Modeling and Characterization ofDielectric-Charging Effects inRF MEMS Capacitive Switches

Xiaobin Yuan, Zhen Peng, and James C. M. HwangLehigh University, Bethlehem, PA 18015

David Forehand, and Charles L. Goldsmith MEMtronics Corporation, Plano, TX 75075

Partially supported by the Air Force Research Laboratory underContract No. F33615-03-C-7003

Funded by DARPA/MTO Harsh Environment,Robust Micromachined Technology (HERMIT) program

Outline

• Introduction

• Experimental setups

• Transient current measurement

• Charging model construction

• Accelerated life tests and model verification

• Temperature dependence

• Equivalent-circuit model

• Bipolar vs. unipolar charging

• Conclusion

Introduction• Many microsystems will include electronics,

optics and MEMS• Main challenges for MEMS are reliability,

packaging, and integration• “Wiggling” is OK; “touching” is touchy; “grinding”

is certain death

• Problems are worse for NEMS - even a low voltage in tight space cause charging problems

• MEMS are more reproducible than NEMS - study of MEMS reliability will help understand NEMS reliability problems

Motivation• RF MEMS switches have low loss, low power, and high linearity• RF MEMS switches for electronically steered antenna represent

the first significant insertion opportunity of MEMS technology into aerospace/defense systems

• Lifetime of RF MEMS contact switches limited by stiction• Lifetime of RF MEMS capacitive switches limited by dielectric

charging • No quantitative model exists to predict lifetime due to charging• Accelerated life test is required because MEMS are slow • Only after the failure mechanisms are understood and

acceleration factors are quantified can life test be properly accelerated

• A dielectric-charging model can be used to design control-voltage waveforms either to accelerate failure or to prolong lifetime

RF Device Modeling/Characterization Lab - One of the Best in Academia

Pulsed I-V and S parameter measurement±100V, 20A, 50GHz, −65-200°C

Pulsed harmonic load-pull power and waveform measurement

Femtoampere transient current measurement, −65-200°C

Experimental Setup

MEMSBias-T Bias-T

VNA DC Source

RF Source

Function Generator

RF Detector

Oscilloscope

VNARF Test Setup• 50 GHz VNA for transient

pulsed S parameters• ±100 V DC Source• Arbitrary waveform

generator

DC Test Setup• Microchamber with temperature

and humidity control• Triaxial probes/cables• fA Precision semiconductor

parameter analyzer• Transient charging/discharging

current directly measured

RF MEMS Capacitive Switches

•120µ x 80µ MIM capacitor

•25V pull down voltage

•8V release voltage

•0.06dB insertion loss @ 35GHz

•15dB isolation @ 35GHz

•10µs switching time

• Sputtered silicon dioxide 0.3µm thick• Linear relationship between actuation-voltage shift and

accumulated charge in dielectric ∆V = qhQ/e0er

• Transient current measurements taken on false switch and used to construct charging model with charge location as an adjustment factor

• h ≈ (1/2) dielectric thickness• Charging model fits actuation-voltage shift of real switch

Real vs. False Switches

Al membrane (GND)

Cr signal line Oxide

Al membrane (GND)

Cr signal line Oxide

Real Switch False Switch

Top vs. Bottom Charging

Eg ~

9 e

V 4.3

eV

0.9 eV

Al

Vacuum Level

4.5

eV

Cr

• Top charging at higher voltage due to surface contamination

• Top charging very fast; top discharging very slow

• Metal/dielectric combination chosen to avoid top charging

V

Al Membrane

Bipolar vs. Unipolar Charging(—) before, (- -) after

Positive charge causes actuation/release voltages to shift left

Negative charge causes actuation/release voltages to shift right

-1

-0.5

0

0.5

1

0 100 200 300 400 500TIME (s)

CU

RR

ENT

(pA

)

-20

0

20

40

60

VOLT

AG

E (V

)

30 V off

30 V on

-1

-0.5

0

0.5

1

0 100 200 300 400 500TIME (s)

CU

RR

ENT

(pA

)

-20

0

20

40

60

VOLT

AG

E (V

)

30 V off

30 V on

Transient Current Measurements

)/exp()]/exp(1)[/exp(2,1

00JD

JOFF

JCON

JJ ttVVQQ ττ∑=

−−−Δ=Δ

1.0E+10

1.0E+11

1.0E+12

1.0E+13

-50 -25 0 25 50CONTROL VOLTAGE (V)

STEA

DY

STA

TE C

HA

RG

E (q

/cm

2 )

