On the unusual electromigration behavior of copper interconnects

Glickman, E.; Nathan, M.

doi:10.1063/1.363330

Cited by 66 publications

(38 citation statements)

References 32 publications

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“…Due to the large number of material parameters involved, we concentrate on the influence of the one which was predicted to greatly affect the grooving process, i.e., the ratio of the GB to surface diffusivity, r d = D gb /D s [9]. It should be noted that (i) the experimentally measured values of diffusivities could vary, according to different sources, by up to three orders of magnitude, and (ii) D s can be smaller than D gb , due to, for example, surface contamination, thus giving r d > 1.…”

Section: Numerical Results: the Electromigration Problemmentioning

confidence: 99%

Numerical Simulation of Grain-Boundary Grooving by Level Set Method

Khenner

Averbuch

Israeli

et al. 2001

Journal of Computational Physics

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A numerical investigation of grain-boundary grooving by means of a level set method is carried out. An idealized polycrystalline interconnect which consists of grains separated by parallel grain boundaries aligned normal to the average orientation of the surface is considered. Initially, the surface diffusion is the only physical mechanism assumed. The surface diffusion is driven by surface-curvature gradients, while a fixed surface slope and zero atomic flux are assumed at the groove root. The corresponding mathematical system is an initial boundary value problem for a two-dimensional equation of Hamilton-Jacobi type. The results obtained are in good agreement with both Mullins analytical "small-slope" solution of the linearized problem (W. W. Mullins, 1957, J. Appl. Phys. 28, 333) (for the case of an isolated grain boundary) and with the solution for a periodic array of grain boundaries (S. A. Hackney, 1988, Scripta Metall. 22, 1731. Incorporation of an electric field changes the problem to one of electromigration. Preliminary results of electromigration drift velocity simulations in copper lines are presented and discussed.

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Section: Numerical Results: the Electromigration Problemmentioning

confidence: 99%

Numerical Simulation of Grain-Boundary Grooving by Level Set Method

Khenner

Averbuch

Israeli

et al. 2001

Journal of Computational Physics

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“…[8]. Here, is the effective charge number, is the charge of an electron 1.6 10 C, is a characteristic width, is the electric field across the extrusion, is the Cu atomic volume 1.2 , and is the specific Cu interface free energy, 1.7 Joules/m [9]. All physical parameters here are appropriate for a quarter micron Cu wire at 600 K [7].…”

Section: Resultsmentioning

confidence: 99%

Temporary extrusion failures in accelerated lifetime tests of copper interconnects

Zhang

Choy²,

Chapman³

et al. 2005

IEEE Electron Device Lett.

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A novel electromigration failure mode was detected in 0.13-m technology, copper dual damascene interconnects. Extrusions formed between the test lead and neighboring monitor lines, resulting in short-circuit failure. However, many of these extrusions were short lived, shrinking within a period of a minute to an hour. These phenomena indicated that a temporary "soft failure" existed in accelerated copper electromigration tests in addition to the traditional permanent failure or "hard failure." These soft failures would be missed unless short sampling intervals (less than a minute) and continuous monitoring of the leakage current between test metal lines and neighboring circuits were carried out. Consistent with our experimental results, physical modeling suggested that capillary forces were able to rupture a long and narrow extrusion and the electric field across the extrusion could accelerate this process.

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“…The theory advocated by Glickman and Nathan (1996) and his group cannot explain this top to toe grain thinning by their proposed vertical grain boundary grooving model coupled with cathode edge surface diffusion using neither type-A nor type-B mechanisms, which is simulated by Nathan et al (2000) and Khenner et al (2001) in polycrystalline samples, since grain boundary grooving no longer takes place along the those GB-planes parallel to longitudinal axis of the specimen rather proceeds top to bottom and where the active GB-planes are perpendicular to the direction of electromigration, similar to our configuration adapted in this work. Therefore, the model presented here can easily be adapted for the grain thinning simulation studies by taking an extra grain boundary transverse direction and thereby having a triad crystalline sample rather than the bicrsytal as used in the present study.…”

Section: Discussionmentioning

confidence: 99%

Cathode edge displacement by voiding coupled with grain boundary grooving in bamboo like metallic interconnects by surface drift-diffusion under the capillary and electromigration forces

Oǧurtani¹,

Akyıldız²

2008

International Journal of Solids and Structures

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The kinetics of cathode edge shrinkage and displacement (drift) coupled strongly with the grain boundary (GB) grooving is investigated using the novel mathematical model developed by Ogurtani, in sandwich type thin film bamboo lines. The computer simulations are performed under the constant current (CC) and the switch-over constant voltage (SOCV) operations. The cathode drift velocity and the cathode failure time show the existence of two distinct phases, depending upon the normalized electron wind intensity parameter v; the capillary (v 6 0.01) and the electromigration (EM) dominating regimes (v > 0.01), having current exponent n, equal to 0 and 1, respectively. Analysis of various experimental data on the cathode drift velocity results a consistent value for the surface drift-diffusion coefficient, 1:0 Â 10 À5 expðÀ1:00 eV=kT Þ m 2 s À1 , for copper interconnects exposed to some contaminations during the processing and testing stages. This is found to be an excellent agreement with the experimental values reported in the literature after applying the proper 1/kT correction on the apparent activation enthalpy associated with Nernst-Einstein mobility relationship. The complete cathode failure time (CCFT) due to the cathode area shrinkage by voiding is also formulated by inverse scaling and normalization procedures, which show exactly the same capillary and EM dominating regimes. This formula can be used to predict very accurate CCFT for metallic lines with bamboo-like, near-bamboo, and even with polycrystalline structures by proper calculation of the cathode-edge path length (CEPL) parameter, in terms of the actual line width, the thickness and the grain size.

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On the unusual electromigration behavior of copper interconnects

Abstract: Statistics of stress migration and electromigration failures of passivated interconnect lines AIP Conf. Proc. 305, 15 (1994); 10.1063/1.45706Characterization of stress migration in submicron metal interconnects AIP Conf.

Cited by 66 publications

References 32 publications

Numerical Simulation of Grain-Boundary Grooving by Level Set Method

Numerical Simulation of Grain-Boundary Grooving by Level Set Method

Temporary extrusion failures in accelerated lifetime tests of copper interconnects

Cathode edge displacement by voiding coupled with grain boundary grooving in bamboo like metallic interconnects by surface drift-diffusion under the capillary and electromigration forces

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