Accurate Modeling of Spiral Inductors on Silicon …literature.cdn.keysight.com/litweb/pdf/5989-9526EN.pdfSpiral Inductor Design on Si with RFDE Momentum 2004 Page 2 Overview Spiral

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Accurate Modeling of Spiral Inductors on Silicon using Planar EM Simulation

Agilent EEsof RFIC SeminarSpring 2004

Accurate Modeling of SpiralInductors on Silicon FromWithin Cadence Virtuoso usingPlanar EM Simulation

Spiral Inductor Design on Si with RFDE Momentum2004

Page 2

Overview

Spiral Inductor Models Availability & LimitationsMomentum Technology OverviewKey Physical Effects Considered in MomentumRFDE Momentum Solution ProcessMomentum Application BenchmarkSummary


Page 3

Spiral Inductor Models Availability & Limitations

•Inductor models can be found in most RFIC Design Kits•Spiral inductors are considered critical components in RFIC design•Foundry Supplied Design Kit inductor models often suffer from:• Limited discrete-parameters set• Limited frequency coverage• Questionable accuracy outside any design/process variations• Static model response to surrounding physical environment


Page 4

Traditional Characterization MethodMeasurement-based Modeling ApproachFabricate a large number of discretely varying topologiesPositives: Good accuracy over predefined frequency range and

discrete parameters’ samplesNegatives: Need to fabricate test wafer(s): Very time consuming and

costly Limited discrete-parameter set hindering design options Static lumped-element models unresponsive to

component’s physical surroundings Need component modeling skills Any updates to existing models can be just as costly as

starting a new model


Page 5

Predictive Modeling & VerificationElectromagnetics-based Modeling Approach Perform electromagnetic (EM) simulation

Use Scattering Parameters (S-parameters) data file in frequency-domain circuitsimulation

Optional: Build lumped element model based on EM data (for time-domaincircuit simulation; increased work and possible accuracy impact)

Positives: Minimal EM modeling insight Good accuracy over predefined frequency range and parameter samples Model’s frequency range can be extended with few simple menu selections Model’s physical parameters can be extended without any need for wafer run Verify model’s performance in its intended physical environmentNegative: Requires good characterization of process parameters (e.g. substrate)


Page 6

Overview



Page 7

Physical Structure

Port 2

E(r)H(r)

Js(r)

ω

source

load

Port 1

sourceload

planar metallization

z

Layer [3] 333 ,, σµε h3

Air

Layer [2] 222 ,, σµε h2

Layer [1] 111 ,, σµε h1

Gnd

multilayered medium

RFDE MomentumElectromagnetic Modeling & Verification

[S]

S-parameters

Your “Virtual Network Analyzer”Your “Virtual Network Analyzer”


Page 8

RFDE MomentumTechnology Process

B1(r) B2(r) B3(r)

I1 I2 I3S1 S2

[Z].[I]=[V]

I1 I2 I3

C11 C22C12

L11

L23

L22

L13L12

L33R22

[S]

Calculate Substrate’s Green’sFunction (system’s “impulseresponse”)Mesh strips, vias and slots withrectangles and triangles (arbitrarysurface mesh & mesh refinement)Model surface current in eachmesh cell (linear distribution)Build and solve matrix equationfor the unknown currentcoefficientsCalculate S-parameters

Calculate Substrate’s Green’sFunction (system’s “impulseresponse”)Mesh strips, vias and slots withrectangles and triangles (arbitrarysurface mesh & mesh refinement)Model surface current in eachmesh cell (linear distribution)Build and solve matrix equationfor the unknown currentcoefficientsCalculate S-parameters


Page 9

Comparison of Models

• quasi-static inductance . . . . . . • quasi-static capacitance . . . . . • DC conductor loss (σ) . . . . . . . .• DC substrate loss (σ) . . . . . . . . • dielectric loss (tgδ) . . . . . . . . . . . . . . . . . . . . . . . . . . .• skin effect loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .• substrate wave radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .• space wave radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Spiral Inductors

S-parameters

RF

Spice model S-parameters

MW

DC Spice Momentum RF Momentum MW


Page 10

Momentum Microwave & RF – ApplicationsAPPLICATIONS

RFIC (Silicon) RF Module (MCM, LTCC) Microwave - hybrid (Alumina) Microwave - MMIC (GaAs)

Initial design/optimization

Final design/optimization

High-Speed Digital (SI, BGA)RF Board (FR4, Duroid)RF Package (Plastic)