QJ = Q0J exp(V/V0

J)

∆ Trap 1□ Trap 2

Steady-State Charge Density

0

25

50

75

100

-50 -25 0 25 50CONTROL VOLTAGE (V)

TIM

E C

ON

STA

NT

(s)

□ Trap 1 Charging+ Trap 1 Discharging

Δ Trap 2 Chargingх Trap 2 Discharging

Charging/Discharging Time Constants

Model Parameters

)/exp()]/exp(1)[/exp(2,1

00JD

JOFF

JCON

JJ ttVVQQ ττ∑=

−−−Δ=Δ

Positive Voltage

J τC (s) τD (s) ΔQ0 ( cm-2 ) V0 (V)

1 6.6 6.8 3.1×1010 13

2 54 62 1.6×1011 15

Negative Voltage

J τC (s) τD (s) ΔQ0 ( cm-2 ) V0 (V)

1 6.5 7.0 2.4×1010 12

2 53 75 6.0×1010 11

Modeled vs. Measured Transient Currents

1E-15

1E-14

1E-13

1E-12

1E-11

0 100 200 300 400 500

TIME (S)

CU

RR

ENT

(A)

20 V

30 V

40 VDischarging

Charging

1E-15

1E-14

1E-13

1E-12

1E-11

0 100 200 300 400 500

TIME (S)

CU

RR

ENT

(A)

1E-15

1E-14

1E-13

1E-12

1E-11

0 100 200 300 400 500

TIME (S)

CU

RR

ENT

(A)

20 V

30 V

40 VDischarging

Charging

1E-15

1E-14

1E-13

1E-12

1E-11

0 100 200 300 400 500TIME (S)

CU

RR

ENT

(A)

-30 V

-20 V

-40 V

Charging

Discharging

1E-15

1E-14

1E-13

1E-12

1E-11

0 100 200 300 400 500TIME (S)

CU

RR

ENT

(A)

1E-15

1E-14

1E-13

1E-12

1E-11

0 100 200 300 400 500TIME (S)

CU

RR

ENT

(A)

-30 V

-20 V

-40 V

Charging

Discharging

• Model constructed for charging under both positive and negative actuation voltages

• Good fit between modeled and measured transient currents

Charging under Square-Wave Control

TIME

A

B C

DE

CHARGING DISCHARGING

CH

AR

GE

DEN

SITY

tOFFtON

SOn Time

Off Time

A B

DC

E

On Time

Off Time

A B

DC

E

• Net charge accumulation per switching cycle depends on ratchet action of charging/discharging

• Injected charge will saturate when the charging/discharging processes are balanced

0

2

4

6

0 5000 10000 15000 20000NUMBER OF CYCLES

AC

TUA

TIO

N V

OLT

AG

E SH

IFT

(V)

DUTY FACTOR = 75 %

50 %

25 %

PEAK VOLTAGE = - 30V, f = 100 Hz0

2

4

6

0 5000 10000 15000 20000NUMBER OF CYCLES

AC

TUA

TIO

N V

OLT

AG

E SH

IFT

(V)

DUTY FACTOR = 75 %

50 %

25 %

PEAK VOLTAGE = - 30V, f = 100 Hz

Duty Factor Acceleration

0

2

4

6

8

0 5000 10000 15000 20000NUMBER OF CYCLES

AC

TUA

TIO

N V

OLT

AG

E SH

IFT

(V)

DUTY FACTOR = 50%, f = 100 Hz

PEAK VOLTAGE = - 35 V

-30 V

-25 V

0

2

4

6

8

0 5000 10000 15000 20000NUMBER OF CYCLES

AC

TUA

TIO

N V

OLT

AG

E SH

IFT

(V)

DUTY FACTOR = 50%, f = 100 Hz

PEAK VOLTAGE = - 35 V

-30 V

-25 V

Voltage Acceleration

0

2

4

6

1 10 100 1000 10000FREQUENCY (Hz)

AC

TUA

TIO

N V

OLT

AG

E SH

IFT

(V)

PEAK VOLTAGE = - 30V, 160 s

DUTY FACTOR = 75 %

50 %

25 %

0

2

4

6

1 10 100 1000 10000FREQUENCY (Hz)

AC

TUA

TIO

N V

OLT

AG

E SH

IFT

(V)

PEAK VOLTAGE = - 30V, 160 s

DUTY FACTOR = 75 %

50 %

25 %

Frequency Independence

Temperature Dependence)/exp()]/exp(1)[/exp(0

JDOFF

J

JCONJ

J ttkTEaQQ ττ −−−−=∑

9

10

11

12

13

2 3 4 5INVERSE TEMPERATURE (1000/K)

