Fabrication of three-dimensional microstructures using capillary forces

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Fabrication of three-dimensional microstructures using capillary forces Paper ID : 105 (Page 1 / 4)

Main topic : Microfluidics

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FABRICATION OF THREE-DIMENSIONAL

MICROSTRUCTURES USING CAPILLARY FORCES

J.W. van Honschoten

1

, J.W. Berenschot

1

, R.G.P. Sanders

1

, L. Abelmann

1

, N.R. Tas

1

,

M. Elwenspoek

1, 2

1

MESA+ Research Institute, University of Twente, the Netherlands

2

Freiburg Institute of Advanced Studies (FRIAS), University of Freiburg,

79104 Freiburg, Albertstr. 19, Germany

---Abstract

In this paper we describe the fabrication of three-dimensional microstructures by means of capillary forces. Using an origami-like technique, planar structures are folded to produce 3D-objects. To this purpose use is made of capillary interactions and surface tension forces. Capillarity is a particularly effective mechanism since it becomes dominant at small scales (where surface tension forces dominate over bulk forces), the process benefits therefore from miniaturization. Planar microstructures of silicon nitride of various geometries with lateral dimensions of about 100 µµµµm and thickness 1 µµµµm and thin hinges for rotation, have been fabricated. Preliminary experiments in which liquid drops are deposited on these structures show that mechanical bending forces can be overcome and that folding out-of-plane can be realized. Capillary folding is therefore shown to be a very promising technique to fabricate 3D micro- and nanostructures.

Keywords : Threedimensional microstructures,

capillarity, surface tension, origami

I- Introduction

Microfabrication in 3D is difficult using the inherently planar techniques associated with projection photolithography1,2. The most commonly used method for the fabrication of 3D-structures is stereolithography3,4, employing serial writing of patterns in layers in photosensitive polymers. Other strategies include micromilling using microtool sets5,6 and shell plating onto die-cast mandrills7. Elaborate systems exist8 to project planar patterns for photolithography onto spherical substrates. Although these methods provide access to complex structures, they are complicated and limited in the connectivities of the structures they generate.

The strategy of folding, however, is a promising approach to fabricate non-planar structures, it reduces for instance the size of deployable structures in space industry9, as well as in nature10 (plant leaves fold in a bud).

Capillary interactions and surface tension forces seem to be the perfect candidate for this objective, since they scale favorably to miniaturization: at small scales capillary forces (that scale as dimension2) become dominant over bulk forces (scaling as dimension3). Besides, they can well be tailored by varying the interfacial free energy of liquid-liquid or solid-liquid interfaces. Examples of elastocapillary forces in every-day life are abundant: when a paintbrush is dipped into a pot of paint and withdrawn, surface tension forces cause the individual hairs in the brush to coalesce; the wet fur of a dog coming out of a pool assembles into bunches11,12. From practical point of view, the deformation of flexible structures due to surface tension can have severe consequences in micro- and nanoscale fabrication13-15, in the formation of complex structures like nanotube‘carpets’16-17 and plays a dominant role in lung airway closure (respiratory distress syndrome). Capillary attraction is also employed usefully by for example the tarsi of insects18and in biomimetic adhesives19.

It was demonstrated recently20 that capillary interactions can induce the spontaneous wrapping of a droplet by an elastic sheet: ‘capillary origami’. Also, a similar folding technique using molten solder was demonstrated for millimeter sized structures21. However, until now capillarity has not been used to create really 3D-shapes on (sub) micronscale. The microfabrication technique we present here involves the rotation of elements of a planar SiN structure out of that plane through the elastocapillary forces of a liquid deposited onto it and its eventual evaporation. Since many objects can be created from one wafer in parallel, eventually mass production may become possible as well.

II- Theory

When a liquid droplet is deposited on a flexible structure, the surface tension of the liquid tends to reduce the liquid-air interface resulting in a force on the structure and inducing a deformation. The total energy of the system is the sum of the mechanical bending energy of the stiff structure and the surface energy of

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--- the liquid-air interface. The mechanical deformations

reduce the liquid-air area A and thus the surface energy

γA (γ being the surface tension) at the cost of increasing the elastic energy. For a plate of thickness t, length l0 and radius of curvature R (which is an appropriate description of the thin hinge shown in Fig. 1a), the isometric bending energy density is defined locally as 2B/R2, where B = Et3/12(1-ν2) is the bending stiffness (E is the Young’s modulus, ν the Poisson’s ratio)22. We adopt a two-dimensional analysis, of which a schematic view is given in Fig. 1b, and assume further that all deformation energy of the structure is localised in the rotation hinges. The total solid surface is assumed to be covered by liquid.

