A Mehdaoui

M B Pisani

D Tsamados

F Casset

P Ancey

A M Ionescu

MEMS TUNABLE CAPACITORS WITH FRAGMENTED ELECTRODES AND ROTATIONAL ELECTRO-THERMAL DRIVE

Keywords: MEMS tunable capacitor, rotational electrothermal actuations, Above-IC integration

This paper reports on the design, simulation and fabrication of tunable MEMS capacitors with fragmented metal (AlSi 4%) electrodes. We examine a rotational electro-thermal actuation. An analytic model of the rotational effect thermal actuator was established in order to show the periodicity of the capacitance when the angle increases. Evaluation of the impact of fringing fields on the capacitance has been carried out using finite element analysis (FEA). The MEMS capacitors were fabricated using metal surface micromachining with polyimide sacrificial layer. The maximum rotation, corresponding to a maximum angle of 7°, was obtained near 1.2 V and 299 mA. The proposed capacitor has a practical tuning range of 30 %. FEA has shown that this figure can be improved with design optimization. The MEMS architecture based on rotational effect and fragmented electrodes does not suffer from the pull-in effect and offers a practical solution for future above-IC capacitors.

INTRODUCTION

Many types of MEMS tunable capacitors have been proposed over the last years, essentially focusing on new architecture solutions to increase their tuning range. Two or three parallel plate capacitors with vertical electrostatic actuation (air-gap variation) show a limited tuning range due to the pull-in effect (non equilibrium between electrostatic and elastic forces) [START_REF] Young | A micromachined variable capacitor for monolithic low-noise VCOS[END_REF][START_REF] Dec | Micromachined Electro-Mechanically Tunable Capacitors and their applications to RF IC's[END_REF]. Some other works [START_REF] Yoon | A high Q Tunable Micromechanical Capacitor with movable dielectric for RF Applications[END_REF][START_REF] Liu | Micromachined variable capacitors with laterally positioned suspended plates[END_REF] have demonstrated effective solutions by varying the effective area or dielectric constant of capacitors. This paper reports on the design, simulation fabrication of tunable capacitors with fragmented metal (AlSi 4%) electrodes that are rotationally driven by electro-thermal actuators and avoid the pull-in effect. The proposed new capacitor is shown in Fig. 1. It is made of two fragmented electrodes: (i) a bottom fixed electrode and (ii) a top rotationally movable electrode suspended over a 1.4 µm air gap. Both metal electrodes have a circular comb form and the top electrode is rotationally driven by electro-thermal actuators. We used two arms connected on each part of the small central disk structure to rotate the top electrode and change the capacitance. The electro-thermal drive gives more flexibility in terms of design, dimensions and applied voltages. However, this comes at the price of an increased power consumption compared to the classical tunable capacitor configuration.

MEMS CAPACITOR WITH FRAGMENTED ELECTRODES AND ROTATIONAL ELECTRO -THERMAL ACTUATION

Analytic modeling and simulation

The schematic of a MEMS capacitor with fragmented electrodes using arms electro-thermal actuation is presented in Fig. 2. We used two arms connected on each part of the small central disk structure to rotate the top electrode and change the capacitance. When a current passes through the arms, the injected power induces a net thermal expansion of the arm

T l l ∆ = ∆ α
, α is the thermal expansion, l the length of the beam and ∆T the thermal gradient that creates a moment that rotates the entire structure. The amplification (effective displacement of the outer disk) depends on the dimensions of the actuator and the ratio between the radius of the inner and outer disk. We have designed electro-thermal actuators with various dimensions and a case study is presented on the following geometry of arms: width = 4 µm, length = 200 µm and thickness = 4 µm. Fig. 1 shows the shape and the area of ' and θ e are the initial-state angle of the top electrode, the initial angle of the finger and the rotational angle respectively. N is the number of fingers.

Figure 1. Rotational effect thermal actuator

The capacitance as a function of θ e has been studied by finite element analysis (ANSYS TM ). Fig. 2 shows the periodicity of the capacitance when the angle increases, with the minimum value periodically decreasing because of the decrease of S2 and S3, which are the non-fragmented parts of the disk area. We compare the analytical and simulated tuning range results.

Figure 2. Capacitance versus angular displacement

For an angular displacement of 7°, we obtained, for the analytical and simulated results, a tuning range more than 70% and 30%, respectively. This discrepancy between analytical and simulated results is due to the fringing capacitance, which is not accounted for in our model. Moreover this tuning range is limited by the design of the capacitor (area) and the buckling in the arm. By a proper design (minimization of S1, S2 and S3 and more favorable fragmentation) this can be increased in excess of 100%.

Optimization

The design has been optimized by FEA, using ANSYS TM simulator. The optimization goal was to obtain the maximum tuning range. So, the fringing capacitance should be minimized. First, we studied the influence of, θ 0 ', then, the angle between two fingers (pitch), and finally the surface of the non-fragmented areas.

