Design and Fabrication of Novel Devices Using the
Casimir Force for Non-contact Actuation
Emma L Carter, Michael Ward, Carl Anthony
School of Mechanical Engineering
University of Birmingham
Birmingham, UK
The Casimir force has been found to be the cause of stiction
1
problems in MEMS devices resulting in permanent adhesion of
close adjacent surfaces. However, it has also been proposed that
the Casimir force can be harnessed to achieve non-contact
actuation in MEMS sensors. One way of achieving this is to use
the lateral component of the Casimir force through suitably
constrained moving parts and designed surfaces. Three devices
were designed and fabricated using UV lithography and dry
etching. Device 1 is designed to demonstrate non-contact
actuation using the normal Casimir force in the wafer plane,
device 2 uses the lateral Casimir force for parallel motion noncontact actuation and device 3 uses the lateral Casimir force for
perpendicular non-contact actuation. All devices use similar
comb drives and capacitive sensors. The design of the devices,
fabrication limitations and expected qualitative results are
discussed.
I.
INTRODUCTION
The Casimir force is a manifestation of the quantum
electromagnetic field and can be understood as a retarded Van
der Waals attraction between interacting macroscopic bodies
rather than the Van der Waals interaction between constituent
atoms and molecules – the retardation being a consequence of
the finite velocity of light being significant with respect to the
increased separation [1]. In 1958, Hendrick Casimir presented
his work on the attraction between two perfectly conducting
plates with its ubiquitous equation (1) relating the force, Fc, to
the area, A, of the plates and the separation, d, between them
[2].
electrostatic charge drowning out the relatively small Casimir
force and uneven pull-down of parallel plates due to the rapid
drop off of the force with separation prompting most to resort
to a sphere and plate configuration [3, 4]. Also, to compare
these experiments with Casimir's original theory, several
modifications and approximations must be made to account
for real materials with finite conductivity [5, 6], thermal
effects [6, 7], varying slab thickness and material properties
[6, 8], sphere-plate configuration (requiring the ‘proximity
theorem’ approximation) [3, 4] and surface roughness [6]. To
experimental physicists studying the gravitational effects of
small bodies, however, the Casimir force is actually so
relatively large as to drown out the gravitational
measurements [9]. To manufacturers of MEMS1 sensors, the
Casmir force can be a primary cause of stiction resulting in
loss of function, and is therefore, again, something to be
avoided. To others, it is a force that can be manipulated by
altering surface geometry [10] or designing ‘metamaterials’
with artificial optical properties [11], which can reduce the
Casimir force (thereby mitigating the problem of stiction) or
even reverse it, creating a repulsion within a limited waveband
[12, 13]. Also, it has been proposed that the attractive normal
and lateral Casimir force can be used to achieve non-contact
actuation in MEMS and more significantly in NEMS2 devices
[14, 15]. This paper aims to begin to explore the feasibility,
design, fabrication and proposed testing of various devices
which use either normal or lateral Casimir force coupling.
II.
DESIGN, MODELING & FABRICATION
The Casimir force is noticeable at separations of less than
500 nm and significant at separations of less than 100 nm so
π =cA
(1) MEMS devices are really on the borderline of being
FC = −
influenced by the Casimir force whereas for NEMS devices,
240d 4
the Casimir force would dominate. (However, it should be
Since then it has been considered from several different noted that the Casimir force has been demonstrated at
perspectives each with their corresponding challenges: Those separations between 0.6 - 6μm [3]). The greatest challenge,
simply wishing to measure the force and study its dependence therefore, is to design and fabricate a device to produce
on material properties and geometry etc. face the problem of measurable displacements due to Casimir force coupling,
particularly the lateral Casimir force. For static displacements,
2
This work has been sponsored by the EPSRC
1
Micro Electro-Mechanical Systems
978-1-4244-5335-1/09/$26.00 ©2009 IEEE
2
229
Nano Electro-Mechanical Systems
IEEE SENSORS 2009 Conference
this would be very difficult, but with micro-scale devices a
high Q-factor3 is achievable (in this case Q = 8000) so that
when they are driven at resonance, the resulting amplification
of these very small forces and correspondingly small
displacements is sufficient to be measureable with capacitive
sensors.
In order to gauge how measurable the Casimir force is
between parallel plates but with relatively large separations, an
initial Matlab model was done for a parallel plate device
where one plate is fixed and the other is supported on springs
with a starting separation of 4μm and with plate area
dimension and spring stiffness comparable with the devices
presented in this paper (Fig. 1). The free plate is moved
electrostatically towards the fixed plate by increasing the
applied voltage, both with and without the existence of the
Casimir force (red and pink respectively). The resulting
capacitance is given on the right-hand axis, both with and
without the Casimir force (dark blue and light blue
respectively), showing a measurable change in capacitance.
