http://holst.stanford.edu/~CPYue [email protected] On-Chip Spiral Inductors for Silicon-Based Radio-Frequency Integrated Circuits C. Patrick Yue Center for Integrated Systems Stanford University, CA http://holst.stanford.edu/~CPYue [email protected] Outline • Overview • A physical model for on-chip inductors • Effects of process and layout parameters • Design methodology • Inductors with patterned ground shields • Substrate noise coupling • Conclusions http://holst.stanford.edu/~CPYue [email protected] Worldwide Wireless Market 20M 36% Annual Growth (7%) (Source: CTIA, 1996.) Asia Pacific North America 5M 80M (27%) (6%) 125M (41%) Asia Pacific North America 19M (22%) 38M (43%) Europe Europe 75M (25%) 25M (29%) 1996 Total: 87M 2000 Total: 300M http://holst.stanford.edu/~CPYue [email protected] A Typical Cellular Phone RF front-end component count: Inductor 11 Capacitor >100 Resistor >50 IC 5 Transistor 12 Crystal 1 Filter 2 (Source: Bosch, 1997.) http://holst.stanford.edu/~CPYue [email protected] Advantages of Integration • Cost: assembly and packaging • Power: fewer parasitics • Design Flexibility: signals stay on chip •Size • Reliability • Tolerance http://holst.stanford.edu/~CPYue [email protected] Discrete Inductors • L: 2 to 20 nH (2 to 10%) • Q: 50 to 200 (1 to 2 GHz) inch • srf: 4 to 10 GHz mm (Source: Coilcraft, 1997.) http://holst.stanford.edu/~CPYue [email protected] Active Inductors i 1 -gm 1 i in • Excess Noise + + C v vin c • Extra Power g – m 2 – i2 • Limited Linearity C L = ---------------- gm1gm2 http://holst.stanford.edu/~CPYue [email protected] Bond Wire Inductors • Predictability • Unwanted Couplings • Repeatability • Limited Inductance (Source: ISSCC’95, pp. 266) http://holst.stanford.edu/~CPYue [email protected] A Typical Planar Spiral Inductor Number of Turns Outer Dimension Spacing Width http://holst.stanford.edu/~CPYue [email protected] Multilevel Interconnects (Source: Semiconductor International, 1997.) http://holst.stanford.edu/~CPYue [email protected] A Typical Inductor On Silicon Al SiO2 Si 3 µm 3D Perspective View Top View http://holst.stanford.edu/~CPYue [email protected] Model Description Cs Csi Cox Rsi Ls Rs http://holst.stanford.edu/~CPYue [email protected] Model Description Cs Ls Rs Cox Cox Rsi Csi Csi Rsi http://holst.stanford.edu/~CPYue [email protected] Model Description Physical Model of Inductor on Silicon Effects L : Greenhouse Method Mutual s Couplings ρ ⋅ l Eddy Rs = ------------------------------------------–t⁄δ- w ⋅δ ⋅()1e– Current R ε C s 2 ox Feed-Through ox ⋅⋅------------------ C C s =nw Capacitance s tox M1-M2 1 ε Oxide R C L ⋅⋅ ⋅ox si si s Cox =-- l w ------- Capacitance 2 tox 1 Si Substrate C =-- ⋅⋅l wC ⋅ si 2 Sub Capacitance 2 Si Substrate R = ------------------------- si ⋅⋅ Ohmic Loss l wGSub http://holst.stanford.edu/~CPYue [email protected] Skin Effect Co-axial E Field Current Conductor Microstrip http://holst.stanford.edu/~CPYue [email protected] Effective Metal Thickness Current t Density - x / δ t = ∫ e ⋅ dx eff 0 J 0 - t / δ =δ ⋅()1e– Actual Metal 0 t