Influence of the angle

' 0 θ
The design presented in Fig. 1 was used as a base for the optimization. First we have tried to increase the tuning range by changing the angle θ 0 '. Each finger is distant by θ 0 '. Fig. 3 shows the capacitance versus the angular displacement for different values of θ 0 '. different angle θ 0 ' Table 1 shows the tuning range for these 4 angles θ 0 '. We can see that the tuning range is optimal for θ 0 '=13° in case of a rotation of θ e =13°. Table 1 : Tuning range of the Tunable Capacitor for different angle θ 0 '

Influence of the pitch

In this part, the influence of the interdigital angle is studied (pitch). Three cases have been investigated : fingers of 5°, 7° and 9° with separating angle of 7°, 9° and 11° respectively. Fig. 4 shows the capacitance versus the angular displacement for different values of pitch.

0.12 0.17 To minimize the fringing capacitance and increase the tuning range, one solution is to minimize the nonfragmented area. The drawback in this case is that the total capacitance is diminishing.

Conclusion of the design optimization

To obtain a maximum tuning range, we have to minimize the fringing capacitance. For that, three possible approaches exist :

-increase the angle θ 0 ' -increase the angle between two fingers -minimize the non fragmented area Finally, we find a new optimized design with a tuning range of more than 100% (110%). Fig. 5 shows the capacitance versus angular displacement for fingers of 9° separated by 11° and R 2 = 195 (µm) .

FABRICATION USING POLYIMIDE SACRIFICIAL LAYER

Fig. 6 depicts the simplified successive steps of the process with AlSi 4%. The silicon substrate is p-type with resistivity larger than 8kΩ.cm. This process needs three levels of masks and one chemical-mechanical polishing step (CMP). First a silicon dioxide layer (with a thickness of 2 µm) is grown in a wet atmosphere as shown in Fig. 6a. The next step, as shown in Fig. 6b, is the deposition of AlSi 1% bottom electrode (1 µm). The patterning of AlSi 1% metal layer is performed by a chlorine-based plasma chemistry (Fig. 6b). Then, a spin-on polyimide layer (pyralin PI -2610 from Dupont) defines the sacrificial layer (Fig. 6c). We use a solution of 3aminopropyltriethoxysilane on isopropyl alcohol as adhesion promoter before the deposition and a long postdeposition bake of 200°C/1h followed by 300°C/1h in nitrogen atmosphere to have a solvent-free polyimide film [START_REF] Pisani | Copper/Polyimide fabrication process for Above-IC integration of high quality factors inductors[END_REF]. A CMP is needed to level the sacrificial layer (Fig. 6c). Then, a step consists in etching through the polyimide layer (plasma O 2 ) to prepare the mechanical anchors to the bottom electrode for the suspended electrode (Fig. 6d). The next step of the etching through the polyimide layer (plasma O 2 ) to prepare the mechanical anchors to the bottom electrode for the suspended electrode (Fig. 6d). The next step of the process consists in metal layer deposition AlSi 4% (4 µm) by sputtering (Fig. 6e). The patterning of AlSi 4% metal layer is performed by a chlorine-based plasma chemistry (Fig. 6e). Then the suspended metal membranes are released by dry etching of the polyimide sacrificial layer in oxygen plasma (O 2 ) as shown in Fig. 6f. Figure 6. Fabrication process of fragmented AlSi 4% tunable capacitor using polyimide sacrificial layer

CHARACTERIZATION

Figure 7 shows an SEM image of the MEMS tunable capacitor with electrothermal actuator. Figure 8 shows the top fragmented electrode. Figure 9 shows a cross section of 1 µm AlSi 1% + 1.2 µm air gap + 4 µm AlSi 4%. For our fabricated MEMS capacitors (Fig. 7-8-9) the input power need for actuation ranges from 0 to 300mW, which turns into an operating voltage range of 0 to 1.2 V. At zero voltage, the bottom and top electrode are intentionally misaligned. When increasing the applied voltage, the capacitance decreases and increases again (Fig. 10).

Bottom electrode AlSi1%

Top electrode AlSi 4% The measurements have been carried out by extracting the capacitance from S-parameter measurements made in the 2-5GHz range (see also Fig. 11) with a network analyzer HP 8719 D. We obtain a maximum rotation near 1.2 V and 299 mA: the bottom and top electrode being aligned. -The general trend shown by FEA, decrease of the capacitance and then increase, is reproduced in the experiment.

-The value of the measured capacitance is higher than in simulation or that predicted analytically. This could be attributed to the influence of the parasitic capacitances. Further, experiments should clarify this issue.

-At 1V of polarization, the profilometer shows that the bottom and top electrodes are aligned. So, we would expect to get the highest capacitance as predicted by FEA and analytical model. However, experimental data show that although electrodes are aligned, the capacitance is lower than for 0V. In addition, profilometer measurements during actuation show that the structure begins to move out of plane even for a 0.6V bias, increasing the gap and therefore decreasing the total capacitance (Fig. 14, Table 4).

