Download New ways of measuring pull-in voltage and transient

NEW WAYS OF MEASURING PULL-IN VOLTAGE AND TRANSIENT BEHAVIOR OF
PARALLEL-PLATE CAPACITIVE MEMS TRANSDUCERS
C. Glacer1,2 , A. Dehé2 , M. Nawaz2 and R. Laur1
1
Institute for Electromagnetic Theory and Microelectronics (ITEM), University of Bremen, Bremen, Germany
2
Infineon Technologies AG, Neubiberg/Munich, Germany
Abstract — In this paper we introduce two
new ways of measuring the pull-in voltage
and the transient behavior of parallel-plate
capacitive MEMS transducers. The advantages
in measurement speed and resolution of the socalled fast MEMS test will be discussed as well as
an enhanced method, the time-resolved dynamic
measurement. With the second method we can
visualize the integral displacement of a membrane
while measuring the voltage drop of a high
frequency signal over a shunt resistor/capacitor.
This offers us a new robust and cheap option for
tracing moving structures without the need of an
optical line of sight.
Keywords: MEMS testing, Silicon Microphone,
laser Doppler vibrometer, pull-in voltage
I – Introduction
Acoustical parallel-plate microelectromechanical
systems (MEMS) especially for mobile applications
are strongly upcoming the last years. With ongoing
miniaturization of mobile phone components and
the desire for automatic reflow solder processes
the requirements for microphones are increasing.
Conventional electret condenser microphones suffer
from humidity and temperature influences. The
Infineon Silicon MEMS Microphone chip set delivers
a small size, good reproducibility and stability, low
sensitivity to vibration and the ability of low-cost batch
fabrication along with a sufficient sound recording
quality [1].
Figure 1: Schematic of the Infineon Silicon MEMS Microphone [1]. The membrane (red) and the fixed counterelectrode (blue) can bee seen.
The Infineon microphone uses a pressure sensitive
diaphragm made out of in poly-Silicon. Along with a
preamplifier, the microphone chip converts an impinging sound wave into an electrical output signal with
a capacitive transducing concept. Although there is a
big market and millions of devices are produced every
year, the membrane behavior in such a microphone
system is not fully transparent and understood. Especially in case of large deflections, mechanical shocks
or extreme sound pressure levels it needs a (scanning)
laser Doppler vibrometer (LDV) and a complex sample
preparation to monitor the membranes motion.
Belong those special measurement setups for further
investigations of some systems; every chip has to pass
a final inspection. The pull-in voltage (Vp ) can become
a key parameter for this purpose. It marks the equilibrium point of the electrostatic attraction force and the
mechanical resilience in a voltage controlled capacitive
system. This delivers insights about the membrane compliance (k) with a given air gap (d0 ) and area (A) [2].
s
8kd03
(1)
Vp =
27εA
Despite a simple pass-fail test the system sensitivity
(S) can be derived [1] by determining Vp .
r
8d0
V0
S=
·
(2)
Vp
27εAk
Several methods to detect the pull-in event are existing. The probably simplest way is to look at the
membrane while increasing the stimulus voltage step by
step. When the pull-in voltage is reached, the closing of
the air-gap between the two electrodes will lead to interference fringes which are visible with a microscope.
More advanced equipment like a Doppler vibrometer
will do the same purpose. Another common method to
detect Vp is the usage of a LCR meter. The displacement
of the membrane towards the electrode leads to a higher
capacitance which can be monitored. As a consequence,
the membranes motion over the excitation voltage can
be plotted. The voltage where the pull-in acceleration
phase begins can be made visible as Vp . This event can
be even heard, so that a acoustical detection is another
method.
In this work new approaches for testing parallelplate sensors and actuators - the fast MEMS test and
the time-resolved dynamic measurement - will be
presented. This measurement techniques deliver new
insights in the transient motion of a micro-mechanically
fabricated membrane as well as a fast and exact test
method for the pull-in voltage and system resonances.