Thickness http://holst.stanford.edu/~CPYue [email protected] Measurement Setup HP 8720B Open Structure P P G R R G S O O S G B B G E E Device Under Test Probe Station http://holst.stanford.edu/~CPYue [email protected] Parameter Extraction Procedure S to Transmission De-embedded Matrix Conversion S Parameters S S 11 12 → AB S21 S22 CD Solve for Propagation Constant ( Γ ) and Characteristic Impedance ( Z0 ) coshΓl Z sinhΓl AB 0 = CD –1 Γ Γ Z0 sinh l cosh l R 2Z0 s Γ⋅⋅ --------- = = l Z0 Γ ⋅ l Rp Cp Cs Ls http://holst.stanford.edu/~CPYue [email protected] Measured and Modeled Values of Ls and Rs 10 25 R C s ox C 8 20 s R C L si si s ) 6 15 ) H Ω n ( ( s s R L 4 10 Copper 2 5 Aluminum (Cs =28fF) 0 0 Model 0.1 1 10 Frequency (GHz) http://holst.stanford.edu/~CPYue [email protected] Substrate Modeling C ox 2Z0 R C = --------- p p Γ ⋅ l R C si si Physical Model Extracted Capacitance and Resistance http://holst.stanford.edu/~CPYue [email protected] Measured and Modeled Values of Rp and Cp R 25 250 C s ox C s 20 200 R C L ) si si s Ω 15 k 150 ( (fF) p p C R 10 100 Copper 5 50 Aluminum 0 0 Model 0.1 1 10 Frequency (GHz) http://holst.stanford.edu/~CPYue [email protected] Definition of Inductor Quality Factor ω V cos t R 0 s R C C L p p s s Peak Magnetic Energy– Peak Electric Energy π------------------------------------------------------------------------------------------------------------- Q2= Energy Loss in One Oscillation Cycle ω L R 2 () s p R s C p + C s --------- × ------------------------------------------------------------------- ×1 – ------------------------------- –ω 2 L ()C + C R []()ω ⁄ 2⋅s p s s R p +L s R s +1Rs Ls Substrate Loss Factor Self-Resonance Factor http://holst.stanford.edu/~CPYue [email protected] Measured and Modeled Value of Q 10 8 6 Q 4 Copper 2 Aluminum 0 Model 0.1 1 10 Frequency (GHz) Substrate Loss Factor http://holst.stanford.edu/~CPYue 0.0 0.2 0.4 0.6 0.8 1.0 0.1 1 10 Measured andModeledValues of Frequency (GHz) Substrate Factors 0.0 0.2 0.4 0.6 0.8 1.0 Self-Resonance Factor [email protected] Model Aluminum Copper http://holst.stanford.edu/~CPYue [email protected] Comparison to Published Results 20 15 10 Line Width 5 5 µm 9 µm Q Predicted by Our Model 14 µm 0 µ 0 5 10 15 20 19 m 24 µm Measured Qpeak presented by Ashby et al. http://holst.stanford.edu/~CPYue [email protected] Effect of Metal Scheme on Q 8 R C s ox C s 6 R C L si si s Q 4 3 levels of 1 µm in parallel 2 3 µm Al 2 µm Al 0 1 µm Al 0.1 1 10 Frequency (GHz) Model http://holst.stanford.edu/~CPYue [email protected] Effect of Oxide Thickness on Q 8 R C s ox C s 6 R C L si si s Q 4 6.5 µm Oxide 2 4.5 µm Oxide 2.5 µm Oxide 0 Model 0.1 1 10 Frequency (GHz) http://holst.stanford.edu/~CPYue [email protected] Effect of Substrate Resistivity on Q 8 R C s ox C s 6 R C L si si s Q 4 10 Ω-cm Si: × -3 µ 2 Csub = 1.6 10 fF/ m 2 × -8 µ 2 Gsub = 4.0 10 S/ m 6 Ω-cm Si: × -3 µ 2 Csub = 6.0 10 fF/ m 0 G = 1.6×10-7 S/µm2 0.1 1 10 sub Frequency (GHz) Model http://holst.stanford.edu/~CPYue [email protected] Effect of Layout Area on Q 8 R C s ox C s 6 R C L si