A sensitive electronic capacitance measurement system to measure comb

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					A sensitive electronic capacitance measurement system to measure comb drive
motion of surface micromachined MEMS devices

W. Merlijn van Spengen1,2 and Tjerk H. Oosterkamp1
  Leiden University, Kamerlingh Onnes Laboratory, P. O. Box 9504, 2300RA Leiden,
The Netherlands
  Also with Falco Systems, Gelderlandplein 75L, 1082LV Amsterdam, The Netherlands

Email principal author: spengen@physics.leidenuniv.nl

Keywords: MEMS, capacitance measurement, comb drive, stiction
We have developed a method to measure the displacement of a MEMS comb drive using
a probe station, by monitoring the minute capacitance changes between the fingers due to
the motion. Probe station measurements of the capacitance changes of small comb drives
are usually hampered by the relatively large parasitic capacitances present. This can be
reduced by using a proper measurement layout design for minimal on-chip capacitance,
in combination with a resonant LCR-circuit to counteract the effect of the probe station
cable capacitance. The method results in a measurement that, after averaging, enables us
to see the motion of a MEMS comb drive with 4nm peak-to-peak noise sensitivity,
corresponding to a capacitance change around 10aF. Both the effect of comb drive lateral
motion and that of levitation are observed.

With the increasing use of MEMS (Micro-ElectroMechanical System) devices, the need
to monitor the position of a moving MEMS component with high sensitivity is becoming
more and more important. Not only in sensor applications, where the position of a
moving part may be the variable to measure a certain physical property (like in
acceleration sensors), but also in precise positioning systems.
One way to readout the position of a moving part of a MEMS device is by optical
methods. For out-of-plane motions, interferometric techniques [1] and laser Doppler
vibrometry can be employed. Doppler vibrometers [2] are usually employed at relatively
high speeds but are not well-suited for semi-static measurements. Interferometric
techniques are usually low-frequency, but can be used in a configuration with a
stroboscope [3] or a laser TV-holography system [4] for high-speed imaging. The
sensitivity of these methods can be in the sub-nm range, but they are limited to out-of-
plane motions and require rather bulky setups and shiny surfaces. Optical measurements
of in-plane movements are much more restricted. Systems that use a curve fitting
algorithm to obtain detail below the optical resolution limit [1] can be used but are
generally slow and not always easy to apply.
The SEM (scanning electron microscope) can be used to accurately monitor the position
of moving MEMS, but the image can be distorted by the high actuation voltages required
in electrostatic MEMS, and the induced charge can even cause parts to get stuck. In
addition, the MEMS has to be electrically operated in a vacuum environment which is not
necessarily the same as the environment in which the MEMS device is eventually going
to be used in a real-life application. Depending on the application this can be vacuum, a
well-defined under-pressure, normal or dry air, or even a specially selected gas
On the level of individually packaged MEMS chips, electronic readout is a common way
to monitor the position. MEMS acceleration measurement systems and MEMS
gyroscopes depend for their functionality to a large extent on the possibility to readout
capacitance changes on-chip with high sensitivity. The designs of these devices are
usually made such that the capacitance change is as large as possible and the parasitic
capacitances are small. The readout electronics is integrated on a separate chip and wire-
bonded right next to the MEMS die in the same package, or even integrated on the same
chip, as is the case with the Analog Devices accelerometer range of devices. The way to
measure the capacitance is to send a relatively high-frequency signal through the
capacitor to be measured and monitoring the impedance. Several chips have been
optimized for this purpose [5 - 7].
In a laboratory situation, this type of detection is generally not employed, although its use
without dedicated chips has been reported on larger scale devices [8, 9]. A probe station
is typically used in a laboratory environment for electrical contact with the MEMS device
under test, and the connecting coaxial cables easily add 100pF/m of parasitic capacitance
to the measurement setup. To make matters worse, the coaxial cable capacitance is never
truly constant and changes with the temperature of the room and with mechanical
vibrations (sound in the measurement room, coupled either directly by air to the cable or
via the optical table on which the setup is positioned). This is the reason why the accurate
electronic readout of the position of laterally moving MEMS is virtually never reported in
the scientific literature when discussing laboratory experiments with a probe station. To
alleviate these problems, we have developed a very sensitive method to monitor small
capacitance changes in MEMS in the presence of large non-constant parasitic
capacitances, which is discussed in this paper. We show that with this technique it is
possible to measure the position of a moving MEMS device with 4nm peak-to-peak noise
The setup is very easy to use once it has been set up. Performing a single experiment is
comparable in complexity to measuring transistor performance parameters with a curve
tracer. Because the setup has a large bandwidth (currently 1kHz but this can be tailored to
the requirements of the device), high speed motion changes can be observed, contrary to
the approaches in [8] and [9]. The technique can be beneficial to the understanding of
parasitic and non-linear motions in prototype MEMS devices, and makes changing from
one device to the next in a testing environment very easy compared to wire-bonding each
device independently to an appropriate interface semiconductor chip. In principle, the
setup could be extended to a fully automated system for measuring capacitance change
versus actuation voltage curves on wafer level of many devices one after the other, but
this has not been implemented.

