  Single-layer atom or vacancy clusters in the presence of electromigration are
studied theoretically assuming an isotropic medium. A variety of distinctive
behaviors distinguish the response in the three standard limiting cases of
periphery diffusion (PD), terrace diffusion (TD), and evaporation-condensation
(EC). A general model provides power laws describing the size dependence of the
drift velocity in these limits, consistent with established results in the case
of PD. The validity of the widely used quasistatic limit is calculated. Atom
and vacancy clusters drift in opposite directions in the PD limit but in the
same direction otherwise. In absence of PD, linear stability analysis reveals a
new type of morphological instability, not leading to island break-down. For
strong electromigration, Monte Carlo simulations show that clusters then
destabilize into slits, in contrast to splitting in the PD limit.
Electromigration affects the diffusion coefficient of the cluster and
morphological fluctuations, the latter diverging at the instability threshold.
An instrinsic attachment-detachment bias displays the same scaling signature as
PD in the drift velocity.