The reason for this behavior can be found in the mechanics of the structure. The central part of the top electrode is free to move vertically, so the total suspended length of the actuation beams becomes quite considerable. Thermal stress in the beams, which is compressive in our case, increases with voltage, and as a result when this stress goes beyond the critical value for buckling, the whole structure moves up instead of turning. A solution to this problem has been found by changing the position of the actuators and optimization of their design is under way. Figures 14a and14b show the profile measurement of the top electrode, at 0V and 0.9V respectively.

CONCLUSION

In this paper, we validate for the first time the principle of the rotational electro-thermal actuator for MEMS tunable capacitors showing 30% experimental tuning range.The experimental maximum angle is obtained at 7°, so less than one period. The experimental tuning range is somewhat smaller than the 70% predicted by simulation and the analytical model developed. We attribute this to the influence of parasitic capacitances.

Optimization of the design has been studied. By implementing certain design changes a tuning range of the capacitance of more than 100% should be obtainable.

The MEMS architecture based on rotational actuation and fragmented electrodes does not suffer from pull-in limiting effects, characteristic of conventional tunable capacitors, and offers a practical solution for future above-IC MEMS varicaps.

  and linear variation when the rotational angle increases . R 1 = 190 µm, R 2 = 210 µm, R 3 = 60 µm, r = 10 µm, θ 0 = 85°, θ 0 ' = 5°, d = 1.2 µm. θ 0 , θ 0

Figure 3 .

 3 Figure 3. Capacitance versus angular displacement fordifferent angle θ 0 ' Table1shows the tuning range for these 4 angles θ 0 '. We can see that the tuning range is optimal for θ 0 '=13° in case of a rotation of θ e =13°.

Figure 4 .

 4 Figure 4. Capacitance versus angular displacement for different value of pitch.

Figure 5 .

 5 Figure 5. Capacitance versus angular displacement (TR 110%)

Figure 7 .Figure 8 .Figure 9 .

 789 Figure 7. SEM image of the MEMS tunable capacitor with electro-thermal actuator

Figure 10 .

 10 Figure 10. Capacitance versus tuning voltage (experiment)

Figure 11 .

 11 Figure 11. Capacitance versus frequency (experiment)However, this maximum displacement is limited by buckling in the arms at high temperature (>400°C) (Fig.12).

Figure 12 .

 12 Figure 12. Microscope picture of the structure :a. under zero voltage, b. under 0.8V and 270 mA, c. under 1.2 V and 299 mA

Figure 13 .

 13 Figure 13. Profile measurement of the top electrode : a. under zero voltage, b. under 0.9V. Vertical displacement occurs increasing the gap and decreasing the total capacitance

Table 2

 2

	shows the tuning range for these three cases. We
	can see that the tuning range is the most interesting for
	structures with fingers of 9° spaced by 11°. With this
	design we can obtain a maximum tuning range of 60%

Table 2 :

 2 Tuning range of the Tunable Capacitor for different value of pitch2.3.3. Influence of the non-fragmented areaWe keep the optimal angle θ 0 ' = 13°. The pitch is 13°. We tried to minimize the area of the non fragmented part, by using a ring of 5 µm width as the middle part instead of a full circle. Then, we simulated the capacitance versus angular displacement for different values of R 2 .Table3shows the tuning range for three values of R 2 .

	R 2 (µm)	TR (%)
	195	39.5
	200	28.3
	205	28

Table 3 :

 3 Tuning range of the Tunable Capacitor for different value of R 2

Table 4 .

 4 A. Mehdaoui, M.B.Pisani, D. Tsamados, F. Casset, P. Ancey, A.M. Ionescu MEMS TUNABLE CAPACITORS WITH FRAGMENTED ELECTRODES AND ROTATIONAL ELECTRO-THERMAL DRIVE Vertical displacement relative to initial position

	Applied Voltage	Vertical	Vertical
	(V)	Displacement	Displacement
		relative to initial	relative to initial
		position (µm)	position (µm)
		(middle part)	(extreme part)
	0.6	7	0.1
	0.8	8.5	0.1
	0.9	11.8	0.8

Acknowledgements

Thanks to the EPFL-CMI staff for the support given on the technological steps development.


S.-H H Ng

Z.-F F Wang

R.-T T Tjeung

N F De Rooij

N De

Rooij Process

PROCESS ISSUES FOR A MULTI-LAYER MICROELECTROFLUIDIC PLATFORM

published or not. The documents may come

INTRODUCTION

Microfluidic devices can be classified into limitedfunction lab-on-chip (LOC) and micro total analysis system (µTAS). Most LOCs are single function and single layer devices such as mixers, separation channels, etc. Micro total analysis systems, on the other hand, are more complicated and can perform many functions such as mixing, reaction, separation, etc on a single chip. It can also consist of active valves and pumps to direct flow of fluids and metal electrodes for detection. Earlier microfluidic devices are mostly made of silicon, silicon oxide or glass partly due to the adoption of the microelectro-mechanical systems (MEMS) fabrication processes [START_REF] Lichtenberg | A Microchip Electrophoresis System with Integrated In-plane Electrodes for Contactless Conductivity Detection[END_REF]. Structural integrity and dimensional control are very good when using these materials and processes.

