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
http://holst.stanford.edu/~CPYue [email protected]
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
http://holst.stanford.edu/~CPYue [email protected]
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.)
http://holst.stanford.edu/~CPYue [email protected]
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.)
http://holst.stanford.edu/~CPYue [email protected]
Advantages of Integration
• Cost: assembly and packaging
• Power: fewer parasitics
• Design Flexibility: signals stay on chip
• Size
• Reliability
• Tolerance
http://holst.stanford.edu/~CPYue [email protected]
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
http://holst.stanford.edu/~CPYue [email protected]
Active Inductors
-gm 1
gm 2C
i1
iin
i2
vin–
+vc–
+
LC
gm1gm2----------------=
• Excess Noise
• Extra Power
• Limited Linearity
http://holst.stanford.edu/~CPYue [email protected]
Bond Wire Inductors• Predictability
• Repeatability
• Unwanted Couplings
• Limited Inductance
(Source: ISSCC’95, pp. 266)
http://holst.stanford.edu/~CPYue [email protected]
A Typical Planar Spiral Inductor
WidthSpacing
Number of Turns
Outer Dimension
http://holst.stanford.edu/~CPYue [email protected]
Multilevel Interconnects
(Source: Semiconductor International , 1997.)
http://holst.stanford.edu/~CPYue [email protected]
A Typical Inductor On Silicon
3D Perspective View
Top View
Si
SiO2
3 µm
Al
http://holst.stanford.edu/~CPYue [email protected]
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
http://holst.stanford.edu/~CPYue [email protected]
Skin Effect
Co-axial
Microstrip
E Field
Current
Conductor
http://holst.stanford.edu/~CPYue [email protected]
Effective Metal Thickness
Current
Actual
Density
t
J0
0Metal Thickness
teff e- x / δ
dx⋅0
t∫=
δ 1 e- t / δ
–( )⋅=
http://holst.stanford.edu/~CPYue [email protected]
Measurement Setup
HP 8720B Open Structure
Probe Station
PROBE
G
GS
G
GS
Device Under Test
PROBE
http://holst.stanford.edu/~CPYue [email protected]
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
http://holst.stanford.edu/~CPYue [email protected]
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
http://holst.stanford.edu/~CPYue [email protected]
Substrate Modeling
CpRpCsi
Cox
Rsi
2Z0
Γ l⋅---------=
Physical Model Extracted Capacitanceand Resistance
http://holst.stanford.edu/~CPYue [email protected]
Measured and Modeled Values of Rp and Cp
0.1 1 10Frequency (GHz)
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
CopperAluminum Model
http://holst.stanford.edu/~CPYue [email protected]
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
http://holst.stanford.edu/~CPYue [email protected]
Measured and Modeled Value of Q
0.1 1 10Frequency (GHz)
0
2
4
6
8
10
Q
CopperAluminum Model
http://holst.stanford.edu/~CPYue [email protected]
Measured and Modeled Values ofSubstrate Factors
0.0
0.2
0.4
0.6
0.8
1.0
Self-
Reso
nanc
e Fa
ctor
0.1 1 10Frequency (GHz)
0.0
0.2
0.4
0.6
0.8
1.0
Subs
trate
Los
s Fa
ctor
CopperAluminum Model
http://holst.stanford.edu/~CPYue [email protected]
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
http://holst.stanford.edu/~CPYue [email protected]
Effect of Metal Scheme on Q
0.1 1 10Frequency (GHz)
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
http://holst.stanford.edu/~CPYue [email protected]
Effect of Oxide Thickness on Q
0.1 1 10Frequency (GHz)
0
2
4
6
8
Q
Rs
Ls
Cs
Csi
Cox
Rsi
6.5 µm Oxide4.5 µm Oxide 2.5 µm OxideModel
http://holst.stanford.edu/~CPYue [email protected]
0.1 1 10Frequency (GHz)
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
http://holst.stanford.edu/~CPYue [email protected]
0.1 1 10Frequency (GHz)
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
http://holst.stanford.edu/~CPYue [email protected]
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
http://holst.stanford.edu/~CPYue [email protected]
