A model for linewidth-dependent electromigration lifetime and its application to design rule scaling for narrow interconnects

Fu, Kuan–Yu

doi:10.1063/1.348659

Cited by 10 publications

(8 citation statements)

References 7 publications

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“…The variations in MTTF and DTTF with linewidth w (assumed equal to pd 0 [26]) are shown in figure 7. The dependence is as expected from several other studies [15,16,[18][19][20][21][22].…”

Section: Analysis Of Early Failuressupporting

confidence: 90%

“…The failure-unit, or structural defect, model has received quite general usage in electromigration theory, and versions of it have been considered as descriptions for electromigration failure on many occasions (e.g. [9,[15][16][17][18][19][20][21][22]). The model was originally developed by Agarwala et al [17] to describe the behaviour of the failure distribution as a function of the line length, and it was later developed by Cho and Thompson [19] to include the important dependence on linewidth.…”

Section: Failure-unit Modelmentioning

confidence: 99%

“…They have also investigated the manner in which the average number of failure-units, N, depends upon both the linewidth, w, and the current density, j , and demonstrated that, for near-bamboo lines, the average number of failure-units decreases with decreasing linewidth. However, along with others [15,9,[19][20][21][22], they have assumed that all lines are alike and equivalent to the average line. They have consequently used the approximation…”

Section: Failure-unit Modelmentioning

confidence: 99%

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An analysis of the weakest-link model for early electromigration failure

Dwyer¹

2004

J. Phys. D: Appl. Phys.

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The application of the weakest-link or failure-unit model to electromigration failure is discussed in relation to a simple model that should describe the early failures in fine-line, as-patterned aluminium reasonably well. The earliest failures are expected to be due to the presence of at least one polygranular cluster longer than some critical (Blech) length, while the next earliest are assumed to arise from linked shorter clusters. Using a simple model of the microstructure, the probability density function for the number of each of these types of failure-unit is determined as a function of the linewidth. For this simple model the overall failure distribution may be calculated essentially exactly using the Theory of Runs; consequently we can compare these exact results with some common approximations. It is demonstrated through Jensen's inequality that a common approximate method is in fact a rigorous upper bound for the failure distribution. The model exhibits the expected increase in median-time-to-failure and deviation-in-time-to-failure values with decreasing linewidth when forcing a lognormal distribution. Although this would suggest an eventual decrease in reliability with scale reduction, the exact results show that this is not the case.

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“…The variations in MTTF and DTTF with linewidth w (assumed equal to pd 0 [26]) are shown in figure 7. The dependence is as expected from several other studies [15,16,[18][19][20][21][22].…”

Section: Analysis Of Early Failuressupporting

confidence: 90%

Section: Failure-unit Modelmentioning

confidence: 99%

Section: Failure-unit Modelmentioning

confidence: 99%

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An analysis of the weakest-link model for early electromigration failure

Dwyer¹

2004

J. Phys. D: Appl. Phys.

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“…In single crystal segments, surface diffusion is the dominant transport path, while in polycrystalline segments, grain boundary diffusion dominates transport. We quantify the proportion of the total line length of polycrystalline segments as the parameter p. This parameter was used to explain the effects of microstructure on Al interconnect mass transport [18]. However, Cu interconnects are fabricated through a damascene process.…”

Section: Modeling Of Drift Velocity For Polycrystalline Conductormentioning

confidence: 99%

Electromigration mechanisms in Cu nano-wires

Lin

Lee

Oates

2010

2010 IEEE International Reliability Physics Symposium

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In this article, we propose a new drift velocity technique to measure electromigration at temperatures of 125 o C to directly assess electromigration transport at use conditions. We present measurements of the temperature of the drift velocity of Cu conductors with small and large polycrystalline grain size. A significant grain size dependence of drift velocity was found, indicating a large flux of atoms through grain boundaries when the fraction of polycrystalline segments is a significant fraction of the conductor length. A physical model is proposed to explain the drift velocity behavior in Cu nano-wires and we determine the diffusion parameters from grain boundary diffusion and interface diffusion.

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“…Some researchers observed the failure time of polycrystalline lines to increase slowly with linewidth [3][4][5][6]. It was suggested that such lines be better described as serial/parallel combinations of failure elements [6].…”

Section: N Ineqs(2)and(3) Asmentioning

confidence: 99%

Two electromigration failure modes in polycrystalline aluminum interconnects

Atakov

Clement

Miner

1994

Proceedings of 1994 IEEE International Reliability Physics Symposium RELPHY-94

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Grain-boundary (GB) erosion-type voids and transgranular slit-like voids are found to be two competing elecaomigration (EM) failure modes in partly-bamboo interconnects. The effects of metal microstructure, passivation thickness, line width and length, and EM sbess conditions on the two failure modes were studied. The kinetics for GBtype failures is strongly affected by the threshold effect in polycrystalline segments and is well described by the MultiLognormal (MLN) function with stress-dependent number of elements. The model @cts that the EM resistance of partly-bamboo lines at VLSI operating conditions is limited by the slit failure mode, rather than by GB-type failures.not only time is saved, but the statistical error brackets are reduced. The problem of Joule heating can be alleviated by optimizing the test " r e layout.In this work, we evaluated the effect of line length on the parameters of the failure time distribution. 1 mm long lines were typically used to characterize the EM kinetics and the effect of process variables for wider, partly-bamboo lines, while 14 mm or 19 mm long lines were used to characterize narrow, bamboo lines. The effect of linewidth on EM lifetime was studied for both 1 mm and 14 mm long lines.The experimental results are interpreted in terms of the MLN model. The effect of material characteristics and EM stress conditions on the model parameters is discussed.

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A model for linewidth-dependent electromigration lifetime and its application to design rule scaling for narrow interconnects

Cited by 10 publications

References 7 publications

An analysis of the weakest-link model for early electromigration failure

An analysis of the weakest-link model for early electromigration failure

Electromigration mechanisms in Cu nano-wires

Two electromigration failure modes in polycrystalline aluminum interconnects

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