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## Critical Area Calculation

Carafe begins bridge fault extraction between two layers of material by finding all 2-way bridge faults, or bridge fault primitives. Carafe finds intra-layer bridge fault primitives by taking the material of a node and searching around it on all sides within a distance of the maximum defect diameter. Any material in a different electrical node within this distance in the same layer has a potential bridge. Carafe creates fault primitives that characterize the critical area for the bridges. These characterizations are independent of the defect radius and are called Length-Widths. This defect independent characterization allows the same set of fault primitives to be used for the extraction of several different defect radii less than the maximum. Figure 4.4 shows the three types of length-widths for intra-layer bridges which depend on the orientation of the conductive material being bridged. Figure 4.5 shows the critical areas for these length-widths. Figure 4.4: The three different length-widths for intra-layer bridge fault primitives, depending on the orientation of the conductive material: (a) diagonal, (b) horizontal, (c) vertical. Figure 4.5: Critical areas for length-widths: (a) diagonal, (b) horizontal, (c) vertical. Note that these critical areas were computed with fringe on.

For inter-layer bridges, Carafe looks for regions where the two layers overlap. The length-width for an inter-layer bridge is simply the areas of overlap between the two layers of material, and the critical area is the area of the length-width extended on all four sides by the radius of the defect.

Once all bridge fault primitives between two layers have been found, Carafe computes the critical area for each fault primitive given some defect radius less than or equal to the maximum defect radius. Carafe then takes these defects and intersects them to find the faults, as described in section 4.1.1. After all compound faults for that defect radius have been extracted, Carafe can recompute the fault primitive critical areas for another defect radii and repeat the process. If a fault primitive does not cause a bridge at a defect smaller than the maximum defect size, it is ignored for that smaller defect size.

The total critical area of a fault is the sum of all critical areas affecting the same objects in each layer for each defect radius. The probability of that fault is then computed by scaling the critical areas for each layer using the defect distributions given in the fabrication file. If a bridge fault is given a probability of zero in the fabrication file, but is listed in the bridge section of the technology file, bridges between those layers for that defect size are skipped.

Figure 4.6 shows the fault primitive critical areas for the circuit shown in Figure 4.2 given some defect radius. Figure 4.7 shows the four regions formed by these overlapping fault primitives. The following bridging faults would be reported by Carafe:

• A defect falling in region 1 would bridge Node 2 to Node 3.
• A defect falling in region 2 would bridge Node 1 to Node 3.
• A defect falling in region 3 would bridge Node 1 to Node 2.
• A defect falling in region 4 would bridge Node 1 to Node 2 to Node 3. Figure 4.6: Fault primitive critical area between: (a) Node 2 and Node 3, (b) Node 1 and Node 3, and (c) Node 1 and Node 2. Figure 4.7: Intersection of three fault primitive critical areas.    Next: Limitations Up: Bridges Previous: Bridges

David Dahle Wed Jan 24 11:51:06 PST 1996