Metal Width Variation (Summary)

Summary of Metal Width Variation

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)

Now, I think this much is sufficient for the width variation. Let’s revise few of them.

Below figure has

• Ideal shape (which we draw on layout or say theoretical shape)
• Practical Shape (Which will come after different manufacturing variation effect).
• Here, I have flipped the shape of “practical shape” which we have discussed till now to show you that if you understand this then you can model any type of shape.

Below figure explain about the modeling as per variation Type2:

• Red color dotted shape is Ideal shape / Layout shape or say Theoretical Shape.
• Light brown color shape is Desired Shape.
• Green color shape is modeled shape (as per variation type 2)
• In variation type 2, top and bottom delta are same.
• Since modeling is with respect to theoretical shape’s edges, it’s difficult to model exact delta either on Top side or bottom side. But this one is more closure to the desired shape.

Below figure explain about the modeling as per variation Type3:

• Red color dotted shape is Ideal shape / Layout shape or say Theoretical Shape.
• Light brown color shape is Desired Shape.
• Green color shape is modeled shape (as per variation type 3)
• In variation type 3, top and bottom delta can be different and that’s the reason we are able to match top and bottom delta width properly (except right hand side bottom delta).
• This is because Variation type 3 has condition that
• top width delta on either side should be same
• Bottom width delta on either side should be same.

Below figure explain about the modeling as per variation Type4 along with the variation Type3:

• Red color dotted shape is Ideal shape / Layout shape or say Theoretical Shape.
• Light brown color shape is Desired Shape.
• Green color shape is modeled shape (as per variation Type3 and Type4)
• In variation type 3, top and bottom delta can be different and that’s the reason we are able to match top and bottom delta width properly and in type 4 right and left side variation can be different and that the reason we are able to match right hand side bottom delta (which were missing in the type 3).

In the above figure related to non-linear top-to-bottom variation can be modeled with the help of Variation type 5.

Below figure explain about the modeling as per variation Type6 (basically it will explain now from the Top view – which also include the length of the metal wire)

• Red color dotted shape is Desired Shape (which will come after manufacturing). (Note: here just changed the color scheme)
• Light green shapes are as per modeling (after applying variation type6)
• Dark green (in reference to above point) shapes are Ideal shape / Layout shape or say Theoretical Shape.

For variation type 7 below figure is self-explanatory. I think it’s not required to give much more details of that. Just remember that these 2 wires are oriented differently (one in vertical and other in horizontal).

For variation type 8 again below figure is self-explanatory. Just point to noted that it is because of n number of non-uniformities. It effects differently for Resistance and Capacitance. This variation type can be combined to any other variation type and accordingly can be modeled.