embedded integrated inductors with a single layer...
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Embedded Integrated Inductors With A Single Layer Magnetic Core:
A Realistic Option- Bridging the gap between discrete inductors
and planar spiral inductors -
Dok Won Lee, LiangLiang Li, and Shan X. Wang
Department of Materials Science and EngineeringDepartment of Electrical Engineering
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Outline
I. Introduction
II. Analytical Models and Inductor Design
III. Fabrication of Integrated Inductors
IV. Measurement of Fabricated Inductors
V. Analysis of Magnetic Inductors on Si
VI. Conclusion
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Use of Inductors in Our Daily Lives
Texas Instruments Tag-itTM
• Traffic light• Red-light camera
• Metal detector • RFID tag
• Voltage regulator module • Cell phone
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4R.K. Ulrich and L.W. Schaper, “Integrated Passive Component Technology”, 2003
Fully integratedelectronics
Why Integrated Inductors?
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IC containinggate driver andpower MOSFETs
Inductor
Capacitors
IC containinggate driver andpower MOSFETs
Inductor
Capacitors
Enpirion EN5330 PSoC (Power-System-on-a-Chip)
70% of pc-board area saved
Passive components are discreteand occupy large areas
Example: Power Management
DC-DC converter
* R. Allen, Electronic Design, May 2004
*
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Inductance Requirement for Power Management
100 kHz 1 MHz 10 MHz 100 MHz 1 GHz 10 GHz
10 uH
1 uH
100 nH
10 nH
1 nH
100 pH
From A. Ghahary, Power Electronics Technology, Aug. 2004
Frequency
Indu
ctan
ceDiscrete inductors Large inductance
Large volumePoor AC performance
Planar spiral inductors Small area consumption
Small inductanceLimited performance insub-GHz applications
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Transmission line Spiral inductor Solenoid inductor
Small resistanceSmall inductanceUsually two magneticlayers needed
Schematics of Magnetic Inductor Designs
Close to the planar spiralLimited inductance gainOne or two magneticlayers
Magnetically efficientRelatively complexstructure
One magnetic layer
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Brief Rev of Integrated Magnetic Inductors
Tohoku
Taken from Lee et al, Embedded Inductors with Magnetic Cores,Book Chapter in press (Springer)
Intel, Tyndall
CEA-LETI
≥
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IEEE Trans. Magn.2002, p.3168-70
A.M. Crawford, et al.
Planar spiral inductor with CoTaZr core,CMOS compatibility,Q ~ 2.7 @ 1 GHz
On-package solenoid inductor with CoFeHfO core,Q = 22 @ 200~300 MHz,Rdc ~ 10 mΩ
IEEE Trans. Advanced Packaging (accepted 2008)
L. Li, D. W. Lee, et al.
Magnetic Inductors from Stanford & Cowork
Planar transmission line inductor with CoTaZr core,Q = 6 @ 700 MHz
Intermag 08, CV 01P. K. Amiri, et al.
Planar solenoid inductor with CoTaZr core,Inductance enhancement over air core = 34x Q>6 @ 26 MHz
Intermag 08, AG 01 (invited)D. W. Lee, et al.
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I. Introduction
II. Analytical Models and Inductor Design
III. Fabrication of Integrated Inductors
IV. Measurement of Fabricated Inductors
V. Analysis of Magnetic Inductors on Si
VI. Conclusion
• Analytical models for key device properties• Material selection• Optimization of design parameters• Inductor design concepts
II. Analytical Models and Inductor Design
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wM
lA, lM
lC
sV
tMtA
tCsV
g
wV
gV
wA
wC
Top view Cross-section view
Schematics of Integrated Solenoid Inductor
• Solenoid inductor design was mainly considered in this work.
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Key Device Properties
• Inductance L
• Resistance R
• Quality factor Q
• Device area
• Useful bandwidth
RL
TndissipatioPowerstoredEnergyQ ωπ =
⋅=
2
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0 1x10-8 2x10-8 3x10-8 4x10-8 5x10-80
1x10-8
2x10-8
3x10-8
4x10-8
5x10-8
HFSS simulations Linear fit
∆Lsi
mul
ated
(H)
∆Lcalculated (H)
Inductance of magnetic inductor LMC:
• For a finite-sized magnetic core, there is ademagnetizing field inside the magnetic core,which effectively reduces µr.
• Demagnetizing field is not uniform inside the magnetic core,and the numerical solutions should be used for µr > 1.