LOG

CH

AR

GE

DEN

SITY

(q/c

m2 )

▬ Trap 1 Modeled□□ Trap 1 Extracted

--- Trap 2 ModeledΔΔ Trap 2 Extracted

0

30

60

90

120

150

200 250 300 350 400TEMPERATURE (K)

TIM

E C

ON

STA

NTS

(s)

0

30

60

90

120

150

200 250 300 350 400TEMPERATURE (K)

TIM

E C

ON

STA

NTS

(s)

ΔΔ Trap 2 Chargingxx Trap 2 Discharging

□□ Trap 1 Charging++ Trap 1 Discharging─ Averaged Values

•Steady-state charge density exhibits Arrhenius temperature dependence

•Time constants independent of temperature

Temperature Acceleration

0

2

4

6

8

10

0 50 100 150 200 250STRESS TIME (s)

AC

TUA

TIO

N-V

OLT

AG

E SH

IFT

(V)

50°C25°C0°C

(curve) modeled(symbol) measured

Actuation-Voltage Shift under -30 V

-12

-10

-8

-6

2 3 4 5INVERSE TEMPERATURE (1000/K)

LOG

CU

RR

ENT

DEN

SITY

(A/c

m2 ) Steady-State Current Density under -30 V

•Model agrees with measured increase in actuation-voltage shift as a function of temperature

•Switch more prone to stiction at higher temperature due to both increased charging of dielectric and decreased stiffness of membrane electrode

•Steady-state leakage current through dielectric increases with temperature, but did not help bleed away trapped charge

)/exp()]/exp(1)[/exp(0JDOFF

J

JCONJ

J ttkTEaQQ ττ −−−−=∑

Equivalent-Circuit Model

RRd5R=74.7 Ohm

RRc5R=52.5 Ohm

RRd4R=7 Ohm

RRc4R=6.5 Ohm

DiodeDIODE7

DiodeDIODE6

CC5C=1.0 F

VtPulseSRC8

t

VtPulseSRC6

t

CC3C=1.0 F

DiodeDIODE5

DiodeDIODE1

C = 1 F

C = 1 F

RC1 = τ C1

RD1 = τ D1

RC2 = τ C2

RD2 = τ D2

VS1 = Q01exp(V/V01)

VS2 = Q02exp(V/V02)

RRd5R=74.7 Ohm

RRc5R=52.5 Ohm

RRd4R=7 Ohm

RRc4R=6.5 Ohm

DiodeDIODE7

DiodeDIODE6

CC5C=1.0 F

VtPulseSRC8

t

VtPulseSRC6

t

CC3C=1.0 F

DiodeDIODE5

DiodeDIODE1

C = 1 F

C = 1 F

RC1 = τ C1

RD1 = τ D1

RC2 = τ C2

RD2 = τ D2

VS1 = Q01exp(V/V01)

VS2 = Q02exp(V/V02)

• Compact model to simulate circuits of multiple MEMS and electronic devices under complex control waveforms

• Equivalent-circuit model an approximation of equation-based model

• Transient SPICE model implemented in Agilent’s ADS circuit simulator

Complex Control Waveforms

-45

-30

-15

0

15

30

45

60

75

90

-25 0 25 50 75 100 125TIME (ms)

CO

NTR

OL

VOLT

AG

E (V

)

0-15-30

0

0

-15-30

-15-30 tP = 5 ms

tP = 25 ms

tON = 50 ms tOFF = 50 ms

-45

-30

-15

0

15

30

45

60

75

90

-25 0 25 50 75 100 125TIME (ms)

CO

NTR

OL

VOLT

AG

E (V

)

0-15-30

0

0

-15-30

-15-30 tP = 5 ms

tP = 25 ms

tON = 50 ms tOFF = 50 ms

0

2

4

6

0 50 100 150 200TIME (s)

AC

TUA

TIO

N-V

OLT

AG

E SH

IFT

(V)

2.612

2.614

2.616

2.618

2.62

172.1 172.15 172.2 172.25 172.3TIME (s)

AC

TUA

TIO

N-V

OLT

AG

E SH

IFT

(V)

tP

tON tOFF

2.612

2.614

2.616

2.618

2.62

172.1 172.15 172.2 172.25 172.3TIME (s)

AC

TUA

TIO

N-V

OLT

AG

E SH

IFT

(V)

tP

tON tOFF

•Equivalent-circuit simulation correctly predict reduced charging under dual-pulse control wave

•Envelope simulation more efficient similar to that for wireless communication under complex modulation such as CDMA

Bipolar vs. Unipolar Charging

Eg ~

9 e

V 4.3

eV

0.9 eV

Al

Vacuum Level

4.5

eV

Cr

• Top charging at higher voltage due to surface contamination

• Top charging very fast; top discharging very slow

• Avoid bipolar charging!

