I don't think it's comparing apples to apples, though. If you attempt to work out the cost per wafer (multiply the given unit cost by the number of working units) you end up with a figure around $2745 for the three larger sizes, where the wafer fab is the most expensive step.
On the three smaller sizes, though, the total cost is much higher ($11750, $13700, and $18650 respectively), so the final price is obviously constrained by something other than the wafer fabrication step. So the quoted figures are comparing figures derived from one cost estimate (for the larger chips) to figures based on a different estimate for a different step in the process. That said, however, the overall qualitative conclusion (that costs rise prohibitively as the chip size increases) is correct. Changing the costs of the other processes may shift the per-unit cost a handful of dollars either way. This is significant when you're talking about a $8.19 part, but doesn't make much difference on a $2745 item. > Seen on the Pentax group on dpreview. > > Joe > > --------------------- > > I thought I'd do the maths. Well, I borrowed the company cost model for estimating > silicon chip cost, and got it to do the math. > > Some things to understand - this isn't REAL: the cost model is not up to date with > all the latest information and anyway it relates to a particular silicon fabrication > plant which certainly isn't suitable for making CCD imagers (though it might at a > push make CMOS ones). Also, I had to lie to the model - tell it that the chip had > repairable structures - since it has no way of accepting chips that aren't perfect: > in a conventional IC, if one thing is broken, that's it: in an image sensor, if one > or even five pixels are broken, then provided they're not badly broken - sell it! I > hope that saying things are repairable gets it over the hump (anyway, without this > the larger imagers do not yield at all...) but it may be wrong in magnitude. > > And I couldn't derive values for process improvements. If you make the same silicon > chip over a number of years, then you get better at doing it - the defectivity > number falls. For the big chips, I couldn't do this since I needed the best > defectivity at the beginning - this represents the state of the art after 2-3 years > of production. > > Anyway, the overall shape of the numbers is convincing and some of the modelling is > just pure maths like the number of possible die per wafer. I used 12" wafers, since > again the largest sensors simply didn't yield well enough - thus, this modelling > already assumes that larger sensors will move to more modern fab lines. (On 8" or > smaller wafers, then all costs will rise...) > > 1/2.7" - 5.27x3.96mm - 2910 raw die per wafer, 2277 working die per wafer (78.3% > yield) - cost: $8.19 > > 1/1.8" - 7.18x5.32mm - 1593 raw die per wafer, 1036 working die per wafer (65.1% > yield) - cost: $13.23 > > 2/3" - 8.8x6.6mm - 1045 raw die per wafer, 551 working die per wafer (52.8% yield) - > cost $21.32 > > APS C - 23.7x15.6mm - 61 raw die per wafer, 9 working die per wafer (15.6% yield) - > cost $309 > > 1.3x crop - 27x18mm - 42 raw die per wafer, 3 working die per wafer (8.1% yield) - > cost $920 > > FF - 36x24mm - 23 raw die per wafer, 2 working die per wafer (11.6% yield) - cost > $1373 > > If that doesn't look bad enough, I had to reduce the defectivity by a factor of 2 > for the Full Frame sensor: otherwise, the model only gave a yield of 1.8% (i.e. no > working die per wafer on average). I was sort of happy to do this on the assumption > that it translates into many more pixels that don't work on an FF sensor than on the > others. Clearly, one might say even more dead pixels are acceptable and ask for > further modelling with changed defectivity assumptions, but remember that this > number doesn't only relate to dead pixels - the electronics of the sensor has to > work, too: if there's a fault that takes out a whole row or column, then the sensor > is probably useless. This is actually a pretty rosy view of the cost of an FF sensor > - if I'd only reduced the defectivity by 1.5, then the cost is $2745 (yield falls to > 6.1%). And the whole notion of repair (which is assumed in this model) is a bit > bogus - you can't fix a dead pixel like you can a dead RAM cell by swapping in n e! > w lines... > > Of course, a sensor manufacturer may end up with very different numbers - there's > packaging and test which might be very different from my assumptions for example, > and someone has to weld the anti-alias filter on. (packaging and test raise the cost > of the smaller die quite a bit...) This is cost, too - if you want to do research > and development, that's more money. > > I guess I'm not holding my breath for a Full Frame camera to be affordable. Even a > 1.3x crop factor looks quite expensive! > > Hope this is helpful. And again, I repeat the caveat - this is only a model: all the > numbers are wrong, really! > > --Sophie > > > >
