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 v; the capillary (v 6 0.01) and the electromigration (EM) dominating regimes (v > 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 À5 expðÀ1:00 eV=kT Þ m 2 s À1 , 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.

Analysis of multistate models for electromigration failure

“…͑3͒. [27][28][29] These calculations are able to demonstrate complex morphological changes similar to those of real voids in encapsulated metal lines, 24,25,[27][28][29] including a void splitting mechanism in which, in the presence of a strong anisotropy, a cylindrical void can develop side features which may then detach from the mother void, [27][28][29] and a description of the migration of voids toward the cathode and a model of void pinning at grain boundaries. 22,31 To understand failure statistics, it is necessary to limit such problems, such as by starting with a single mode, such as viabelow failure in M2 lines, and considering such growth complexities at a later stage.…”

“…[20][21][22][23][24][25][26][27][28][29][30][31] Each of these factors depends on the local microstructure, leading to anisotropies which may affect the void growth direction and consequently its shape factor in Eq. ͑3͒.…”

Morphological evolution in a strained-heteroepitaxial solid droplet on a rigid substrate: Dynamical simulations

“…Therefore, we have implicitly assumed that the substrate is rigid, and the displacement is supplied as a Dirichlet boundary condition along the interface, which is calculated from the misfit strain forces. 32 The network remeshing is continuously applied using the criteria advocated by Pan and Cocks, 33 and the curvature and normal line vector are evaluated at each node using a discrete geometric relationship in connection with the fundamental definitions of the radius of curvature.…”

Generic role of the anisotropic surface free energy on the morphological evolution in a strained-heteroepitaxial solid droplet on a rigid substrate

“…The detailed description of the indirect boundary elements method (IBEM), and its implementation 30 are presented very recently in two comprehensive papers by Ogurtani and Akyildiz 31,32 in connection with the void dynamics in metallic interconnects under the effect of electromigration forces. In this study, we utilized the simplest implementation of the IBEM that employs the straight constant line elements in the evaluation of the hoop stress at the free surface of the droplet, as well as along the interface between droplet and the substrate.…”