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On-Chip Spiral Inductors for
RF Applications
Juin J. Liou
Electrical and Computer Engineering Dept.University of Central Florida, Orlando, FL, USA
University ofCentral Florida
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Research Activities
Affiliation: Professor, Electrical and Computer Engineering Dept.
Director, Solid State Electronics Lab and Device
Characterization Lab, University of Central Florida
Research Area: Semiconductor device modeling/simulation, RF device/IC
design, and semiconductor manufacturing
L
is
t ofRe
ce
nt Proje
cts:
1. Study and modeling of reliability of GaAs heterojunction bipolar transistors
(Air Force, Alcatel Space)
2. RF CMOS reliability modeling and simulation (Intersil Corp., Conexant
Systems)
3. Design and modeling of on-chip electrostatic discharge (ESD) protection
structures (Semiconductor Research Corp., Intersil Corp., Intel Corp., NIST,TSMC)
4. Parameter extraction of VBIC bipolar transistor model (Lucent Tech.)
5. Statistical modeling of Si devices and ICs (Lucent Tech.)
6. Design and modeling of junction field-effect transistors (Texas
Instruments/SRC)
7. Design and modeling of passive components for RF ICs
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Outline
Background
Design and Modeling Concept Advanced Inductor Structures
Advanced Inductor Modeling
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In contrast with digital circuits which use mainlyactive devices, on-chip passive components arenecessary and imperative adjuncts to most RFelectronics. These components include inductors,capacitors, varactors, and resistors
For example, the Nokia 6161 cellphone contains 15ICs with 232 capacitors, 149 resistors, and 24inductors
Inductors in particular are critical components in
low noise amplifiers, oscillators and other tunedcircuits
The lack of an accurate and scalable model for on-chip spiral inductors presents a challenging
problem for RF ICs designers
Motivations
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RF Low Noise Amplifier(LNA)
Inductorsoccupy a large percentageofthechip
areaandareoftenthe performanceandcost
limitingelementsin RF ICs
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Outline Background
Design and Modeling Concept
Advanced Inductor Structures
Advanced Inductor Modeling
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Typical Square Shaped Spiral Inductor
builton Si Substrate
On-chip spiral inductors are used when a relatively small inductance
(i.e., several nH) is needed. Otherwise off-chip inductors are used
Performance of the spiral inductor depends on the number of turns, line
width, spacing, pattern shape, number of metal layers, oxide thickness
and conductivity of substrate
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Equivalent Circuitofa Lumped (Single-
) Model forSpiral Inductors
Except for the series
inductance, all
components in the modelare parasitics of the
inductor and need to be
minimized
This model is widely used,but it is not very accurate
and not scalable
SiC SiR
oxC
sL
sR
sC
SiC SiR
oxC
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ComponentsofLumpedModel
SiC SiR
oxC
sL
sR
sC
SiC SiR
oxC
LS consists of the self
inductance, positive
mutual inductance, and
negative mutual
inductance
CS is the capacitance
between metal lines
RS is the series resistanceof the metal line
COX
is the capacitance of
oxide layer underneath the
spiral
RSi and CSi are the coupling
resistance and capacitance
associated with Si substrate
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Quality Factorand Self-Resonant Frequency
The quality factorQ is an extremely important figure of merit for theinductor at high frequencies. The most fundamental definition forQ is
Basically, it describes how good an inductor can work as an energy-
storage element. In the ideal case, inductance is pure energy-storage
element (Q approaches infinity), while in reality, parasitic resistance and
capacitance reduce Q. This is because the parasitic resistance consumesstored energy, and the parasitic capacitance reduces inductivity (the
inductance can even become capacitive at high frequencies).
Self-resonant frequencyfSR marks the point where the inductor turns to
capacitive.
!
ederDissipatAveragePow
edEnergyStorQ [
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Quality Factor
pR pC sC
sR
sL
Equivalent circuit of the
one terminal grounded
inductor
? A
! psss
pss
sssp
p
s
s CCLL
CCR
RRLR
R
R
LQ 2
2
21
1[
[
[
2
2
22
1
ox
poxSi
Siox
p
R
RR
!
[
222
22
1
1
SiSiox
SiSiSiox
oxpRCC
RCCCCC
!
[
[
torsonanceFacSelfossFactorSubstrateLR
L
s
s Re![
Note: RP and CP give rise to substrate eddy and displacement currents, respectively
WhenRPapproaches infinity, the substrate loss factor approaches unity (ideal case)
Q can be improved by making the silicon substrate either a short or an open
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Physical MechanismsofSubstrate Loss
Both the eddy and displacement currents contribute to the
substrate loss and degrade the inductor RF performance
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Effectof InductorQfactoron Circuit
Performance
;! KR 2
1Term
nHLg 6!
nH
s 5.0!