Planar Antennas

Momentum RF Momentum MW

frequency

physicalsize

200 GHzDC


Page 11

Overview



Page 12

Substrate Coupling & Radiation

Resistive loss of metallizationResistivity of Si substrateCapacitive coupling effects to Si substrate

Silicon h = 500 µmεr = 11.9 σ = 7.41 S/m

W = 15 um

SiO2 h = 5 µm εr = 4

Copper, t = 4 µm


Passivationh = 4 µm εr = 3.6

Copper, t = 0.66 µm

σ=4.5107S/m

Ground


Page 13

Current Return Path & Frequency Dependency

Impedance = R + jωLImpedance = R + jωL

frequencyDC 100 MHz 350 MHz 1.4 GHz

Current follows the path of “least resistance”impedance


Page 14

Current Distribution & Skin Effects

Current distribution in cross section of thick conductor as function of frequency

Example: RFIC process copper, w=15µm, t=4µm

w

t

t < δsw < 2δs

t < δsw > 2δs

2δs > t > δsw > 2δs

edge effectsingle-sidedskin effect

frequencyDC

High

Low

Current Density100 MHz 350 MHz

w = 2δs t = δs

σ=4.5e7 S/m1 MHz 75 µm10MHz 23.7 µm100MHz 7.5 µm1 GHz 2.37 µm

Skin depth of copper

ωµσδ 2=s

t > 2δsw > 2δs

double-sidedskin effect

1.4 GHz

t = 2δs

OR

isolated conductorconductor withground planeuniform current

distribution


Page 15

t = 2 um t = 4 um t = 8 um

t=2um

t=4um

t=8um

sheet conductorthick conductor

thick conductor

Influence of the thickness on the external inductance of the trace-Using edge mesh to include edge effect-Using Ohms/square resistance (no skin effect)-Using thick conductor model

port 1 port 2

length = 100 µm

L(ω)R(ω)


W = 15 um


Copper, t = 2, 4, 8 µm




σ=4.5107S/m

Increased thickness: -lower resistance -lower external inductance

Thick Conductors Effects


Page 16

Thick Conductor Modeling IssuesEdge Effect & Skin EffectHow does Momentum address Edge Effect and Skin Effect?•The edge mesh concept takes the edge effect into account

•The surface impedance concept takes the skin effect into account

How does the inclusion of the edge effect and the skin effect influencethe resistance and inductance of a trace?

port 1 port 2

length

L(ω)R(ω)

⋅σ=

)wt(lengthRDCNote:


W = 15 um


Copper, t = 4 µm




σ=4.5107S/m


Page 17

Influence of the edge effect on the resistance and inductance of the traceusing Ohms/square resistance (no skin effect)

no edge edge mesh

Ω=⋅σ

= 037.0)wt(

lengthR DC

Edge effect: -higher resistance -lower inductance

Edge effect

R(ω)

L(ω)

port 1 port 2

length = 100 µm

L(ω)R(ω)

port 1 port 2

length = 100 µmno edge mesh

with edge mesh


Page 18


W = 15 um


Copper, t = 4 µmSiO2 h = 3 µm εr = 4



Influence of the skin effect on the resistance and inductance of a traceusing edge mesh to include edge effect- using surface current (sheet) model- using thick conductor expansion

port 1 port 2

length = 100 µm

L(ω)+ ∆L(ω)R(ω)

Skin effect: -higher HF resistance -higher internal inductance -lower external inductance

Skin effect: -higher HF resistance -higher internal inductance -lower external inductance

sheet model 1sheet model 2sheet model 3thick model

LHF

∆LDC

LDC∆LHF

RDC

RHF

single-sided skin effect

double-sided skin effect

single-sided skin effect

double-sided skin effect

no skin effect

t = δs t = 2δs

no skin effect

Skin Effects


Page 19

Skin Effect – Discretization Problems

01

N

T

L

WH

Thick conductor is subdivided into Nlayers of thickness T/N and conductivity σ

Volume current is modeled with piecewiseconstant current filaments

How does a 3D volume meshing technology handles thick conductors?

N = 2N = 4N = 8N = 16N = 32N = 64

Need at least 3 subdivisionper skin depth forconvergence !!!

σ=4.5e7 S/m1 MHz 75 µm10MHz 23.7 µm100MHz 7.5 µm1 GHz 2.37 µm

Skin depth of copper

ωµσδ 2=s


Page 20

Momentum Modeling of Thick MetalField Equivalence Theorem: decomposition into external and internal problem

port 1 port 2

metal trace

L(ω)+ ∆L(ω)R(ω)

Thick conductor

w

t

h

σ

)( )( rJrE σ=

=

)( Z)( sss rJrE =

External Problem

t +Js(r)

Internal Problem

),(t,Zs ωσ

)L(j)(R ω∆ω+ω)L(j ωω

Surface current

L(ω)=external inductance∆L(ω)=internal inductance

Takes skin effect into account!

w

tσ

Surface impedance

PatentPending!


