1. EE4271 VLSI Design
VLSI Channel Routing

2. Objectives Definition of VLSI channel routing problem
How to perform channel routing for width optimization
Lower bound proof for channel routing
Understand that channel routing problem is difficult to solve

3. Routing to reduce the area
Routing Problem
Routing to reduce the area

4. Routing Anatomy 3D view Top view Symbolic Layout Metal layer 3 Via
Top layers have more spacing between wires
Top layers higher aspect ratio (like walls)
Metal layer 3
Via
Metal layer 2
Metal layer 1
©Bazargan

5. Vertical Routing Track Horizontal Routing Track
Routing Grid
Vertical Routing Track
Horizontal Routing Track

6. Channel Routing Terminology
Terminals (Gate Pins)
Via
Upper boundary
Width
(# of Horizontal Routing Tracks)
Tracks
Lower boundary
Assume that there are only one horizontal layer and only one vertical layer, i.e., no overlap among horizontal wires and no overlap among vertical wires will be allowed.

7. Channel Routing Problem - I
Input:
Two vectors of the same length to represent the pins on two sides of the channel.
One horizontal layer and one vertical layer in the routing grid.
Output:
Connect pins of the same net together such that there is no overlap among horizontal wires and there is no overlap among vertical wires.
Minimize the channel width.

8. Channel Routing Problem - II1 2 2 3 4 1 2 3 3 4 4
Example: ( )
( )
where 0 = no terminal
Route all the pins with the same index

9. A Channel Routing Example
How good
is it?

10. Is this routing with the minimum width?
A Simpler Example - I
Is this routing with the minimum width?

11. Is this routing with the minimum width?
A Simpler Example - II
Is this routing with the minimum width?

12. Lower Bound on Channel Width1 6 1 2 3 5 6 3 5 4 2 4 1 6 1 2 3 5 1 2 3
Channel density =
Maximum local density 4 5 6 6 3 5 4 2 4
Local
density 1 3 4 4 4 4 2
Lower bound = 4
Lower bound on channel width = Channel density

13. Exercise
Use minimum number of tracks to route the following nets. Is your result the best possible one?

14. Lower Bound Always Achievable?
Is the channel routing lower bound always achievable for any channel routing problem? 1 2

15. A More Complex Example # columns =174, # nets=72, density =19
Routing result:
number of tracks=20

16. # routes actually on a track max # routes allowed on a track
Realistic Design
Different colors refer to different wire densities. Red color means large congestion.
# routes actually on a track
max # routes allowed on a track
Congestion=
From DAC Knowledge Center

17. Summary Definition of VLSI channel routing problem
Channel routing for width optimization
Lower bound for channel routing
Local Density and Channel Density
Lower bound is not always achievable