It will be elucidated how the fast MEMS test works
and which equipment is necessary for acquisition
and data processing. Moreover possible application
25
II – Measurement Setup
20
Measured voltage drop over Cmeas
15
10
Voltage drop over CMeas [mV]
fields will be shown and initial results will be presented.
Input signal Vstim [V]
The concept of the fast MEMS test is relatively
simple and bases upon the well-known current mea15
5
surement with a shunt resistor. For the simplest case,
the Vp determination, the voltage drop across a resistor
10
0
in series to the capacitive transducer will be metered
with an oscilloscope (L E C ROY MSO 44MX S -B). The
5
−10
excitation is realized with a biased signal generator
(AGILENT 33220A) which delivers for example a tri0
−10
angular waveform with 0 to 20V back to 0V in 1ms.
0
0.2
0.4
0.6
0.8
1
1.2
Time [ms]
If the pull-in voltage is inside this voltage ramp, the
capacitance of the parallel-plate actuator will quickly Figure 3: Measured voltage drop across the shunt capacitor. It
increase and influence the current through the circuit shows the pull-in event (time index: ≈ 0.5ms) and the release
and so the resistors voltage drop. Fig. 2 shows the basic (≈ 0.9ms).
setup. In our case, the usage of a shunt capacitor instead
of resistor delivered a higher output voltage with a better
signal to noise ratio (SNR).
1kHz triangular waveform. This delivered a resolution
of 8mV/step for the given signal.
Scope
GPIB-Control
The big disadvantage of this method is that the response
signal directly follows the input stimulus fstim .
PC with
Measurement
Therefor we can only extract the pull-in and release
MatLab
C
voltage but not the membranes free motion. Also it is
DUT (e.g. SiMic)
not possible to resolve the membrane movement when
1
2
the excitation is a mechanical stimulus instead of an
C
R /C
electrical. To get rid of this problem, the time-resolved
Simplified equivalent circuit
1 2
dynamic measurement is introduced.
For this method we use a series AC voltage source
Biased AC stimulus
+
- +
with a sinusoidal signal fHF of small amplitude and
high frequency. This signal superimposes the electromechanical stimulus or acts alone with a mechanical
Figure 2: Simplified model of the pull-in detection measureexcitation. For a given frequency of typically 1MHz or
ment setup. Containing the electrical circuit and an simplified
more, the membrane is not capable to follow the signal
equivalent circuit of the MEMS capacitances.
which lies clearly above the membranes resonance frequency (≤120kHz). The number of scan points s within
After the equilibrium point of the acting forces, the one period of the stimulus which can be achieved with
membrane encounters a large acceleration due to the this methods can be calculated by s = fHF / fstim .
To extract Vout,HF from Vout = Vout,stim +Vout,HF it is
increasing electrostatic force. This normally happens at
necessary
to apply an electrical filter. In this case we
around 1/3 of the systems air gap [2]; the el. potential
use
a
software
Butterworth band pass filter generated
where this large acceleration event starts can be taken
in
M
AT
L
AB
to
get
rid of Vout,stim and noise. The signal
as the pull-in voltage. Due to our capacitive shunt setup
processing
contains
the following steps:
it was necessary to form the second derivative to figure
out the largest acceleration of the membrane which is
1. Measurement and data transfer; e.g. 100k Samples
proportional to the largest change in output voltage.