Page 21

Thick Conductor Modeling

• Volume of thick conductor is divided into two equal sheet conductor layers, one atthe top surface and one at the bottom surface, with same conductivity and half of thethickness

• Additional via layer (perfect conducting) to short out differential mode• Actual distribution of top and bottom layer currents not enforced, but follows from

solution of EM equations, yielding improved model for resistance and inductance• Accuracy decreasing (horizontal currents on via layers missing) when w/t decreases

(w/t < 2) (this will be addressed in a future release)

)( ),,(Z)(

)( ),,(Z)(

2,s2t

s2,s

1,s2t

s1,s

rJrE

rJrE

ωσ=

ωσ=

External Problem

t +Js,1(r) wtσ

Internal Problem

),(t,Zs ωσSurface impedanceSurface current

Js,2(r)2-layers surface current

[1]

[2][3] σ, t/2

σ, t/2h2=t

h1

h3

3 substrate layers 2 strip layers + 1 via layer


Page 22

Overview



Page 23

RFDE MomentumSolution Process Steps• Define Substrate stack & layer mapping• Make Momentum cell from design• Map Momentum ports to Cadence pins• Define simulation options: frequency plan, mesh settings…• Perform simulation and review results• Transpose new model to schematic for more accurate circuit

simulation


Page 24

RFDE Momentum Solution ProcessStep 1 – Define Substrate stack & layer mapping


W = 15 um


S = 5 um

Copper, t =1.75 µmSiO2 h = 3 µm εr = 4 Copper, t = 0.66 µm


Page 25



Page 26



Page 27

RFDE Momentum Solution ProcessStep 2 – Make Momentum Cell


Page 28

Momentum PortsMomentum Ports Cadence PinsCadence Pins

RFDE Momentum Solution ProcessStep 3 – Assign Ports to Cadence Pins


Page 29

+ref -ref

port

RFDE Momentum Design FlowStep 3 – Assign Ports to Cadence Pins

Physical portsPhysical ports

Unphysical portsUnphysical portselectrically long distance

electrically short distance

electrically short distance


Page 30

Frequency planMesh settingsMetallization properties…

RFDE Momentum Solution ProcessStep 4 – Define Simulation Options


Page 31

RFDE Momentum Solution ProcessStep 5 – Perform EM Simulation & Review Results


Page 32



Page 33



Page 34

RFDE Momentum Solution ProcessStep 6 – Make Schematic View for New Model


Page 35

RFDE Momentum Solution ProcessStep 6 – Transpose New EM Model to Schematic

Schematic Actions:1. Insert Momentum

components in Composer2. Set/Alter simulation control:

identical to case where noMomentum components areused

3. Run circuit simulation4. View/Analyze results

MomentumComponent

Momentum from Composer

Momentum from Composer

Can be used with Agilentcircuit simulator and CadenceSpectre (v5.0.33)

Can be used with Agilentcircuit simulator and CadenceSpectre (v5.0.33)


Page 36

Overview



Page 37

Momentum – Application Benchmark“Momentum validated against results forstandard parts… This leads to a substantialimprovement in phase noise of a 4GHz testoscillator” Dr. M P Wilson

Source: “Modeling of integrated VCOresonators using Momentum” Dr. M PWilson, Tality UK.

Source: “Modeling of integrated VCOresonators using Momentum” Dr. M PWilson, Tality UK.


Page 38

Momentum – Application Benchmark

2.5 Turn Octagonal Spiral Inductor

“Three test inductors were compared with measuredresults. All three inductor examples show good agreementwith measured results, showing that we could producereliable Momentum models for the particular processused.” Dr. M P Wilson.

“Three test inductors were compared with measuredresults. All three inductor examples show good agreementwith measured results, showing that we could producereliable Momentum models for the particular processused.” Dr. M P Wilson.


