# Substrates and Metals for IC Inductors

Question asked by BURTON.C on Oct 13, 2006
Latest reply on Oct 17, 2006 by ELTZ
I have some questions regarding the user's guide for Momentum in ADS2005A:

1.  On page 3-5, there is a note at the bottom of the page under the "Defining an Interface Layer" heading, that says thick substrates should be less than 0.5 wavelength in thickness.  An example is given, that a 10-mil substrate with a cover height of air of 300 mils is good up to 20 GHz (it's not listed in the example, but I calculate the free space wavelength as 590 mils at 20 GHz, so a half wavelength is 295 mils).  I don't understand how this distance relates to the substrate--a 10 mil substrate is nowhere near 295 mils.  Is this an error in the example?

2.  On page 3-16, there is an equation for the high frequency equivalent sheet impedance, ZHF = (1+j)/(2*conductivity*skin_depth).  Can you provide some information as to where this equation comes from?  I find by looking in textbooks that the surface resistance is given by 1/(conductivity*skin_depth), but I cannot find where the remainder of the equation comes from.  Also, why does this equation not contain a term for the conductor thickness?  What if the conductor thickness is less than a skin depth?

3.  On page 3-18, there is a sentence that says "Typically, when the height/thickness aspect ratio is smaller than a factor of 5, the effect of accounting for the finite thickness of the conductors will need to be allowed for in Momentum simulations."  What is the "height" that this statement is referring to? I would think a thick conductor would be relative to the width/thickness ratio.

4.  I'm trying to model rectangular spiral inductors on an IC that has many layers of metals.  I'm looking for an accurate value for both inductance and Q.  We've been using sheet metals and giving them "thickness" using vias within the substrate layers.  As I've read through the Momentum manual, I'm wondering what benefit there is to this approach, and if it would be better for us to use the thick conductor model.  Are the vias doing anything other than contributing to the loss/Q calculation?  Or do they affect the inductance?  In this case, the via has the same shape as the strip metal traces.  I believe my question could be rephrased as, does Momentum compute current flow in the vias, or does it simply use the vias to determine the voltage/potential of the various layers that they connect?

Thanks.