CONTROLLING THE ADHESION FORCE FOR ELECTROSTATIC ACTUATION OF

MICROSCALE MERCURY DROP BY PHYSICAL SURFACE MODIFICATION

WENJIANG SHEN, JOONWON KIM, and CHANG-JIN “CJ” KIM

Mechanical and Aerospace Engineering Department

University of California at Los Angeles, Los Angeles, CA 90095, USA

mercury and electrode pad is not compromised. Second,

ABSTRACT thanks to the high surface tension and non-wetting nature of
mercury, the surface modification can be made with even
Under electrostatic actuation, mercury droplet can act as a usual lithographic micromachining.
contact and moving part in a microswitch system. In order
to reduce the actuation voltage while keeping the electrical We have demonstrated various droplet-based microswitches
advantages of liquid-solid contact, the contact properties of in the past [5-8]. In microscale, the strong adhesion of
mercury droplet on structured surfaces are investigated in droplets provides the stability against disturbances and
this paper. Forces to actuate a mercury droplet on different makes the switch naturally bistable. However, relatively
structured surfaces are theoretically analyzed and large forces are needed to actuate the droplets against
experimentally tested. Both results confirm our claim that adhesion. Since adhesion keeps mercury droplets in place
the adhesion forces of liquid metal droplets on a solid even at tens of thousands of G’s in microscale, reducing the
surface can be designed by physical modification of the adhesion is acceptable and perhaps the only way to reduce
surface. The criteria for detaching a mercury droplet from the driving voltage. This paper will present a set of
solid surface was predicted and verified by experimental experimental and theoretical results of controlling adhesion
results. force by physical surface modification.

INTRODUCTION
SAMPLE PREPARATION
This paper reports that adhesion forces of liquid droplets on
solid surfaces can be designed by physical surface We employed simple line patterns for surface modification,
modification (as opposed to chemical treatment). For solid- made by DRIE, to keep the analysis manageable. A series of
to-solid contact, it is well known that the effective adhesion line patterns, shown in Fig. 1(a), are made with contact ratio
force is reduced on rough surface. We expect a similar (i.e., line width per pitch, which is B/A) ranging from 0.3 to
condition for liquid metals on a solid surface. Our approach 0.7, while keeping the pitch at 10 µm. After DRIE, a 2000Å
to design this adhesion force is to control the contact surface thin Cr/Ni layer is deposited on this line-patterned surface to
area between droplet and a solid surface by micromachining ensure good electric conductivity during testing.
the solid surface. A B

We first develop theoretical understanding of the

phenomena through mechanical analysis and contact angle
measurements on simple structured surfaces. The
knowledge is then applied to two different modes of
(a) A: Pitch (kept at 10 µm), B: Line width
electrostatic actuation of a mercury droplet – sliding on and
detaching from the surface.

Mercury microswitching, where a mercury droplet acts as

the moving and contact part, is an excellent candidate to
benefit from this surface modification. The liquid-to-solid
electrical contact brings significant advantages over (b)
conventional MEMS switch [1-4] with solid-to-solid Silicon Cr/Ni SiO2
contact, such as lower contact resistance, and lower contact
surfaces degradation. There are two main reasons to use this Fig. 1 Testing samples (a) Surface-patterned wafer (b)
kind of surface modification in mercury microswitching Actuation wafer
system. First, chemical modification of electrode surface
needs to be avoided so that the contact resistance between

