due to the direct action of the applied electric
field on the charge of the proton. The wind force comes
from the scattering of the current carrying electrons off the proton.
Until 1962 there was a common belief that the direct force was determined by
the force on the bare proton, having a charge equal to the
elementary charge. At most
a small deviation from that value could arise from the electrons
in the metallic environment of the ion. In 1962 Bosvieux and Friedel
predicted a complete cancellation of the direct force due to screening
effects, so that only the wind force would remain. By that
prediction the controversy was born. It was not easy to decide matters
by a measurement, and a satisfactory theoretical answer was lacking
as well.
In 1975 Kumar and Sorbello published an exact
linear response expression for the driving force. After that
is was considered as being just a matter of a careful evaluation
of that expression in order to settle the problem. This did not
turn out to be the case. Either lowest order evaluations were
given only, for example by Sham and Schaich, or an unconclusive complete
evaluation was given by Rimbey and Sorbello. In 1989 the present author
obtained a result which supported the view of Bosvieux and Friedel.
However, a careful analysis of the different evaluations did not exist yet
in the literature. This he has taken as the challenge for the year 2003.
This search has led to a surprising and conclusive result.
In 2005 he succeeded to resolve the controversy
completely by pointing at a fatal error in the 1962-paper. On top of that,
he has shown that the starting formula of Bosvieux and Friedel
just reproduces the standard linear-response result for T = 0.
These findings were published in Europhysics Letters 72 (2005)
774, which paper carries the title "Electromigration theory unified".