Simulation of the effect of microstructure on electromigration induced failure of interconnects

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 1997.Includes bibliographical references (leaves 85-87).by Walid R. Fayad.M.S

Microstructure evolution and interconnect realiability

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2000.Includes bibliographical references (leaves 207-213).In the context of predicting the effects of geometry, microstructure, and processing conditions on electromigration (EM) induced interconnect failure, normal grain growth in thin films was studied, analytic models were built for the grain structure statistics in 2D and 3D interconnects, and simulation programs were developed for generation of process and complex-geometry-sensitive interconnect structures. The models were validated through simulations and experiments and were integrated into tools for circuit-design level interconnect reliability predictions. The universal scaling behavior of 2D normal grain growth was demonstrated and characterized using a simulation of 2D grain growth (GGSim). We showed that the constant rate of change of the average grain area is equal to the grain boundary mobility constant pt. We also found that the steady state grain size distribution obtained using our simulation technique, as well as those reported in experiments on simple model systems and those reported for very different simulation techniques, are all very well fit by a Weibull distribution function with the dimensionless parameter p = 5/2, and are better fit by this function than the log normal, Gamma or Rayleigh functions. The 2D simulation was used to simulate the development of film structures with drag induced lognormal grain size distributions from which interconnect strips were etched and then annealed, in order to analyze the statistics of as-patterned, as well as post-pattern annealed, interconnect grain structures. These statistics were characterized as a function of the ratios of the line-widths to the initial-grain-sizes. Among the important findings is that polygranular cluster and bamboo segment length distributions for as-patterned lines are best fit by Weibull distribution functions. Analytic formulae describing grain structure statistics were reported, for usage in EM simulations and reliability predictions. A differential model predicting the evolution of the polygranular cluster length distribution during post-patterning annealing was developed. It was shown that the rate of bamboo-segment nucleation per unit time and unit of untransformed length is proportional to [mu]/w 3 , and is negligible in the growth-dominated steady-state. The cluster shrinkage velocity was demonstrated to reach a constant steady-state value proportional to [mu]/w (assuming constant and uniform [mu]). This was shown to lead to a time-invariant, steady-state exponential cluster length distribution with an average cluster length proportional to the strip width, and a cluster length fraction decaying exponentially with U=[mu]/w2 . The distribution of grain lengths in the resulting final bamboo grain structure is well fit by a log normal distribution, with a median grain length scaling with the line width, and a line-width-independent normalized deviation in the grain length. This result was used to show, using an EM simulation, that grain-orientation-dependent variations in surface diffusivities constitute a likely cause for the variabilities in lifetimes observed experimentally. The 2D simulation GGSim was also substantially modified to simulate the patterning of interconnect features of general shapes from polygranular thin film structures, as well as to simulate further grain structure evolution due to post-patterning annealing in these complex shapes. A grain structure extraction tool, PolySeg, was developed to allow extraction of the atomic transport details in the case of complex interconnect trees for EM reliability predictions using EM simulations. To assess the 3D effects on grain structure evolution, and therefore on interconnect reliability, a soap froth experiment was used to study 3D normal grain growth in long rectangular prisms. The kinetics were found to scale with the normalized time [mu]/w 2 (with w being the largest of the two prism cross-sectional dimensions). It was found that the normalized duration of the conversion from 3D (non-columnar) to 2D (columnar) structures and the normalized duration of the initial phase during which the structure was polygranular became longer as w/h approached 1. The same results obtained in the 2D case for the scaling behaviors of the bamboo nucleation rate and the polygranular cluster shrinkage rate were demonstrated. Based on a 2D approach, a prism-geometry-sensitive analytic model was developed for the transformation to fully-bamboo structures. These results were compared with preliminary results obtained using a 3D grain growth simulation and qualitative agreement was demonstrated. We have successfully captured with simple analytic models as well as elaborate simulations the physics of microstructure evolution in complex patterned thin-film structures. In particular, we have developed an array of models and simulations that can be used to investigate the impact of geometry and process history on microstructure evolution, and ultimately on EM-induced failure statistics.by Walid R. Fayad.Ph.D