Sunday, October 4, 2015

Metal Width Variation (Type 1 and Type 2)

Metal Width Variation (Part 1)

In the previous articles, we have discussed a lot about the Etching, CMP, Lithography and their effects. Now it’s the time to know
  1. How these variations are modeled in real?
  2. How foundry provide the corresponding data?
  3. How to read that one and provide the info to different tools?

Let’s start with the Summary figures of last post.

Note: Blue is what we need ideally and brown is what we will get actually/practically.

As we have discussed in last few post that there are basically 3 parameters which are affected a lot.
  • Width of metal
  • Thickness of Dielectric and
  • Thickness of Metal.

From the above figure and also from statement, you can easily conclude that there are 2 mainly type of variation – In width and In height. Let’s start one by one.

Width Of Metal:

There are different ways to model variation information of this parameter. Different EDA vendors code this info in different way (I will summarize this in the last of this Article series). Similarly, Foundries also provide this info in different way.

Width Variation Type 1:

Most common and simpler form of variation is “variation in percentage” or “absolute numbers” in the form of table.

Table 1: In the form of variation %
Metal Width (um) variation in % (+/-)
Metal 1 0.02 8
Metal 2 0.04 8
Metal 3 0.04 9
Metal 4 0.04 10

Structure wise after applying the variation type 1, we may get below patterns or we can say that we are modeling only below type of variation in the shapes.

In this type of variation, we assume that width variation is same from top to bottom OR if there is any difference, their effect in Capacitance and Resistance are negligible. I have just used 2 words, CAPACITANCE and RESISTANCE, so it’s my moral duty to ask this question- “How, above type of width variation impact the CAP and RES of the Circuit?” :)

I would say – think and if you forget then please refer Parasitic Interconnect Corner article. It will help you to refresh your concept And don’t worry I will also summarize this later on.

Width Variation Type 2:

In this we will remove the restriction of Type 1 (same bottom and top width variation). It’s now more closure toward the practical shape. And foundry consider this for 180nm and below nodes.

Ideal Width of Metal = W (Rectangle shape)
Because of several fabrication steps (already discussed in last few Articles of this series), final shape of the Metal is not rectangular. It’s trapezoidal, so we have to define 2 widths.

Top_width = W+2A
Bottom_Width = W-2A


  • Here we are considering that “bottom delta” = “top delta”.
  • In case, top_width_delta=bottom_width_delta, we can model this by using the angle Ɵ also. Where tan Ɵ = 2B/2A and known as Tangent.

So, in all the above case the table (or say info provided by Foundry) can be any of the following.

Table 2: In the form of absolute Numbers (final width)
Metal Width (um) Top_width/bottom_width
Metal 1 0.2 0.21/0.19
Metal 2 0.4 0.41/0.39
Metal 3 0.4 0.41/0.39
Metal 4 0.4 0.41/0.39

Table 3: In the form of absolute variation number
Metal Width (um) Top_delta/bottom_delta
Metal 1 0.2 +0.01/-0.01
Metal 2 0.4 +0.01/-0.01
Metal 3 0.4 +0.01/-0.01
Metal 4 0.4 +0.01/-0.01

Table 4: In the form of % delta variation number
Metal Width (um) %Top_delta/%bottom_delta
Metal 1 0.2 +5%/-5%
Metal 2 0.4 +10.0%/-10.0%
Metal 3 0.4 +10.0%/-10.0%
Metal 4 0.4 +10.0%/-10.0%

Table 5: In the form of Tangent (angle)
Metal Width (um) Thickness (A) tan Ɵ
Metal 1 0.2 1000 5
Metal 2 0.4 1200 6
Metal 3 0.4 1200 6
Metal 4 0.4 1200 6

Structure wise after applying the variation type 2, we may get below patterns or we can say that we are modeling only below type of variation in the shapes.

I am sure you are able to co-relate these with the real structure or shapes (Snapshot of last few article summary). But if you are still confused, please refer below figure.

After seeing above figure, you may be thinking that it’s not 100% matching. For that variation Type 3 can help you.
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