Hirotaka Sugawara, Yoshiaki Yoshihara, Hiroyuki Ito, Kenichi Okada, and Kazuya Masu Precision and Intelligence Laboratory, Tokyo Institute of Technology, Japan MEMS Variable Inductor for Multi-band RF CMOS Circuits 3. Measurement Results 1. Background 2. Principle of Variable Inductor On-chip inductors The demand has been increasing for RF Si CMOS circuits. Parallel-plate Actuator MEMS Actuator Comb actuator stationary electrode movable electrode Parallel-plate actuator stationary electrode movable electrode W. C. Tang, M. G. Lim, and R. T. Howe: J. Microelectromechanical Systems 4 (1992) 170. V. M. Lubecke, and J. -C. Chiao: The IEEE 4 th Int. Conf. on Telecommunications in Modern Satellite, Cable and Broadcasting Services, 1999 p. 1 The actuators are driven by electrostatic force. By generating DC bias between the stationary electrode and the movable electrode. MEMS actuator is used for moving the metal plate above the spiral inductor Variable Inductor consists of a planar-type spiral inductor and a metal plate. Metal Plate Spiral Inductor h x Moving The inductance continuously varies depending on the position of the metal plate. The metal plate shields the magnetic flux which penetrate the inductor. The inductance value can be also varied by changing the height of the metal plate. Small h Variable range of inductance increases. Parasitic Capacitance increases. Shielding Magnetic Mechanism Metal Plate L [nH] 0.8 1.8 Relative Permeability m 0.01 1 10000 100 1.0 1.2 1.4 1.6 L [nH] 0.8 1.8 Conductivity s [S/m] 1 10 2 1.2 10 6 10 8 10 4 10 10 1.4 1.6 1.0 L [nH] 1.8 1.4 1.6 Thickness of Metal Plate [mm] 0.01 0.1 100 10 1 1.2 1.0 0.8 x h Thickness Spiral Inductor Turns : 2.5 Line width W : 20 mm Line space S : 10 mm Outer dimension D : 250 mm L=1.8 nH Simulated by HFSS (Ansoft) Metal Thickness of over Skin Depth Magnetic flux can be shielded by the metal plate 2 Depth Skin = Skin Depth 2mm @1GHz 2 Depth Skin = Skin Depth 2mm @1GHz 2 Depth Skin = Skin Depth 2mm @1GHz ωσμ Measurement Method Effect of Parasitic Capacitance Input Impedance Equivalent circuit model sub sub 2 sub met met 2 met ) ( ) ( s s in L jω R M L j R M L j R Z ω ω ω ω + + + + + = The magnetic flux penetrates the metal plate. Eddy current flows in the metal plate. Eddy current flows in the metal plate. Induced a counteractive magnetic field according to Lenz’s Law. Induced a counteractive magnetic field according to Lenz’s Law. The metal plate shields the magnetic flux. The metal plate shields the magnetic flux. Inductance change Change of the magnetic flux l L + - + + + + + + = 2 sub 2 sub sub 2 sub 2 met 2 met met 2 met 2 sub 2 sub sub 2 sub 2 met 2 met met 2 met ) ( ) ( ) ( ) ( - s ) ( ) ( ) ( ) ( s L R L M L R L M L j L R R M L R R M R ω ω ω ω ω ω ω ω ω ω Purpose To realize a variable inductor on Si CMOS chip ( ) ( ) in Re in Im Z Z Q = The variation Q is smaller than that of L The wireless communication system has several frequency bands which are required to cover several frequency bands. Variable RF Inductor Wide-range oscillation of VCO Wide-tunable impedance matching Multi-band solutions are required to cover several frequency bands. Multi-band solutions are