Cathode edge displacement by voiding coupled with grain boundary grooving in bamboo like metallic interconnects by surface drift-diffusion under the capillary and electromigration forces

Abstract

The kinetics of cathode edge shrinkage and displacement (drift) coupled strongly with the grain boundary (GB) grooving is investigated using the novel mathematical model developed by Ogurtani, in sandwich type thin film bamboo lines. The computer simulations are performed under the constant current (CC) and the switch-over constant voltage (SOCV) operations. The cathode drift velocity and the cathode failure time show the existence of two distinct phases, depending upon the normalized electron wind intensity parameter χ; the capillary ( χ ⩽ 0.01) and the electromigration (EM) dominating regimes ( χ > 0.01), having current exponent n, equal to 0 and 1, respectively. Analysis of various experimental data on the cathode drift velocity results a consistent value for the surface drift-diffusion coefficient, 1.0 × 10 - 5 exp ( - 1.00 eV/ kT ) m 2 s - 1 , for copper interconnects exposed to some contaminations during the processing and testing stages. This is found to be an excellent agreement with the experimental values reported in the literature after applying the proper 1/ kT correction on the apparent activation enthalpy associated with Nernst–Einstein mobility relationship. The complete cathode failure time (CCFT) due to the cathode area shrinkage by voiding is also formulated by inverse scaling and normalization procedures, which show exactly the same capillary and EM dominating regimes. This formula can be used to predict very accurate CCFT for metallic lines with bamboo-like, near-bamboo, and even with polycrystalline structures by proper calculation of the cathode-edge path length (CEPL) parameter, in terms of the actual line width, the thickness and the grain size.