A Macroscopic Model of Electromigration: Comparison with Experiment
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Comparison of theory and experiment is critical in microelectronic reliability. In this work, a model which has been previously used for electromigration time to failure predictions (developed by Harrison) is extended to include predictions for numbers of voids and void sizes. Predictions from the model are compared to experimental measurements. The model makes reasonable predictions for mean lifetimes, numbers of voids, and void areas with very few free parameters. The model, however, does not adequately reproduce the range of lifetimes found in experiment.
INTRODUCTION Much work has been done to understand, and thereby to control, the damage and the ultimate failure of microelectronic parts due to electromigration in metal interconnects.
From a pragmatic view, the characteristic of critical importance is the lifetime of the interconnect. Most of the theoretical work, and much of the experimental work as well, has focused primarily on lifetime measurements. However, other characteristics, such as the total area of electromigration voids on a stripe, can be measured, and our understanding of the electromigration process can only be complete when these other
characteristics as well as the lifetimes can be predicted accurately. The purpose of this work is test the extent to which characteristics of thin film electromigration damage such as void areas and the number of voids can be adequately simulated by a simple model [1] which has previously been used only to examine changes in the time to failure. The experimental results which are compared to the simulation results are discussed in detail elsewhere [2]. In brief, Al 1% Si meander test stripes, 1600 Ai long, 3.4 p wide, and 0.8 pi thick, were electromigrated to failure at a constant 2 x 106 A/cm 2 . The test stripes were passivated with 0.4 A•of Si0 2 . The test stripes were examined for void damage using a Scanning Electron Microscope (SEM). The void areas, perimeters, lengths, and widths were measured on thirty-eight of the stripes using a Cambridge SEM equipped with a Robinson backscatter detector in conjunction with an Optimas digital image analysis system. MODEL DEVELOPMENT The microstructure and diffusion model adopted for this work is largely from the work of Harrison [1] and is discussed in detail elsewhere [1,3]. For brevity, only the 367 Mat. Res. Soc. Symp. Proc. Vol. 391 01995 Materials Research Society
departures from the Harrison model will be discussed in detail. In this model, the metal grain sizes are assumed to be log normally distributed, with the peak of the distribution at Dbig, full width half maximum of Wbig, and a skew of Pbig. The grains are then placed into segments at random positions along the stripe, continuing to add grains to each segment (as it is randomly chosen) until the width of the stripe is reached. The interface between the metal stripe and the passivation at the sides of the stripes is also included as a grain boundary capable of passing material along the stripe. This is a departure from Harrison's model. These interfa
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