1

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

2

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

3

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

4R.K. Ulrich and L.W. Schaper, “Integrated Passive Component Technology”, 2003

Fully integratedelectronics

Why Integrated Inductors?

5

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

*

6

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

7

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

8

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

≥

9

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.

10

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

11

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.

12

Key Device Properties

• Inductance L

• Resistance R

• Quality factor Q

• Device area

• Useful bandwidth

RL

TndissipatioPowerstoredEnergyQ ωπ =

⋅=

2

13

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

23

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.

27

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

30

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

31

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

32

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

33

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.

34

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)

35

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

37

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.