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 Engineering
Department of Electrical Engineering
1
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
2
Use of Inductors in Our Daily Lives
• Traffic light
• Red-light camera
• Metal detector
• RFID tag
Texas Instruments Tag-itTM
• Voltage regulator module
• Cell phone
3
Why Integrated Inductors?
Fully integrated
electronics
R.K. Ulrich and L.W. Schaper, “Integrated Passive Component Technology”, 2003
4
Example: Power Management
DC-DC converter
Passive components are discrete
and occupy large areas
IC containing
gate driver and
power MOSFETs
Inductor
Capacitors
Enpirion EN5330 PSoC (Power-System-on-a-Chip) *
70% of pc-board area saved
* R. Allen, Electronic Design, May 2004
5
Inductance Requirement for Power Management
Discrete inductors
☺ Large inductance
Large volume
Poor AC performance
10 uH
Inductance
1 uH
100 nH
Planar spiral inductors
☺ Small area consumption
Small inductance
Limited performance in
sub-GHz applications
10 nH
1 nH
100 pH
100 kHz
1 MHz
10 MHz
100 MHz
1 GHz
10 GHz
Frequency
From A. Ghahary, Power Electronics Technology, Aug. 2004
6
Schematics of Magnetic Inductor Designs
Transmission line
☺ Small resistance
Small inductance
Usually two magnetic
layers needed
Spiral inductor
☺ Close to the planar spiral
Limited inductance gain
One or two magnetic
layers
Solenoid inductor
☺ Magnetically efficient
Relatively complex
structure
☺ One magnetic layer
7
Brief Rev of Integrated Magnetic Inductors
Intel,
Tyndall
≥
Tohoku
CEA-LETI
Taken from Lee et al, Embedded Inductors with Magnetic Cores,
Book Chapter in press (Springer)
8
Magnetic Inductors from Stanford & Cowork
P. K. Amiri, et al.
Intermag 08, CV 01
Planar transmission line
inductor with CoTaZr core,
Q = 6 @ 700 MHz
A.M. Crawford, et al.
IEEE Trans. Magn.
2002, p.3168-70
Planar spiral inductor
with CoTaZr core,
CMOS compatibility,
Q ~ 2.7 @ 1 GHz
L. Li, D. W. Lee, et al.
IEEE Trans. Advanced
Packaging (accepted 2008)
On-package solenoid
inductor with CoFeHfO core,
Q = 22 @ 200~300 MHz,
Rdc ~ 10 mΩ
D. W. Lee, et al.
Intermag 08, AG 01 (invited)
Planar solenoid inductor with
CoTaZr core,
Inductance enhancement over
air core = 34x
9
Q>6 @ 26 MHz
II. Analytical Models and Inductor Design
I.
Introduction
II. Analytical Models and Inductor Design
•
•
•
•
Analytical models for key device properties
Material selection
Optimization of design parameters
Inductor design concepts
III. Fabrication of Integrated Inductors
IV. Measurement of Fabricated Inductors
V. Analysis of Magnetic Inductors on Si
VI. Conclusion
10
Schematics of Integrated Solenoid Inductor
• Solenoid inductor design was mainly considered in this work.
Top view
Cross-section view
wM
lC
wV
wC
sV
tM tA
tC
lA, lM
g
gV
sV
wA
11
Key Device Properties
• Inductance L
• Resistance R
• Quality factor Q
Q = 2π
Energy stored
ωL
=
Power dissipation ⋅ T
R
• Device area
• Useful bandwidth
12
Inductance of Magnetic Inductor
LMC
Inductance of magnetic inductor LMC:
µ0 µeff N 2 wM tM
µ0 µr N 2 wM tM
where ∆L =
=
lM [1 + N d ( µr − 1)]
lM
N d = Demagnetizing factor of rectangular prism
µeff ≡
µr
1 + N d ( µr − 1)
• For a finite-sized magnetic core, there is a
demagnetizing field inside the magnetic core,
which effectively reduces µr.
