If you thin a silicon die enough it becomes flexible. I suspect they're using a standard planar fab then thinning the die and mounting it on some curved substrate.

They may even just be using relief cuts in the die to produce the effect. Reliefs have a number of advantages, including reducing twisting and buckling.

But not flexible in 3 dimensions...

(Ie. You can curve it around a cylinder, but not around a sphere)

If you want to dive deeper into the issues look into Developable Surfaces https://en.wikipedia.org/wiki/Developable_surface

Wouldn't different thicknesses allow this?

Take a sheet of paper and wrap it around a ball. Notice how it folds?

If you could take a flat surface and have it represent the surface of a sphere without warping (or vice-versa), we wouldn't have constant debates about what kind of map projections are best.

Maybe you could make it like an orange peel and bend it mostly sideways? Depends on how rigid it is. Or cut ridges like a fresnel lens? Or like lasik? All depends on the material properties.

Yes, I agree. What I mean is that by varying the thickness, you can get it very close to or exactly a sphere.

Good question. I don't know but I know from another effort that was at Sun way back in the day it is really difficult to create curvature in a system that wants flat optical masks and flat processing.

There are at least two challenges, one is curve itself, and the other is laying out the sensor to be linear across the curved surface. I'm wondering if they are going to do a Hot Chips presentation, that has been where most of the coolest advances in chip making have been detailed.

A friend speculated they might be doing a mems sort of thing where they make a 'thick' chip and then etch down to the layers of sensors, perhaps polishing, as a glass lens might be made, but for me that seems like it would be too risky. Thinning and bending is a possibility of course you need to account for the final topology in your layout.

Definitely a fun puzzle to speculate about.

Although wafers seem easy to make flat, I wonder if lithography itself might work better on a curved target.

there are lenses in the lens assembly that flattens the image. Thus if you wanted to make curved wafers you could remove these. But then the curve would be across the water itself and maybe not what you want on the individual chip level.