on-chip spiral inductors for silicon-based radio-frequency...

http://holst.stanford.edu/~CPYue [email protected]

On-Chip Spiral Inductors forSilicon-Based Radio-Frequency

Integrated Circuits

C. Patrick Yue

Center for Integrated SystemsStanford University, CA


Outline

• Overview

• A physical model for on-chip inductors

• Effects of process and layout parameters

• Design methodology

• Inductors with patterned ground shields

• Substrate noise coupling

• Conclusions


Worldwide Wireless Market

1996 Total: 87M 2000 Total: 300M

North America125M (41%)

Europe75M (25%)

Asia Pacific80M (27%)

North America38M (43%)

20M(7%)

5M(6%)

Asia Pacific19M (22%)

Europe25M (29%)

36% Annual Growth(Source: CTIA, 1996.)


A Typical Cellular Phone

RF front-end component count:

Inductor 11

Capacitor >100

Resistor >50

IC 5

Transistor 12

Crystal 1

Filter 2

(Source: Bosch, 1997.)


Advantages of Integration

• Cost: assembly and packaging

• Power: fewer parasitics

• Design Flexibility: signals stay on chip

• Size

• Reliability

• Tolerance


Discrete Inductors

• L: 2 to 20 nH(2 to 10%)

• Q: 50 to 200(1 to 2 GHz)

• srf: 4 to 10 GHz

(Source: Coilcraft, 1997.)

mminch


Active Inductors

-gm 1

gm 2C

i1

iin

i2

vin–

+vc–

+

LC

gm1gm2----------------=

• Excess Noise

• Extra Power

• Limited Linearity


Bond Wire Inductors• Predictability

• Repeatability

• Unwanted Couplings

• Limited Inductance

(Source: ISSCC’95, pp. 266)


A Typical Planar Spiral Inductor

WidthSpacing

Number of Turns

Outer Dimension


Multilevel Interconnects

(Source: Semiconductor International , 1997.)


A Typical Inductor On Silicon

3D Perspective View

Top View

Si

SiO2

3 µm

Al


Model Description

Ls

CsCsi

Rs

Rsi

Cox


Model Description

Ls

Cs

Rs

CsiRsi

Cox

RsiCsi

Cox


Model DescriptionPhysical Model of Inductor on Silicon Effects

MutualCouplingsEddy Current

Feed-Through Capacitance

Oxide Capacitance

Si SubstrateCapacitance

Si SubstrateOhmic Loss

Ls: Greenhouse Method

Rsρ l⋅

w δ 1 et– δ⁄

–( )⋅⋅-------------------------------------------=

Cs n w2 εox

tox M1-M2------------------⋅ ⋅=

Cox12-- l w

εox

tox-------⋅ ⋅ ⋅=

Csi12-- l w CSub⋅ ⋅ ⋅=

Rsi2

l w GSub⋅ ⋅-------------------------=

Rs

Ls

Cs

Csi

Cox

Rsi


Skin Effect

Co-axial

Microstrip

E Field

Current

Conductor


Effective Metal Thickness

Current

Actual

Density

t

J0

0Metal Thickness

teff e- x / δ

dx⋅0

t∫=

δ 1 e- t / δ

–( )⋅=


Measurement Setup

HP 8720B Open Structure

Probe Station

PROBE

G

GS

G

GS

Device Under Test

PROBE


Parameter Extraction ProcedureS to TransmissionMatrix Conversion

Solve for Propagation Constant ( Γ )and Characteristic Impedance ( Z0 )

A BC D

Γlcosh Z0 Γlsinh

Z01– Γlsinh Γlcosh

=

S11 S12

S21 S22

A BC D

→

Γ l Z0⋅ ⋅=2Z0

Γ l⋅--------- =

De-embeddedS Parameters

Cs

Rs

LsCpRp


0.1 1 10Frequency (GHz)

0

2

4

6

8

10

L s (n

H)

0

5

10

15

20

25

R s ( Ω

)

