Hexagonal Die

By: Math Nerd (math.nerd.delete@this.nerds.com), June 27, 2022 5:05 am
Room: Moderated Discussions
> 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
< Previous Post in ThreadNext Post in Thread >
TopicPosted ByDate
OK dumb question timeDoug S2022/06/24 01:31 PM
  OK dumb question timeanon52022/06/24 01:38 PM
  Silicon ingots are round.Mark Roulo2022/06/24 02:29 PM
    Silicon ingots are round.Squarehead2022/06/24 02:38 PM
      Silicon ingots are round.Mark2022/06/24 03:00 PM
        Silicon ingots are round.Gary Kopp2022/06/24 03:20 PM
      Silicon ingots are round.Adrian2022/06/24 11:34 PM
    Silicon ingots are round.tarlinian2022/06/24 03:38 PM
      Silicon ingots are round.Doug S2022/06/24 11:13 PM
        Silicon ingots are round.anon2022/06/25 11:34 AM
          Silicon ingots are round.Doug S2022/06/25 11:39 AM
            Silicon ingots are round.Groo2022/06/26 09:41 AM
              Silicon ingots are round.Doug S2022/06/26 12:05 PM
                Silicon ingots are round.Gtoo2022/06/26 02:55 PM
          Silicon ingots are round.rwessel2022/06/25 11:43 AM
            Not reallyGroo2022/06/26 09:39 AM
              Not reallydmcq2022/06/26 10:56 AM
                Not reallyGroo2022/06/26 02:58 PM
              Not reallyanon22022/06/26 05:22 PM
              Why not triangles? Anon2022/06/27 03:34 AM
                Why not triangles? Math Nerd2022/06/27 04:52 AM
                Why not triangles? Math Nerd2022/06/27 05:45 AM
                  Don't forget Penrose Tiling (NT)ananon2022/06/27 06:06 AM
                  Why not triangles? Doug S2022/06/27 07:43 AM
                  Why not triangles? Anon2022/06/27 08:33 AM
                    Die shape that minimizes wasted area on circular wafersMath Nerd2022/07/01 09:20 PM
                      Die shape that minimizes wasted area on circular wafersBrett2022/07/02 02:35 PM
                        Die shape that minimizes wasted area on circular wafersMath Nerd2022/07/02 04:15 PM
                        Die shape that minimizes wasted area on circular wafersMark Roulo2022/07/02 04:41 PM
                          Die shape that minimizes wasted area on circular wafersDoug S2022/07/02 06:44 PM
                          Die shape that minimizes wasted area on circular wafersBrett2022/07/03 12:31 AM
                            Die shape that minimizes wasted area on circular wafersAdrian2022/07/03 10:25 PM
                              Die shape that minimizes wasted area on circular wafersanon22022/07/03 11:33 PM
                                Die shape that minimizes wasted area on circular wafersBrett2022/07/04 12:45 AM
                                  Die shape that minimizes wasted area on circular wafersdmcq2022/07/04 06:09 AM
                                    Die shape that minimizes wasted area on circular wafersJames2022/07/04 09:52 AM
                                      Die shape that minimizes wasted area on circular wafersdmcq2022/07/04 10:26 AM
                                        Die shape that minimizes wasted area on circular wafersAdrian2022/07/05 03:28 AM
                                      Cannon Lake vs Kaby LakeMark Roulo2022/07/04 10:30 AM
                                        C-class bonusesblue2022/07/04 12:27 PM
                                          C-class bonusesanonymou52022/07/04 03:23 PM
                                  Die shape that minimizes wasted area on circular wafersanon22022/07/04 06:53 AM
                                    Die shape that minimizes wasted area on circular wafersBrett2022/07/04 12:32 PM
                                      Die shape that minimizes wasted area on circular wafersFoyle2022/07/04 01:30 PM
                                        Die shape that minimizes wasted area on circular wafersAnon2022/07/04 01:37 PM
                                          What is a mirrored die?Mark Roulo2022/07/04 02:59 PM
                                            What is a mirrored die?Brett2022/07/04 03:32 PM
                                              What is a mirrored die?Doug S2022/07/04 10:08 PM
                                        Die shape that minimizes wasted area on circular wafersanonymou52022/07/04 03:12 PM
                                          Die shape that minimizes wasted area on circular wafersFoyle2022/07/05 10:41 AM
                                      Die shape that minimizes wasted area on circular wafersanon22022/07/04 04:52 PM
                                        Die shape that minimizes wasted area on circular wafersUngo2022/07/05 06:24 PM
                                          Die shape that minimizes wasted area on circular wafersBrett2022/07/05 07:56 PM
                                            Die shape that minimizes wasted area on circular wafersanonymou52022/07/06 05:46 AM
                                              Die shape that minimizes wasted area on circular wafersdmcq2022/07/06 02:55 PM
                                                Die shape that minimizes wasted area on circular wafersMark Roulo2022/07/06 04:09 PM
                                                Die shape that minimizes wasted area on circular wafersDoug S2022/07/06 05:31 PM
                                      Example of mirrored wafer?Mark Roulo2022/07/04 06:01 PM
                                  Not the same as 3-core CPU from a 4-core dieMark Roulo2022/07/04 09:31 AM
                                Wafer probingAdrian2022/07/05 03:08 AM
                                  Great comment, thank you (NT)anon22022/07/06 12:00 AM
                crystal latticehobold2022/06/27 12:09 PM
                  crystal latticedmcq2022/06/27 03:58 PM
                  Given path dependency I doubt it ...Mark Roulo2022/06/27 06:02 PM
                    Given path dependency I doubt it ...Adrian2022/06/27 10:01 PM
              Hexagonal DieMath Nerd2022/06/27 05:05 AM
                Hexagonal DieAdrian2022/06/27 10:24 PM
                  Hexagonal Diedmcq2022/07/06 03:00 PM
          Silicon ingots are round.dmcq2022/06/25 02:38 PM
            Silicon ingots are round.dmcq2022/06/25 02:43 PM
          Silicon ingots are round.aaron spink2022/06/25 03:05 PM
      Notch on Silicon WafersEric P2022/07/01 04:07 PM
        Still there, I think ...Mark Roulo2022/07/01 04:47 PM
          Still there, I think ...Eric P2022/07/01 05:26 PM
            Still there, I think ...tarlinian2022/07/01 06:50 PM
              Still there, I think ...David Kanter2022/07/02 09:14 AM
            Still there, I think ...Mark Roulo2022/07/01 09:31 PM
              Still there, I think ...Eric P2022/07/02 12:10 AM
  OK dumb question timeanonymouse2022/06/24 03:47 PM
Reply to this Topic
Name:
Email:
Topic:
Body: No Text
How do you spell tangerine? 🍊