Strong-coupling theory for the driving force in electromigration

The linear-response formalism of Kumar and Sorbello for the driving force in electromigration is applied to the strong electron-impurity coupling regime for an impurity in an electron gas (jellium). The off-energy-shell integrals over the $T$ matrix provide bound-state contributions to the effective charge $Z^{*}$ for sufficiently strong coupling. It is also shown that not all scattering terms can be included in the force correlation function through the $T$ matrix. Analogous to the conductivity problem, calculation of all contributions higher order in $\frac{1}{k_{F}l}$ appear to be intractable. The size of these higher-order contributions depends on the particular model assumed for the impurity scattering potential and may lead to significant corrections to the current-independent part of the driving force. An approximate model calculation is presented. The role of electron screening, bound-state polarization, and the complications introduced by a Bloch-function description of electrons are also discussed.