si s Q 4 Outer Dimension Line Width 2 550 µm, 41 µm 400 µm, 24 µm 0 300 µm, 13 µm 0.1 1 10 Frequency (GHz) Model http://holst.stanford.edu/~CPYue [email protected] Application of Model 1 f = ---------------------- C L C 2π LC⋅ , → f C = 1.6 GHz C1.2= pF L= 8 nH fC Circuit Requirements L ? Inductor Design with Area (Design Tool) Optimal Q Technology Substrate Constraints Factors http://holst.stanford.edu/~CPYue [email protected] Contour Plots of Q Measured Q Measured Q 1.7 3.4 2.9 4.6 10 0.6 GHz 1.0 GHz 8 1 1 6 3 3 4 5 5 Inductance (nH) 2 7 9 0 0 100 200 300 400 0 100 200 300 400 Outer Dimension (µm) Outer Dimension (µm) http://holst.stanford.edu/~CPYue [email protected] Contour Plots of Q Measured Q Measured Q 4.0 5.2 6.1 4.0 10 1.6 GHz1 4 3.0 GHz 1 4 8 3 2 5 4 6 5 4 7 7 Inductance (nH) 9 2 9 0 0 100 200 300 400 0 100 200 300 400 Outer Dimension (µm) Outer Dimension (µm) http://holst.stanford.edu/~CPYue [email protected] Outline • Overview • A physical model for on-chip inductors • Effects of process and layout parameters • Design methodology • Inductors with patterned ground shields • Substrate noise coupling • Conclusions http://holst.stanford.edu/~CPYue [email protected] Overview • Challenges - Q degraded by substrate loss - Substrate coupling - Modeling and characterization - Process constraints • Approaches - Etch away Si substrate - Patterned Ground Shield http://holst.stanford.edu/~CPYue [email protected] Suspended Inductors Wafer Backside Polyimide Membrane ~550 µm http://holst.stanford.edu/~CPYue [email protected] Electromagnetic Fields of Conventional On-Chip Inductors H Csi Cox E Rsi Ls Rs http://holst.stanford.edu/~CPYue [email protected] Problems with Solid Ground Shield Induced Loop Current and Magnetic Field http://holst.stanford.edu/~CPYue [email protected] EM Fields of On-Chip Inductors with Patterned Ground Shield http://holst.stanford.edu/~CPYue [email protected] Patterned Ground Shield Design • Pattern - Orthogonal to spiral (induced loop current) • Resistance - Low for termination of the electric field Ground Strips - Avoid attenuation of Slot between Strips the magnetic field Induced Loop Current http://holst.stanford.edu/~CPYue [email protected] Effect of Aluminum Ground Shields on L 10 8 Patterned 6 Solid (nH) s None L 4 (19 Ω-cm) 2 None (11 Ω-cm) 0 0.1 1 10 Frequency (GHz) http://holst.stanford.edu/~CPYue [email protected] Effect of Aluminum Ground Shields on R 25 20 Patterned ) 15 Solid Ω ( s None R 10 (19 Ω-cm) 5 None (11 Ω-cm) 0 0.1 1 10 Frequency (GHz) http://holst.stanford.edu/~CPYue [email protected] Effect of Aluminum Ground Shields on C 300 250 Patterned 200 Solid (fF) 150 p None C 100 (19 Ω-cm) 50 None (11 Ω-cm) 0 0.1 1 10 Frequency (GHz) http://holst.stanford.edu/~CPYue [email protected] Effect of Polysilicon Ground Shields on L 10 8 6 Patterned (nH) Solid s L 4 Patterned 2 Aluminum 0 0.1 1 10 Frequency (GHz) http://holst.stanford.edu/~CPYue [email protected] Effect of Polysilicon Ground Shields on R 25 20 ) 15 Patterned Ω ( s Solid R 10 Patterned 5 Aluminum 0 0.1 1 10 Frequency