Electromigration of single-layer clusters

We describe the steady states, fluctuations, dynamics, and instabilities of atom and of vacancy single-layer-height islands during electromigration, a ssuming an isotropic medium. We emphasize the dependence on cluster size an d on the three standard limiting cases of mass-transport mechanism: periphe ry diffusion (PD). terrace diffusion (TD). or evaporation-condensation (EC) , as well as the differences between atom and vacancy clusters. A general m odel provides power laws describing the size dependence of the drift veloci ty in these limits, consistent with established tin the case of PD) results . For PD, atom and vacancy islands drift in opposite directions; otherwise they drift in the same direction. The validity of the widely used quasistat ic limit is calculated. Linear stability analysis reveals a new type of mor phological instability, not leading to island break-down. We find non-circu lar steady states for EC vacancy islands. Analytical calculations are corro borated by both Monte Carlo simulations and numerical integration. For weak electromigration the cluster responds isotropically for TD and PD but not EC. In EC, clusters elongate perpendicular to the drift axis. In PD a morph ological instability at strong electromigration leads to cluster splitting, in contrast to destabilizing into slits in the other cases. TD or EC induc es a new instability for vacancy clusters above a threshold. Using Langevin formalism, we derive the non-equilibrium cluster diffusion constant and st udy morphological fluctuations. Electromigration affects the diffusion coef ficient of the cluster and morphological fluctuations, which diverge at the instability threshold. An intrinsic attachment-detachment bias displays th e same scaling signature as PD in the drift velocity. (C) 2001 Published by Elsevier Science B.V.