for fHF = 5MHz
To do the necessary data processing a software
solution with M ATH W ORKS M AT L AB was used. The
2. Spline interpolation in M AT L AB to regain the siAC source as well as the digital storage oscilloscope
nusoidal signal shape
are controlled by the General Purpose Interface Bus
3. Butterworth band pass filtering; e.g. with 4th order
(GPIB) interface. After a measurement the results will
and fc = 5MHz ± 0.2MHz
be transferred to the PC, derivated twice and the point
of the biggest acceleration of Vout gets linked to the
4. Creating the envelope to figure out the amplitude
stimulus voltage Vstim . The number of read-out samples
of each period
are directly influencing the data transfer time and the
5. Result: Signal proportional to the integral of the
resolution of the measurement. We worked with a
membrane displacement and its capacitance sum
compromise of 5000 samples while stimulating with a
Measurement Results
Static
Pull-In
Meas
meas
Change of pull-in voltage over frequency
2.5
III – Results and Discussion
A. Fast dynamic pull-in detection
To gain statistical values with the introduced pull-in
detection method we investigated several wafers containing silicon microphones. For this we used a GPIB
controlled lab wafer prober from S UESS M ICROT ECH.
Figure 4 shows a distribution of the pull-in voltages
across an experimental test wafer containing >10k silicon microphones in total. It can be demonstrated how
fine the gradients in the pull-in voltage determination
are, so that even technology effects on this wafer can
be made visible. When we measure the same wafer
again without changing the setup, the median of the
deviations particular chips show in their pull-in voltages
is Vp,di f f = 8.7mV , which is nearly within the measurement resolution of 8mV /step.
16V
80
60
15V
40
Wafer y
20
Change in pull-in voltage [V]
2
1.5
1
0.5
Change of Vp, electrical fast MEMS test
Standard deviation, electrical
Change of Vp, optical LDV
0
−0.5
0
0.5
1
1.5
2
2.5
3
Frequency [kHz]
3.5
4
4.5
5
Figure 5: Change of pull-in voltage over frequency. Determined by fast MEMS test and proven by optical measurement.
as shown in fig. 5.
Here the fast MEMS test is a promising method
as the decrease in pull-in voltage over frequency is
repeatable for every chip. According to this a correction
factor can be extracted and also no steep (rectangular)
steps appear in the excitation voltage.
B. Time-resolved dynamic measurement (TRDM)
0
14V
−20
−40
13V
Since a LCR meter delivers exact capacitance values
but has in our test setting a minimum settling time
of around 2.8ms per point, this tool is not appropriate
to perform transient measurements of MEMS microphones.
−60
−80
−80
−60
−40
−20
0
Wafer x
20
40
60
80
(a)
(b)
(c)
(d)
12V
Figure 4: Pull-in voltage distribution across an experimental
test wafer. After 2/3 of the wafer stepping the prober tips lost
contact. This resulted in noise which will be filtered out in
further measurements.
Another advantage of the fast MEMS test is its high
measuring speed. With the given resolution the contact
time of a chip amounts 2.5ms which includes a safe
prober tip contact, the time to trigger and acquire the
waveform by the oscilloscope and the command to start
stepping to the next chip for the prober.
A point which has to be minded is the dynamic effect
of different excitation frequencies to the pull-in voltage.
In vacuum a steeper excitation slope leads to a higher
membrane acceleration and contributes more energy to
the system. With a higher measurement frequency and
the same maximum amplitude value the slope steepness
increases [3]. Compared to a quasi-static pull-in event,
the bigger kinetic energy at e.g. 1kHz test frequency
leads to a lower effective pull-in voltage. Under normal
air pressure this effect gets obliterated by the air damping. With higher frequencies the pull-in voltage drops
Figure 6: With a scanning laser Doppler Vibrometer measured
displacement of the membrane at certain time points during a
pull-in and release event.
The motion of a parallel-plate capacitive transducer
encountered from a triangular stimulus is shown in
figure 6. This measurement was done with a SLDV
from P OLYTECH through the perforation holes of the
overhead (fixed) counter electrode. It shows the slow
deflection of the membrane (a), the first contact between
the electrodes (b), the widening of the contact area due
to higher voltage (c) and the overshoot after the release
(d).
The ability of scanning through different measure-
ferent transducer types, that the fast MEMS test method
is working and delivers good results. It produces a
high measurement resolution with a measurement time
which only needs one period of a stimulus signal (e.g.
