A study of stress-driven diffusive growth of voids in encapsulated interconnect lines
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Stress-driven diffusive growth of voids in encapsulated interconnect lines is studied. By calculating the rate of growth of a single void in a passivated line subjected to an initial hydrostatic tension stress and by assuming that failure occurs when the void reaches a critical size, a model for failure of encapsulated interconnect lines by stress voiding can be developed. The model for the prediction of void growth and failure is based on two limiting kinds of void growth. In one limit, which applies at short times, radial displacements occur by diffusional flow processes around the growing void and relax the local hydrostatic tension stress. In the long time limit, vacancies flow to the void from distant parts of the line by diffusion along grain boundaries, thereby relaxing the stress in a growing section of the line. A model based on a combination of these behaviors leads to a failure law for aluminum lines of the form tfcr2jd = 10 192 exp(Q/RT) where tf is the failure time in seconds, a is the initial hydrostatic tension stress in the line in Pa, d is the grain size in meters, and the activation energy, Q = 80.9 kJ/mol, is close to that for grain boundary diffusion in aluminum. The model predictions appear to be in good agreement with the few experiments on stress voiding that have been conducted.
I. INTRODUCTION In 1984, reports of stress-induced failure of aluminum based interconnects began to appear in the literature. Since then a number of observations of this phenomenon have been made.1"6 The occurrence of these failures has paralleled the trend of smaller feature sizes in integrated circuit structures. As the linewidths in microelectronic structures get smaller, the thermal stresses that develop within the lines are expected to increase and this, in turn, is expected to exacerbate the problem of stress voiding in conductor lines. In this way, stress-induced failure of interconnect structures is well recognized as a serious reliability problem in the integrated circuit industry. In order to understand and control stress-induced voiding of interconnect lines, it is necessary to understand both the driving forces responsible for void growth, i.e., the thermal stresses, and the mechanism of void growth itself. Several recent studies have focused on the calculated or measured thermal stresses in encapsulated lines,7"13 so that this aspect of the problem is now reasonably well understood. The void growth process itself, however, is not so well understood. Several efforts have been made recently to model the growth of voids in encapsulated lines.13"21 Most authors have suggested that void growth occurs by grain boundary diffusion, and many of the existing models for stress voiding employ this mechanism. Li et al.19 used a simple flux expression (based on grain boundary diffusion) and a geometric formulation to estimate the J. Mater. Res., Vol. 7, No. 5, May 1992 http://journals.cambridge.org
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percentage of lines that fail during an aging test. Sugano et al.20 modeled their own failure
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