∆Lsimulated (H)
LMC = LAC + ∆L
5x10
-8
4x10
-8
3x10
-8
2x10
-8
1x10
-8
Slope = 1.01 ± 0.01
HFSS simulations
Linear fit
0
0
1x10
-8
2x10
-8
3x10
-8
4x10
-8
5x10
-8
∆Lcalculated (H)
• Demagnetizing field is not uniform inside the magnetic core,
and the numerical solutions should be used for µr > 1.*
Inductance enhancement:
∆L LMC − LAC
A
=
≈ µeff MC
LAC
LAC
AAC ,eff
Much less than µr
but still significant
AMC
AAC,eff
* D.-X. Chen et al., IEEE Trans. Magn., 41, 2077 (2005)
13
Resistance of Magnetic Inductor
RMC
Resistance of magnetic inductor RMC:
• From the classical electromagnetism:*
1
Magnetic contribution to the energy stored E Magnetic = ∫∫∫ µ ' H 2 dV
2
Magnetic power loss PMagnetic = ∫∫∫ ωµ" H 2 dV
⎛ µ" ⎞
PMagnetic ≈ 2ω ⎜⎜ ⎟⎟ EMagnetic
⎝ µ' ⎠
• Representing in terms of the device properties:
PMagnetic = ( RMC − RAC ) I 2 = ∆RI 2 where ∆R ≡ RMC − RAC
EMagnetic = EMagnetic inductor − E Air core inductor =
1
1
1
LMC I 2 − LAC I 2 = ∆LI 2
2
2
2
⎛ µ" ⎞
∴ RMC = RAC + ∆R = RAC + ω ⎜⎜ ⎟⎟∆L
⎝ µ' ⎠
R
∆R for large ∆L
∆R for small ∆L
RAC
Freq.
⎛ µ" ⎞
∆R = ω ⎜⎜ ⎟⎟ ∆L
⎝ µ' ⎠
Both ω and (µ”/µ’) increase with
frequency. Hence ∆R becomes
significant as the frequency increases.
The more inductance enhancement
we obtain by using a magnetic core,
the more resistive losses we introduce
at high frequencies.
* R.F. Harrington, “Time-Harmonic Electromagnetic Fields”, 1961
14
Quality factor
Q
Quality factor of air core inductor QAC:
Quality factor of magnetic inductor QMC:
10
Quality factor
8
6
LAC
RAC
QMC = ω
LMC
=ω
RMC
LAC + ∆L
⎛ µ" ⎞
RAC + ω ⎜ ⎟∆L
⎝ µ' ⎠
∆L/LAC=1
∆L/LAC=10
∆L/LAC=30
QAC
µ'/µ"
4
∆L << LAC
QMC ~ QAC at low frequencies
∆L >> LAC
QMC ~ µ’/µ” at high frequencies
fMC can be considered as the useful bandwidth
of the magnetic inductor.
2
0
6
10
Q AC = ω
10
7
10
8
Frequency (Hz)
fMC
10
9
15
Material Selection
Conductor: Copper due to its low electrical resistivity
Magnetic core:
• Amorphous Co90Ta5Zr5 (at. %) alloy:
- µ’ ~ 600
- Hc < 1 Oe
- ρ ~ 108 µΩ-cm
- fFMR ~ 1.5 GHz
2500
Relative permeability
• Desirable properties:
- High permeability
- Soft magnetic material (low coercivity)
- High resistivity
- High ferromagnetic resonance (FMR)
frequency
0.2 μm CoTaZr magnetic film
2000
µ'
µ"
1500
1000
500
0
6
10
10
7
10
8
10
9
Frequency (Hz)
16
Inductor Designs
“Spiral”
Planar spiral inductor
with or without magnetic plane
“Scale-down”
“Standard”
N = 4.5, 8.5, 17.5
N = 4.5
Solenoid inductor with
lateral parameters scaled
down by a factor of 2
while maintaining vertical
parameters unchanged
N = 4.5, 8.5, 17.5
“Series”
“Closed core”
Solenoid inductor with
different magnetic core
arrangement or shape
N = 4.5, 8.5, 17.5
17
III. Fabrication of Integrated Inductors
I.
Introduction
II. Analytical Models and Inductor Design
III. Fabrication of Integrated Inductors
• Fabrication steps
• Images of fabricated inductor devices
• Magnetic properties of processed magnetic core
IV. Measurement of Fabricated Inductors
V. Analysis of Magnetic Inductors on Si
VI. Conclusion
18
Image of Fabricated Wafer
Wafer (4”-dia.) map
Die map
“Air core inductors”
“De-embedding
structures”
“Magnetic inductors”
19
SEM Images of Fabricated Inductor Devices
“Spiral”
“Standard”
“Scale-down”
400 µm
400 µm
400 µm
“Series”
400 µm
“Closed core”
400 µm
20
FIB Cross-section Images of Fabricated Inductors
Top Cu layer
6.6 um
Polyimide 0.5 um
Magnetic core 2.2 um
Polyimide
2.0 um
Bottom Cu layer
4.4 um
Thermal oxide
50 µm
Si substrate
2 µm
• FIB images confirm the successful fabrication of multi-layered inductor devices.
