Disclaimer: I am not an electrical engineer and have no special knowledge about any of this.
Some time ago Thom Hogan estimated the cost of an FX camera sensor to be around $500 (I don’t have the reference, but I’m pretty sure this is true since he said as much recently in a comment thread). Similarly, E. J. Pelker, who is an electrical engineer, estimated an FX sensor to cost around $385 based on industry standard cost and defect rates in 2006. So it seems like there’s this general acceptance of the idea that an FX sensor costs more than 10x than a DX sensor (Pelker estimates $34 for a Canon APS sensor, which is slightly smaller than DX, and $385 for a 5D sensor).
My assumptions can be dramatically off but the result will be the same.
I don’t mean to be mean to Pelker. It’s a great and very useful article — I just think it’s not that the assumptions he knows he’s making are off, it’s that he’s made tacit assumptions he doesn’t realize he’s made are completely and utterly wrong.
The assumption is that if you get an 80% yield making DX sensors then you’re get a 64% (80% squared) yield from FX sensors (let’s ignore the fact that you’ll get slightly fewer than half as many possible FX sensors from a wafer owing to fitting rectangles into circles).
Here are Peltzer’s “unknown unknowns”:
Sensors are fault-tolerant, CPUs aren’t
First, Peltzer assumes that a defect destroys a sensor. In fact if all the defect is doing is messing up a sensel then the camera company doesn’t care – it finds the bad sensel during QA, stores its location in firmware, and interpolates around it when capturing the image. How do we know? They tell us they do this. Whoa — you might say — I totally notice bad pixels on my HD monitors, I would totally notice bad pixels when I pixel peep my 36MP RAW files. Nope, you wouldn’t because the camera writes interpolated data into the RAW file and unless you shoot ridiculously detailed test charts and examine the images pixel by pixel or perform statistical analysis of large numbers of images you’ll never find the interpolated pixels. In any event (per the same linked article) camera sensors acquire more bad sensels as they age, and no-one seems to mind too much.
Sensor feature sizes are huge, so most “defects” won’t affect them
Next, Peltzer also assumes industry standard defect rates. But industry standard defect rates are for things like CPUs — which usually have very small features and cannot recover from even a single defect. The problem with this assumption is that the vast majority of a camera sensor comprises sensels and wires hooking them up. Each sensel in a 24MP FX sensor is roughly 4,000nm across, and the supporting wiring is maybe 500nm across, with 500nm spacing — which is over 17x the minimum feature size for 28nm process wafers. If you look at what a defect in a silicon wafer actually is, it’s a slight smearing of a circuit usually around the process size — if your feature size is 17x the process size, the defect rate will be vanishingly close to zero. So the only defects that affect a camera sensor will either be improbably huge or (more likely) in one of the areas with delicate supporting logic (i.e. a tiny proportion of any given camera sensor). If the supporting logic is similar in size to a CPU (which it isn’t) the yield rate will be more in line with CPUs (i.e. much higher).
This eliminates the whole diminishing yield argument (in fact, counter-intuitively, yield rates should be higher for larger sensors since their feature size is bigger and the proportion of the sensor given over to supporting logic is smaller).
(Note: there’s one issue here that I should mention. Defects are three dimensional, and the thickness of features is going to be constant. This may make yields of three dimensional wafers more problematic, e.g. BSI sensors. Thom Hogan recently suggested — I don’t know if he has inside information — that Sony’s new (i.e. BSI) FX sensors are turning out to have far lower yields — and thus far higher costs — than expected.)
To sum up — an FX sensor would cost no more than slightly over double a DX sensor (defect rates are the same or lower, but you can fit slightly fewer than half as many sensors onto a die owing to geometry). So if a DX sensor costs $34, an FX sensor should cost no more than $70.