Slope = 1.01 ± 0.01
)1(1
prism rrectangula offactor ingDemagnetiz )]1(1[
where2
02
0
−+≡
=
=−+
=∆
∆+=
rd
reff
d
M
MMeff
rdM
MMr
ACMC
N µ
Nl
twNNl
twNL
LLL
µµ
µµµ
µµ
Inductance of Magnetic Inductor LMC
* D.-X. Chen et al., IEEE Trans. Magn., 41, 2077 (2005)
Inductance enhancement:
effAC
MCeff
AC
ACMC
AC AA
LLL
LL
,
µ≈−=∆ Much less than µrbut still significant
AMC AAC,eff
*
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Resistance of magnetic inductor RMC:
• From the classical electromagnetism:
MagneticMagnetic EP ⎟⎟⎠
⎞⎜⎜⎝
⎛≈'"2
µµω
LRRRR
LIILILEEE
RR∆RRIIRRP
ACACMC
ACMCinductorcoreAirinductorMagneticMagnetic
ACMCACMCMagnetic
∆⎟⎟⎠
⎞⎜⎜⎝
⎛+=∆+=∴
∆=−=−=
−≡∆=−=
'"
21
21
21 where)(
222
22
µµω
LR ∆⎟⎟⎠
⎞⎜⎜⎝
⎛=∆'"
µµω
• Representing in terms of the device properties:
* R.F. Harrington, “Time-Harmonic Electromagnetic Fields”, 1961
Resistance of Magnetic Inductor RMC
dVHP
dVHE
Magnetic
Magnetic
∫∫∫∫∫∫
=
=
2
2
" losspower Magnetic
'21 storedenergy the tooncontributi Magnetic
ωµ
µ
Both ω and (µ”/µ’) increase withfrequency. Hence ∆R becomessignificant as the frequency increases.
The more inductance enhancementwe obtain by using a magnetic core,the more resistive losses we introduceat high frequencies.
R
Freq.
RAC
∆R for small ∆L
∆R for large ∆L
*
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Quality factor Q
LR
LLRLQ
AC
AC
MC
MCMC
∆⎟⎠
⎞⎜⎝
⎛+
∆+==
'"
µµω
ωω
fMC106 107 108 109
0
2
4
6
8
10 ∆L/LAC=1 ∆L/LAC=10 ∆L/LAC=30 QAC µ'/µ"
Qua
lity
fact
or
Frequency (Hz)
AC
ACAC R
LQ ω=
∆L << LAC QMC ~ QAC at low frequencies
∆L >> LAC QMC ~ µ’/µ” at high frequencies
fMC can be considered as the useful bandwidthof the magnetic inductor.
Quality factor of air core inductor QAC:
Quality factor of magnetic inductor QMC:
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• Desirable properties:- High permeability- Soft magnetic material (low coercivity)- High resistivity- High ferromagnetic resonance (FMR)
frequency
• Amorphous Co90Ta5Zr5 (at. %) alloy:- µ’ ~ 600- Hc < 1 Oe- ρ ~ 108 µΩ-cm- fFMR ~ 1.5 GHz
Material Selection
Conductor: Copper due to its low electrical resistivity
Magnetic core:
106 107 108 1090
500
1000
1500
2000
2500
µ' µ"
Rel
ativ
e pe
rmea
bilit
y
Frequency (Hz)
0.2 μm CoTaZr magnetic film
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Inductor Designs
“Standard”
“Spiral”“Scale-down”
“Series” “Closed core”
N = 4.5, 8.5, 17.5
N = 4.5N = 4.5, 8.5, 17.5
N = 4.5, 8.5, 17.5
Planar spiral inductorwith or without magnetic plane
Solenoid inductor withlateral parameters scaled
down by a factor of 2while maintaining verticalparameters unchanged
Solenoid inductor withdifferent magnetic corearrangement or shape
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I. Introduction
II. Analytical Models and Inductor Design
III. Fabrication of Integrated Inductors
IV. Measurement of Fabricated Inductors
V. Analysis of Magnetic Inductors on Si
VI. Conclusion
• Fabrication steps• Images of fabricated inductor devices• Magnetic properties of processed magnetic core
III. Fabrication of Integrated Inductors
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Image of Fabricated Wafer
Wafer (4”-dia.) map Die map
“Magnetic inductors”
“Air core inductors”
“De-embeddingstructures”
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400 µm
400 µm
400 µm
400 µm 400 µm
“Standard”“Spiral”
“Scale-down”
“Series” “Closed core”
SEM Images of Fabricated Inductor Devices
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50 µm
FIB Cross-section Images of Fabricated Inductors
Top Cu layer 6.6 um
Bottom Cu layer 4.4 um
Polyimide 2.0 um
Magnetic core 2.2 um
Si substrate
Polyimide 0.5 um
Thermal oxide
2 µm
• FIB images confirm the successful fabrication of multi-layered inductor devices.
