Surface evolution in bare bamboo-type metal lines under diffusion and electric field effects

Averbuch, Amir; Israeli, M.; Nathan, M.; Ravve, Igor

doi:10.1016/s0021-9991(03)00199-2

Cited by 22 publications

(14 citation statements)

References 56 publications

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“…11 Their treatment involves a governing equation obtained rigorously from the irreversible thermodynamic theory, instead of assuming the self-similar enlargement ͑which keeps the void shape invariant during growth͒ of a void with a constant rate of growth, as employed by Kraft et al 18 The EM-driven evolution of transgranular edge voids has been treated extensively in the literature, 9,14,16 while that of intergranular edge voids in "bamboo" metal lines, which was studied thoroughly by Oren and Ogurtani, has received little attention, 19 as mentioned by Averbuch et al 20 and Nathan et al 21 Thermal stresses generated by differential thermal expansion in encapsulated metal interconnects in ultralarge scale integration ͑ULSI͒ chips have long been recognized as an important subject. 4 The importance arises from the fact that the stresses can be large enough to cause immediate or, even worse, delayed failure of the metal lines.…”

Section: Introductionmentioning

confidence: 99%

Morphological evolution of voids by surface drift diffusion driven by capillary, electromigration, and thermal-stress gradients induced by steady-state heat flow in passivated metallic thin films and flip chip solder joints. I. Theory

Oǧurtani

Akyıldız

2008

Journal of Applied Physics

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Section: Introductionmentioning

confidence: 99%

Morphological evolution of voids by surface drift diffusion driven by capillary, electromigration, and thermal-stress gradients induced by steady-state heat flow in passivated metallic thin films and flip chip solder joints. I. Theory

Oǧurtani

Akyıldız

2008

Journal of Applied Physics

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“…͑3͒. [27][28][29] These calculations are able to demonstrate complex morphological changes similar to those of real voids in encapsulated metal lines, 24,25,[27][28][29] including a void splitting mechanism in which, in the presence of a strong anisotropy, a cylindrical void can develop side features which may then detach from the mother void, [27][28][29] and a description of the migration of voids toward the cathode and a model of void pinning at grain boundaries. 22,31 To understand failure statistics, it is necessary to limit such problems, such as by starting with a single mode, such as viabelow failure in M2 lines, and considering such growth complexities at a later stage.…”

Section: ͪ ͑1͒mentioning

confidence: 85%

“…[20][21][22][23][24][25][26][27][28][29][30][31] Each of these factors depends on the local microstructure, leading to anisotropies which may affect the void growth direction and consequently its shape factor in Eq. ͑3͒.…”

Section: ͪ ͑1͒mentioning

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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“…This statement was also assumed by Ohring 47 in his analytical studies on electromigration damage in thin film interconnects. Averbuch et al 2 utilized highly sophisticated numerical procedures in their studies, but they still assumed that there is an equilibrium configuration at the TJ, and the TJ displacement velocity can be extrapolated from the projection of normal velocities of neighboring nodes in the direction of intergranular grain boundary. Zhang et al 48 and Xin and Nang 49 also studied the effect of anisotropic surface free energy on thermal grooving by using the standard Herring model with equilibrium dihedral angles.…”

Section: Introductionmentioning

confidence: 99%

Mesoscopic nonequilibrium thermodynamics of solid surfaces and interfaces with triple junction singularities under the capillary and electromigration forces in anisotropic three-dimensional space

Oǧurtani

2006

The Journal of Chemical Physics

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A theory of irreversible thermodynamics of curved surfaces and interfaces with triple junction singularities is elaborated to give a full consideration of the effects of the specific surface Gibbs free energy anisotropy in addition to the diffusional anisotropy, on the morphological evolution of surfaces and interfaces in crystalline solids. To entangle this intricate problem, the internal entropy production associated with arbitrary virtual displacements of triple junction and ordinary points on the interfacial layers, embedded in a multicomponent, multiphase, anisotropic composite continuum system, is formulated by adapting a mesoscopic description of the orientation dependence of the chemical potentials in terms of the rotational degree of freedom of individual microelements. The rate of local internal entropy production resulted generalized forces and conjugated fluxes not only for the grain boundary triple junction transversal and longitudinal movements, but also for the ordinary points. The natural combination of the mesoscopic approach coupled with the rigorous theory of irreversible thermodynamics developed previously by the global entropy production hypothesis yields a well-posed, nonlinear, moving free-boundary value problem in two-dimensional (2D) space, as a unified theory. The results obtained for 2D space are generalized into the three-dimensional continuum by utilizing the invariant properties of the vector operators in connection with the descriptions of curved surfaces in differential geometry. This mathematical model after normalization and scaling procedures may be easily adapted for computer simulation studies without introducing any additional phenomenological system parameters (the generalized mobilities), other than the enlarged concept of the surface stiffness.

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Surface evolution in bare bamboo-type metal lines under diffusion and electric field effects

Cited by 22 publications

References 56 publications

Morphological evolution of voids by surface drift diffusion driven by capillary, electromigration, and thermal-stress gradients induced by steady-state heat flow in passivated metallic thin films and flip chip solder joints. I. Theory

Morphological evolution of voids by surface drift diffusion driven by capillary, electromigration, and thermal-stress gradients induced by steady-state heat flow in passivated metallic thin films and flip chip solder joints. I. Theory

Analysis of multistate models for electromigration failure

Mesoscopic nonequilibrium thermodynamics of solid surfaces and interfaces with triple junction singularities under the capillary and electromigration forces in anisotropic three-dimensional space

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