Physically based models of electromigration: From Black’s equation to modern TCAD models

Orio, R. L. de; Ceric, H.; Selberherr, S.

doi:10.1016/j.microrel.2010.01.007

Cited by 120 publications

(43 citation statements)

References 96 publications

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“…(10) (without the thermal and stress terms) as detailed by R.L. de Orio and his colleagues [25] was compared with the simulation results. The boundary conditions are shown in Eq.…”

Section: Model Validationmentioning

confidence: 99%

Progress in the Development of an Electro-Migration Modelling Methodology

Zhu¹,

Kotadia²,

Xu³

et al. 2014

Proceedings of 10th World Congress on Computational Mechanics

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“…(10) (without the thermal and stress terms) as detailed by R.L. de Orio and his colleagues [25] was compared with the simulation results. The boundary conditions are shown in Eq.…”

Section: Model Validationmentioning

confidence: 99%

Progress in the Development of an Electro-Migration Modelling Methodology

Zhu¹,

Kotadia²,

Xu³

et al. 2014

Proceedings of 10th World Congress on Computational Mechanics

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“…It is this effect which is referred to as electromigration (EM) [1,2] in the literature. The migration is almost entirely due to a vacancy exchange mechanism [3] and the material flux can be described in terms of a vacancy flux J v [4].…”

Section: Introductionmentioning

confidence: 99%

“…Depletion results ultimately in the formation of voids and line failure. Modelling EM has therefore a long tradition and has reached a high level of maturity [4]. The focus has naturally been on how to avoid or delay deterioration of interconnects, i.e.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional simulations of temperature and current-density distribution in electromigrated structures

2014

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We report on the application of a feedback-controlled electromigration technique for the formation of nanometre-sized gaps in mesoscopic gold wires and rings. The effect of current density and temperature, linked via Joule heating, on the resulting gap size is investigated. Our experiments include in situ measurements of the evolution of the electrical resistance and of the structure of the device during electromigration. Experimentally, a good thermal coupling to the substrate turned out to be crucial to reach electrode spacings below 10 nm and to avoid overall melting of the nanostructures. This finding is supported by numerical calculations of the current-density and temperature profiles for structure layouts subjected to electromigration. The numerical method can be used for optimizing the layout so as to predetermine the location where electromigration leads to the formation of a gap.

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“…These models are essentially parametric modifications of Black's Equation. Orio et al [5] study the well-known EM failure models to identify gaps in models and implementation. Shatzkes et al [15] empirically demonstrate that the current density exponent in Black's Equation should be n = 2.…”

Section: Introductionmentioning

confidence: 99%

On potential design impacts of electromigration awareness

Kahng

Nath

Rosing

2013

2013 18th Asia and South Pacific Design Automation Conference (ASP-DAC)

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Abstract-Reliability issues significantly limit performance improvements from Moore's-Law scaling. At 45nm and below, electromigration (EM) is a serious reliability issue which affects global and local interconnects in a chip and limits performance scaling. Traditional IC implementation flows meet a 10-year lifetime requirement by overdesigning and sacrificing performance. At the same time, it is well-known among circuit designers that Black's Equation [2] suggests that lifetime can be traded for performance. In our work, we carefully study the impacts of EM-awareness on IC implementation outcomes, and show that circuit performance does not trade off so smoothly with mean time to failure (MTTF) as suggested by Black's Equation. We conduct two basic studies: EM lifetime versus performance with fixed resource budget, and EM lifetime versus resource with fixed performance. Using design examples implemented in two process nodes, we show that performance scaling achieved by reducing the EM lifetime requirement depends on the EM slack in the circuit, which in turn depends on factors such as timing constraints, length of critical paths and the mix of cell sizes. Depending on these factors, the performance gain can range from 10% to 80% when the lifetime requirement is reduced from 10 years to one year. We show that at a fixed performance requirement, power and area resources are affected by the timing slack and can either decrease by 3% or increase by 7.8% when the MTTF requirement is reduced. We also study how conventional EM fixes using per net Non-Default Rule (NDR) routing, downsizing of drivers, and fanout reduction affect performance at reduced lifetime requirements. Our study indicates, e.g., that NDR routing can increase performance by up to 5% but at the cost of 2% increase in area at a reduced 7-year lifetime requirement.

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Physically based models of electromigration: From Black’s equation to modern TCAD models

Cited by 120 publications

References 96 publications

Progress in the Development of an Electro-Migration Modelling Methodology

Progress in the Development of an Electro-Migration Modelling Methodology

Two-dimensional simulations of temperature and current-density distribution in electromigrated structures

On potential design impacts of electromigration awareness

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