Metal Width Variation (Type 7)

Metal Width Variation (Part 5)

Chapter 3: Manufacturing Effects and Their Modeling
3.1	3.2a	3.2b	3.3a	3.3b	3.3c	3.4
Introduction	Effect Of Etching Process	Effect Of Etching Process	Chemical Mechanical Planarization	Importance Of CMP process	Dishing & Erosion (CMP effects)	Lithography
3.5a	3.5b	3.5c	3.5d	3.5e	3.5f	3.5g
Metal Width Variation (Type:1-2)	Metal Width Variation (Type3)	Metal Width Variation (Type:4-5)	Metal Width Variation (Type6)	Metal Width Variation (Type7)	Metal Width Variation (Type8)	Metal Width Variation (Summary)

Width Variation Type 7:

Now what?? What is remaining now?:) :)Anyways – still few things are remaining. Have we discussed anything about the wire orientation? Wire width variation based on wire orientation.
Please refer the below figure and think how can you model such scenario.

Don’t think that I am creating variation type unnecessary :) it’s the scenario for lower nodes (like 28nm and below). Soon you will get the all the explanation of this. But right now, modeling is important.:). So what’s the solution? Yes you are thinking in the right direction that we will add one more parameter “Direction” along with the normal wire variation parameter. So as per you, Horizontal and Vertical are 2 different direction and we can specify 2 different biasing tables for these. But I would like to generalize this.

Usually, foundry provides the info with respect to the some reference orientation. Actually this direction concept come from the manufacturing instrument (just explained in layman language). Every machine has different accuracy margin between left-right (horizontal) and top-bottom (vertical). So orientation thing comes into the picture.

Your deign will have structure only in 2 direction (45degree structure or any other degree orientated structure are now obsolete in lower nodes) and once you decide that your reference direction (may be based on maximum structure in a particular direction or with respect to any other reason), you will apply those rules. Once your reference direction is decided, machine will be orientated for that direction.

Structure in that direction will have rules corresponding to that and for other structure (which are in other orientation) machine will behave differently (so different rules). So this reference direction is important.

Foundry will provide the rules as per Reference direction.

• Parallel_to_Reference
• Perpendicular_to_Reference

Variation info can be in the following way.

Note: I just took the example from variation type 1, but same concepts can be applied for other tables or other type of variation parameter also.

Table 9: In the form of absolute variation number
Metal Layer	Width (um)	Variation in % (+/-)(Parallel_to_Reference)	Variation in % (+/-)(Perpendicular_to_Reference)
Metal 1	0.2	8	9
Metal 2	0.4	8	9
Metal 3	0.4	9	10
Metal 4	0.4	10	11