Void Nucleation on a Contaminated Patch
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Void nucleation on a contaminated patch B. M. Clemens, W. D. Nix, and R. J. Gleixner Department of Materials Science and Engineering, Stanford University, Stanford, California 95305–2205 (Received 7 October 1996; accepted 27 January 1997)
The energetics of a simple model of void nucleation on a contaminated patch between the sidewall and metal in an integrated circuit interconnect are examined to determine void nucleation behavior. The conditions under which there is no void nucleation barrier are represented by a simple relationship between the volume driving force, the equilibrium contact angle, the surface energy of the metal, and the contaminated patch radius. The void nucleation barrier, when it exists, is a strong function of these same parameters, and increases sharply as the driving force decreases, and under some conditions, increases with increasing equilibrium contact angle.
I. INTRODUCTION
Voiding in interconnect metal lines caused by thermal stresses and electromigration has emerged as an important reliability problem for integrated circuits.1–3 Once voids have been nucleated, they can grow without bound, both by vacancy adsorption and by void migration and coalescence, eventually severing the line completely and leading to an open circuit.4–8 Here we focus our attention on the earliest stage of this failure process: the void nucleation stage. Recently Gleixner et al.2 have shown that even the very high tensile stresses typically present in aluminum interconnect lines are not sufficient to cause void nucleation to occur by vacancy condensation. Even for the most favorable geometries and interfaces, the critical sizes and formation-free energies of the embryos are much too large to permit void nucleation by vacancy clustering. Flinn has suggested that void nucleation under these conditions can occur on a patch of contaminated interface between the metal line and the passivation sidewall.1 Such a mechanism can account for the observation of void formation in interconnect lines that were initially void-free. With the contaminated patch nucleation mechanism, it is imagined that there is no bonding between the metal and sidewall in the region within the contaminated patch, so that a void can easily grow there. We examine a simple model incorporating this idea, and extend it to include the growth of the void beyond the region of the contaminated patch. We use a continuum approach which ignores the complex geometries of small atomistic voids. We find that, under some conditions, the free energy will monotonically decrease as the void volume increases, so that nucleation can occur without a barrier. We also calculate the barrier in the cases where the free energy 2038
J. Mater. Res., Vol. 12, No. 8, Aug 1997
does not monotonically decrease as a function of void volume. II. VOID CONFINED TO PATCH
We first consider the free energy of a spherical cap void growing on a circular patch of radius RP , where the contact area between the void and the sidewall is constr
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