A model for electromigration in thin metal film interconnects is presented that includes two components of diffusion. The grain-boundary and lattice components of mass transport are considered in terms of their temperature dependence and the metallurgical ‘‘structure’’ of patterned planar interconnects. Interconnect structure is defined in terms of single- and polycrystalline line segments, which result from the local grain microstructure for a patterned interconnect line. The dependence of the diffusional flux on the length and type of line segment is included in the model. The results indicate that the grain structure of the film plays an important role in determining the relative contribution of the diffusion components to mass transport. The model assumes that the length and type of interconnect line segment determines the relative contribution of grain boundary and lattice diffusion components, and provides a means for extrapolating accelerated test results for planar interconnects by taking into consideration the temperature dependence of the diffusion mechanisms, and the effect of the local microstructure on diffusion. The model also indicates that extrapolations made using Black’s equation may result in an overestimate of safe operating conditions. Calculations show that the effective activation energy depends on the median grain size and its distribution parameter, D50 and σ, respectively, and the interconnect linewidth W. Model calculations of electromigration lifetime t50 were compared to experimental results obtained on patterned interconnects using sputter-deposited Al-1.5% Cu alloy films. The experimental data support a linewidth-dependent electromigration activation energy and show that the dependence of t50 on linewidth for W≤3D50 results from a change in the dominant diffusion mechanism with temperature, linewidth, and local interconnect ‘‘structure.’’

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An existing cell-based percolation model with parameter correlation can find its potential applications in assessing soft-breakdown (BD) statistics as long as the oxide thinning due to the localized physical damage near the SiO2/Si interface is accounted for. The resulting model is expressed explicitly with the critical trap number per cell nBD and the remaining oxide thickness tox′ both as parameters. Reproduction of time-to-bimodal (soft- and hard-) breakdown statistical data from 3.3-nm-thick gate-oxide samples yields nBD of 3 and 4 for soft and hard breakdown, respectively. The extracted tox′ of 1.0 nm for soft breakdown, plus the transition layer thickness of 0.5 nm in the model, is fairly comparable with literature values from current–voltage fitting. The dimension and area of the localized physically damaged region or percolation path (cell) are quantified as well. Based on the work, the origins of soft and hard breakdown are clarified in the following: (i) soft breakdown behaves intrinsically as hard breakdown, that is, they share the same defect (neutral trap) generation process and follow Poisson random statistics; (ii) both are independent events corresponding to different tox′ requirements; and (iii) hard breakdown takes place in a certain path located differently from that for the first soft breakdown.

Analytical formulae for linewidth-dependent electromigration lifetime, as represented by a log-normal distribution, are derived based on a linewidth-independent log-normal grain size distribution. This formulation can quantitatively explain the experimentally observed increase of both the Median-time-to-failure and standard deviation (σ) as the linewidth decreases to become comparable to or less than the median grain size. Comparison between the theoretical prediction and experimental data for three metallization systems all show reasonable agreement. Due to its analytical nature, the model can also be applied to define design rules versus linewidth for a given metallization technology down to the submicron linewidth. Conditions in limiting the process variations in order to optimize the scaling of design rules are discussed.

A new model for electromigration in thin metal film interconnects has recently been proposed which includes the effects of film microstructure and temperature on the components of mass transport. In this paper experimental data is presented which supports this model. Our results indicate that the grain structure of the film coupled with the temperature dependence of the lattice and grain boundary diffusivities plays an important role in determining the relative contributions of these diffusion components to mass transport. For line widths in the range of the median grain size the line width dependence of median fail time, '50, results from a change in the relative contribution of these components to the diffusional flux. The model correctly describes the experimental dependence of '50 and activation energy on line width.