INTERFACE SCIENCE 7, 33–44 (1999) c  1999 Kluwer Academic Publishers. Manufactured in The Netherlands. Grain Boundary Resistivity and Electrically Induced Grain Boundary Migration (EIGM) in Metallic Bamboo Microstructures RAND DANNENBERG AND ALEXANDER H. KING Department of Materials Science and Engineering, State University of New York at Stony Brook, Stony Brook NY 11794-2275 Abstract. As VLSI conductor line dimensions continue to decrease, electrotransport properties increasingly effect device lifetimes. Grain boundaries are intimately linked to these processes, providing paths of varying diffusivity, and as mobile defects themselves. Haessner et al. [6] make a challenging finding in experiments with thin gold films: based on calorimetric data, in order to account for the velocity of grain boundaries migrating in high electric current densities, the force on the atoms of a grain boundary would have to be two orders of magnitude larger than what the accepted theory for bulk ions predicts. The failure is attributed to the simplicity of the model which does not account for possible variations of the resistivity and effective valance charge that could occur in the vicinity of a grain boundary. In this paper, expressions are developed for the electron wind force on the atoms near grain boundaries, and they are written in terms of thermodynamic variables: the boundary specific volume expansion and specific resistivity. The enhancement of the wind force of the boundary atoms over the bulk wind force is calculated using published data. This model allows for more than an order of magnitude enhancement in gold, and Haessner’s observation is rationalized. Keywords: resistivity, mobility, grain boundary migration, electromigration, electron scattering 1. Introduction Grain boundaries in metals contribute to the overall electrical resistivity by absorbing energy from the mov- ing conduction electrons. This process can also pro- duce a directed force upon the grain boundaries, poten- tially inducing migration. In this paper, we derive an explicit relationship between the resistivity of a grain boundary and the force generated upon the boundary. We express these quantities in terms of known or mea- surable structural parameters of the grain boundary, such as the specific volume expansion and specific re- sistivity, and we compare our results with published data on grain boundary resistivity and electrically- induced grain boundary migration. The results may be relevant to the behavior of grain boundaries in electrical interconnections in very large scale integrated circuits, which operate at current densities of the order of 10 6 A/m 2 , and the forces applied to grain boundaries may be considerable. When a crystal is subjected to an electric field, forces act on both the electrons and mobile ions, causing the motion of both through quite different mechanisms. Electrons are accelerated in the negative direction of the field, but interact with phonons, defects, and the periodic potential of the lattice which contribute to the net resistivity and lead to ohmic behavior. The ions are influenced by the electric field, the electron cur- rent, the lattice, and the resulting charge distributions in their vicinity. This results in a current of ions, ei- ther with or against the electron current, depending on the strength of each interaction. This effect is known as electromigration, and the damage it produces is a significant practical problem for the microelectronics industry. The most intuitive ways to understand the effect are due to Fiks [1], and Huntington and Grone [2], who proposed that the total force on the ions results from two sources: (1) the electric field acting on the bare ionic charge, termed the direct force; (2) the rate of