RFC
2Term
AQ1010
Low Noise Amplifier
0 1 2 3 4
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
m2:
Freq=2.4 GHz
NF=2.057 dB
F=5
m1:
Freq=2.4 GHz
NF=0.898 dB
F=25
m1
m2
NoiseFigure(dB)
Frequency (GHz)
0 1 2 3 4
2
4
6
8
10
12
14
m2:
Freq=2.4 GHz
S21
=10.487 dB
F=5
m1:
Freq=2.4 GHz
S21
=12.001 dB
F=25
m1
m2
S21
(dB)
Frequency (GHz)
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Effectof InductorQfactoron Circuit
Performance
Colpitts Oscillator
Circuit
AQ500 pFC 2002 !
pC 401!
;! KR 10nHLc
200!
1 10 100 1000
-170
-160
-150
-140
-130
-120
-110
-100
-90
-80
m2:
Noise Frequency=100 KHz
Phase Noise=-126.996 dBc
Quality Factor=10
m1:
Noise Frequency=100 KHz
Phase Noise=-140.841 dBc
Quality Factor=30
m2
m1
Phase
Noise
(dB
c)
Noise Frequency (KHz)
Inductor is often the component
limiting the cost and performance in
RFICs!
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ImprovedModel withMore Accurate
Series Resistance
1siC
1siR
1oxC
2siC
2siR
2oxC
dcLdcR
2sR
2sL
1sR
1sL
1sM 2sM
R increases with increasing frequency skin effect
This model uses several frequency-independent components to
describe frequency-dependent series resistance
0 2 4 6 8 10
0
1
2
3
4
5
6
7
8
QualityFactor
Frequency (GHz)
Measured
Conventional T Model
One LoopTwo Loops
0 2 4 6 8 10
2
4
6
8
10
R
;)
Frequency (GHz)
Measured
Conventional TModel
One Loop
Two Loop
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ImprovedModel with Additional R and
C Components
subC subR
oxC
subC subR
oxC
20
L
20
R
cC
subC subR
oxC
cC
sC
20
R
20
L
21
R 21
R
scR
scR
2m
L2m
L
0.1 1 10
0
2
4
6
8
10
12
14
16
DifferentialQualityFactor
Frequency (GHz)
easurement (w=15 Qm,D=220Qm,N=4)
Proposed odel
Fixed RL mode l
(extracted at f=4GHz)
This model uses a double- frequency equivalent circuit to
account for the frequency-dependent nature ofL and R
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ImprovedModel with Additional
Horizontally Coupled R and C
0.1 1 10
0
1
2
3
4
5
6
7
8
9
Quality
a
tor
Frequen y GHz)
SquareSpiral Indu tor
R=60Qm, W=14.5Qm, S=2Qm
Model w/o Rsub
& Csub
roposedModel
Measurements:
2.5 Turn
6.5 Turn
1siC
1siR
1oxC
2siC
2siR
2oxC
0sL0s
R
sC
subR
subC
1sL
1sR
This model adds R and C to account for the horizontal coupling
in Si substrate
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Outline Background
Design and Modeling Concept
Advanced Inductor Structures
Advanced Inductor Modeling
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Structure with patterned ground shield
0.1 1 10
0
1
2
3
4
5
6
7
8
Q
Frequency (GHz)
PGS
SGS
NGS (19;-cm)
Ground shielding reduces the effective distance between the spiral and groundand thus reduces the substrate resistance. But solid ground shield (SGS) canreflect EM field in the substrate and reduce Q factor. Patterned ground shield canavoid this effect. Drawback of ground shielding is an increased coupling
capacitance due to an reduced distance between the metal and ground.
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Structure with Suspended Spiral
Inductor suspended above the structure to reduce the
substrate coupling resistance and capacitance
0 2 4 6 8 10 12 14 16 18 20
0
2
4
6
8
10
Conventional L
Suspended L
Conventional Q
Suspended Q
Frequency (GHz)
Inductance
(nH)
0
10
20
30
40
50
QualityFactor
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Structure with Substrate Removal
Portions of substrate are moved using deep-trench
technology to reduce the substrate coupling resistance and
capacitance
st1 Metal
nd2 Metal
BPSG
ViaHole
Si Pillar
1 100
2
4
6
8
10
12
14
Q
Fr y ( z)
Induct rw/o Tr nch
Inductorw/ Tr nch
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Structure with Vertical Spiral
Spiral is placed vertically on the substrate to reduce magnetic
field coupling to substrate
0 1 2 3 40
2
4
6
8
10
12
14
Quality
Factor
Fr uency ( z)
Model-Before PDM
Measured-Before PDM
Model-AfterPDMA
Measured-AfterPDMA
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Structure with Multiple Metal Layers and
Vertical Shunt
The series resistance is reduced with increasing number of
vertical shunt among the metal layers (case of M3 has no
vertical shunt). But this approach can increase COX
and thus
reduce the self-resonant frequency.