required to cover several frequency bands. The metal plate is moved by DC bias between the stationary electrode and the movable electrode Lower Power Consumption The variable inductor is an indispensable device for high-frequency and multi-band circuits. MEMS actuator requires high manufacturing cost, and the reliability is not so high at the present time. h Spiral Inductor Metal Plate Stationary Electrode Arm current does not flow between the electrodes De-embedding Open and short pad are used open short open meas ind 1 1 1 Y Y Y Y Y - - - = De-embedding Open and short pad are used open short open meas ind 1 1 1 Y Y Y Y Y - - - = ( ) ( ) ( ) d e d m d m Z R Z I Q Z I 1 L = = ( ) 2 ind 12 ind 22 ind 11 ind 12 ind 12 ind 11 d Y Y Y 2Y Y Y Z - + + = ω DUT Open pad Short pad Frequency [GHz] 0.1 1 10 L [nH] 0 12 8 4 16 h=100 mm h=10 mm Frequency [GHz] 0.1 1 10 Q 1 2 4 0 3 5 h=100 mm h=10 mm Height of plate h [mm] 3.5 L [nH] 0 20 80 6.5 4.5 5.5 60 40 100 f =2.45 GHz x=500 mm Height of plate h [mm] 2 Q 0 20 80 5 3 4 60 40 100 f =2.45 GHz x=500 mm Variable Range:34.6% Variable Range:26.3% The parasitic capacitance is induced between the spiral inductor and the metal plate LC f 2 1 SR = π Degrade the inductor characteristics Height of plate h [mm] 0 0 20 80 0.10 60 40 100 C [pF] 0.08 0.06 0.02 0.04 Height of plate h [mm] 5 0 20 80 8 6 7 60 40 100 fSR [GHz] h decreases f SR decreases Effect of parasitic capacitance is not dominant Parasitic capacitance is not increased so much by metal plate Height of plate h [mm] 50 0 20 80 100 70 90 60 40 100 Im(Zin) 80 60 f =2.45 GHz Re(Zin) Height of plate h [mm] 20 0 20 80 30 25 60 40 100 35 40 f =2.45 GHz LS RS Lmet Rmet Metal Plate Spiral Inductor Lsub Msub Rsub Zin Mmet h decreases Mmet increases Im(Zin) decreases Msub decreases Re(Zin) decreases h decreases Mmet increases Im(Zin) decreases Msub decreases Re(Zin) decreases Variation of Q is small Appendix. Redistributed Layers Si SiO2 Al Cu Resin Cu:10 mm Resin:10 mm Al:1.5 mm SiO2 :0.5 mm Si:525 mm Si resistivity A: 2-6 Ωcm B: 1k Ωcm DUT with pad Open pad Height of plate [mm] 0 4 50 3 2 150 100 200 5 A (ρ=2-6 Ωcm) B (ρ>1 kΩcm) Variable range:53.1% Variable range:52.4% L [nH] 10 50 20 30 Height of plate [mm] 0 50 150 100 200 40 0 60 A (ρ=2-6 Ωcm) B (ρ>1 kΩcm) Variable range:48.8% Variable range:61.0% Q Frequency [GHz] L [nH] 2 0 4 0.1 1 10 10 6 8 A (ρ=2-6 Ωcm) B (ρ>1 kΩcm) Frequency [GHz] 0.1 1 10 Q 0 10 50 20 30 40 60 A (ρ=2-6 Ωcm) B (ρ>1 kΩcm) @ f=2 GHz The variable range of L 53 % in Inductor A 52 % in Inductor B The variable range of Q 50 % in Inductor A 62 % in Inductor B WL-CSP wafer-level chip-scale packages Lead free bump 2 nd Resin Inductor Die 1 nd Resin Cu rerouting Al pad K. Itoi, M. Sato, H. Abe, H. Sugawara, H. Ito, K. Okada, K. Masu, and T. Ito: IEEE MTT-S Int. Microwave Symp. Digest, Fort Worth, 2004 p. 197. WL-CSP Advantages Thick Cu conductor Resin layer between the conductor and Si substrate Reduction in substrate loss High-Q WL-CSP The CMOS chip's pads are connected to the board's pads through lead free bumps and redistributed layers. Inductance is implemented using redistributed layer Metal Plate [without inserting] [with inserting]