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 Another wafer needed to conduct testing is the actuation Fs = γL cos(π − θ adv ) − γL cos(π − θ rec ) (1)
wafer, where the high voltage is applied to attract the where γ: the mercury/air surface tension
mercury placed on the line-patterned wafer. A thermal oxide L: the effective contact length between mercury
layer is grown on silicon wafer. A layer of Cr/Ni (2000 Å) is droplet and solid surface, which can be expressed as
then deposited on top of this silicon dioxide. Final oxide π
layer is deposited on the nickel surface by PECVD to L = η ⋅ 2 R cos(θ − ) , η : contact ratio
2
prevent electrical shorting in case the liquid metal droplet θadv and θrec: advancing and receding contact angle
touches both actuation wafer and surface wafer. Finally, part The contact angle hysteresis is small enough for us to
of PECVD oxide is removed by HF to make opening for reasonably assume that
electrical contact, as shown in Fig. 1(b). 1 1
θ adv = θ + ∆θ ; θ rec = θ − ∆θ
2 2
FORCE ANALYSIS So the force in Eqn. 1 can be expressed as
1
By using a high performance goniometer (First Ten Fs = γη ⋅ 4 R sin 2 θ sin( ∆θ ) (2)
Angstrom FTA4000), apparent contact angles of mercury 2
droplet on controlled sample surfaces can be measured. As where θ is contact angle of mercury, which is related to
contact ratio B/A decreases, we confirm that apparent contact ratio η, and ∆θ is contact angle hysteresis.
contact angle of mercury droplet increases (Fig. 2), and the For a droplet detaching, a driving electrode is placed
apparent contact area of droplet decreases (Fig. 3), parallel above the droplet to pull and detach it from a solid
suggesting us that the adhesion force will decrease. surface (Fig 5), the actuation force needs to overcome the
surface tension. This force can be expressed as
Fd = γη ⋅ 2πR sin 2 θ
160

158
(3)
156

154
Contact Angle

152
FF
d
150

148
R R
146
θ θ
144

142 γ γ

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Contact Ratio
(a) (b)

Fig. 2 Contact angles of mercury droplet on different Fig. 5 Detaching a droplet from a solid surface (a) cross-
surfaces section view (b) contact area
By comparing these forces, we can see that the force to slide
a droplet on a surface is smaller than the force to detach a
droplet from a surface by a factor of 2 sin( 1 ∆θ ) .
π 2
Non-pattern 0.7 contact ratio 0.3 contact ratio Combing with the contact angle data on surfaces with
different contact ratio, shown in Fig. 2, we can get relative
Fig. 3 Apparent contact area of mercury droplet on different force on surfaces with different contact ratio from Eqn. (2)
surfaces and Eqn. (3). Fig. 6 predicts the force on microstructured
For sliding, a drive electrode is placed laterally near the surfaces relative to the actuation force on flat surface (η=1)
droplet and pulls it parallel to the surface. The actuation 1.0

force needs to overcome the resistant force due to the

hysteresis of contact angle, shown in Fig. 4 0.8
Relative Force

0.6

Fs
F
0.4

R R
0.2
θ adv θrec

γ γ 0.0
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

(a) (b) Contact Ratio

Fig. 6 Predicted trend of the adhesion force on various
Fig. 4 Sliding a droplet on a solid surface (a) cross-section
contact surfaces relative to the one on flat surface
view (b) contact area