Glass is also popular because its capillary and electroosmotic effects with water are strong. However, as the demand for microfluidic devices increases, cost becomes an issue. Cheaper materials such as polymer and mass production replication technologies would have to be implemented, especially for single-use devices. In addition, the trend would be towards cheap, disposable microfluidic devices to eliminate contamination issues. Hence, there has been a huge interest in the fabrication of microfluidic devices out of polymers in recent years [START_REF] Bohl | Multi-layer Su-8 Lift-off Technology for Microfluidic Devices[END_REF]. The complexity of the devices has also been increasing to include on chip detection and active components such as micro-pumps, as in seen in µTAS. This would require some sort of electrical components on the devices, rather than a purely fluidic-based device such as a micro-mixer. At present, most of the devices are single layer devices with all components on a single layer of substrate. As the demand for the performance of the devices increases, multi-layer devices consisting of fluidic channels and electrical circuits would be required.

HOT EMBOSSING

In this research, the creation of micro channels on PMMA was achieved through the hot embossing process. This is a low-cost process suitable for mass production. We attempt to look at the process through a parametric study and material characterization of the polymer material.

Polymer flow: thick film versus thin film

In hot embossing lithography (HEL), also called nanoimprint lithography (NIL), two common applications are: thin film patterning as an alternative to photolithography, and the creation of micro channels for microfluidic devices. In the first case, a thin polymer film with a thickness typically a few hundred nanometers, is spin coated on a semiconductor wafer. After baking the polymer which is commonly a photoresist, the pattern on the stamp is transferred to the polymer through a hot embossing process. The residual layer which remains is then removed by plasma etching. The process can even replicate features down to a ten nanometers [START_REF] Chou | Imprint Lithography with Sub-10 nm Feature Size and High Throughput[END_REF]. This process has great potential to replace conventional photolithography due to its simplicity and ability to S.H. Ng, Z.F. Wang, R.T. Tjeung, N.F. de Rooij Process Issues For A Multi-Layer Microelectrofluidic Platform replicate nano features. However, there are some issues such as its embossing uniformity, to be addressed before it can be implemented in the industry. In the second case, the target is a thick polymer substrate normally around one millimetre in thickness. The hot embossing process is used because it is simple, fast and can produce high fidelity features such as the micro channels for microfluidic devices. In such application, the feature dimensions (channel width and depth) are normally in the tens of microns.

One popular model for the hot embossing process is the squeeze film effect from hydrodynamic theory [START_REF] Scheer | A Contribution to the Flow Behaviour of Thin Polymer Films during Hot Embossing Lithography[END_REF]. Assuming the polymer to be exhibiting ideal fluid behaviour, a fluid pressure distribution will exist in the polymer subjected to changes in the polymer film thickness. The normal load component, L, for a rigid circular plate approaching a rigid plane in parallel alignment can be derived from the Reynolds equation [START_REF] Hamrock | Fundamentals of Fluid Film Lubrication[END_REF]:

3 4 2 3 h w R L πη = ( 1
)
where η is the absolute viscosity, R is the radius of the plate, w is the squeeze velocity and h is the film thickness.

A positive pressure is generated in the fluid film existing between the plate and the plane when the two surfaces are moving towards each other. When they are moving apart, negative fluid pressures will result and this can lead to cavitation. A higher squeeze velocity and low film thickness will result in a larger load support. This provides a very important cushioning effect in bearings especially it takes a finite time to squeeze the oil from the gap. The Reynolds equation is derived from the Navier-Stokes and continuity equations for application in the hydrodynamic lubrication theory. One of the key assumptions in the derivation of the Reynolds equation is that the fluid film thickness is much smaller than the other dimensions such as the width and diameter of a journal bearing. The film thickness, in practice, is typically 3 orders of magnitude smaller than the journal dimensions. Hence, in the order-of-magnitude analysis to derive the Reynolds equation, some terms in the Navier-Stokes equations are neglected. In a further derivation of Equation ( 1) from the Reynolds equation, the film thickness is assumed to be "thin" so that the fluid pressure can be assumed to be constant across it. With this in mind, it is possible to look at the situation happening in the hot embossing process. Considering a typical 100 mm diameter wafer stamp pressing against a polymer, spin coated polymer film thickness can be in the range from tens of nanometers to tens of microns. Typical bulk polymer sheets have thickness from hundreds of microns to a couple of millimeters. In any case, the wafer diameter is many times the thickness of the polymer. Hence, at the wafer level, there is no violation of the thin film assumption when the squeeze film equation is applied to the hot embossing process.

