Metal Width Variation (Part 4)
Width Variation Type 6:After the previous variation type (especially Type4), where I made a sentence that “width variation also depends on the surrounding environment (like metal density or say space with respect to neighboring metal layer)”, you may have a lot of questions or questions came in your mind. Like what will happen in the below scenario.
I am sure you can say that as per the diagram and as per foundry data, small segments of wire (enclosed by dotted red box) see a very large spacing in the horizontal direction. However the next section (enclosed by dotted green box) of the same wire shows a much closure spacing. As per the modeling (whatever we have discussed till now), if large and small spacing concept are used, width (silicon width) changes drastically which we know very well that it’s practically impossible.
What does it mean???
It means … Our list of variation type is not complete. :)
Practically, the above structure will be in somewhere like below shapes after manufacturing. You can notice that the place where spacing is drastically change (Common boundary of red and green dotted box), manufactured shape is not drastically changed. There is a curve/slope or say gradient in the width variation from low value to high value.
Since our goal is to model the variation as close as possible, foundry provide these info also. So that EDA vendors can model such portion also (which can impact RES and CAP values – especially in lower technology nodes).
Info will be somewhere in the following form.
S =space between 2 wires,
L = minimum parallel distance between 2 wires,
dD = delta distance after L length.
dW = Delta width variation = X
data/info will be as per following function
dW(W, S, L, dD) = X ;
dW(0.5, 0.5, 0.5, 0.0) = 0.01 ;
dW(0.5, 0.5, 0.5, 0.05) = 0.02 ;
dW(0.5, 0.5, 0.5, 0.1) = 0.03 ;
dW(0.5, 1.0, 1.0, 0.0) = 0.04 ;
Again this type of info can be provided in “n” no of ways and I can’t discuss all those (because that may create an issue from confidential point of view). I have just provided the concepts here which can help you to understand. If you have worked on such cases anyhow, you can easily correlate and if you haven’t (till now), then such concept is sufficient for you.:)
After modeling as per variation type 6, above wire structures will be converted into following structures (which is very closure to the actual one).