Cantilever motion
In the following, we discuss why the capacitive readout of the lateral position of surface
machined MEMS is such a challenge. The position, voltage and force in typical MEMS
comb drive are related by the following equations [10] when edge effects are neglected
(Fig. 1).

                                                                Fx =        V2
                       l                                                g

             g                                                  Ftotal = nFx
                                                                Ftotal = k xδ x
                   Top view
                                                                       ε tn
                                                               δx =           V2
                                                                 kx g
Figure 1. Typical comb drive actuator with the important geometric variables indicated.
ε = permittivity of free space
V = applied actuation voltage
n = number of comb fingers
t = thickness of combs
Fx = electrostatic force in the x-direction
δx = displacement of the comb drive in the x-direction
kx = spring constant of supporting beam in x-direction

The capacitance of the comb drive can be calculated by assuming a parallel-plate type of
geometry, for which the following equation can be derived,

                                           C=          ,                                 Eq. 1

in which the factor 2 is coming from the fact that both sides of a comb finger form a
capacitor with the opposite finger next to them. When we calculate typical values
encountered in surface micromachined MEMS, we find that typical values are between 1
– 100fF for “real life” comb drive capacitances. The maximum change in this small
capacitance due to comb drive motion is even 1.5 – 4 times smaller. This means that to
monitor the position of a moving MEMS part with a comb drive by the capacitance
change in the comb drive with a few nanometer sensitivity, it is required to measure
changes well into the low atto-Farad range (1aF = 10-18F). With 1m of coaxial cable
connected in parallel, representing 100pF, this means that we have to measure the already
small capacitance of 100pF with an accuracy of 1 part out of 107 to obtain 10aF
resolution. This is generally not possible since the coaxial cable itself is not stable to such
a degree, so a different solution has to be found.
In addition to the coaxial cable, other parasitic capacitances may be present on the chip.
Large conductive areas like bonding pads and signal lines can constitute a significant
capacitance via the substrate path (Fig. 2).

                             Comb drive capacitors

                                                                     Structural layer

                                                                     Insulating layer


                  Large capacitors to the (grounded) substrate

        Figure 2. The substrate forms a large capacitor with all conductive parts.
Comb drive levitation
Comb drives do not only move laterally, but generally also exhibit a significant out-of-
plane motion, contrary to what one would expect from Fig. 1 [11]. This happens because
the electric field forcing a comb drive to move is not symmetrical (Fig. 3). However, the
levitation stops at a certain height when an equilibrium is found, which, if the x- and z-
axis spring constants are more or less equal, happens already at relatively low actuation
voltages [11]. At higher actuation voltages, mostly the lateral deflection will change the

             Stationary                                             Stationary
                           Vact            GND              Vact
                  finger                                            finger


                                           GND (ground)

Figure 3. Cross-section of a comb drive. The field lines coming from the top cannot be
counteracted by the field lines from below, because they are screened by the lower layer

Measuring small capacitance changes in the presence of large parasitic capacitors
In the following section, we will show using a real device how the detrimental effects of
the parasitic capacitances on a low-level capacitance measurement can be minimized.
This demonstrator device is called the “nano-battering ram” and used to measure sidewall
surface forces [12]. It was made in the MUMPS process (multi-user MEMS process) by
The device is schematically depicted in Fig. 4 and a SEM (scanning electron microscope)
image is given in Fig. 5. It consists of a central beam with a set of actuation comb drives
and a set of measurement comb drives. The actuation combs are used to move the beam
forward until the head of the beam touches the counter-surface by applying an actuation
voltage on Vact. The capacitance change in the measurement combs is used to track the
position of the beam as a function of the actuation using contact pad Vret. The “nano-
battering ram” can move forward by exactly 2.0µm before it touches the counter-surface.
The difference between the actuation voltage required to make contact with the counter-
surface, and the (lower) actuation voltage at which the head snaps back is used for
determining the adhesion of the head to the counter-surface (see results section).

