Integrated On-Chip Inductors using Magnetic Films Donald S. Gardner, Gerhard Schrom, Fabrice Paillet, Tanay Karnik, Shekhar Borkar, Circuits Research Lab & Future Technology Research Intel Labs Intel Corporation
Outline Magnetic material properties Magnetic hysteresis loops Complex permeability spectra Magnetic anisotropy Inductor measurements Structure cross sections Inductance measurements Sheet and shunt inductance Measurement analysis and modeling Eddy current and skin effect Time constant and Quality factor Effectiveness of laminations
RF CMOS Integrated Circuit Inductors make up 24% of this chip Inductance density of spirals is small (<100 nh/mm 2 )
100~480 MHz Switching Regulator V IN =1.2V, V OUT =0.9V, L=6.8nH, F=233MHz Φ 3 Φ 2 Discrete Φ 1 Inductors Φ 0 4.3ns High frequency Hysteretic multi-phase topology 1ns response 88% efficiency Schrom, Gardner, et.al., IEEE PESC 2004 and IEEE VLSI Symp. 2004.
Comparison of DC Converters [3] [4] [5] [6] [7] Pavo-1 Year 1996 1999 2000 2002 2002 2004 Tech [µm] n/a 0.25 n/a 0.25 n/a 0.09 # phases 1 1 1 1 1 4 V IN [V] 4 3 4 2.5 3.6 1.2 V OUT [V] 3.3 2 3 1.4 2.7 0.9 f [MHz] 1.6 0.5 3 0.75 1.8 233 Eff. [%] 85 94 83.3 95 80 83.2 L TOT [µh] 3 10 1 15.2 1 0.0017 C [µf] n/a 47 1 21.6 n/a 0.0025 I MAX [A] 0.3 0.25 0.33 0.25 0.3 0.3 100x higher f 1000x Smaller L and C Area [mm 2 ] n/a 0.46 20 0.35 n/a 0.14
Inductor Test Chips Circa 1997~2000 Circa 2001~2005 Circa 2005~2008 Thin Aluminum Thin CoZrTa GHz response demonstrated Thick Aluminum Thick CoZrTa High inductance demonstration Thick Cu/Polyimide Thick Lam. CoZrTa High Q inductors demonstrated
Peak Qu uality Factor Inductance Densities vs. Q-Factor 100 10 1 0.1 6 4 2 6 4 2 6 4 2 Song 2001 from the Literature Fukuda 2003 Saleh 1970 Orlando 2006 O'Donnell 2008 Viala 2004 Gardner 2007 Lee 2008 Yamaguchi 1991 Yachi 1991 Yamaguchi Kim 1997 Ahn 1994 Planar Spiral Gardner 2006 Elongated Spiral Stripline Toroidal Meander Liakopoulos 1999 Gardner 2008 10 0 10 1 10 2 10 3 10 4 Inductance Density (nh/mm 2 ) Gardner, Jamieson, et.al. IEEE Trans. Magnetics, 45, pp. 4760, 2009.
Flux Density B (T) 1.5 1.0 0.5 0.0-0.5-1.0-1.5 Magnetic Hystersis Loops for CoZrTa Hard axis Easy axis Slope µ = 1050-0.1 0 0.1-20 -10 0 10 20 Applied Magnetic Field H (Oe) Coercivity < 0.02 Oe minimizing hysteretic losses.
Permeability vs. Applied Magnetic Field Permea ability (Gauss/Oe) 1000 800 600 400 200 0 0.5 µm 1.5 µm 1.5 µm, 3 lams 4 µm 10 µm 0 5 10 15 Applied Magnetic Field Bias (Oe) 20 Magnetic anisotropy H k has two components: The intrinsic induced anisotropy from the deposition The demagnetizing energy caused by the sample shape
Complex Permeability Model δ = 2ρ ωµ i µ o δ = skin depth ρ = resistivity of magnetic film ω = frequency µ i = relative dc permeability d = film thickness Skin depth (µm m) 10 1 0.1 4 2 4 2 10 µm CoZrTa 4 µm CoZrTa 2 µm CoZrTa 0.5 µm CoZrTa 10 2 4 100 2 4 1000 2 Frequency (MHz) µ = 2 δ (1 + j ) d µ i tanh (1 + j) d 2δ High resistivity materials are needed to reduce the eddy currents and increase the skin depth. CoZrTa ρ = 100 µω-cm
Permeability Spectra of CoZrTa Real Component Imaginary Component Permeability 1000 100 10 0.1 µm 0.5 µm 2 µm 4 µm 10 100 1000 Frequency (MHz) 0.1 µm 0.5 µm 2 µm 4 µm 10 100 1000 Frequency (MHz)
Inductance Modeling of Wire with Magnetic Material Magnetic Material Wire Magnetic Material Maximum Increase in Inductance 1 layer magnetic film 2 2 layers magnetic film µ r
Spiral and Transmission Line Inductors Hard Easy Structures take advantage of the uniaxial magnetic anisotropy.