1ms at fstim = 1kHz) while the chip is contacted. Aside
from that, the needed equipment is, with a function
generator and a digital oscilloscope, common and cheap
so that in most labs the setup can be easily implemented.
The problem of an overshoot due to high voltage steps
around the pull-in point is avoided here.
Extracted prop. membrane displacement
The enhanced measurement setup, the time-resolved
1
dynamic measurement, can partly compare to optical
transient measurements with an SLDV. A disadvantage
is that only integral values of the displacement will be
delivered, comparable to the capacitance of the MEMS
device in the circuit. It is also necessary to compensate
0.5
10
parasitic elements to get correct capacitance readings
out of both measurement methods. This will happen
in a future step. On the other hand the measurement
technique shows several benefits compared to the measurement with an SLDV. Starting by the equipment cost
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
which are only on a fraction of those of a SLDV and
Time [ms]
going over to the application areas. Because of the fact
Coupled oscil. after pull in
Membrane oscil. after release
that no line of sight is needed, the measurement will
0.12
0.1
also work with build-in and moving chips and offers
0.85
0.08
new ways of monitoring the membrane deflection, so
0.06
the method can be also applied to pressure or bulge tests
0.8
0.04
or any overload test.
0.75
All in all the new fast MEMS test and the time0.72
0.74
0.76
0.78
0.36
0.38
0.4
Time [ms]
Time [ms]
resolved dynamic measurement are interesting, easy to
use and robust methods to determine pull-in voltage
Figure 7: Proportional integral membrane motion measured
with the time-resolved dynamic measurement with averaging and membrane motion which offers us new fields of
(above). Coupled oscillation and mebrane oscillation after application.
Prop. displacement [normed]
Prop. displacement [normed]
Stimulus low pass filtered [V]
Prop. displacement [normed]
ment points on the membrane is not given with the
TRDM since only the voltage drop over a resistor/capacitor in series is measured. Instead the integral
movement of the membrane will be recorded. This is
of course a disadvantage but sufficient in most applications. A bigger problem is that higher oscillation
modes can cancel out their results because of an antiphase vibration. This has to be taken into account and is
unavoidable with the current setup.
pull in/release.
Acknowledgements
Figure 7 shows nicely how the membrane gets
attracted and suddenly accelerates when the pull-in
voltage is reached. In contact membrane and electrode
performing a coupled oscillation and the contact area
gets bigger with increasing excitation voltage. When
Vstim is lowered again, the membrane detaches from the
electrode in a different behavior because the mechanical
restoring force is now acting. When a certain voltage
is reached, the last contact point releases from the
electrode which vanishes the adhesion force and causes
the membrane to accelerate again. The membrane
performs an overshoot over its resting position and
oscillates a few times around it. In this case a Fourier
transform of the free membrane oscillation after the
release delivers a membrane resonance frequency
of 65.4kHz under normal pressure and a coupled
resonance of 97.5kHz after the pull in event. This fits
to measurements done with other equipment under the
influence of a bias voltage.
IV – Conclusion
It has been shown on several thousand chips and dif-
The authors would like to thank Dr. Andreas Kenda
from the Carinthian Tech Research AG, Austria for
making the SLDV results available.
References
[1] Marc Fueldner. Modellierung und Herstellung
kapazitiver Mikrofone in BiCMOS-Technologie.
PhD thesis, Technical Faculty University ErlangenNuremberg, Munich, Germany, 2004.
[2] Rafael Nadal Guardia. Current Mode Drive of Electrostatic Microactuators. PhD thesis, Universitat
Politecnica de Catalunia, 2001.
[3] G. Nielson and G. Barbastathis. Dynamic pull-in of
parallel-plate and torsional electrostatic mems actuators. Journal of Microelectromechanical Systems,
15(4):811–821, 2006.