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Design >> Analog Design >> Substrate resistance calculation
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Message started by Visjnoe on Mar 3^rd, 2009, 12:43pm

Title: Substrate resistance calculation
Post by Visjnoe on Mar 3^rd, 2009, 12:43pm

Dear all,

is it possible to have a first-order calculation of the substrate resistivity between 2 points? I know this can be done by dedicated extraction tools, but can one make an estimation by handcalculations?
Furthermore, the substrate resistivity is expressed in Ωcm], e.g. 20Ωcm. But I don't understand this unit. Resistance is multiplied by length (instead of divided by length)?

Regards

Peter

Title: Re: Substrate resistance calculation
Post by thechopper on Mar 3^rd, 2009, 6:29pm

Hi,

Ωcm] is the unit for the material resistivity. Remember that resistivity is defined as ρ=R×A/L, where R is the resistance, A the section and L the lenght.
For diffusion resisitor is it usual to spec their resistivity instead of sheet resistance.

Regards
Tosei

Title: Re: Substrate resistance calculation
Post by Visjnoe on Mar 3^rd, 2009, 11:42pm

Dear Tosei,

Yes, I know that formula. I was confused with the unit Ωcm because I focused on the '1/L' term. But together with the 'A' term you end up indeed with a single dimension, thus indeed cm.

Given that number, how can you proceed to have an estimate of resistivity between 2 points on a die? You could just measure the distance I guess and apply the above formula, but since you have several parallel paths...
Maybe it's just too complicated to estimate by hand.

Regards

Peter

Title: Re: Substrate resistance calculation
Post by ci on Mar 4^th, 2009, 8:54am

The substrate resistance between two points depends also on the current distribution, which then depends on the substrate type, doping profile, and what devices are placed between these two points. Diffusions or deep trench isolations that cut into channel stopper layer increase the resistance. Near end and far end effects also matter. In general the sheet resistance given in the design guide of the fabrication technology is a good starting approximation; however, this alone is not enough to be able to estimate the noise coupling through the substrate.

Regards,
Cosmin
http://www.noisecoupling.com

Title: Re: Substrate resistance calculation
Post by Visjnoe on Mar 4^th, 2009, 9:10am

Thanks for all your inputs.

At the moment, I take as rough estimate the above formula,
where I take for A = w*h with w the width of the chip and h the substrate thickness,
for l the distance between both points and ρ provided by the foundry (10Ωcm in my case).

Regards

Peter