Page 39

Momentum – Application Benchmark

“It can be seen that the Balun circuit improves phasenoise by means of an increase in the effective Q of theresonator. This clearly shows the benefit of the custommodeling facility given by Momentum.”Dr. M P Wilson

“It can be seen that the Balun circuit improves phasenoise by means of an increase in the effective Q of theresonator. This clearly shows the benefit of the custommodeling facility given by Momentum.”Dr. M P Wilson


Page 40

Overview



Page 41

Summary

• Spiral inductors are critical RFIC design components• Foundries’ supplied models may limit design options• Electromagnetic-based modeling approach has many advantages• Method-of-Moments EM technique is best suited for modeling spirals• Momentum industry track record• RFDE Momentum solution process is a simple few steps process• RFDE Momentum is fully integrated with Cadence Virtuoso• RFDE Momentum added accuracy greatly enhances first-pass design

success


Page 42

Appendix

• Momentum Substrate Stack Definition• Modeling Metal Losses


Page 43

Momentum Substrate Definition

Momentum uses a text file for the description of the substratedefinition, which includes:

• Layers stack definition• Dielectric layers physical properties• Metal layers physical properties


Page 44

1. Layers Stack Definition


Page 45

2. Dielectric Layers’ Physical Properties


Page 46

3. Metal Layers Physical Properties


Page 47

Momentum Substrate Definition – Example


Page 48

Modeling Metal LossesDefault Model: Sheet Conductor Model

)( Z)( sss rJrE =

external problem

t +Js(r) w

tσ

internal problem

),(t,Zs ωσSurface impedanceSurface current

• Surface impedance based on 1-dimensional field approximation (only variation in z-direction), valid for good conductors (σ > ωε) with a high width/thickness ratio(typically w/t > 5)

• Models a uniform current distribution over entire cross section at low frequencies,yielding the correct DC resistance value

• Models a concentrated current distribution over skin depth δs at high frequencies, overestimates HF resistance (depending on closeness of return current in ground plane)

• Models the external inductance for zero thickness with higher internal inductance (skineffect), hence over estimates inductance


Page 49

Modeling Metal LossesSurface Currents – Sheet Conductors

• Volume of thick conductor is modeled as an infinitely thin conductor layer• Surface current flows in one sheet conductor layer• External inductance L(ω) is independent of conductor thickness (t)

σt

thick conductor

J(r)

1-layer surface current

Js(r)un

strip (σ, t)

)( Z)( sss rJrE =

)L(j ωω


Page 50

Modeling Metal LossesSurface Currents – Thick Conductors

•Volume of thick conductor is divided into two equal conductor layers, one at thetop surface and one at the bottom surface, with same conductivity and half of theconductor thickness

•Additional via layer (perfect conducting) included to short out differential mode•Actual distribution of top and bottom layer currents not enforced, but follows fromsolution of EM equations

•External inductance L(ω) is dependent on conductor thickness•As conductor thickness (t) increases: mutual inductance decreases externalinductance decreases; also, high frequency resistance decreases

σt

thick conductor

J(r)

2-layers surface current

un

via (perfect conducting)strip (σ, t/2)

strip (σ, t/2)Js,2(r)

Js,1(r)

t


Page 51

Modeling Metal Losses1-dimensional surface impedance model

• Distribution of the current inside the conductor is based on 1-dimensional fieldapproximation (only variation in z-direction), valid for good conductors (σ > ωε)with a high width/thickness ratio (typically w/t > 5)

• Yields analytic model for the surface impedance Zs(t,σ,ω)• Resistance R(ω) and interior inductance ∆L(ω) are dependent on: conductor

thickness, conductivity, and frequency (skin effect)

σt

thick conductor

J(r) )tjkcoth(Z),,t(Z ccs =ωσ

)j(jjk

jj Zwith

c

c

ωε+σωµ=

ωε+σωµ=

)( Z)( sss rJrE =


Page 52

)tjkcoth(Z),,t(Z ccs =ωσ

3tj

t1),,t(Zs

µω+σ

→ωσ

low frequencies (LF):

high frequencies (HF):( )

ωµσ=δ+

σδ→ωσ 2depth skin j11),,t(Z s

ss

LF current runs in entire crosssection of the metallization

drawn on single layer (σ, t)

HF current runs in SINGLE skin depthsurface layer (proximity of ground)

δsσσ t

)j(jjk

jj Zwith

c

c

ωε+σωµ=

ωε+σωµ=

RDC + jω∆LDC

RHF + jω∆LHF

Modeling Metal Losses1-dimensional surface impedance model

SINGLE-SIDED SKIN EFFECT

Typical Application: microstrip circuit

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Printed in USA, April 05, 2004 5989-9526EN

Documents

Accurate Modeling of Spiral Inductors on Silicon …literature.cdn.keysight.com/litweb/pdf/5989-9526EN.pdfSpiral Inductor Design on Si with RFDE Momentum 2004 Page 2 Overview Spiral