• The successful polyimide planarization is also confirmed, resulting in the
continuous magnetic core layer.
21
Magnetic core shape affects permeability!
B-H loops
Easy
Hard
Relative permeability
Normalized B
1.0
Permeability spectra
0.5
0.0
-0.5
-1.0
µ', blanket
µ", blanket
µ', processed
µ", processed
600
Kerr microscope image
Bottom conductor
Magnetic core
400
200
0
-150 -100
-50
0
50
Field (H)
100
150
10
7
10
8
Frequency (Hz)
10
9
Easy
axis
100 µm
• Magnetic test structures identical to the actual magnetic cores were included in
the wafer layout and processed in parallel with the inductor fabrication.
• Magnetic measurements confirm that the magnetic core in the fabricated inductor
maintains the desired soft magnetic properties.
• The permeability spectra of blanket film and processed magnetic core structures
are not identical to each other.
22
On-package Inductors on 8-inch Substrate
Easy axis of CoFeHfO
12
13
21
22
23
24
31
32
33
34
42
43
Notch
23
Surface roughness affects permeability!
Ra=128.6 nm
Permeability spectra of patterned CoFeHfO
bars on dielectric material
Surface roughness of
dielectric material
The rough surface of dielectric material degrades the magnetic properties of
CoFeHfO deposited on it (even before patterning).
24
IV. Measurement of Fabricated Inductors
I.
Introduction
II. Analytical Models and Inductor Design
III. Fabrication of Integrated Inductors
IV. Measurement of Fabricated Inductors
• Measurement method
• Circuit model of integrated inductor
• Measurement results of “Standard” inductors
V. Permeability of CoTaZr Magnetic Cores
VI. Conclusion
25
Device Properties of “Standard” Inductors - L
Air core inductors
Magnetic inductors
-7
-7
1x10
1x10
N = 4.5
N = 8.5
N = 17.5
-8
-8
8x10
Inductance (H)
Inductance (H)
8x10
-8
6x10
-8
4x10
N = 4.5
N = 8.5
N = 17.5
-8
6x10
-8
4x10
-8
-8
2x10
2x10
0
7
10
8
10
Frequency (Hz)
9
10
0
6
10
7
10
8
10
9
10
Frequency (Hz)
• With the use of magnetic core, inductance is 70.2 nH for N = 17.5, and the
inductance enhancement is as high as 34×.
• The device area for N = 17.5 is 0.88 mm2, corresponding to an inductance
density of 80 nH/mm2.
26
Device Properties of “Standard” Inductors - R
Air core inductors
Magnetic inductors
10
10
8
Resistance (Ω)
Resistance (Ω)
8
N = 4.5
N = 8.5
N = 17.5
6
4
6
4
2
2
0
6
10
N = 4.5
N = 8.5
N = 17.5
7
10
8
10
9
10
0
6
10
Frequency (Hz)
7
10
8
10
9
10
Frequency (Hz)
• Resistance at low frequencies is less than 1 Ω.
• Resistance of magnetic inductors increases greatly at high frequencies due to
the magnetic power losses.
27
Device Properties of “Standard” Inductors - Q
Air core inductors
Magnetic inductors
10
N = 4.5
N = 8.5
N = 17.5
8
Quality factor
Quality factor
8
10
6
4
2
0
6
10
N = 4.5
N = 8.5
N = 17.5
6
4
2
7
10
8
10
Frequency (Hz)
9
10
0
6
10
7
10
8
10
9
10
Frequency (Hz)
• Quality factor of magnetic inductor is above 6 at 20 MHz for N = 17.5, and the
enhancement over air core is well above 10×. However, it starts to decrease as
the frequency increases due to the magnetic power losses.