The electrical equivalent schematic of the device, as measured with a conventional
capacitance-meter, contains 7 capacitors (Fig. 6) in addition to the cable capacitances.
         Counter-surface                      Gap



                                    Support         Spring

Figure 4. Schematic top view of the test vehicle: the nano-battering ram.


            Figure 5. SEM-image of the nano-battering ram
Figure 6. Equivalent schematic of the capacitors present in the nano-battering ram (Vact
= actuation voltage, Vgnd = low frequency ground, Vret = measurement voltage (Vret is
 for “retract”, this comb can also be used to retract the ram if the restoring spring force
  would be lower than the stiction force between the head of the ram and the counter-
                     surface), Vsub = substrate (backside) connection)

The parasitic capacitances, both on chip, and those represented by the cables (another
170pF from all 4 contact points to Vsub), are so large that a sensitive measurement at
first sight might seem to be impossible. However, by a careful planning of the
experiment, it can be done.
We use a HF measurement signal that is so high in frequency that the varying impedance
of the small capacitance to be measured can cause a significant change in the amplitude.
At the same time, it is also so low that we can use normal probe setups without having to
resort to delicate and expensive RF equipment, probes and on-chip co-planar waveguide
(CPW) layouts. The test signal we use has a frequency of 10.7MHz, and 3V peak-peak

          Figure 7. Measurement circuit to compensate the parasitic capacitors

The technique which we propose to minimize the parasitic effects (Fig. 7) involves the
following steps:
    1. Identify the comb drive (variable) capacitors of which the values are a measure
       for the displacement (in this case C5 and C7). In the case of the nano-ram,
       because it has four measurements combs, Eq. 1 has to be multiplied by 4,
       resulting in a calculated equilibrium capacitance of 16fF, which changes to 11fF
     when the ram head touches its counter-surface. The total change is 5fF, a small
     value indeed!
2.   Make sure that the actuation scheme is such that there is no actuation voltage over
     one of these capacitors (if we apply an actuation voltage on Vact, C5 will have the
     full actuation voltage over it, while C7 has more or less the same voltage on both
     sides). If this is not possible, like for example in capacitive RF MEMS shunt
     switches, a different, less sensitive method has to be used, detailed features of
     which can be found in [13] and [14].
3.   Indicate the parasitic capacitance that is directly over the capacitor to be
     measured, in this case only C6, being 2pF. All the other capacitors are at least in
     series with another capacitor before they contribute to the parasitic capacitance
     over C7
4.   Choose the high-frequency (HF) ground such, that the parasitic capacitance to the
     ground from one side of the comb drive capacitor to be measured is as small as
     possible. In this case, it is done by making the Vsub the HF ground. On one side,
     C7 sees C3 to ground, which is only 19pF, and on the other side C2, which is
5.   Apply the HF measurement frequency directly on the side that has the highest
     capacitance to ground (here Vsub). In that way the HF voltage on the Vgnd node
     is fixed, even if some displacement currents through the large parasitic capacitors
     would change its impedance to the HF ground Vsub.
6.   The measurement electrode is the other side of C7. However, if we monitor the
     HF signal strength there, it will be very low, because most of it will leak away
     through C3 and the capacitance of the connected probe with its coaxial cable. This
     results in a very poor signal to noise ratio in the amplifier/detector that has to
     monitor the amplitude of the HF signal as a function of the position of the MEMS
7.   To prevent this, C12 and the coaxial cable capacitance are used as the capacitor
     in a parallel LC resonance circuit with damping resistor P1, adjusted to the
     frequency of the HF measurement signal (Fig. 7). This increases the signal
     strength, while at the same time reducing the influence of variations in C3 and the
     probe cable, because the top of an LC resonance circuit amplitude is flat. To
     obtain maximum sensitivity, P1 should be adjusted such that the LCR circuit at
     resonance has the same impedance as the impedance of C6 and C7 together (Fig.
8.   The HF signal, that is amplitude modulated by the changes in the position of the
     MEMS device, is finally sent to a low-noise amplitude modulation (AM) detector.
9.   Please Note: If the signal-to-noise ratio is too low for the application, averaging
     can be used to obtain an even clearer measurement, as usual. Be careful, however,
     to avoid ground loops, as this setup is extremely sensitive to them. We found that
     it was necessary to place the whole probe station including most of the
     measurement electronics in a vibration and sound isolated Faraday cage.
 Figure 8. To obtain the largest signal variations, the voltage divider consisting of the
capacitance to be measured (Z1) and the impedance of the AM-detector input (Z2) with
 the LCR-circuit should have a ratio of 1:1. If Z2 is much lower than Z1, Vout will be
close to 0V, no matter what the variations in Z1 are. If Z2 is much higher than Z1, Vout
will be close to Vin, even if the variations in Z2 are relatively large. Both result in a poor
                      signal to noise ratio at the AM-detector output.

