Back-of-envelope calculation of native quad-core production

Semiconductor chip yield is one of the most guarded secret in the industry. There is no way an outsider could have "guess-timated" an accurate value, except by chance (which is also extremely low). Yet sometimes observations can be made from some big, obvious facts. In this article we will make some (strictly) back-of-envelope calculations of AMD and Intel's yields on dual-core processors, and make implications on native quad-core "manufacturability" from both companies.

The observation and assumptions

For the purpose of discussion, we will make the following assumptions -

1. In mid-late 2006, Intel occupies ~80% market share with three 300mm 65nm fabs, while AMD occupies ~20% with only 90nm FAB30 (200mm) and FAB36 (300mm).
2. AMD's FAB30 has the same wafer throughput as Intel's 65nm fabs. FAB36, while under 90-to-65nm transition and having low utilization, further increases production volume by 50%.
3. Intel's main production in 3Q 2006 is Core 2 Duo and dual-core Netburst, with Core 2 Quad volume small enough to be negligible to our discussion (e.g., 10% or less).
   
4. The most significant factor except those described above are the yield of the fabs, and AMD's FSB36 has about the same dual-core K8 yield as its 90nm counterparts.
   

The assumptions above may be utterly wrong, or they may be good enough for the "back-of-envelope" purpose. My point here is not to commend their validity; rather it is to make clear that the arguments below will hold true only if these assumptions do. Note that Intel's last 65nm fab (Ireland) of the three started production output by July 2006, while AMD's FAB36 started 65nm output in the later part of 4Q that year. Thus at least for 3Q 2006 the above market-share and relative technology differences are known to be true.

The calculations

Potentially, three 300mm 65nm fabs would have 3*2*2 = 12x capacity of one 200mm 90nm fab, if the yields of all fabs are the same. Thus, counting into AMD's FAB36, Intel would've had 12x/1.5 = 8x capacity of AMD with the same (dual-core processor) yield. However, Intel's market share during the period is only 4x that of AMD's. There is thus a 2x discrepancy between Intel's potential capacity (8x of AMD's) and its true capacity (4x of AMD's), which is presumably affected by a lower yield of its fabs. In other words, to reach the expected market share, AMD's FAB30 and FAB36 would have yields twice as good as Intel's 65nm 300mm fabs.

Apparently, this conclusion is not possible. A factor of two in terms of yield is too large, and Intel simply can't be that bad in manufacturing. A few factors may have affected the estimation accuracy here:

• Intel's 65nm fabs may have lower wafer throughput or utilization than AMD's FAB30 and FAB36 combined, particularly the Ireland fab which was ramping for just 4 months, and D1D which is also used for 45nm research & development.
  
• Intel may be making much more Core 2 Quad, which effectively cuts production volume in half (two Core 2 Duo dies make one Core 2 Quad).

Taking into consideration of the two factors above, we'll adjust the estimated yield difference from 2x down (quite arbitrarily) to 1.5x. Note that a high percentage of Netburst-related products from Intel actually makes the discrepancy larger, since Netburst chips are smaller in size per die, much matured, and should have better yield than the cutting-edge Core 2 Duo.

The Implication

So how does this 1.5x yield difference affect "native" quad-core manufacturing? Suppose AMD's dual-core K8 yield is 81%; Intel's Core 2 Duo yield would be just 54% (1/1.5x). By 1st-order estimate, AMD's native quad-core would have a yield of roughly 65% (0.81*0.81), whereas Intel's would have 29% (0.54*0.54). In other words, out of 100 quad-core dies, AMD is able to make 65 functional quad-core processors, while Intel only 29, less than 50% of its smaller competitor. It is not difficult to see why AMD is going native but Intel won't until late 2008.

Lets for the purpose of discussion turn the parameters further in Intel's favor, and assume it has just 1.25x lower yield (instead of 1.5x) from AMD's. If we again suppose dual-core K8 has yield 81%, then Core 2 Duo would have almost 65%, making Intel's MCM quad-core approach as productive as AMD's native quad-core approach. What we see here is that a yield just a quarter better than the competitor could've made a huge difference in terms of native quad-core manufacturability. In fact, Not only is Intel late to native quad-cores, it was also late to native dual-cores for about 6 months even with a better technology (65nm vs. 90nm).

The conclusion is clear, that Intel is telling the truth that it can't make native quad-core cost-effectively. For AMD, it might be very hard, but probably still doable, based on a simple capacity observation and this back-of-envelope calculation.

