By: Adrian (a.delete@this.acm.org), June 27, 2022 10:24 pm

Room: Moderated Discussions

Math Nerd (math.nerd.delete@this.nerds.com) on June 27, 2022 5:05 am wrote:

> > It is a tad more expensive but not a significant cost in relation to a finished wafer on a modern

> > process. The biggest reason you don't want to do it is the loss of edge area for I/O.

>

> The perimeter of a rectangle with a 2:1 aspect ratio is only 14% more than the perimeter of a regular

> hexagon with the same area. The perimeter of a square is only 7% more than the perimeter of a regular

> hexagon with the same area. If anyone would make a hexagonal die, it would be for the largest die,

> because they have the most wasted area on a circular wafer. The largest die today all use flip chip

> area bonding, not edge bonding. There seems to be a trend to use chiplets today instead of large

> dies and that reduces the wasted area near the circumference of the wafer.

>

> In any case, the ability to make non-rectangular die is very interesting and surprising,

> which I’m sure was the main reason you mentioned it. One semi-practical use for this technology

> could be making microscopic chips where it would be better to not have sharp rectangular

> corners, such as RFID tags for pets or sensors implanted under human skin.

>

> For the record, here is how I calculated that the perimeter of a rectangle with a 2:1

> aspect ratio is 14% more than the perimeter of a regular hexagon with the same area:

>

> Perimeter of 2:1 aspect ratio rectangle with smaller side a is 6a (rectangle is a x 2a).

> Perimeter of regular hexagon with side b is 6b.

> Ratio is perimeters is a/b.

> Area of a 2:1 aspect ratio rectangle with smaller side a is 2 a^2.

> Area of a regular hexagon with side b is b^2 (3/2) sqrt[3].

> Set areas equal: 2 a^2 = b^2 (3/2) sqrt[3]

> a/b = sqrt[ (3/4) sqrt[3] ] = 1.14

While making triangular dies would be almost as easy as making rectangular dies, they would have a higher risk of corner breakage during manufacturing and the internal areas near the corners might be used inefficiently due to difficulties in placing there devices and routing their connections without excessive crowding.

Making hexagonal dies is certainly much more expensive, as there are no straight lines to separate the dies. The only way to cut the dies would be with a laser that cuts completely through the wafer.

Especially for smaller hexagonal dies, there would be a problem how to manipulate the dies at the moment when they are cut loose. Picking the dies one by one, e.g. with a vacuum suction cup, would be very slow and expensive.

The traditional cheap method was to glue the wafer on an elastic membrane, scribe the straight lines between the dies and then expand the elastic membrane to separate the dies. Thus the die separation was extremely fast and the individual dies remained attached to the membrane, there was no need for some special means to catch each die when it is detached, to prevent its fall.

> > It is a tad more expensive but not a significant cost in relation to a finished wafer on a modern

> > process. The biggest reason you don't want to do it is the loss of edge area for I/O.

>

> The perimeter of a rectangle with a 2:1 aspect ratio is only 14% more than the perimeter of a regular

> hexagon with the same area. The perimeter of a square is only 7% more than the perimeter of a regular

> hexagon with the same area. If anyone would make a hexagonal die, it would be for the largest die,

> because they have the most wasted area on a circular wafer. The largest die today all use flip chip

> area bonding, not edge bonding. There seems to be a trend to use chiplets today instead of large

> dies and that reduces the wasted area near the circumference of the wafer.

>

> In any case, the ability to make non-rectangular die is very interesting and surprising,

> which I’m sure was the main reason you mentioned it. One semi-practical use for this technology

> could be making microscopic chips where it would be better to not have sharp rectangular

> corners, such as RFID tags for pets or sensors implanted under human skin.

>

> For the record, here is how I calculated that the perimeter of a rectangle with a 2:1

> aspect ratio is 14% more than the perimeter of a regular hexagon with the same area:

>

> Perimeter of 2:1 aspect ratio rectangle with smaller side a is 6a (rectangle is a x 2a).

> Perimeter of regular hexagon with side b is 6b.

> Ratio is perimeters is a/b.

> Area of a 2:1 aspect ratio rectangle with smaller side a is 2 a^2.

> Area of a regular hexagon with side b is b^2 (3/2) sqrt[3].

> Set areas equal: 2 a^2 = b^2 (3/2) sqrt[3]

> a/b = sqrt[ (3/4) sqrt[3] ] = 1.14

While making triangular dies would be almost as easy as making rectangular dies, they would have a higher risk of corner breakage during manufacturing and the internal areas near the corners might be used inefficiently due to difficulties in placing there devices and routing their connections without excessive crowding.

Making hexagonal dies is certainly much more expensive, as there are no straight lines to separate the dies. The only way to cut the dies would be with a laser that cuts completely through the wafer.

Especially for smaller hexagonal dies, there would be a problem how to manipulate the dies at the moment when they are cut loose. Picking the dies one by one, e.g. with a vacuum suction cup, would be very slow and expensive.

The traditional cheap method was to glue the wafer on an elastic membrane, scribe the straight lines between the dies and then expand the elastic membrane to separate the dies. Thus the die separation was extremely fast and the individual dies remained attached to the membrane, there was no need for some special means to catch each die when it is detached, to prevent its fall.