What shapes can IC dies be?

Question

I know an IC die can be cut into a rectangular shape. Apparently triangles and rhombuses are also possible, but not used. What other tesselations can they be cut into?

Answer 1

The main restriction is that the easiest and cheapest way to cut a wafer is in straight lines that go all the way across the wafer. It's hard to start and stop cutting in the middle of the wafer, which would be required for tightly-packed hexagonal dice:

(image source)

Note how there are no lines here that go on indefinitely; they all stop in the middle of the wafer.

If you really wanted hexagonal dice, and you can afford to sacrifice a bit of wafer area, you could use a trihexagonal tiling like so:

(image source)

Note how here, the extra triangles mean that all the cuts do go on indefinitely, so this could be made with a couple passes through an ordinary wafer sawing machine. You'd need three passes instead of two as for rectangular dice, but that's not a big deal.

Triangles and parallelograms (which includes rectangles) tile with zero wasted space with straight-line cuts. There's never any advantage that I'm aware of to making triangular or non-rectangular parallelogram dice, though, so they're all rectangles.

(image source)
Note that in these triangular tilings, you make three sets of cuts. If you make just two sets of cuts (remove one set of parallel lines), you get parallelogram tilings.

It would also be possible to cut a wafer into slices like a pizza, but there's little reason to do that either. That's a good metric for it though: Any shape you can cut pizza into is a shape you could cut a wafer into.

The one other shape you sometimes see used is circular, where the entire wafer is used to make a single device with no cutting involved at all. This is used for extremely high-current diodes and thyristors, which can be recognised by their distinctive hockey-puck or coaster-like shape:

(image source)
(this device is rated for 103 kiloamps peak!)

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It is possible to cut dice into arbitrary complex shapes by using other cutting methods, but these are much more expensive than simply using diamond saws. The disadvantages outweigh the advantages, for most applications.

Answer 2

Occasionally you see some unusual shapes, especially when the target structure is circular:

https://www.photonics.com/Buyers_Guide/ProdSpec/Sensors_Detectors/Photodiode_-_AXUV20A/psp7337

Aside from cost I don't think there are any hard limitations, and occasionally you'll see MEMS devices where the silicon is cut into complex or even curved edges.

Answer 3

While the questions asks What other tesselations can they be cut into?, a counter argument is what are the reasons why rectangular shapes are used.

From searching found other answers which gives the reasons for using rectangular shapes:

1. If silicon wafers can only be made round, why are the chips we make not hexagons instead of squares to cover the edges more efficiently? says:

   2. Areas around the edge of a wafer (and some internal spots) that you think might be wasted are actually used for test circuits. These test transistors are evaluated by the manufacturing fab to validate that the wafer was processed correctly before giving them to the customer. If the test transistors anywhere around the edge are out of tolerance then this means something in the process shifted and yield of the die may suffer.
   3. It is easier to cut straight across the wafer with a saw.

2. Why aren't semiconductor wafers diced into triangles? has the following in a comment:

   Sharper corners would result in more stress at the corners of the die which could result in failure of the IC.