However, at the feature level, while the squeeze film effect can be applied to the case where a thin film is embossed, it cannot be applied to the case where a thick film is embossed. Fig. 1 shows the difference in the two cases. The stamp feature dimensions can range from the nanometers to microns. Hence, the squeeze film effect can be applied to the situation in Fig. 1(a) if the spin coated polymer film thickness, h, is many times smaller than the feature length. Laminar flow of material throughout the polymer thickness will occur between every feature and the silicon substrate. Material squeezed out between two adjacent features would be forced into the recess between them. In Fig. 1(b), the film thickness, h, is typically many times the feature length. Hence, Equation (1) will not be applicable. In addition, the flow across the film thickness will be very different from that of a Poiseuille flow as predicted by Equation ( 1). Assuming a 1 mm thick polymer substrate and 100 µm features, the situation would be analogous to placing the tip of a finger on the surface of a 1 m deep tank of water! Most of the material flow will occur around the feature rather than throughout the thickness.

There is a fundamental difference in the polymer flow mechanism between hot embossing on thin, spin coated polymer films and hot embossing on thick polymer substrates. The mechanism in the second case should be likened to that of an indentation model (especially for well spaced out protruding features) since the contact length is much smaller than the substrate thickness. The actual situation would be much more complicated than a single indentation due to pattern dependency effects. Neighbouring patterns or features will have an effect on the embossing performance of a feature.

In both cases shown in Fig. 1, the squeeze film effect will occur at the wafer level once the polymer level hits the field region of the stamp. This will occur earlier for a stamp with recessed features than in the other extreme, a stamp with protruding features. The squeeze film effect at the wafer level can be seen when the average polymer thickness across the wafer decreases with time during embossing.

S.H. Ng, Z.F. Wang, R.T. Tjeung, N.F. de Rooij Process Issues For A Multi-Layer Microelectrofluidic Platform

Experiments

Hot embossing was conducted on 1 mm thick PMMA sheets using a hybrid stamp based on the FR4 printed circuit board material. The hybrid stamp consisted of a 1.6 mm thick FR4 glass fibre reinforced epoxy topped with a 34 µm layer of copper. A pattern of raised structures from one of these copper surfaces was created by nickel electrolytic plating. The feature in this study was a channel array of about 70 µm width with 100 µm pitch. Figure 2 shows a typical profilometric scan across the array on the stamp as well as on an embossed PMMA. Channel depth was uniform with values of about 10 µm. The walls of the stamp features were not vertical but have a slight relief angle that aided stamp release after embossing. The stamp used in the experiments was measured to be 55 mm x 48 mm x 1.6 mm.

As illustrated in Fig. 3, the process consisted of a stamp or mould (with positive and negative relief structures) that was pressed against a polymer substrate that has been heated to a temperature that was normally above the glass transition temperature of the polymer material. A holding time was necessary under heat and pressure to allow the polymer to flow completely to form the patterns. Upon cooling down and separation (demoulding step) of the stamp and polymer substrate, a reversed image of the stamp pattern would be imprinted on the polymer surface. The hot embossing machine used was a bench-top hydraulic press with a capacity of 15 tonnes load. It was fitted with two 100 mm diameter heated platens (top and bottom) and these were connected to a temperature controller. A thermocouple was embedded into the top platen. Cooling was achieved through natural air cooling and through water cooled plates attached to the platens. A chiller circulated water through the two cooling plates.

Three sets of experiments were conducted to look at the effects of load, temperature and holding time on the fidelity of the embossed channels. Table 1 shows the three sets of experimental runs.

MULTI-LAYER MICROELECTROFLUIDIC PLATFORM

One of the most straight forward approaches to fabricate a three-dimensional network of embedded fluidic channels will be to create two-dimensional networks of the channels and laminate the layers together. Inter-layer interconnecting channels will have to be created also. The most challenging step in this method is the bonding process, especially for polymer-based devices. While techniques for the bonding of two flat surfaces of polymers have been established, e.g. adhesive bonding and thermal bonding, bonding two structured polymer surfaces is a much trickier business. A good bonding of surfaces containing micro channels and metal traces would be characterized by 1) minimal number of trapped air bubbles, 2) complete flow of polymer around metal traces, 3) hermetic sealing of fluidic channels, 4) minimal blockage of channels and maintaining channel dimensions. With standard thermal bonding process, the microstructures deform easily, clogging the channels since temperatures and pressures are high in order for bonding to occur. Hence, plasma or X-ray assisted thermal bonding processes have been developed. In the case of the plasma assisted process [START_REF] Wu | Polymer microchips bonded by O 2 -plasma activation[END_REF], both surfaces of the polymers are activated by plasma and at the same time become more hydrophilic. Thermal bonding can then be achieved with lower temperature and pressure, reducing the risks of channel deformation or even worse, channel blockage. Another popular method is the use of adhesives to bond two surfaces of polymers together. B. Bilenerg et al. [START_REF] Bilenerg | PMMA to Su-8 Bonding for Polymer Based Lab-on-a-chip Systems with Integrated Optics[END_REF] demonstrated the use of spin on solvated PMMA to bond an Su-8 surface with a Pyrex glass surface, creating embedded micro channels. The technique requires the bonding to be carried out in an evacuated environment. Precise control of the viscosity of the adhesive just before bonding and the bonding force is essential in preventing excessive adhesive flow into the channels.

