# What shapes can IC dies be?

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?

• Conceivably you could cut them into rhombus shapes or triangles. What problem are you trying to solve here? Commented Nov 18, 2023 at 23:22
• I feel an explanation is necessary for my off-topic flag. It should be obvious that in principle the material used could be cut into any shape, given the proper tools. Since the question explictly mentions "tesselations", however, it seems that the intent is "what shapes can be used to tesselate a sheet of material?" (i.e., cut it into identical pieces without material left over except at the edges). That, in turn, is just an application of a pure math problem. It has nothing to do with electronics, and no understanding of electronics is necessary to answer. Commented Nov 19, 2023 at 20:31
• @KarlKnechtel: I think you're reading to much or too little into the phrasing of "can they be cut into?". They don't mean just math, they mean "... can they practically / usefully be cut into, considering any factors that are relevant for an IC die?" e.g. that triangles have sharp corners, and more of the area farther away other parts of the chip than shapes with more faces. From the question title, and the fact it's posted here, answerers were easily able to infer that meaning and post useful and interesting answers, e.g. that straight cuts across the wafer are highly preferable. Commented Nov 20, 2023 at 0:36
• There are probably other things to consider like yield when cutting. Commented Nov 20, 2023 at 15:45

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:

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:

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!)

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.

• Interesting hex/triangle mix. Do people ever mix two different designs, one on the triangles and one on the hexes? I'd guess that's rare since the area ratios are fixed, but I guess one or the other shape could just have some unused space. It also means the production quantity ratios are fixed (modulo yield and ability to use part of a die with a defect), unless you also have a wafer of just triangles (which tiles the plane with straight cuts). Maybe P-core vs. E-core for stacked packaging? Or I/O + cache substrate vs. cores? Or just different chips to package separately. Commented Nov 19, 2023 at 18:22
• I don't think anyone uses anything other than rectangular. Which also has the advantage that you can choose width and height independently. Commented Nov 20, 2023 at 0:06
• @PeterCordes You theoretically could, but I have never heard of anyone doing so. It's rare enough that you'd have any reason to use non-rectangular dice in general, I can't imagine a situation where you'd want hexagonal and triangular dice. More likely you'd cut it like that and send the triangles back to the wafer plant to melt down into silicon for future wafers. That's what gets done with parts that come out bad, anyway. Commented Nov 20, 2023 at 0:16
• Another example is that Canon made a 200 mm × 200 mm camera sensor, which is essentially a whole silicon wafer: dpreview.com/articles/7964414898/canonlargestsensor Commented Nov 20, 2023 at 0:55
• Cerabras has made whole wafer size chips. anandtech.com/show/16626/… Commented Nov 20, 2023 at 19:19

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

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.

• I wonder if that was fabbed as a honeycomb, or if as triangles with corners chopped as shown in one of the other answers. Commented Nov 20, 2023 at 19:27

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:
1. 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.
2. 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.

• Note that areas too close to the edge are unusable for test circuits due to edge effects; even product dice too close to the edge of the wafer are frequently discarded without testing, simply because the chance of them working is near zero. Your PCM (test circuits), when needed, should be mixed in with the product dice, in my experience typically replacing one or more product dice. Commented Nov 26, 2023 at 4:11