The results of this approach are given in Fig. 9. After 10,000x averaging, with a
bandwidth of 1kHz, we see the capacitance change of the nano-battering ram introduced
in Fig. 4, with high resolution (the whole scale is about 5 fF). When the ram is actuated,
the force would be expected to increase with the square of the actuation voltage if the
out-of-plane motion of the combs would not play a role. Because the restoring springs are
linear, this would results in a quadratic dependence of the position on the actuation
voltage as given in Fig. 1.
The decrease of the curve at the beginning is due to the capacitance changes
corresponding to the influence of the out of plane force. Because we measure the comb
drive capacitance of the measurement combs as indicated in Fig. 4, their capacitance goes
down with the lateral displacement. The fact that the levitation counteracts this, instead of
aggravating the effect, is caused by the following. The comb drive moves up with the
actuation, until it reaches its equilibrium height, where it “feels” as many field lines as
possible. This is the situation of the highest capacitance between the two parts of the
comb, although the direct overlap of the fingers is somewhat smaller. Hence the
levitation movement is showing up as a “capacitance increase”, even though intuitively
one would expect a capacitance decrease if we do not take into account fringe fields. The
accuracy of the vertical scale added to Fig. 9 is difficult to judge due to the influence of
the levitation on the low voltage end of the curve.
When the battering ram hits the counter-surface, it cannot move any further. This
immediately gives a rough (!) calibration opportunity, as the geometry of the device is
well-known from the MEMS design or subsequent SEM investigation. In our case, the
gap that is closed is 2.0µm, so that a rough scale in µm can be linked to the arbitrary units
of the capacitance measurement in Fig. 9, without even knowing the exact value of the
capacitance changes. To do this, a parabola is fitted through the data according to the
theory of Fig. 1 and Eq. 1. However, the scale is only correct for the upper part of the
curve, where the levitation effect is negligible.
                Fitted “deflection” (
                                    (µm)                         Measured capacitance change (a.u.)
         only true for upper part of the curve                             Full scale ±5fF

                       2.0               Effect of adhesion to
                                         the counter -surface                        4



                       0.5                                                           1
                                                              Fitted parabola
                       0.0                                                           0
                             0      10       20      30      40        50       60

                                            Actuation voltage (V)

Figure 9. Measurement of the capacitance change of the ram. The measured curve has no
     parabolic shape because of the vertical levitation effect. The fitted curve of the
 “displacement” is the “quick and dirty” approach to the capacitance change that would
   have been the result of only the lateral motion of the ram. The parabolic fit has been
 made using the upper part of the parabolic part of the graph only, because the effect of
                            the levitation is the smallest there.

A comprehensive discussion of the exact shape of the capacitance versus actuation
voltage curve and the effect of levitation, both the theory and experiments, is currently in
press elsewhere [15]. The analysis presented in [15] shows that the horizontal and the
vertical motion and their combined effects on the capacitance change can be very
accurately separated using the measured capacitance data. The result the analysis is that
the lateral position of the device can be extracted with high accuracy as shown in Figure
                   Position (µm)

                                 True parabola
                                 Retract                              200nm

                                Effect of low drive voltage
                               mostly visible at low actuation
                                 voltage (most levitation)                  Effect
                     1.0                                                  of adhesion


                           0       10        20        30        40           50    60
                                            Actuation voltage (V)

Figure 10. Calibrated lateral position as a function of the actuation voltage by using the corrected
measured capacitance data using the method of [15]. In addition, a true parabola is shown, which
 would be the theoretical motion if there were no levitation. The parabola starts 30nm below the
 0µm position, because the comb drive does not experience the full driving force of the actuation
                    voltage when it is not yet fully levitated (details in [15]).