For a rotation φ of the flap, the bending energy per unit length is simply (see Fig. 1a) :

0 2 2

1

_B

_{/ l}

U

_b

=

φ

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while the surface energy can be written in terms of θ and φ (using r=w(cosφ+1/2)/sin(θ/2), see Fig. 1b)

) sin( ) cos( 2 2 1 θ φ θ γ + = w U_s (2)

The total energy, normalised per unit length, can thus be written as 2 2 2 1 ) sin( ) cos(φ _βφ θ _θ+ + = U (3)

where the important parameter β = Bl0/γw characterizes the ratio between mechanical bending forces and surface tension. φ R t l0 θ r w φ w F_s θc Fb Fp

Figure 1a : Schematic of the hinge in the 2D model, of thickness t and rotated over an angle φ. Figure 1b : Definition of the angles and parameters for

a threefold structure of width w, rotated over an angle

φ, with opposing torques due to the surface tension Fs, and due to the Laplace pressure Fp and mechanical

bending, Fb.

Minimisation of the energy yields the final equilibrium angle φe. As Fig. 2 shows, two parameters determine the final equilibrium angle : both β and the initial volume of the drop, characterised by the parameter σ = S/w2 with S the cross-sectional surface of the liquid (Fig. 1b.)

Fig. 1b shows that the equilibrium situation can equally be found by equating the opposing torques working on the structure : on the one hand the torque due to the surface tension Fs and on the other the torque due to Laplace pressure, Fp, and the bending stiffness, Fb.

0 0.5 1 1.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 n o rm a lis e d e n e rg y U /γ w angle φ σ = 2 ; β = 0 σ = 4 ; β = 0 σ = 6 ; β = 0 σ = 4 ; β = 1 σ = 4 ; β = 2 σ = 4 ; β = 3

Figure 2 : Normalised energy as a function of rotation angle φ, for varying values of β (the ratio bending stiffness and surface tension) and σ (the drop volume).

III-Fabrication

Planar silicon nitride structures of varying geometries (depicted in Fig. 3) of approximately 100 µm length and 1 µm thickness were fabricated. A relatively simple surface micromachining approach was used to fabricate the silicon nitride structures, by depositing the SiN directly on the silicon wafer. The essential process steps are illustrated by Fig. 4.

Figure 3 : Some of the planar geometries for the capillary folding

The hinges were created by plasma etching of the stripes of the silicon nitride and depositing a thin layer (about 100 nm) of SiN afterwards. To realize free-hanging folding flaps, the silicon wafer was isotropically underetched until a final supporting ‘pillar’ under the structure remained. See Fig. 4. The dimensions of the hinges were varied, for all geometries, and ranged between l0 = 1 to l0 = 10 µm, with t = 100 nm.

Fig. 5 shows one of the rectangular SiN geometries with the free hanging folding wings and the silicon support below. The thin hinges can be clearly seen in the close up of Fig. 5.

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--- Fig. 4a Fig. 4b Fig. 4c Fig. 4d Fig. 4e

Figure 4 : Schematic of the fabrication process. A SiN layer of 1 µm thickness (dark grey) is deposited directly

on the silicon wafer (light grey), (Fig.4a). The hinges for rotation are created by etching away parts of the SiN (4b) and depositing a second, 100 nm thin, layer of

SiN (4c). To obtain free-hanging folding flaps, the silicon is underetched and a central support remains

(4e).

IV-Experiments

A liquid dispenser system designed for UV nano-imprint lithography was used to create and deposit small liquid droplets on the substrate. The apparatus allowed for the creation of picoliter-size droplets of a photosensitive liquid, and the accurate positioning of these on a substrate. Preceding to the experiment, the wetting parameters of the liquid on silicon, on silicon nitride and gold were investigated.

Droplets of 1.8 pL were deposited on the individual structures, in the middle, while the process was recorded using a standard microscope and camera. Also, the liquid evaporation could be monitored. Typical evaporation times were 100 s.

After deposition, the folding wings of most of the investigated structures were rotated out-of-plane, and while the liquid slowly evaporated, a return to the original planar configuration was observed.

Since the dispenser system offers as well the possibility to ‘freeze’ the liquid by UV illumination, this allows for accurate determination of the final rotation angle. The latter option is currently under investigation, and is promising for further optimisation of the process.

V- Conclusion

In this work several planar SiN structures of micrometer size, that could be folded into three-dimensional structures by means of capillary forces, have been

fabricated using a straightforward surface micromachining process. Small liquid droplets of picoliter-size could accurately be deposited on these structures, inducing mechanical deformations. We thus demonstrated the feasibility of the spontaneous formation into 3D objects, starting from a planar geometry, using capillary forces. To our knowledge, capillary folding of structures on micrometer scale has never been demonstrated before.

An analytic description shows that the final equilibrium angle of the rotated flaps is essentially determined by the ratio of mechanical bending stiffness to the surface tension, and the initial drop volume.

Since the process can be further optimised, for example with respect to the tuning of the droplets and the folding configurations, and the possibility to ‘freeze’ the liquid during folding, the capillary folding is seen to be a very promising technique to fabricate 3D microstructures.

Figure 5 : Microscopic image of one of the fabricated devices. Shown above is the rectangular geometry, with

free hanging folding flaps of 100 mm squared, supported by the central silicon pillar. The hinges are

shown in the close-up below.

VI-References

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