Stress That Counteracts Electromigration: Threshold Versus Kinetic Approach

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142432, Moscow District, Russia

Abstract The paper analyzes electromigration (EM) conditions and material properties that determine the maximum EM induced stress, aa, and stress gradient, Va, which counteract EM flow in interconnects. The first systematic data on the drift velocity vs. stripe length, L, current density, j, and temperature are presented for Al lines. In contrast to the conventional approach to the Blech problem with aa taken to be a material constant ("yield strength"), the observations suggest that aa increases with j. The stress adjustment is shown to result from the imperative coupling of the net flux of material directed to the downwind end of the stripe with the flux of plastic flow (creep) responsible for stress relaxation. The effect of parameters of the constitutive equation assumed to describe the plastic flow kinetics, namely that of strain rate exponent, threshold stress, and creep, effective viscosity, on the stress cya is considered. To account for the creep viscosity, T1, obtained unpassivated aluminum stripes from EM experiments, a model for the attachment-controlled Coble creep is suggested.

Introduction The conventional approach to the interaction of EM generated mechanical stress with EM flux in interconnects is based on the key assumption that the maximum compressive stress at the anode end of the stripe, aa, equals to some threshold value, at, loosely referred to as "the yield strength of the film" and independent of the current density, j, or the stripe length, L. This, with Va ; crt/L, leads to the Blech-Schreiber formulae (BSF) for the EM displacement rate, V [1-3].

V/Vd

- Lt/L = 1 - A/jL

(1)

Or, in dimensionless variables, = I - S-' Here Vd is the EM rate for L -+ oo, Lt is the threshold length, A = artf/pz

(1-a) is the threshold, p is

specific resitivity, Q is atomic volume, Z is effective charge, while S = V/Vd and S = L/Lt. Although the BSF for displacement kinetics captures the length and current density EM thresholds and

is widely used for analysis of the Blech-mode fkilures at contact windows, vias and other sites of perfect EM flux divergences, it has never been verified experimentally. As regards the principal assumption of this Threshold--Sharp Yield Stress Approach that the maximum stress, aa, material can sustain equals a

yield strength, ast, it was shown not to be generally valid [4-7]. The Kinetic Approach predicts that EM induced stress and stress distribution along the line should be dictated by the kinetics of time-dependent plastic flow (creep) and should "tune in" to the current density. In the present work we test, for the first time, the validity of the BSF in the drift velocity in situ experiments with aluminum stripes. The observed deviations from the behavior predicted by Eq.(l-a) will be explained in terms of stress adjustment resulting from the coupling of the flux of material directed to the anode end with the flux of diffusional creep, which is assumed to be responsible for stress relaxation. 477

Mat. Res. Soc. Symp. Proc. Vol. 356 @1995

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