• The successful polyimide planarization is also confirmed, resulting in thecontinuous magnetic core layer.
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Magnetic core shape affects permeability!
-150 -100 -50 0 50 100 150
-1.0
-0.5
0.0
0.5
1.0
Easy
Nor
mal
ized
B
Field (H)
Hard
107 108 1090
200
400
600
µ', blanket µ", blanket µ', processed µ", processed
Rel
ativ
e pe
rmea
bilit
y
Frequency (Hz) 100 µm
B-H loops Permeability spectra Kerr microscope image
• Magnetic test structures identical to the actual magnetic cores were included inthe wafer layout and processed in parallel with the inductor fabrication.
• Magnetic measurements confirm that the magnetic core in the fabricated inductormaintains the desired soft magnetic properties.
• The permeability spectra of blanket film and processed magnetic core structuresare not identical to each other.
Easyaxis
Magnetic coreBottom conductor
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22 23
32
12 13
42 43
21
31
24
3433
Notch
Easy axis of CoFeHfO
On-package Inductors on 8-inch Substrate
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Surface roughness affects permeability!
Permeability spectra of patterned CoFeHfO bars on dielectric material
Surface roughness of dielectric material
Ra=128.6 nm
The rough surface of dielectric material degrades the magnetic properties of CoFeHfO deposited on it (even before patterning).
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I. Introduction
II. Analytical Models and Inductor Design
III. Fabrication of Integrated Inductors
IV. Measurement of Fabricated Inductors
V. Permeability of CoTaZr Magnetic Cores
VI. Conclusion
• Measurement method• Circuit model of integrated inductor• Measurement results of “Standard” inductors
IV. Measurement of Fabricated Inductors
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106 107 108 1090
2x10-8
4x10-8
6x10-8
8x10-8
1x10-7 N = 4.5 N = 8.5 N = 17.5
Indu
ctan
ce (H
)Frequency (Hz)
107 108 1090
2x10-8
4x10-8
6x10-8
8x10-8
1x10-7
N = 4.5 N = 8.5 N = 17.5
Indu
ctan
ce (H
)
Frequency (Hz)
Device Properties of “Standard” Inductors - L
Air core inductors Magnetic inductors
• With the use of magnetic core, inductance is 70.2 nH for N = 17.5, and theinductance enhancement is as high as 34×.
• The device area for N = 17.5 is 0.88 mm2, corresponding to an inductancedensity of 80 nH/mm2.
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106 107 108 1090
2
4
6
8
10
N = 4.5 N = 8.5 N = 17.5
Res
ista
nce
(Ω)
Frequency (Hz)106 107 108 109
0
2
4
6
8
10
N = 4.5 N = 8.5 N = 17.5
Res
ista
nce
(Ω)
Frequency (Hz)
Device Properties of “Standard” Inductors - R
• Resistance at low frequencies is less than 1 Ω.
• Resistance of magnetic inductors increases greatly at high frequencies due tothe magnetic power losses.
Air core inductors Magnetic inductors
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106 107 108 1090
2
4
6
8
10
N = 4.5 N = 8.5 N = 17.5
Qua
lity
fact
or
Frequency (Hz)106 107 108 109
0
2
4
6
8
10
N = 4.5 N = 8.5 N = 17.5
Qua
lity
fact
orFrequency (Hz)
Device Properties of “Standard” Inductors - Q
• Quality factor of magnetic inductor is above 6 at 20 MHz for N = 17.5, and theenhancement over air core is well above 10×. However, it starts to decrease asthe frequency increases due to the magnetic power losses.
Air core inductors Magnetic inductors
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Five-Turn Magnetic Inductor on Package
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I. Introduction
II. Analytical Models and Inductor Design
III. Fabrication of Integrated Inductors
IV. Measurement of Fabricated Inductors
V. Analysis of Magnetic Inductors on Si
VI. Conclusion
V. Analysis of Measurement Results
• Comparison with analytical models• Effect of magnetic core shape• Effect of scaling down
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0 5 10 15 20 250
2x10-9
4x10-9
6x10-9
8x10-9
1x10-8 Air core, measurement Air core, simulation Air core, calculation
Number of turns
L AC (H
)
0
2x10-8
4x10-8
6x10-8
8x10-8
1x10-7
Magnetic, measurement Magnetic, simulation Magnetic, calculation L
MC (H
)34×
Comparison with Analytical Models (I)
Inductance (@ 10 MHz) Coil resistance
• The good agreements confirm that the analytic models can accurately describethe inductances of air core and magnetic inductors and their coil resistances.
