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.