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

That's basicaly how non-rectangular dies are separated too as described in a link earlier. The laser doesn't completely separate them, it weakends the lines like perforated paper and then the pulling separates them.