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 • Metal detector • RFID tag •Red-light camera
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 Inductor gate driver and power MOSFETs 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 10 uH ☺ Large inductance Large volume Poor AC performance 1 uH
100 nH
Planar spiral inductors 10 nH ☺ Small area consumption Inductance Small inductance Limited performance in 1 nH sub-GHz applications
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 Spiral inductor Solenoid inductor
☺ Small resistance ☺ Close to the planar spiral ☺ Magnetically efficient Small inductance Limited inductance gain Relatively complex Usually two magnetic One or two magnetic structure layers needed layers ☺ 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 A.M. Crawford, et al. inductor with CoTaZr core, IEEE Trans. Magn. Q = 6 @ 700 MHz 2002, p.3168-70 Planar spiral inductor with CoTaZr core, CMOS compatibility, Q ~ 2.7 @ 1 GHz
L. Li, D. W. Lee, et al. D. W. Lee, et al. IEEE Trans. Advanced Intermag 08, AG 01 (invited) Packaging (accepted 2008) Planar solenoid inductor with On-package solenoid CoTaZr core, inductor with CoFeHfO core, Inductance enhancement over Q = 22 @ 200~300 MHz, air core = 34x R ~ 10 mΩ dc Q>6 @ 26 MHz 9 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 t tC wV w tM A C sV
g lA, lM
gV
sV wA
11 Key Device Properties
• Inductance L
• Resistance R
Energy stored ωL • Quality factor Q Q = 2π = Power dissipation ⋅T R
• Device area
• Useful bandwidth
12 Inductance of Magnetic Inductor LMC
Inductance of magnetic inductor LMC: = + ∆ 5x10-8 LMC LAC µ L µ Slope = 1.01 ± 0.01 2 N 2w t 4x10-8 ∆ = 0 r N wM tM = 0 eff M M where L µ µ µ l [1+ N ( −1)] l -8 M d r M (H) 3x10 N = Demagnetizing factor of rectangular prism d -8 µ simulated 2x10 L µ ≡ r ∆ HFSS simulations eff + µ − -8 1 Nd ( r 1) 1x10 Linear fit
0 • For a finite-sized magnetic core, there is a -8 -8 -8 -8 -8 0 1x10 2x10 3x10 4x10 5x10 demagnetizing field inside the magnetic core, ∆L (H) µ calculated which effectively reduces r. • Demagnetizing field is not uniform inside the magnetic core, µ and the numerical solutions should be used for r > 1.*
Inductance enhancement:
AMC AAC,eff ∆L L − L A µ = MC AC ≈ µ MC Much less than r eff but still significant LAC LAC 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 2 µ Magnetic contribution to the energy stored EMagnetic ' H dV ω ⎛ " ⎞ 2 ∫∫∫ P ≈ 2 ⎜ ⎟E Magnetic ⎜ µ' ⎟ Magnetic Magnetic power loss P = ωµ" H 2 dV ⎝ ⎠ Magnetic ∫∫∫ µ • Representing in terms of the device properties: P = (R − R )I 2 = ∆RI 2 where ∆R ≡ R − R Magnetic MC AC MC AC ω µ ∆ = ⎛ " ⎞∆ 1 1 1 R ⎜ ⎟ L E = E − E = L I 2 − L I 2 = ∆LI 2 ⎝ µ' ⎠ Magnetic Magnetic inductor Air core inductor 2 MC 2 AC 2 ω ⎛µ " ⎞ ∴R = R + ∆R = R + ⎜ ⎟∆L MC AC AC ⎜ µ' ⎟ ⎝ ⎠ Both ω and (µ”/µ’) increase with frequency. Hence ∆R becomes ∆R for large ∆L significant as the frequency increases. R The more inductance enhancement ∆ ∆ R for small L we obtain by using a magnetic core, R the more resistive losses we introduce AC at high frequencies.
Freq. * R.F. Harrington, “Time-Harmonic Electromagnetic Fields”, 1961 14 Quality factor Q
L Quality factor of air core inductor Q : Q = ω AC AC AC ω RAC ω L L + ∆L Q = MC = AC Quality factor of magnetic inductor QMC: MC ω µ RMC + ⎛ " ⎞∆ RAC ⎜ ⎟ L ⎝ µ' ⎠
10 ∆ L/LAC=1 ∆ L/LAC=10 ∆ 8 L/LAC=30
QAC µ'/µ" ∆L << L Q ~ Q at low frequencies 6 AC MC AC µ µ ∆L >> LAC QMC ~ ’/ ” at high frequencies 4