Hirotaka Sugawara, Yoshiaki Yoshihara, Hiroyuki Ito, Kenichi Okada, and Kazuya MasuPrecision 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 inductorsThe demand has been increasing for RF Si CMOS circuits.

Parallel-plate ActuatorMEMS 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 4th 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 Inductorconsists 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 whichpenetrate 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 [n

H]

0.8

1.8

Relative Permeability µ0.01 1 10000100

1.01.21.41.6

L [n

H]

0.8

1.8

Conductivity σ [S/m]1 102

1.2

106 108104 1010

1.41.6

1.0

L [n

H]

1.8

1.41.6

Thickness of Metal Plate [µm]0.01 0.1 100101

1.21.00.8

x

h

Thickness

Spiral InductorTurns : 2.5Line width W : 20 µm Line space S : 10 µmOuter dimension D : 250 µmL=1.8 nH

Simulated by HFSS (Ansoft)

Metal Thickness of over Skin Depth

Magnetic flux can be shielded by the metal plate

2Depth Skin =　

Skin Depth≒2µm @1GHz

2Depth Skin =　

Skin Depth≒2µm @1GHz

2Depth Skin =　

Skin Depth≒2µm @1GHz

ωσµ

Measurement Method

Effect of Parasitic Capacitance

Input Impedance

Equivalent circuit model

subsub

2sub

metmet

2met )()(ssin

LjωRM

LjRMLjRZ

ω

ωωω

++

+++=

The magnetic fluxpenetrates 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

+−

++

++

++=

2sub

2sub

sub2

sub2

met2

met

met2

met

2sub

2sub

sub2

sub2

met2

met

met2

met

)()(

)()(-s

)()(

)()(s

LRLM

LRLMLj

LRRM

LRRMR

ωωω

ωωω

ωω

ωω

PurposeTo realize a variable inductor on Si CMOS chip

( )( )inRe

inImZZQ =

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 InductorWide-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

openshortopenmeas

ind

111

YYYY

Y

−−

−

=

De-embedding･ Open and short pad are used

openshortopenmeas

ind

111

YYYY

Y

−−

−

=

( )

( )( )de

dm

dm

ZRZIQ

ZI1L

=

=

( )2ind12

ind22

ind11

ind12

ind12

ind11

dYYY2YYYZ

−

++=

ω

DUT

Open pad

Short pad

Frequency [GHz]0.1 1 10

L [n

H]

0

12

8

4

16h=100 µmh=10 µm

Frequency [GHz]0.1 1 10

Q

12

4

0

3

5h=100 µmh=10 µm

Height of plate h [µm]

3.5

L [n

H]

0 20 80

6.5

4.5

5.5

6040 100

f =2.45 GHzx=500 µm

Height of plate h [µm]

2

Q

0 20 80

5

3

4

6040 100

f =2.45 GHzx=500 µm

Variable Range:34.6% Variable Range:26.3%

The parasitic capacitance is induced between the spiral inductor and the metal plate

LCf

21

SR =π

⇒Degrade the inductor characteristics

Height of plate h [µm]

00 20 80

0.10

6040 100

C [p

F]

0.080.06

0.020.04

Height of plate h [µm]

50 20 80

8

6

7

6040 100

fSR [G

Hz]

h decreases⇒fSR decreasesEffect of parasitic capacitance is not dominant

Parasitic capacitance is not increased so much by metal plate

Height of plate h [µm]

500 20 80

100

70

90

6040 100

Im(Z

in)

80

60 f =2.45 GHz

Re(

Zin)

Height of plate h [µm]

200 20 80

30

25

6040 100

35

40

f =2.45 GHz

LS

RS

Lmet

Rmet

Metal PlateSpiral Inductor

Lsub

Msub

RsubZin

Mmet

h decreasesMmet 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

CuResin

Cu:10 µmResin:10 µmAl:1.5 µmSiO2 :0.5 µmSi:525 µmSi resistivity A: 2-6 Ωcm B: 1k Ωcm DUT with pad Open pad

Height of plate [µm]0

4

50

3

2150100 200

5

A (ρ=2−6 Ωcm)

B (ρ>1 kΩcm)Variable range:53.1%

Variable range:52.4%

L [n

H]

10

50

20

30

Height of plate [µm]0 50 150100 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 [n

H]

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

60A (ρ=2−6 Ωcm)B (ρ>1 kΩcm)

@ f=2 GHz

The variable range of L

53 % in Inductor A 52 % in Inductor BThe variable range of Q

50 % in Inductor A 62 % in Inductor B

WL-CSP wafer-level chip-scale packagesLead free bump

2nd Resin Inductor

Die

1nd ResinCu reroutingAl pad

K. Itoi, M. Sato, H. Abe, H. Sugawara, H. Ito, K. Okada, K. Masu, and T. Ito: IEEE MTT-SInt. 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-CSPThe 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]