How is critical area calculated?
The value of critical area varies for different particle sizes. For a given layout, the bigger the particle size is, the larger the critical area becomes. The average critical area can be calculated based on the following formula:
How can critical area be used to measure the impact on yield?
Critical area has a direct impact on yield. Yield is improved by reducing the critical area. Instead of assuming that yield loss may occur anywhere in the layout, critical area can be applied as a yield metric to assess whether or not optimizations will improve yield.
Applying such a metric during physical design implementation can help designers predict loss characteristics and improve yield. To illustrate how this can be implemented practically, let’s look at a joint project between Synopsys Inc. and Toshiba Corp.
First step: concept validation
The first step is to validate the concept of using critical area as a yield metric for designers. Toshiba Corporation, a leader in information and communications systems, consumer products and power systems, is one of the first semiconductor companies to realize the importance of critical area as a first-order metric for yield. Following Toshiba’s guidance, Synopsys concluded that critical area is a suitable proxy for yield.
Second step: correlation with foundry results
To optimize a design for critical area, implementation tools must offer an analysis engine that correlates well with foundry results. The sign-off tools used at foundries have proven critical area analysis engines that help to ensure a golden level of accuracy. The second step of our project was to correlate the design tool’s critical area analysis engine with Toshiba’s foundry-certified calculations.
Toshiba validated the correlation between the critical area analysis engine in Synopsys’ implementation tools and their internal tape-out solution using a 90nm design with six metal layers. Some of their results are illustrated in figures 3 and 4.
Figure 3 Correlation results short critical area.
Figure 4 Correlation results open critical area.
Third step: Critical area reductions through yield optimizations
The third step was to use critical area as the yield metric to guide various routing optimizations. Once the critical area of a routing layer is calculated, the router can apply several optimization techniques to reduce critical area and increase yield.
After the optimization step, critical area analysis can validate the effectiveness of the optimizations for yield. The complete optimization flow is illustrated in figure 5.
Figure 5 Yield optimization flow.