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
0 100 200 300 400Outer Dimension (µm)
http://holst.stanford.edu/~CPYue [email protected]
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
0 100 200 300 400Outer Dimension (µm)
0 100 200 300 400Outer Dimension (µm)
0
2
4
6
8
10
Indu
ctan
ce (n
H)
1
http://holst.stanford.edu/~CPYue [email protected]
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
http://holst.stanford.edu/~CPYue [email protected]
Overview
• Challenges
- Q degraded by substrate loss
- Substrate coupling
- Modeling and characterization
- Process constraints
• Approaches
- Etch away Si substrate
- Patterned Ground Shield
http://holst.stanford.edu/~CPYue [email protected]
Suspended Inductors
PolyimideMembrane
Wafer Backside
~550 µm
http://holst.stanford.edu/~CPYue [email protected]
Electromagnetic Fields of Conventional On-Chip Inductors
E
H
Ls
Rs
Rsi
CsiCox
http://holst.stanford.edu/~CPYue [email protected]
Problems with Solid Ground Shield
Induced Loop Current and Magnetic Field
http://holst.stanford.edu/~CPYue [email protected]
EM Fields of On-Chip Inductors with Patterned Ground Shield
http://holst.stanford.edu/~CPYue [email protected]
• 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
http://holst.stanford.edu/~CPYue [email protected]
Patterned
Solid
None (19 Ω-cm)
None(11 Ω-cm)
0.1 1 10Frequency (GHz)
0
2
4
6
8
10
L s (n
H)Effect of Aluminum Ground Shields on L
http://holst.stanford.edu/~CPYue [email protected]
Patterned
Solid
None (19 Ω-cm)
None(11 Ω-cm)
0.1 1 10Frequency (GHz)
0
5
10
15
20
25
R s ( Ω
)Effect of Aluminum Ground Shields on R
http://holst.stanford.edu/~CPYue [email protected]
Effect of Aluminum Ground Shields on C
Patterned
Solid
None (19 Ω-cm)
None(11 Ω-cm)
0.1 1 10Frequency (GHz)
0
50
100
150
200
250
300
C p (f
F)
http://holst.stanford.edu/~CPYue [email protected]
Patterned
Solid
PatternedAluminum
0.1 1 10Frequency (GHz)
0
2
4
6
8
10
L s (n
H)Effect of Polysilicon Ground Shields on L
http://holst.stanford.edu/~CPYue [email protected]
Patterned
Solid
PatternedAluminum
0.1 1 10Frequency (GHz)
0
5
10
15
20
25
R s ( Ω
)Effect of Polysilicon Ground Shields on R
http://holst.stanford.edu/~CPYue [email protected]
Patterned
Solid
PatternedAluminum
0.1 1 10Frequency (GHz)
0
50
100
150
200
250
300
C p (f
F)Effect of Polysilicon Ground Shields on C
http://holst.stanford.edu/~CPYue [email protected]
Ls
Rs
Cox
Circuit Models of On-Chip Inductors
Ls
Rs
Rsi
CsiCox
Conventional Design With Patterned Ground Shield
http://holst.stanford.edu/~CPYue [email protected]
Effect of Aluminum Ground Shields on Q
Patterned
Solid
None (19 Ω-cm)
None(11 Ω-cm)
0.1 1 10Frequency (GHz)
0
2
4
6
8
Q
http://holst.stanford.edu/~CPYue [email protected]
Patterned
Solid
PatternedAluminum
0.1 1 10Frequency (GHz)
0
2
4
6
8
QEffect of Polysilicon Ground Shields on Q
http://holst.stanford.edu/~CPYue [email protected]
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%
http://holst.stanford.edu/~CPYue [email protected]
Noise Coupling Measurement
PROBE
G
GS
G
GS
PROBE
HP 8720B
Probe Station
http://holst.stanford.edu/~CPYue [email protected]
Patterned
None (19 Ω-cm)
None(11 Ω-cm)
Probes up
0.1 1 10Frequency (GHz)
-90
-80
-70
-60
-50
-40
|s21
| (dB
)Effect of Polysilicon GS on Isolation
http://holst.stanford.edu/~CPYue [email protected]
A Single-Chip CMOS GPS Receiver
http://holst.stanford.edu/~CPYue [email protected]
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.
http://holst.stanford.edu/~CPYue [email protected]
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
http://holst.stanford.edu/~CPYue [email protected]
Acknowledgments
• Center for Integrated Systems Industrial Sponsors
• National Science Fundation (MIP-9313701)
• National Semiconductor FMA Fellowship (Dr. G. Li)
http://holst.stanford.edu/~CPYue [email protected]
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