The model also shows the point at which the plates latch
together. As the area of the plates is increased, the Casimir
force is larger but the plates latch together at a larger
separation.
The same comb drive system was used in all the devices
for both driving one side of the device and sensing
displacement from the opposite side. The finger width and gap
widths were 3μm. There are 264 fingers on each section (one
section can be used to drive the device and the other to
measure the displacement). The whole structure had a
resonant frequency of approximately 13kHz and the
supporting springs had a stiffness constant of approximately
20 N/m according to FEA modeling of the 20μm device layer
version. The mask layout was designed using Layout Editor
and transferred onto a chrome-on-soda lime mask by Delta
Mask using a Helium/Cadmium laser (0.8μm spot size). The
-6
-12
Lateral Casimir device
x 10
x 10
2.18
3.88
2.16
Plate displacement (m)
3.86
2.14
3.84
2.12
3.82
2.1
3.8
2.08
3.78
2.06
3.76
2.04
3.74
2.02
3.72
3.7
8.41
Capacitance (F)
3.9
8.42
8.43
8.44
8.45
8.46
8.47
Applied voltage (V)
8.48
8.49
2
8.5
Figure 1. Matlab model of Casimir attraction and capacitance between
parallel plates
3
Quality Factor
Figure 2. Device fabrication process
smallest achievable line-width for this process is 1.5μm [16].
The fabrication methodology used is bulk micromachining of
BESOI4 wafers of varying Si device layer thicknesses (10μm,
20μm and 100μm respectively) and 2um SiO2 layer (Fig. 2a).
S1813 photo-resist was applied to the wafer followed by UV
lithography with the mask in hard contact for an equivalent
exposure time of 9 seconds. It was developed in Microposit
MF-319 and then dry etched (DRIE5) to remove the parts of
the device layer exposed by the pattern (Fig. 2b). After dicing
into chips, the resist was removed using PG1165 remover at
80°C and O2 plasma clean. For the 100μm device layer wafer,
the small component dimensions (the comb fingers and
springs were only 3μm wide) resulted in an aspect ratio which
was too high for the DRIE process. However, excellent results
were achieved with the 10μm and 20μm device layer wafers.
Due to the benefit of increased plate area with thicker device
layers, future work will involve testing of a 50μm device layer
wafer. To release the moving structures, the chips were placed
in an HF solution6 for 6 minutes to etch the SiO2 (Fig. 2c). The
chips were then rinsed in water followed by IPA which was
allowed to evaporate slowly over a few days to reduce the risk
of moving parts adhering to the substrate due to capillary
action. This HF etch process is still being refined for the new
devices.
A. Parallel plate normal Casimir device
The first device presented was intended as a control device
designed to demonstrate non-contact actuation using the
normal Casimir force in the wafer plane (similar in concept to
the device presented recently by Ardito [17]). As the top part
of the device is driven at resonance, the bottom part should
start to move under Casimir attraction alone since both parts
are connected to ground. An SEM image of one of the
fabricated devices is shown in Fig. 3. Initial separations were
fabricated at 2μm, 3μm and 4μm.
B. Lateral Casimir friction device
The second device was designed to use the lateral
component of the Casimir force or Casimir friction. The
parallel plates here have corrugations so that the lateral motion
of one side with respect to the other induces a lateral Casimir
force – or Casimir friction [18]. There are 55 corrugations in
4
Bonded and Etched back Silicon On Insulator
5
Deep Reactive Ion Etch
6
Hydrofluoric acid
230
Figure 5. SEM image of Casimir friction device showing 2 parts each
supported by 4 springs with Casimir coupling between them in the middle
Figure 3. SEM image of device for demonstrating Casimir attraction
between parallel plates in the wafer plane.
TABLE I.
each device and the width of each one is 5μm, with an
adjacent gap of 4μm (Fig 4). As one part of the device is
driven electrostatically at resonance, the other part (a mirror
image) is coupled by Casimir attraction alone, causing it to
move parallel to the driven device (Fig 5). Different versions
of the new device were designed with varying fixed
separations between the two plates; 1.0μm, 1.5μm and 2.0μm.