(Cs = 28 fF)

Rs

Ls

Cs

Csi

Cox

Rsi

CopperAluminum Model

Measured and Modeled Values of Ls and Rs


Substrate Modeling

CpRpCsi

Cox

Rsi

2Z0

Γ l⋅---------=

Physical Model Extracted Capacitanceand Resistance


Measured and Modeled Values of Rp and Cp


0

5

10

15

20

25

R p (k

Ω)

0

50

100

150

200

250

C p (f

F)

Rs

Ls

Cs

Csi

Cox

Rsi



Definition of Inductor Quality Factor

V0 ωtcos Rs

LsCsCpRp

Q 2πPeak Magnetic Energy Peak Electric Energy–

Energy Loss in One Oscillation Cycle-------------------------------------------------------------------------------------------------------------=

ωLs

Rs---------

Rp

Rp ωLs Rs⁄( ) 2 1+[ ] Rs⋅+-------------------------------------------------------------------× 1

Rs2 Cp Cs+( )

Ls-------------------------------– ω2Ls Cp Cs+( )–

×

Self-Resonance FactorSubstrate Loss Factor


Measured and Modeled Value of Q


0

2

4

6

8

10

Q



Measured and Modeled Values ofSubstrate Factors

0.0

0.2

0.4

0.6

0.8

1.0

Self-

Reso

nanc

e Fa

ctor


0.0

0.2

0.4

0.6

0.8

1.0

Subs

trate

Los

s Fa

ctor



Comparison to Published Results

0 5 10 15 20Measured Qpeak presented by Ashby et al.

0

5

10

15

20

Q P

redi

cted

by

Our

Mod

el

5 µm9 µm

Line Width

14 µm19 µm24 µm


Effect of Metal Scheme on Q


0

2

4

6

8

Q

Rs

Ls

Cs

Csi

Cox

Rsi

3 levels of 1 µm in parallel3 µm Al 2 µm Al1 µm AlModel


Effect of Oxide Thickness on Q


0

2

4

6

8

Q

Rs

Ls

Cs

Csi

Cox

Rsi

6.5 µm Oxide4.5 µm Oxide 2.5 µm OxideModel



0

2

4

6

8

Q

Rs

Ls

Cs

Csi

Cox

Rsi

10 Ω-cm Si:Csub = 1.6×10-3 fF/µm2

Gsub = 4.0×10-8 S/µm2

6 Ω-cm Si:Csub = 6.0×10-3 fF/µm2

Gsub = 1.6×10-7 S/µm2

Model

Effect of Substrate Resistivity on Q



0

2

4

6

8

Q

Rs

Ls

Cs

Csi

Cox

Rsi

Outer Dimension Line Width550 µm, 41 µm400 µm, 24 µm300 µm, 13 µmModel

Effect of Layout Area on Q


Application of Model

LCfC

12π L C⋅----------------------=

fC 1.6 GHz= C 1.2 pF=, L→ 8 nH=

InductorDesign with Optimal Q

CircuitRequirements

TechnologyConstraints

?

(Design Tool)Area

SubstrateFactors

L

fC


Contour Plots of Q

Measured Q3.4

0 100 200 300 400Outer Dimension (µm)

0

2

4

6

8

10

Indu

ctan

ce (n

H)

5

3

1 1

3

5

7

9

0.6 GHz 1.0 GHz

1.7 Measured Q

4.62.9



Contour Plots of Q

21

53

79

4

4

5

4

79

1.6 GHz 3.0 GHz

Measured Q4.06.1

Measured Q5.24.0



0

2

4

6

8

10

Indu

ctan

ce (n

H)