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 ACTUATION EXPERIMENTS AND
RESULTS
During sliding testing, a CCD and microscopy system is
used to monitor and record the behavior of liquid metal
droplet under experiment. Table 1 is the testing result of (a) (b) (c)
sliding a droplet of 550 µm on microstructured surfaces with Fig. 8: Detaching experiment. (a) Electric breakdown,
the initial gap between the mercury surface and driving (b) Bridging, and (c) Detaching during detach testing
electrode as 20 µm.
Table 1 Actuation voltage to slide a droplet on CRITERIA FOR DETACHING
microstructured surfaces
Contact Driving Relative Relative Because our system is in microscale, we can estimate the
ratio voltage (V) driving force breakdown voltages for each gap by Paschen curve. At the
voltage same time, our testing conditions such as air pressure,
0.3 42 0.37 0.14 humidity, temperature, etc, will make the breakdown curve
deviate from Paschen curve. The actual breakdown curve is
0.4 49 0.43 0.18 obtained experimentally and included in Fig. 9. To
0.5 62 0.54 0.29 successfully detach a droplet from solid surface, the critical
0.6 70 0.61 0.37 voltage cannot be larger than the breakdown voltage.
0.7 77 0.67 0.45
1 115 1 1 The droplet under electrostatic actuation will deform before
it is moved. For the sliding case, this deformation effect
leads to the contact angle hysteresis (∆θ ~ 5o). Considering
Because electrostatic force is proportional to the voltage
the contact angle θ is 142o and contact angle hysteresis is 5o,
square, we can get the relative force on each surface. If we
we can convert this contact angle hysteresis to the droplet’s
plot these data into the theoretic curve in Fig. 6, we can see
that the data follows the theoretic curve very well, as shown deformation as: ∆l = 0.035 ⋅ R , where R is the radius of the
in Fig 7. The adhesion force on patterned surface with 0.3 droplet.
contact ratio is only about 10% of that on flat (i.e., non-
patterned) surface, confirming our claim that adhesion of For the detaching case, the droplet deformation may cause
surface can be designed by lithography. the bridge effect. Based on Eqn. (2) and Eqn. (3), the force
to detach a droplet is about 35 times larger than the force to
1.0
slide a droplet on the same surface, so we can reasonably
0.9
Experimental Data assume that the deformation for detaching case is 35 times
0.8

0.7 Theoretical curve larger than that of the sliding case. We can estimate the
maximal droplet sizes allowed for detaching on a given
Relative Force

0.6

0.5
surface with different actuation gaps. Table 2 shows the
0.4
analysis results for detach on a microstructure surface with
0.3 0.3 contact ratio.
0.2
Table 2: Critical droplet size for each actuation gap
0.1

0.0
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Actuation Gap (µm) 10 20 30 40
Contact Ratio Critical Radius (µm) 60 120 180 240
Fig. 7 Sliding test results fit with predicted curve
For the case of sliding a droplet on a flat surface with a
For detaching, a drive electrode is placed horizontally above given actuation gap, the driving voltage was found to
the droplet and pulls it up. The resistance against detaching decrease with the increase of droplet size [8]. We can expect
is expected higher than that of against sliding, as the the same trend of driving voltage for the case of detaching.
detachment process requires creating new free surfaces [9]. So each maximum droplet size in the Table 2 for a given gap
As a higher voltage is applied, electric breakdown may represents the minimum voltage needed to avoid bridging
occur (Fig. 8a). Furthermore, the droplet may deform effect. Based on these analytical data, we can plot the
enough to contact both electrodes under electrostatic bridging line in Fig. 9. The criteria in Fig. 9 clearly indicate
actuation (Fig. 8b). These two adverse effects must be that detachment can occur only between these two lines.
considered to find out the criteria for detaching mercury
droplet.

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 good understanding in designing a mercury microswitching
550 Droplet size 350 µm system with lower driving voltage. In order to decrease
Droplet size 480 µm driving voltage, the microstructured patterns can be made on
500
Breakdown curve solid surface of switch cells to reasonably reduce the
450 adhesion without losing the advantage of liquid contact such
Voltage (V)

400
as bistable operation, low contact resistance.
Bridging curve
350

300
ACKNOWLEDGEMENT
250 This work has been supported by the National Science
200
Foundation (NSF) CAREER Award ECS-9702875, NSF
20 25 30 35 40 45 50 Engineering Microsystems: XYZ on a chip” Program CMS-
Initial gap (µm) 99-80874, and NASA research grant NAG5-10397. Thanks
Fig. 9 Criteria for detaching a droplet (breakdown curve to R. Timothy Edwards of the Johns Hopkins University
and bridging curve) on a surface with 0.3 contact ratio and Applied Physics Laboratory for his advice and helpful
experimental data suggestions.

To verify these detaching criteria, the goniometer (First Ten

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