A Comparison of Electromigration in Bulk and Thin - Film Aluminum
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DRIFT VELOCITY MEASUREMENTS Electromigration arises because of momentum exchange between conduction electrons and host metal atoms (the "electron wind"). The flux of atoms arising from electromigration is given by:
j = ND ez*jpkT e jkT
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=N D-eZr* p(j-j.)= NVD 277
Mat. Res. Soc. Symp. Proc. Vol. 391 ©1995 Materials Research Society
(1)
Here vd is the drift velocity for electromigration,
D is the diffusivity and Z* the effective charge
for the appropriate diffusion mechanism, j is the current density, N is the atom density, p is resistivity, •2 is the atomic volume, •9•/•lix is the stress gradient induced by electromigration, the electronic charge and kT has the usual meaning, jc is the current density threshold electromigration defined by (jel) = QA• / eZ*p, where l is the stripe length and Aa is maximum stress difference that the stripe can maintain without plastic deformation.
the e is for the
The drift velocity of a thin - film conductor is readily determined from measurements of the displacement of the cathode edge of a thin - film stripe on a refractory substrate during current stressing. Test structures for this purpose consist of Al alloy stripes on a refractory substrate such as W or TiN 4. Experimentally this technique can also be implemented with circuit structures designed to investigate electromigration at contacts to silicon or intermetal via contacts 5. These latter structures consist of contacts / vias linked by Al stripes on refractory underlayers, and vd may be estimated from the rate of Al depletion on the stripe joining the contacts or vias. The drift may be observed directly, but for multilayer conductors the drift also generates a resistance increase that can also be used to measure vd. Assuming that vd is constant, the resistance change with time is linear and is given by: dR w vd = --
(2)
where w is the width of the stripe, Rs is the sheet resistance of the refractory metal layer and dR/dt is the rate of resistance change due to the drift of the cathode edge. In polycrystalline films Cu depletion occurs prior to the motion of the cathode end of the stripe and reduces the electromigration flux until the Cu depletion distance, L,,, extends beyond a critical distance, Lc. As Lp increases beyond Lc, vd increases until it reaches a steady state value equivalent to that in pure Al when Lp >> Lc. Clearly, under these circumstances vd is non - linear and estimates obtained from the initial stages of the drift will be lower than the "true" value obtained from the steady state regime. Since this effect arises because of a restriction of Al motion along grain boundaries, one should not expect a similar situation a priori in the bamboo microstructures. It will depend on the dominant mechanism of transport. Studies for bamboo microstructures are conflicting, with both no measurable effectI and a retardation in drift reported 6 in A1Cu alloys. For bulk Al, Cu in solution appears to enhance the rate of Al electromigration 7 . The variability in thin - film results may indicate that Cu precipita
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