Microstructure and electromigration in copper damascene lines

Arnaud, L.; Tartavel, G.; Berger, T.; Mariolle, D.; Gobil, Y.; Touet, I.

doi:10.1016/s0026-2714(99)00209-7

Cited by 67 publications

(28 citation statements)

References 9 publications

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“…With continuing void growth, the line resistance increases, eventually leading to failure of the line. The corresponding failure times usually follow a lognormal distribution with the median lifetime depending on the quality of the interface, which controls the mass transport [Hu 1999, Arnaud 2000, Hau-Riege 2001, Ogawa 2002b, Meyer 2002, Hauschildt 2004a, Hauschildt 2004b. Since EM experiments are conducted at higher current densities and temperatures compared to operating conditions, extrapolations are needed to assess reliability at operating conditions.…”

Section: Chapter 1: Introductionmentioning

confidence: 99%

Statistical Analysis of Electromigration Lifetimes and Void Evolution for Cu Interconnects

Hauschildt

Gall²,

Thrasher³

et al. 2004

MRS Proc.

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Electromigration (EM) failure statistics and the origin of the lognormal deviation (σ) for Cu interconnects have been investigated by analyzing the lifetime statistics and void size distributions at various stages during EM testing. Experiments were performed on 0.18 μm wide Cu interconnects with tests terminated after specific amounts of resistance increases, or after a specified test time. Void size distributions of resistance-based, as well as time-based EM tests were obtained using focused ion beam (FIB) microscopy. The lifetime and void size distributions were found to follow lognormal distribution functions. The σ values of EM lifetime and time-based void size distributions decrease with higher percentages of resistance increase, reaching an asymptotic value of σ ∼ 0.14. In contrast, σ values of resistance-based void size distributions are significantly smaller and do not show an obvious dependence on time. The statistics of resistance-based void size distributions can mainly be accounted for by geometrical variations of the void shape, while the statistics of time-based void size distributions requires consideration of kinetic aspects of the EM process. The σ values of EM lifetime distributions at long times can be simulated based on measured void size distributions, taking into account geometrical and experimental factors of EM. In contrast, for short times the statistics of initial void formation and the kinetics of interfacial mass transport have to be considered.

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Section: Chapter 1: Introductionmentioning

confidence: 99%

Statistical Analysis of Electromigration Lifetimes and Void Evolution for Cu Interconnects

Hauschildt

Gall²,

Thrasher³

et al. 2004

MRS Proc.

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“…w and h are the linewidth and height, and d 50 is the mean metal grain diameter. In copper interconnect, diffusion along the interface between the copper and the nitride caplayer generally dominates D A ͑Refs.…”

Section: ͪ ͑1͒mentioning

confidence: 99%

“…If t f is distributed lognormally then log͑t f ͒ is normally distributed and may be described by parameters , the mean of log͑t f ͒, and TTF its standard deviation. Almost all EM failure data is plotted on lognormal paper and consequently tends to come quoted with it a median value t 50 equal to exp͑͒ and a value of TTF . The pdf for a lognormally distributed t f is given by ͓LN͑ , TTF ͔͒…”

Section: Gamma Versus Lognormalmentioning

confidence: 99%

Analysis of multistate models for electromigration failure

Dwyer

2010

Journal of Applied Physics

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Additional Information:• This article was published in the Journal of Applied Physics [ c Amer- The application of a multistate Markov chain is considered as a model of electromigration interconnect degradation and eventual failure. Such a model has already been used ͓Tan et al., J. Appl. Phys. 102, 103703 ͑2007͔͒, maintaining that, in general, it leads to a failure distribution described by a gamma mixture, and that as a result, this type of distribution ͑rather than a lognormal͒ should be used as a prior in any Bayesian mode fitting and subsequent reliability budgeting. Although it appears that the model is able to produce reasonably realistic resistance curves R͑t͒, we are unable to find any evidence that the failure distribution is a simple gamma mixture except under contrived conditions. The distributions generated are largely sums of exponentials ͑phase-type distributions͒, convolutions of gamma distributions with different scales, or roughly normal. We note also some inconsistencies in the derivation of the gamma mixture in the work cited above and conclude that, as it stands, the Markov chain model is probably unsuitable for electromigration modeling and a change from lognormal to gamma mixture distribution generally cannot be justified in this way. A hidden Markov model, which describes the interconnect behavior at time t rather than its resistance, in terms of generally observed physical processes such as void nucleating, slitlike growth ͑where the growth is slow and steady͒, transverse growth, current shunting ͑where the resistance jumps in value͒, etc., seems a more likely prospect, but treating failure in such a manner would still require significant justification.

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“…With j =20 mA m −2 , the jl product for a 50 m line is 10 4 A cm −1 which is comfortably greater than that suggested for void nucleation in copper lines. 33,34 We assume that grain diameters are distributed lognormally, with a median value of d 50 = 0.5 m and lognormal deviation of d = 0.36, values obtained for 0.35 m lines, 35 although we shall regard these parameters as variables to some extent.…”

Section: Failure Time Distributionmentioning

confidence: 99%

Modeling the electromigration failure time distribution in short copper interconnects

Dwyer

2008

Journal of Applied Physics

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The electromigration (EM) lifetime in short copper interconnects is modeled using a previously developed means of generating realistic interconnect microstructures combined with the one-dimensional stress evolution equation of Korhonen et al. [J. Appl. Phys. 73, 3790 (1993)]. This initial analysis describes the void nucleation and subsequent growth in lines blocked at one end and terminated with a pad at the other. For short copper interconnects, the failure time is largely spent on void growth, and, for sufficiently short lines (≲50 mm), the growth is largely steady state. This allows for the development of a simple expression for the variation of the failure time with microstructure. Assuming that the diffusion activation energies are normally distributed, the permanence property of summed lognormals leads to a roughly lognormal distribution for EM failure times. Importantly for EM design rules, linear extrapolation on lognormal plot is found to slightly underestimate interconnect reliability.

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Microstructure and electromigration in copper damascene lines

Cited by 67 publications

References 9 publications

Statistical Analysis of Electromigration Lifetimes and Void Evolution for Cu Interconnects

Statistical Analysis of Electromigration Lifetimes and Void Evolution for Cu Interconnects

Analysis of multistate models for electromigration failure

Modeling the electromigration failure time distribution in short copper interconnects

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