28
Five-Turn Magnetic Inductor on Package
29
V. Analysis of Measurement Results
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
• Comparison with analytical models
• Effect of magnetic core shape
• Effect of scaling down
VI. Conclusion
30
Comparison with Analytical Models (I)
Inductance (@ 10 MHz)
6x10
4x10
2x10
-9
-9
34×
-9
8x10
-8
6x10
-8
4x10
-8
2x10
-8
-9
0
0
0
5
10
15
Number of turns
20
25
1.0
LMC (H)
LAC (H)
8x10
-7
Resistance @ 1MHz (Ω)
1x10
1x10
Air core, measurement
Air core, simulation
Air core, calculation
Magnetic, measurement
Magnetic, simulation
Magnetic, calculation
-8
Coil resistance
Air core, measurement
Magnetic, measurement
Calculation
0.8
0.6
0.4
0.2
0.0
0
5
10
15
20
25
Number of turns
• The good agreements confirm that the analytic models can accurately describe
the inductances of air core and magnetic inductors and their coil resistances.
• It indicates that the demagnetization effect plays a major role in determining
the effective permeability of the magnetic inductors.
• The calculated inductance enhancement is about 30× for N = 17.5, which is
very close to the observed enhancement of 34×.
31
Comparison with Analytical Models (II)
Trade-off between ∆L and ∆R
“Standard” with N = 17.5
10
12
∆R (Ω)
6
Measurement
Calculation
8
4
2
0
0.0
5.0x10
-8
1.0x10
∆L (H)
-7
1.5x10
-7
8
6
6
4
4
2
2
0
6
10
10
7
10
8
Quality factor
8
⎛ µ" ⎞
∆R = ω⎜⎜ ⎟⎟∆L
⎝ µ' ⎠
Resistance (Ω)
10
20 MHz
40 MHz
60 MHz
10
R measured
R calculated
Q measured
Q calculated
0
9
10
Frequency (Hz)
• Permeability spectra of the processed magnetic core are used for the calculations
of resistance and quality factor of the magnetic inductor.
• The excellent agreements between the calculation and measurement results
directly confirm the validity of the proposed analytical models.
32
Effect of Magnetic Core Shape (I)
“Series”
Inductance (H)
“Closed
core”
2.0x10
-7
1.5x10
-7
1.0x10
-7
5.0x10
-8
Inductance (@ 10 MHz)
Standard, measurement
Standard, simulation
Series, measurement
Series, simulation
Closed core, measurement
Closed core, simulation
“Standard”
0.0
0
5
10
15
20
Number of turns
• For a given number of turns, the inductance of the “series” inductor is nearly
doubled from those of the “standard” inductor, indicating that the “series”
inductor can be viewed as two “standard” inductors connected in series.
33
Effect of Magnetic Core Shape (II)
Inductance (@ 10 MHz)
“Closed core”
“Two bars”
-7
2.0x10
Closed core, measurement
Closed core, simulation
Two bars, simulation
-7
Inductance (H)
1.5x10
-7
1.0x10
-8
5.0x10
0.0
0
µ’ = 600
5
10
15
20
Number of turns
• Simulation results indicate that the effective shape of the closed magnetic core
should 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 flux
closure significantly, and it can be explained by the tensor nature of permeability
of the magnetic core.
34
Effect of Scaling Down
6x10
-8
5x10
-8
4x10
-8
3x10
-8
2x10
-8
1x10
-8
Resistance
10
N = 4.5
N = 8.5
N = 17.5
8
Resistance (Ω)
Inductance (H)
Inductance
6
4
2
0
10
N = 4.5
N = 8.5
N = 17.5
6
10
7
10
8
Frequency (Hz)
10
9
0
6
10
10
7
10
8
10
9
Frequency (Hz)
• Inductance is 48.4 nH at 10 MHz for N = 17.5, and the device area is reduced by
a 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 be
0.57 Ω for N = 17.5 at 1 MHz.
35
Bridging the Gap
10 uH
Discrete inductors
Inductance
1 uH
100 nH
Integrated magnetic inductors
10 nH
1 nH
Planar spiral inductors
100 pH
100 kHz
1 MHz
10 MHz
100 MHz
1 GHz
10 GHz
Frequency
36
Summary
High-performance integrated magnetic inductors
were successfully designed and fabricated:
•
For the coil resistance less than 1 Ω and the device area below
1 mm2, the inductance as high as 70.4 nH was obtained on Si,
corresponding to the inductance enhancement of 34× over the air
core 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.
37