Cross-Sectional Image of Inductor in 130 nm 6-level Metal CMOS Process Hard Axis CoZrTa Inductor Metal CoZrTa Magnetic Via Cu (M6) Cu (M5) Cu (M4) Cu (M3) Cu (M2) Cu (M1)
Spiral Inductors with Single Magnetic Layer Induc ctance (nh) 10 1 8 turn (mag.) 8 turn (no mag) 4 turn (mag.) 4 turn (no mag) 2 turn (mag.) 2 turn (no mag) 1 turn (mag.) 1 turn (no mag) 0.1 10 7 10 8 10 9 10 10 Frequency (Hz) Increase in inductance is small (10~30% at up to 9.8 GHz)
Spiral Inductors with Two Magnetic Layers Indu uctance (nh) 100 10 1 0.1 9X 10 7 2 4 10 8 2 4 10 9 2 4 10 10 Frequency (Hz) 8 turn (mag) 8 turn (no mag) 4 turn (solid mag) 4 turn (no mag) 2 turn (solid mag) 2 turn (no mag) 1 turn (solid mag) 1 turn (no mag) Inductance increases by 9
Spiral and Stripe Inductors Using 5um thick Copper Hard Easy Structures take advantage of the uniaxial magnetic anisotropy.
Magnetic Via Cross-Sectional Image of Inductor in 90 nm CMOS Process Magnetic Via 90 nm 7-level Metal CMOS Process
Hard Axis Cross-Sectional Image of Inductor
Inducta ance (nh) 6.0 5.0 4.0 3.0 2.0 1.0 0.0 Stripe Inductors With Thick Copper 24X 25X 26X 31X 5 µm mag. 10 µm mag. 20 µm mag. 30 µm mag. 5 µm no mag. 10 µm no mag. 20 µm no mag. 30 µm no mag. 6 810 7 2 4 6 810 8 2 4 6 8 10 9 Frequency (Hz) Inductance increases by up to over 30
Magnetic Flux Density At 1GHz Unlaminated Cobalt alloy B-field (T) 4.0 3.6 3.2 2.8 2.4 2.0 1.6 1.2 0.8 0.4 0.0 Laminated Cobalt alloy Skin-depth effect limits penetration of B-field. Larger skin depth results in lower losses.
Inductance Modeling of Rectangular Line L µ 0 µ r t m 2 l w l = line length w = line width t m = magnetic film thickness µ r = relative dc permeability 1/L w 1/l L sheet 1/L shunt W tot Eqn. from V. Korenivski and R. B. van Dover, JAP, v. 82 (10), 1997
Indu uctance (nh) 4.0 3.0 2.0 1.0 0.0 Magnetic Via Widths 10 µm via 8 µm via 6 µm via 5 µm via 4 µm via thru 6 810 7 2 4 6 810 8 2 4 6 8 10 9 Frequency (Hz) Inductance increases with via width, but the change becomes diminishingly small.
Sheet and Shunt Inductances Sheet inductance (nh/square) 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 10 um via 8 um via 5 um via 4 um via No mag. alloy Simulated 6 10 7 2 4 6 10 8 2 4 6 10 9 Frequency (Hz) Shunt ind ductance (nh/mm) 40 30 20 10 0 6 10 µm via 8 µm via 5 µm via 4 µm via no mag. alloy Sim. 8 µm via 10 7 2 4 6 10 8 2 4 6 10 9 Frequency (Hz) Sheet inductance is independent of the magnetic via width. Shunt inductance increases with increasing via width.
Analytical Modeling of Q-Factor Thinner films give higher Q-factors, but lower inductance.
Analytical Modeling of Q-Factor Laminations increase the Q-factor.
Quality Factor of Inductors With Laminated Magnetic Films 6 4 Q-Factor 1 0.1 2 6 4 2 30 µm (4 lams) 30 µm (8 lams) 10 µm (4 lams) 10 µm (8 lams) 5 µm (4 lams) 5 µm (8 lams) 10 6 10 7 10 8 10 9 Frequency (Hz) Peak quality factor is increased, But quality factor at lower frequencies decreased.
Summary Magnetic materials Permeability Complex spectra (real and imaginary) Need small coercivity CMOS compatibility (thermal, process compatibility) Inductors Single films increase inductance by 30% up to 9.8 GHz 2 magnetic films increase inductance up to over 30 compared to air-core Over 200 nh inductors possible (1,700 nh/mm 2 ) Sheet inductance vs. shunt inductance Effectiveness of laminated structures Time constants and quality factors Measurements, simulations, and analytical models
For More Information IEEE Trans. Magnetics, 45, pp. 4760, 2009. Journal of Applied Physics, 103, pp. 07E927, Apr. 1, 2008. IEEE Trans. Magnetics, 43, pp. 2615, 2007.