1


Outline

• Overview

• A physical model for on-chip inductors

• Effects of process and layout parameters

• Design methodology

• Inductors with patterned ground shields

• Substrate noise coupling

• Conclusions


Overview

• Challenges

- Q degraded by substrate loss

- Substrate coupling

- Modeling and characterization

- Process constraints

• Approaches

- Etch away Si substrate

- Patterned Ground Shield


Suspended Inductors

PolyimideMembrane

Wafer Backside

~550 µm


Electromagnetic Fields of Conventional On-Chip Inductors

E

H

Ls

Rs

Rsi

CsiCox


Problems with Solid Ground Shield

Induced Loop Current and Magnetic Field


EM Fields of On-Chip Inductors with Patterned Ground Shield


• Pattern

- Orthogonal to spiral

(induced loop current)

• Resistance

- Low for termination of

the electric field

- Avoid attenuation of

the magnetic field

Patterned Ground Shield Design

Ground Strips

Slot between Strips

Induced Loop Current


Patterned

Solid

None (19 Ω-cm)

None(11 Ω-cm)


0

2

4

6

8

10

L s (n

H)Effect of Aluminum Ground Shields on L


Patterned

Solid

None (19 Ω-cm)

None(11 Ω-cm)


0

5

10

15

20

25

R s ( Ω

)Effect of Aluminum Ground Shields on R


Effect of Aluminum Ground Shields on C

Patterned

Solid

None (19 Ω-cm)

None(11 Ω-cm)


0

50

100

150

200

250

300

C p (f

F)


Patterned

Solid

PatternedAluminum


0

2

4

6

8

10

L s (n

H)Effect of Polysilicon Ground Shields on L


Patterned

Solid

PatternedAluminum


0

5

10

15

20

25

R s ( Ω

)Effect of Polysilicon Ground Shields on R


Patterned

Solid

PatternedAluminum


0

50

100

150

200

250

300

C p (f

F)Effect of Polysilicon Ground Shields on C


Ls

Rs

Cox

Circuit Models of On-Chip Inductors

Ls

Rs

Rsi

CsiCox

Conventional Design With Patterned Ground Shield


Effect of Aluminum Ground Shields on Q

Patterned

Solid

None (19 Ω-cm)

None(11 Ω-cm)


0

2

4

6

8

Q


Patterned

Solid

PatternedAluminum


0

2

4

6

8

QEffect of Polysilicon Ground Shields on Q


Parallel LC Resonator at 2 GHz

PatternedPolysilicon

None(11 Ω-cm)

LC

QRESONATOR

fC

∆f-----=

1.0 1.5 2.0 2.5 3.0Frequency (GHz)

0.00

0.25

0.50

0.75

1.00

1.25

1.50

Mag

nitu

de o

f Z (k

Ω)

Zmax at fc

∆f~30%


Noise Coupling Measurement

PROBE

G

GS

G

GS

PROBE

HP 8720B

Probe Station


Patterned

None (19 Ω-cm)

None(11 Ω-cm)

Probes up


-90

-80

-70

-60

-50

-40

|s21

| (dB

)Effect of Polysilicon GS on Isolation


A Single-Chip CMOS GPS Receiver


Conclusions

• A compact model for spiral inductors on silicon has been presented.

• Physical phenomena important to limitation and prediction of Q were investigated.

• Effects of various structural parameters on Q have been demonstrated.

• The scalable model can be used as a design tool for optimizing Q.


Conclusions on Patterned Ground Shield

• Improves Q by eliminating substrate loss

(up to 33% at 1-2 GHz)

• Improves isolation by preventing substrate

coupling (up to 25 dB at 1 GHz)

• Simplifies modeling

• Eliminates substrate dependency

• Requires no additional process steps


Acknowledgments

• Center for Integrated Systems Industrial Sponsors

• National Science Fundation (MIP-9313701)

• National Semiconductor FMA Fellowship (Dr. G. Li)


Acknowledgments

• Prof. Simon Wong

• Prof. Dwight Nishimura, Prof. Krishna Saraswat, and Prof. Robert Dutton

• Prof. Calvin Quate

• Prof. Tom Lee

• Rosanna Foster and Ann Guerra

• CIS and SNF Staff Members

• Friends

• Family

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