We have designed and fabricated a multi-layer test device. Four PMMA layers each with hot embossed micro channels were bonded together simultaneously. Prior to bonding, inter-layer via holes were created by micro-drilling.

In addition to creating a network of interconnecting fluidic channels, an electrical network will have to be incorporated into a microelectrofluidic device. One of the ways to lay down conductive traces on polymers will be to use metal deposition through sputtering or evaporation. This can be combined with metal etching or lift-off techniques to create the patterns. For a polymer-based device, these wet processes often pose problems since organic solvents are used. These solvents can be found in the developers and photoresist strippers. Without strong chemical bonding between the

S.H. Ng, Z.F. Wang, R.T. Tjeung, N.F. de Rooij Process Issues For A Multi-Layer Microelectrofluidic Platform

deposited metal film and polymer surface, these solvents can attack the polymer causing metal delamination.

In this work, we adopted a low-cost microprinting technique. A 4-layer electrical test device was designed. A stencil printer from MPM Corporation was used to deposit conductive traces on the PMMA sheets. The paste used was a low temperature cure silver-filled epoxy from Emerson & Cumming. Both electrical traces and inter-layer via holes were filled with this material. A layer by layer trace printing, via filling, thermal cure and bonding process was used.

RESULTS AND DISCUSSION

Figure 4 shows some typical hot embossing results. The filling mechanism of the cavity was a single-peak mode rather than the dual-peak mode reported in some studies [START_REF] Heyderman | Flow Behaviour of Thin Polymer Films Used for Hot Embossing Lithography[END_REF][START_REF] Rowland | Polymer Deformation and Filling Modes during Microembossing[END_REF]. In the dual-peak mode, the phenomenon was seen under a two-dimensional surface profilometric scan, as two peaks climbing up the cavity walls. While frictional heating and shear thinning have been proposed to be causing it, we believed another necessary condition for the dual-peak mode is the squeeze film configuration where the film thickness was much smaller than the feature size.

In our process, the polymer substrate was much thicker than the feature size. Under most conditions, the peak reached the cavity ceiling before lateral filling was completed.

We attempted to quantify three parameters to study the flow behaviour of the polymer: the maximum depth of the imprinted channels, the top and bottom widths of the channels (as illustrated in Fig. 5). In Fig. 2, it was shown that the walls of the stamp features and the embossed channels were not vertical (good for stamp release), resulting in changing widths of the channels in the vertical direction. Depths of the channels were obtained through profilometry results while the channel widths were obtained through cross sectional measurements of the samples under a microscope. Each depth data was averaged over 5 measurements while each channel width data was averaged over 3 measurements. Figure 6 shows the hot embossing results. The error bars were one standard deviation for each set of repeated measurements. The effects of embossing load and time were very minimal. The depths of the channels were almost identical under all the loads and time experimented. Channel top and bottom widths showed small decreases with both increasing load and time. The effect of embossing temperature was more pronounced. Larger decreases in channel top and bottom widths were seen with increasing temperature especially between the 100 o C and 120 o C range. The depth was almost constant at 10 µm except for the case at 100 o C where a depth of about 3 µm was obtained.

The PMMA was commercially available in large 1 mm thick sheets. The material was optically clear with an average surface roughness of 0.02 µm. Since the grades and properties of PMMA could vary, dynamic mechanical

S.H. Ng, Z.F. Wang, R.T. Tjeung, N.F. de Rooij Process Issues For A Multi-Layer Microelectrofluidic Platform

analysis (DMA) was conducted on the samples to determine its viscoelastic and thermal properties. The DMA experiments were conducted on a Q800 from TA Instruments using the single cantilever method. The specimen dimensions were 17.50 mm x 9.70 mm x 1.07 mm. The temperature ranges from 30 o C to 160 o C with isothermal steps of 5 minutes every 2.5 o C. A frequency sweep from 0.1 Hz to 10 Hz was carried out at each isotherm with amplitudes of 20 µm. Figure 7 shows the results from the DMA analysis. Typically, storage modulus was higher for higher frequency deformation. The glass transition temperature shifted to higher values as the frequency is increased. This could be deduced from the rightward shifts of the three plots. Tan delta values peaked well above 1.2 indicating loss modulus exceeding the storage modulus during glass transition. For the 0.1 Hz case (better estimate for the hot embossing process), the loss modulus peaked at 108 o C, indicating the material's exact glass transition temperature. The PMMA was amorphous losing more than 95 % of its storage modulus during the sharp glass transition from about 95 o C to 115 o C. For the test conducted at 0.1 Hz, the drop was from 1180 MPa at 96 o C to 36 MPa at 116 o C. This explained the results from the hot embossing tests conducted at different holding temperatures. There was a huge different in the hot embossing results for the 100 o C and 105 o C temperatures due to the rapid change in material properties in this glass transition range. Above 120 o C, there is no significant difference in the hot embossing results and this was explained by the rubbery plateau in the storage modulus after the glass transition. After glass transition, the material exhibited a gradual decrease in storage modulus (for 0.1 Hz sweep) reaching a minimum of 3.9 MPa at 138 o C. After that was another gradual increase to 6.6 MPa at 160 o C. The maximum change in storage modulus in the 130 o C to 160 o C range is about 2.5 MPa. In summary, the DMA analysis is a useful tool to understand the behaviour of polymer materials used in hot embossing experiments. The exact glass transition temperature for a polymer alone is insufficient information to explain its behaviour; rather, the glass transition range and its behaviour after that are more important. In this case, using hot embossing temperatures above 130 o C (but up to 160 o C) might not necessarily improve performance or shorten embossing time due to reasons explained earlier. Hence, the number of experiments can be reduced when optimizing the process. In other cases such as semi-crystalline polymers, the situation will be different since the glass transition can happen over a much bigger range than PMMA and it exhibits different behaviour after glass transition.