V

Al Membrane

-4

-3

-2

-1

0

1

2

3

4

0 300 600 900 1200 1500

TIME (s)

AC

TUA

TIO

N V

OLT

AG

E SH

IFT(

V)

30V STRESS 140V STRESS 150V STRESS 150V STRESS 2

Stress Added Stress released, waiting for recover

30V40V

50V

-4

-3

-2

-1

0

1

2

3

4

0 300 600 900 1200 1500

TIME (s)

AC

TUA

TIO

N V

OLT

AG

E SH

IFT(

V)

30V STRESS 140V STRESS 150V STRESS 150V STRESS 2

Stress Added Stress released, waiting for recover

30V40V

50V

• Unipolar charging at ≥ 30V; bipolar charging at ≥ 50 V• Unipolar: actuation voltage recovers to original value• Bipolar: long-term actuation voltage drift after bottom

charge dissipates but top charge remains

Bipolar Charging under Positive Voltage

-4

-3

-2

-1

0

1

2

3

4

0 300 600 900 1200 1500

TIME (s)

AC

TUA

TIO

N V

OLT

AG

E SH

IFT(

V)

-30V STRESS 1-40V STRESS 1-50V STRESS 1-50V STRESS 2-60V STRESS 1-60V STRESS 2

-4

-3

-2

-1

0

1

2

3

4

0 300 600 900 1200 1500

TIME (s)

AC

TUA

TIO

N V

OLT

AG

E SH

IFT(

V)

-30V STRESS 1-40V STRESS 1-50V STRESS 1-50V STRESS 2-60V STRESS 1-60V STRESS 2

Stress Added Stress released, waiting for recover

-30V

-50V

-40V-60V

-4

-3

-2

-1

0

1

2

3

4

0 300 600 900 1200 1500

TIME (s)

AC

TUA

TIO

N V

OLT

AG

E SH

IFT(

V)

-30V STRESS 1-40V STRESS 1-50V STRESS 1-50V STRESS 2-60V STRESS 1-60V STRESS 2

-4

-3

-2

-1

0

1

2

3

4

0 300 600 900 1200 1500

TIME (s)

AC

TUA

TIO

N V

OLT

AG

E SH

IFT(

V)

-30V STRESS 1-40V STRESS 1-50V STRESS 1-50V STRESS 2-60V STRESS 1-60V STRESS 2

Stress Added Stress released, waiting for recover

-30V

-50V

-40V-60V

• Threshold for bipolar charging higher than that under positive voltage

• Barrier from Al to SiO2 higher for holes than for electrons

Bipolar Charging under Negative Voltage

Conclusion

• Model extracted from charging/discharging currents• Model validated under accelerated life test conditions• Model can be used to design control-voltage waveforms

either to accelerate failure or to prolong lifetime• Model can be used for quick evaluation of dielectrics• Model provides deeper insight into the dielectric charging

problem and allow more robust MEMS switches to be designed

• Envelope simulation by using equivalent circuit model provides quick approximation under complex control waveforms

• Temperature accelerates charging and softens membrane• Avoid bipolar charging at all cost!

References

1. X. Yuan, J. C. M. Hwang, D. Forehand, and C. L. Goldsmith, “Modeling and characterization of dielectric-charging effects in RF MEMS capacitive switches,” in IEEE MTT-S Int. Microwave Symp. Dig., June 2005.

2. X. Yuan, J. C. M. Hwang, D. Forehand, and C. L. Goldsmith, “A transient charging model to predict actuation voltage shift in RF MEMS capacitive switches,” in Proc. Soc. Optical Engineers, vol. 6111, Jan. 2006, pp. 61110G1-61110G8.

3. C. Goldsmith, D. Forehand, X. Yuan and J. Hwang, “Tailoring capacitive switch technology for reliable operation,” in Dig. Government Microelectronics Applications Conf., Mar. 2006.

4. X. Yuan, J. C. M. Hwang, D. Forehand, and C. L. Goldsmith, “Temperature acceleration of dielectric-charging effects in RF MEMS capacitive switches,” to appear in IEEE MTT-S Int. Microwave Symp. Dig., June 2006.