The friction device with a 1μm gap defined by the mask was
beyond the resolution capability of the UV lithography
process and resulted in the opposing corrugations being
mostly joined together. However, on measuring the
separations of the actual fabricated devices on the SEM, it was
found that the actual gap size was significantly smaller than
that dictated by the mask – in this instance an advantageous
result of the fabrication process (Table 1). Another effect of
the DRIE process etch / passivation cycle is the scalloped side
wall as seen clearly in Fig. 4. As surface roughness has a
significant effect on the Casimir force [6], this is something
that should be addressed, either through tuning the etch /
passivation time, to create smaller scallops, or by skimming
the walls with the FIB to create a smooth surface.
FRICTION DEVICE PLATE SEPARATION
Mask
1.5 μm
2.0 μm
2.5 μm
3.0 μm
4.0 μm
Actual
0.85 μm
1.20 μm
1.90 μm
2.20 μm
3.20 μm
Also different plate depths were fabricated (defined by the
device layer thickness); 10μm, 20μm and 100μm. The lateral
Casimir force was modeled for all three device thicknesses for
both a 0.5μm and 1.0μm fixed separation. The plot for the
20μm device layer and 0.5μm separation is presented in Fig. 6,
showing the estimated lateral Casimir force between
corrugations (y-axis) as one part of the device is moved
laterally with respect to the other. An earlier version of the
friction device was dry etched without the gap which was
subsequently milled by the FIB with a 5000pA beam current
in order to achieve a closer separation (Fig. 7). Although a
much smaller plate separation can be achieved using the FIB,
it was very difficult to maintain a parallel cut at such a high
aspect ratio for the entire length of the device (500μm). For
this reason, the feasibility of minimizing this separation using
only UV lithography and DRIE etching was used in the newer
devices.
Figure 4. SEM image: DRIE etched Casimir friction device (gap of 850nm)
231
Figure 6. Model of lateral Casimir force for 20μm device layer at 0.5μm
separation [19]
Figure 7.
SEM image showing FIB milled gap measuring 400nm
C. Lateral Casmir ratchet device
The third device is also designed to harness the lateral
component of the Casimir force but using asymmetric teeth as
shown in Fig. 8. As the SEM image of the whole device shows
(Fig. 9), the two outer sections are constrained to move only
vertically and the middle section is constrained to move only
horizontally. As the two outer sections are driven in the
direction shown, the two ratchets provide lateral Casimir
coupling, causing the middle section to move in the
perpendicular direction as shown in Fig. 9. As the outer
sections are moved back again, the restoring spring force will
return the middle section in the opposite direction, causing it
to oscillate at the same frequency.
The first attempt at fabricating such a ratchet designed
with teeth 10μm across and 2μm high (Fig. 10a) resulted in a
rounded etched geometry where the top and bottom surfaces
were in phase which would have resulted in no lateral motion
(Fig. 10b). Although attempts were made to mill the desired
profile using the FIB, this proved difficult due to the high
aspect ratio, the high degree of parallelism required for both
opposing surfaces, and the long processing time. The design
was revised with ratchet teeth 20μm across and 4μm high on a
glass mask to improve resolution, resulting in well-defined
ratchet teeth with the same slope angle as before (Fig. 10c).
Since the lateral Casimir device involves driving the plates
together to induce the lateral force, the problem of fabricating
a sufficiently small initial plate separation is less important.
This device is therefore probably the most promising.
Figure 8. Mask showing asymmetric teeth of ratchet device and resulting
perpendicular motion of plates
Figure 9. SEM image of Lateral Casimir ratchet device
Figure 10. Progression of ratchet tooth design and fabrication
232
III.
[3]
CONCLUSIONS AND FURTHER WORK
This work has presented a couple of ideas for microdevices which use the lateral Casimir force for non-contact
actuation. It also highlights some of the limitations of making
devices which use the Casimir force with tradition MEMS
fabrication technology and indeed the difficulty of producing a
measurable Casimir force in the larger sub-micron regime.
The main conclusion of the modeling is that larger plate areas
and smaller separations are required for measurable lateral
Casimir forces. Tests of the devices are still ongoing and will
hopefully give more data on the size of both the normal and
lateral Casimir force in real devices, particularly with regard
to the influence of DRIE scalloped surfaces compared with
smoother FIB-milled surfaces. A new design for the Casimir
friction device is underway which enables reduction of the
plate separation electrostatically after the device has been
fabricated. This will enable a much smaller plate separation to
be achieved which, according to the simulations, should result
in a measurable lateral Casimir force. This would also allow a
range of plate separations to be tested using the same device.
As devices get smaller and smaller, particularly those
developed for biomedical applications, the Casimir force will
become more significant and exploiting it for non-contact
actuation within these devices will become an increasingly
feasible and attractive option.
ACKNOWLEDGMENT
E. L. C. thanks Arash Azari and Ramin Golestanian for the
lateral Casimir force estimations.
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