RF 0.18 um CMOS Inductor Relative Permeability

I've been calculating the inductance of a 0.18u CMOS process inductor in Cadence using several formulas such as Wheeler's, Rosa's and monomial expressions for octagonal spiral inductors. All these formulas give the same amount with very little variation while the real inductance is significantly different. As these calculations depend solely on parameters like width, length and spacing which are obvious as well as the permeability of the material, I guess it's the µr value that I'm getting wrong. I'm assuming the material to be Al, but it probably isn't. I know that the inductor is a combination of metal-6 with 5 and 4, but what is the exact permeability of it?

There are many parasitics that you might be ignoring in your calculations.
Getting the right inductance of a CMOS inductor even using EM simulators is difficult enough (provided that you are an experienced user of these simulators) let alone solely using formulas.

Elecemperor said:

I've been calculating the inductance of a 0.18u CMOS process inductor in Cadence using several formulas such as Wheeler's, Rosa's and monomial expressions for octagonal spiral inductors. All these formulas give the same amount with very little variation while the real inductance is significantly different. As these calculations depend solely on parameters like width, length and spacing which are obvious as well as the permeability of the material, I guess it's the µr value that I'm getting wrong. I'm assuming the material to be Al, but it probably isn't. I know that the inductor is a combination of metal-6 with 5 and 4, but what is the exact permeability of it?

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Are you able to measure on-chip inductance ? If you are, have you ever considered "calibration" of the measurement platform ?
Because I have lived trouble for many times and the calibration errors can be very significant on measurements.

Second thing, process variations can be so high so that the inductor values can be very far from the wanted value..
What about the EM simulation ?? Have you ever done ??

Hamid.Kiumarsi said:

There are many parasitics that you might be ignoring in your calculations.
Getting the right inductance of a CMOS inductor even using EM simulators is difficult enough (provided that you are an experienced user of these simulators) let alone solely using formulas.

Click to expand...

I know it's a tedious process, and may not even make sense when there are EM simulators and software like ASITIC designed particularly for this. But I kind of have to do it. I'm taking the resistive and capacitive parasitics of the metal traces and the substrate,and the metal oxide substrate capacitance into effect.

BigBoss said:

Are you able to measure on-chip inductance ? If you are, have you ever considered "calibration" of the measurement platform ?
Because I have lived trouble for many times and the calibration errors can be very significant on measurements.

Second thing, process variations can be so high so that the inductor values can be very far from the wanted value..
What about the EM simulation ?? Have you ever done ??

Click to expand...

About the first thing, no I unfortunately can't do any measurements. But I have done EM simulations on both Momentum and Sonnet so far, I'm a bit familiar with HFSS too. So, there's no problem simulating the inductor and extracting its complete model. I just have to bring my calculations as close to the real model as possible, and I need to do this as I also replied to Hamid.

Elecemperor said:

I've been calculating the inductance of a 0.18u CMOS process inductor in Cadence using several formulas such as Wheeler's, Rosa's and monomial expressions for octagonal spiral inductors. All these formulas give the same amount with very little variation while the real inductance is significantly different. As these calculations depend solely on parameters like width, length and spacing which are obvious as well as the permeability of the material, I guess it's the µr value that I'm getting wrong.

Click to expand...

You can use µr =1, no need to change that. I have designed hundreds of RFIC inductors with these simple equations, and the measured inductance is usually accurate to 5% or better.

RFIC inductance calculation is simple and robust, no surprises ... as long as you keep the inductor away from solid ground planes and don't have a "closed" metal ring too closely around the inductor.

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BigBoss said:

Are you able to measure on-chip inductance ? If you are, have you ever considered "calibration" of the measurement platform ?

Click to expand...

That's an important issue - measurement of small inductance in the 0.x nH range requires good knowledge of calibration/de-embedding stuff. Sanity check with simple, known DUTs is highly recommended.

volker@muehlhaus said:

You can use µr =1, no need to change that. I have designed hundreds of RFIC inductors with these simple equations, and the measured inductance is usually accurate to 5% or better.

RFIC inductance calculation is simple and robust, no surprises ... as long as you keep the inductor away from solid ground planes and don't have a "closed" metal ring too closely around the inductor.

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That's an important issue - measurement of small inductance in the 0.x nH range requires good knowledge of calibration/de-embedding stuff. Sanity check with simple, known DUTs is highly recommended.

Click to expand...

Thank you so much, volker! Here's the problem: I have an 180nm CMOS inductor in Cadence with an inner radius of r=30u, a width of w=6u, and spacing of s=2u, with one turn. Cadence shows an inductance of L=307.91pH for it, while Rosa's formula yields 142.9pH, Wheeler's 141.14pH, and monomial 142.26pH. What could be the reason for so much difference? I don't have access to equipment to measure the inductance by the way.

Elecemperor said:

Thank you so much, volker! Here's the problem: I have an 180nm CMOS inductor in Cadence with an inner radius of r=30u, a width of w=6u, and spacing of s=2u, with one turn. Cadence shows an inductance of L=307.91pH for it, while Rosa's formula yields 142.9pH, Wheeler's 141.14pH, and monomial 142.26pH. What could be the reason for so much difference? I don't have access to equipment to measure the inductance by the way.

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Do you use RCL extraction to predict inductance value in Cadence ?? If you do, RCL extraction won't give you a correct value.

BigBoss said:

Do you use RCL extraction to predict inductance value in Cadence ?? If you do, RCL extraction won't give you a correct value.

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Why not? How can I get the correct value using Cadence?

Elecemperor said:

Why not? How can I get the correct value using Cadence?

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RC extraction may give some insight about parasitic elements around a circuit but prediction of Inductances are based on simple straight line inductance calculation and it does not take into account proximity effects or real capacitive or inductive couplings with other lines/GND/metallic structures. Therefore EM simulation with a good substrate definition and correct port configuration should be precisely done.

BigBoss said:

RC extraction may give some insight about parasitic elements around a circuit but prediction of Inductances are based on simple straight line inductance calculation and it does not take into account proximity effects or real capacitive or inductive couplings with other lines/GND/metallic structures. Therefore EM simulation with a good substrate definition and correct port configuration should be precisely done.

Click to expand...

Well... Still,the EM simulations give an inductance with a maximum variation of 10pH from the Cadence result, and it's something in the formula that seems wrong.

Elecemperor said:

inner radius of r=30u, a width of w=6u, and spacing of s=2u, with one turn.

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Indeed, I have also seen that these very small inductors (some hundred pH) with one single turn are inaccurate with the simple equations. It seems that current path/field distribution is somewhat special then. Equations are good for 2+ turns, or large single turn inductors.

If you have confirmed your Cadence result with EM, go for it.