Figure 8(a) shows a bonded multi-layer fluidic chip. After thermal bonding the chip was fitted with inlet/outlet connectors (supplied by Nanoport) and was connected to tubing and a syringe. Tests revealed that fluid was able to flow through all 4 layers of channels and via holes without leakage (see Fig. 8(d)). Figure 8(c) shows a cross-sectional scanning electron micrograph of a typical channel. The channel was not blocked and the overall dimensions (width and depth) were maintained. However, the shape deviated from that of a rectangular cross section due to some deformation, especially at the corners. More process control of the bonding process would improve the situation.

Fig. 1

 1 Fig. 1 Thin film (a) and thick film (b) hot embossing. (a) (b)

Fig. 2

 2 Fig. 2 Profilometric scans.

Fig. 4 Fig. 3

 43 Fig. 4 Cross sectional view of embossed micro channels: (a) 1000 kg, 130 o C, 10 min., (b) 1000 kg, 100 o C, 10 min. (a) (b)

Fig. 5

 5 Fig. 5 Embossed feature parameters. Bottom width

Figure 8 (

 8 Figure 8(b) shows a bonded multi-layer electrical interconnect chip. The traces were 200 µm in width and the via holes were 1 mm in diameter. Separate printing tests using a test pattern showed that features down to 100 µm could also be printed. Electrical testing on the chip indicated connection through all the layers of the chip.

Fig. 6 Fig. 8

 68 Fig. 6 Hot embossing results.

Fig. 7

 7 Fig. 7 DMA results.

Table 1

 1 Hot embossing runs.

	Run	Load (kg)	Time (min.)	Temperature ( o C)
	1	1200	10	130
	2	1000	10	130
	3	800	10	130
	4	600	10	130
	5	400	10	130
	6	200	10	130
	7	1000	12	130
	8	1000	8	130
	9	1000	5	130
	10	1000	3	130
	11	1000	1	130
	12	1000	10	150
	13	1000	10	120
	14	1000	10	110
	15	1000	10	105
	16	1000	10	100

ACKNOWLEDGEMENT

This research is funded by the Agency for Science, Technology and Research (A*STAR), Singapore.


Zhang Yong

Zhu Jian

Yu Yuanwei

Chen Chen

Jia Shi

A KU-BAND NOVEL MICROMACHINED BANDPASS FILTER WITH TWO TRANSMISSION ZEROS

Keywords: micromachining, via-hole, tapped-line, interdigital filters, transmission zeros

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Microwave filters are widely used in communication applications to reject spurious signals and to separate different channels in a multichannel communication system. So the characteristics of compact size, high selectivity, and low insertion loss for microwave filters are highly required. To meet these objectives, some key techniques are used in this paper, such as tapped-line interdigital structure, micromachined via-hole and implementation of transmission zeros at finite frequency.

In tapped-line filters design, the first and the end coupling sections are eliminated. Therefore, filters with tapped-line feed can offer space and cost saving advantages. Furthermore, the realizable bandwidth could be much greater [START_REF] Chang | Handbook of RF/Microwave Components And Engineering[END_REF].

Through-silicon-substrate-via-hole is realized by MEMS technique. It is used for the grounding of the microwave resonators in the filter and therefore makes the filter much more compact [START_REF] Zhu | Micromachined Silicon Via-hole and Interdigital Bandpass Filters[END_REF].

To build in prescribed transmission zeros can remarkably improve the selectivity of the filters. Various methods have been introduced for the implementation of the transmission zeros at finite frequencies. Using cross couplings between nonadjacent resonators is the most common way [START_REF] Levy | Filters with single transmission zeros at real or imaginary frequencies[END_REF]. But it usually suffers more complex structures in design. To avoid cross coupling structures, open-loop and hairpin transmission-line resonator filters using tapped-line feed topology to create transmission zeros have also been reported [START_REF] Hsueh | Tunable Microstrip Bandpass Filters With Two Transmission Zeros[END_REF], [START_REF] Tsai | Hairpin filters with tunable transmission zeros[END_REF]. However, their size is usually not as compact as the one with interdigital structure.

