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.

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 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.

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!)

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.

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.

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.

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.

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 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.