An electromigration model that includes the effects of microstructure and temperature on mass transport

Abstract

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.’’

Electromigration model for the prediction of lifetime based on the failure unit statistics in aluminum metallization

“…where the t u50_E is the median lifetime at T E ͑K͒ and j E ͑ϭ1 MA/cm 2 ), T is the absolute temperature, k is the Boltzmann 11 It is an assumption that the preexponential factor, t u50_E for single grain segments and polygrain segments in Black's equations are the same at T ϭT E . The T E of aluminum is typically within the range between 300 and 400°C and the value of T E ϭ 350°C is chosen for our study.…”

“…The T E of aluminum is typically within the range between 300 and 400°C and the value of T E ϭ 350°C is chosen for our study. 11 As a result, if the value of Ea _SG , Ea _PG , and t u50_E were determined, then t u50_PG and t u50_SG can be determined at a given temperature from Eqs. ͑7͒ and ͑8͒.…”

The scaling of electromigration lifetimes

“…In general, the Cu conductor has a near-bamboo grain structure, being composed of single-crystal and polycrystalline segments in series. The polycrystalline fraction, p=Lp/(Lp+Ls), where L p and L s are the mean polycrystalline and single-crystal length (Fig.3), is determined by the trench width [8]. Due to the difficulty in growing grains in narrow trenches, microstructure is increasingly polycrystalline with feature size reduction.…”

The Effects of Microstructures on Normal and Early Failures of Interconnects Caused by Electromigration

“…Considering the effect of microstructure, Dreyer et al developed a model for electromigration lifetimes. 4 The model separates mass transport into two distinct components: grain boundary and lattice diffusions, and expresses the effective diffusivity of an interconnect as sum of contribution from each individual component. However, in a near bamboo structure interconnect, the bamboo segments and polygranular clusters are in series.…”