The arguments

Some people have argued the precision of the above estimates. Their arguments can basically be divided into the following points:

1. Intel's D1D is also making 45nm transition in late 2006, thus should have less than maximum output.
2. Intel's Ireland fab, ramping only 4 months from Jun'06, won't achieve max capacity in Oct'06.
3. Intel's shipping more dual-core processors in 4Q06 than AMD. Specifically, just over 50% of Intel processors are dual-cores, while only 30% of AMD's are.
4. AMD's FAB36, making 300mm wafers and started revenue shipping in Apr'06, should've been making as much silicon as FAB30.
5. By late 3Q06, AMD would also have Chartered's output at hand.
6. Intel's 65nm doesn't actually result in 2x capacity of 90nm, more like 1.7x (1/0.6). As well, Intel's 300mm wafer would result in ~2.25x usable silicon area of 200mm ones.

It's important to note that all these are considered higher-order factors. A slight difference in terms of max wafer throughput per fab (ranging anywhere from 20k to 60k) could've dwarfed any of above. Still, for the sake of discussion, lets still try some more precise estimates from these points.

The first point, it turns out, is wrong. As D1D's making 45nm outputs, its 65nm capacity is moved to the neighboring D1C, which is outputting 65nm chips right after Ireland and purposely/completely ignored by me above. The second point would be valid and reduce 65nm Ireland fab's capacity to some 30% of its max.

The third point above is also true; however it fails to recognize that most of Intel's single-core processors (Celerons and Pentium M's) are made at its 90nm fabs, whereas all of AMD's single-core and dual-core processors are made out of FAB30 & 36 (excluding Chartered), a factor the 17% difference in dual-core ratio isn't even able to compensate.

The fifth and sixth points are minor. Chartered's flex capacity would account for up to 20% of AMD's silicon output, and even less in Oct'06, not 3 months after its first revenue shipping for AMD. Assume Chartered is supplying 15% of AMD's silicon output, it'll effectively make output from AMD's own fabs 85% of the total, or changing the actual Intel-to-AMD output ratio from 4x to 4.7x.


The forth point, which we'll discuss last here, seems quite valid from page 5 of this AMD Jun'06 analyst day presentation (see picture above). At late 3Q06, the 300mm "wafer outs" from FAB36 seems to be 0.4x of the max 200mm from FAB30, equivalent to 0.4*2.25 = 0.9x FAB30's silicon area. Surely this is a great increase of AMD's potential capacity. Unfortunately, it turns out such argument is unfounded and mislead by a graph without y-axis unit and meant to be illustrative only.

If we read the text on page 4 of that presentation (again see picture above), FAB36 is expected to output 25k wafers per month (wpm) by Q4 2007, which will be the total 300mm wafer output at that point (FAB38 won't have wafer outs until Q1 2008). We also know FAB30 is outputting about 30k wpm in Q3 2006. Now go to page 5 again and look! How can green line's 25k wpm (end of 4Q07) be some 60% higher than red line's 30k wpm in 2006? It is absolutely not possible unless the "wafer outs" y-axis actually means wafer area outs, and the 25k 300mm wpm from FAB36 is effectively doubled to 50k, some 66% higher than the 30k 200mm wpm from FAB30.

It turns out my original estimate of FAB36 reaching 50% capacity of FAB30 is actually a bit optimistic. The true number should be calculated as such: (0.8/3.4 * 25000)*2.25/30000 = 0.44, where 0.8 comes from green line at end of 3Q06, 3.4 from end of 4Q07 (both FAB36 only), 25000 is expected green line wpm at end of 4Q07, 2.25 translates 300mm wpm to effective 200mm wpm, and the final 30000 is FAB30 wpm (red line at end of 3Q06).

Overall, a definitely more precise/probably more accurate estimate is the following:

Intel's potential capacity: (2+0.3)*(1/0.6)*2.25 = 8.6
AMD's potential capacity: 1+0.44 = 1.44
Potential capacity ratio: 8.6/1.44 = 6.0x

Intel's actual output: less than 80% market share (excluding 90nm production)
AMD's actual output: 20%*0.85 = 17% (Chartered effects)
Actual output ratio: 80%/17% = 4.7x

Discrepancy between potential and actual output: 6.1/4.7 = 1.28, or almost 28% difference in microprocessor yield, well between the 50% and 25% estimates I made above.