The method employed here is sufficiently sensitive to clearly see the effect of adhesion
forces. When the voltage is reduced with the ram in contact (retract), the ram will remain
stuck due to surface forces when the voltage is lowered to the point where it first touched
in the approach movement. The difference in voltage (or position) between contact and
release is a measure for the magnitude of the surface forces. We calculated from the
geometry of this particular battering ram that the restoring springs are around 1N/m, so
that the 200nm jump that is observed corresponds to 200nN of force between the
sidewalls, with a sensitivity (caused by electronic noise and interference) of 4nm (peak-
to-peak noise) equivalent to 5nN of force on the contact area. If we assume that the comb
drives have the 5fF capacitance change calculated earlier, the system has a capacitance
resolution of 10aF (95% confidence interval) in this measurement. Environmental
conditions were 45% RH and 24°C.

The procedure has been successfully used with a number of measurements on the “nano-
battering ram” design discussed earlier, and on another design, a two-dimensional device
intended for friction measurements that we will report on later. A short preliminary
discussion of this device can be found in [12]. The order of magnitude of the parasitic
capacitances for this device is roughly the same as for the “nano-battering ram” case
discussed here. De measurements are fully repeatable within the electronic noise limits
set by the current instrumentation.
The method can be used to a great extent for other devices, but there are two limitations.
In the first place, the method only works for devices where there is no actuation voltage
over the measurement combs. If this cannot be avoided, one has to provide means to add
the actuation and the measurement signal together which can easily spoil the sensitivity
of the system as described here. In the second place, the system can only be used
quantitatively when all parasitic capacitances are large compared to the measured signal.
Otherwise the small-signal approximation is lost, and the parasitic capacitance will have
to be taken into account during the measurement for quantifying the capacitance change.
As stated in the introduction, there are two papers in which techniques with a similar
measurement objective have been discussed. Lai et al. [8] have presented a bulkier device
with a 50x larger capacitance change, made by laser machining. They used a sensitive
commercial Agilent model 4288A capacitance meter to monitor the capacitance changes.
According to the manufacturer’s specifications, the resolution of this meter is around 1fF,
and Lai et al. [8] do not state the measurement accuracy for their setup. Direct
comparison of the measurements is therefore difficult, but they do not come close to the
10aF resolution obtained by our method.
Kuijpers et al. [9] have used a different technique with a charge amplifier and
synchronous detection. They obtained a capacitance measurement with a noise level of
which the standard deviation was 417aF after averaging 10 times. The method discussed
here has a 10aF resolution with a 95% confidence interval corresponding to a standard
deviation of 5aF if a Gaussian noise is assumed. With 10,000 averages compared to 10,
our approach is a factor 8 better than in [9] if we correct for the number of averages.
However, to obtain a resolution similar to [9] only takes a few seconds in our setup, while
the measurement lasted for over 6 hours in the measurement discussed in [9].

We have designed a measurement setup to very accurately monitor the capacitance
changes in a MEMS comb drive structure and deduct from them the position of the
moving part of the comb drive with high resolution in a laboratory setting with a probe
station. Although it is very well possible to measure small capacitance changes on chip,
as is done in monolithically integrated acceleration sensors, it is much more difficult to
do this on a probe station, where the coaxial cables add a large amount of parasitic
capacitance to the measurement setup.
To measure small capacitance changes in this case, an extensive equivalent schematic of
the device is required, from which all parasitic capacitances can be observed. By
carefully choosing the injection and detection points of a high frequency measurement
signal, it is possible to measure the capacitance changes by monitoring the amplitude
modulation of the high-frequency signal. . In this way, it is possible to electronically
obtain a capacitance resolution of at least 10aF (10-17F) and a position resolution of 4nm
in the position of laterally moving MEMS devices. However, at low actuation voltages,
the capacitance cannot be directly linked to the lateral motion due to the out of plane
motion of the comb drive influencing the capacitance change. To do this a model is
required that separates the effect of the lateral and vertical motion of the comb drive and
their influence on the capacitance change, which is given in [15].

This work is financially supported by the Dutch NWO-STW foundation in the “Veni”
program under ref no. LMF.7302.
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Description: A sensitive electronic capacitance measurement system to measure comb