• It indicates that the demagnetization effect plays a major role in determiningthe effective permeability of the magnetic inductors.
• The calculated inductance enhancement is about 30× for N = 17.5, which isvery close to the observed enhancement of 34×.
0 5 10 15 20 250.0
0.2
0.4
0.6
0.8
1.0 Air core, measurement Magnetic, measurement Calculation
Res
ista
nce
@ 1
MH
z (Ω
)
Number of turns
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0.0 5.0x10-8 1.0x10-7 1.5x10-70
2
4
6
8
10
12 20 MHz 40 MHz 60 MHz
∆R (Ω
)
∆L (H)
Comparison with Analytical Models (II)
106 107 108 1090
2
4
6
8
10 R measured R calculated
Frequency (Hz)R
esis
tanc
e (Ω
)
0
2
4
6
8
10
Q measured Q calculated Q
uality factor
• Permeability spectra of the processed magnetic core are used for the calculationsof resistance and quality factor of the magnetic inductor.
• The excellent agreements between the calculation and measurement resultsdirectly confirm the validity of the proposed analytical models.
Trade-off between ∆L and ∆R “Standard” with N = 17.5
LR ∆⎟⎟⎠
⎞⎜⎜⎝
⎛µµω=∆
'"
MeasurementCalculation
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Effect of Magnetic Core Shape (I)
0 5 10 15 200.0
5.0x10-8
1.0x10-7
1.5x10-7
2.0x10-7
Standard, measurement Standard, simulation Series, measurement Series, simulation Closed core, measurement Closed core, simulation
Indu
ctan
ce (H
)
Number of turns
Inductance (@ 10 MHz)
“Standard”
“Series”
“Closedcore”
• For a given number of turns, the inductance of the “series” inductor is nearlydoubled from those of the “standard” inductor, indicating that the “series”inductor can be viewed as two “standard” inductors connected in series.
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Effect of Magnetic Core Shape (II)
0 5 10 15 200.0
5.0x10-8
1.0x10-7
1.5x10-7
2.0x10-7
Closed core, measurement Closed core, simulation Two bars, simulation
Indu
ctan
ce (H
)Number of turns
“Closed core” “Two bars”
• Simulation results indicate that the effective shape of the closed magnetic coreshould be viewed as two parallel magnetic bars closed by two “bad” soft magnets.
• Hence, the closed magnetic core is not effective in improving the magnetic fluxclosure significantly, and it can be explained by the tensor nature of permeabilityof the magnetic core.
µ’ = 600
Inductance (@ 10 MHz)
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Effect of Scaling Down
106 107 108 1090
1x10-8
2x10-8
3x10-8
4x10-8
5x10-8
6x10-8
N = 4.5 N = 8.5 N = 17.5
Indu
ctan
ce (H
)
Frequency (Hz)106 107 108 109
0
2
4
6
8
10 N = 4.5 N = 8.5 N = 17.5
Res
ista
nce
(Ω)
Frequency (Hz)
Inductance Resistance
• Inductance is 48.4 nH at 10 MHz for N = 17.5, and the device area is reduced bya factor of four to 0.22 mm2, resulting in the inductance density to 219 nH/mm2.
• The coil resistance is not affected by the scale-down and is measured to be0.57 Ω for N = 17.5 at 1 MHz.
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Bridging the Gap
100 kHz 1 MHz 10 MHz 100 MHz 1 GHz 10 GHz
10 uH
1 uH
100 nH
10 nH
1 nH
100 pH
Frequency
Indu
ctan
ce
Integrated magnetic inductors
Planar spiral inductors
Discrete inductors
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Summary
• High-performance integrated magnetic inductors were successfully designed and fabricated:
For the coil resistance less than 1 Ω and the device area below1 mm2, the inductance as high as 70.4 nH was obtained on Si,corresponding to the inductance enhancement of 34× over the aircore equivalent, and the inductance density reached 219nH/mm2.For DC resistance ~ 10 mΩ and device area of ~14 mm2: Q ~ 25 at 200 MHz for magnetic inductor on package.
• An analytical model can accurately describe the actual device properties:
The fundamental trade-offs (∆L vs ∆R) of the integrated magnetic inductors are well understood.The inductor device properties can be further optimized (by materials or design) for a given application or frequency range.