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Yield Modeling

There are a number of yield models reported in the literature that relate fault probability to chip yield Two such models are the Poisson model
YTot = Y0$\displaystyle \prod_{{j=1}}^{{k}}$e-lambda_j
and the Negative Binomial model
YTot = Y0\prod_{{j=1}}^{{k}}(\vphantom{1 + \frac{\lambda_j}{\alpha_j}}1 + {\frac{{\lambda_j}}{{\alpha_j}}}\vphantom{1 + \frac{\lambda_j}{\alpha_j}}\right)^{{-\alpha_j}}_{}
Where Yo is factor which acts as an adjustment to take into account any non-random defects and $ \lambda_{{j}}^{}$ is the average number of faults of type j.
The Poisson and negative binomial yield models.
The Poisson and negative binomial yield models.

The Poisson model tends to give overly pessimistic yield predictions for large chips. The negative binomial model proposed by Stapper includes a clustering parameter $ \alpha_{j}^{}$ (usually of the order 0.3-5) to correct for the effect of defect clustering and so improve predictions for larger chips. However, it can be seen from the graphs that these models only diverge significantly for large average number of faults for a single defect type. Since many fabrication processes have many layers and faults associated with each layer are largely independent the Poisson model is often used with excellent results. The Negative Binomial model is recommended when fault repair (RAM) is used. The figure above shows a graphical representation of both these models. The models require a value of $ \lambda_{{j}}^{}$ for each defect type. For single layer breaks and shorts the value of $ \lambda$ is calculated using

$\displaystyle \lambda$ = $\displaystyle \int_{{x_{min}}}^{{\infty}}$Ac( x)D(x)dx
where xmin is the minimum feature size of the layout, Ac(x) is the critical area for defect size x and D(x) is defect density function. For critical areas that are independent of defect size (pinhole critical areas)
$\displaystyle \lambda$ = AcD0
where Ac is the critical area and D0 is the number of defects per unit area. For contacts $ \lambda$ is determined by
lambda = NiFi
where Ni is the number of contacts and Fi is the failure rate of these contacts.

A yield model requires both critical areas and defect data . The EYES tool can provide all the necessary critical area information and can combine it with process defect data to generate an accurate yield model.



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