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
0
2
4
6
8
10
12
M2/M3/M4M3/M4M2/M3M3
Resistance(;)
Qmax
-Factor
Total metal Layer Thickness ( m)
Qmax
Rdc
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Structure with Horizontal Shunt
The metal line is split into multiple paths so that the effective
series resistance is reduced and Q factor is increased
0.1 1 10
-2
0
2
4
6
8
10
12
14
16
18
20
22
QualityFactor
Frequency (GHz)
1 // Path
2 // Path
3 // Path
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Structure with Tapered Line Width
EM loss is most significant in center of spiral. The metal line
width is tapered to reduce the magnetically induced losses in
the inner turns
0.1 1 10
0
10
20
30
40
50
QualityFactor
Frequency (GHz)
Optimized (Inner Turns Tapered)
W=40Qm
W=25Qm
W=10Qm
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Structure with Stacked Metal Layers
The stacked structure increases effective metal length, which
increases the inductance without increasing the chip area
0 2 4 6 8-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
QualityFactorInductance
Frequency (GHz)
Quality
Factor
-2
0
2
4
6
8
10
12
Inductance
(n
)
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Structure with Non-Symmetrical and
Symmetrical Winding
The symmetrical winding improves the RF performance
because 1) it has less overlap which reduces the series
capacitance and 2) the geometric center is exactly the magnetic
and electric center, which increases the mutual inductance
a b
1 Met l
2 Met l
Via
OverLap
OverLap
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Structure with Non-Symmetrical and
Symmetrical Winding
0 2 4 6 8 10
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
QualityFactor
Fre uency( )
Non- y etr ical Inductor
Sy etr ical Inductor
fS
R
(
)
Inductance(n )
Non-Sy etr ical Inductor
Sy etr ical Inductor
Q factor of the symmetrical inductor is improved, but the self-
resonant frequency is degraded due to an increased ac potential
difference between neighboring turns in the symmetrical inductor
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Dual-Layer Symmetrical Winding
Q factor of the symmetrical inductor can be further increased
using a dual-layer structure
Port 2Port
2Metal
1Metal
Via
0.
0.
0.
.0 1.
1.
1.
1.
.0 2.2 2.
2.
2.
0.0
0.5
1.0
1.5
2.0
2.5
.0
3.5
.0
4.5
5.0
Quali
actor
QBW
)
Fr
uency
!z)
Single"
#
urns
Dual"
#
urns
Single 3#
urns
Dual 3#
urns
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Structure with Non-Square Pattern
For hexagonal and octagonal inductors, less metal length is needed to achievethe same number of turns. Thus series resistance is compressed and Q factor
improved. On the other hand, the square shaped inductor will be more area
efficient. For example, for a square area on the wafer, square shape will utilize
100% of the area, whereas hexagonal, octagonal and circular shapes use 65%,
82.8% and 78.5% respectively
0 1 2 3 4 5
0
1
2
3
4
5
6
7
Qu
$
lit
%F
$
&
to
'
F( )
qu)
n0 1
(2
Hz)
3
qu4 ( )
H)
x4
gon4
l
5
0
t4
gon4
l
Ci( 0
ul4 (
Fixed
inductanceof 5 nH
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Structure with Non-Square Pattern
0 2 4 6 8 10 12
0
1
2
3
4
5
6
L
eff
(nH)
Frequency (GHz)
Octagonal Inductor
Square Inductor
The square inductor possesses a higher peak inductance but a lower self-resonant frequency (i.e., frequency at which L is zero). This is because
the longer metal line of square inductor induces a larger metal to substrate
capacitance, which reduces the inductance at high frequencies. For low
frequencies, the inductor depends mainly on the length of the spiral wire,
and the square pattern possesses a larger inductance.
Fixed outer
diameter
0 2 4 6 8 10 12
0
2
4
6
8
10
12
14
16
18
QualityFactor
Frequency (GHz)
Octagonal Inductor
Square Inductor
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