In this paper, a Ku band micromachined tapped-line interdigital bandpass filter with two transmission zeros is presented. It is easy to realize in the physical structure. Each transmission zero can be freely placed at desired frequency to achieve demand attenuation in the stopband. The locations of the transmission zeros can be calculated. All the grounded sections of the filter are realrized by micromachined via-hole. Finally, an eight-order bandpass filter is fabricated and measured. The measured performance shows good agreement with the desin theory. The chip size is only 9.6mm×4mm.

ANALYSES AND DESIGN OF Ku-BAND MICROMACHINED BANDPASS FILTERS

Micromachined interdigital filters with via-hole

The basic structure of the filter is using interdigital microstrip quarter-wave lines with short-circuited line at the ends. The filter specification is 8 poles, 0.2dB Chebyshev ripple, and 15% fractional bandwidth. Table .  1. shows the normalized element values (from g 0 to g 9 ) for Chebyshev response. [START_REF] Alessio | Interdigital Design Forms Lowcost Bnadpass Filters[END_REF] Table . The coupling coefficient (k) is related as

1 1 , + + = j j j j g g w k (1) where 0 1 2 f f f w - =
Zhang Yong, Zhu Jian, Yu Yuanwei, Chen Chen, Jia Shi Xing A Ku-Band Novel Micromachined Bandpass Filter with Two Transmission Zeros 2 f and 1 f are the high and low resonant frequencies [START_REF] Matthaci | Micowave Filters, Impedance-Maching Networks, and Coupling Structures[END_REF].

The mutual coupling matrix (M) can be calculated from [START_REF] Chang | Handbook of RF/Microwave Components And Engineering[END_REF]. Then, the physical size (w 0 , w 1 , w 2 … w 8 , w 9 , s 01 , s 12 , s 23 …s 78 , s 89 ) of filter can be calculated [START_REF] Matthaci | Micowave Filters, Impedance-Maching Networks, and Coupling Structures[END_REF].

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = 0

Micromachined tapped-line interdigital filters

After the physical size of the filter is determined, the first and end coupling lines are then changed into tappedline structure. The measured results show a relatively good performance and make a good agreement with the simulated ones. However, the attenuation on lower side is still need to be improved. This problem can be solved by the realization of the transmission zero.

Zhang Yong, Zhu Jian, Yu Yuanwei, Chen Chen, Jia Shi Xing A Ku-Band Novel Micromachined Bandpass Filter with Two Transmission Zeros

Micromachined tapped-line interdigital filters with two transmission zeros

As open-loop and hairpin filters are, the micromachined interdigital filter with two transmission zeros in this paper is also on the base of the tapped-line feed topology. However, the first and end sections are skillfully changed. As shown in Fig. 2., each resonator element of the traditional tapped-line interdigital filters is a quarter-wave length long at midband frequency and is short-circuited at one end and open-circuited at the other end. As a result, there can't be two transmission zeros close to the passband. Thus a new structure is proposed by changing the first and end resonators into transmission lines with both ends short-circuited. That is, Both the first and the end section have two grounded points.

The length of the first and end transmission lines can be longer than the other resonators of the filter, and also the width may be changed a lot. The location of transmission zeros can be calculated from

re l c f ε 2 = (4)
where l is the length from one grounded point of the first or the end transmission lines to the corresponding tap point. re ε is the effective permittivity.

To achieve high attenuation and low insertion loss, the transmission zeros desired should be within the frequency of 10 GHz and 11 GHz on the lower side, 15 GHz and 16 GHz on the upper side. So the length is calculated within 3860 µm and 4250 µm for the transmission zero on the lower side, 2830 µm and 2650 µm for the transmission zero on the upper side. However, the location of the transmission zeros can also affect the coupling condition of the first and the end section. It may cause the overcoupled situation [START_REF] Alessio | Interdigital Design Forms Lowcost Bnadpass Filters[END_REF]. Thus there will be a hump in the passband. To get proper coupling condition, the transmission zeros can be tuned in a very narrow frequency range and it just affect the property of the filter very slightly. The critically coupled condition is given by

u e Q Q K 1 1 + = (5)
where K is the coupling coefficient, e Q is the external Q , and u Q is the unloaded Q of the resonator [START_REF] Matthaci | Micowave Filters, Impedance-Maching Networks, and Coupling Structures[END_REF].

After calculation, the final structure of the filter is obtained and then electromagnetic (EM) simulation is done. The comparison of simulated results of two types of filters is shown in Fig. 4. A is the results of the filter described in Chapter 2.2 and B is that of the filter with two transmission zeros. It shows that the improvement of the out-of-band attenuation is remarkble. In A, the attenuation at 10.6 GHz is 36.8 dB. While in B, it is 48.3dB at the same frequency. To achieve more compact size, matched microstrip corners are introduced. That is, the first and the end lines are designed into folded structure. That affects the location of the transmission zeros very slightly.

EXPERIMENTAL RESULTS OF FABRICATED FILTERS

The filter is fabricated on the 4〞 high resistivity silicon substrate. Inductively coupled plasma (ICP) process is used for the fabrication of the silicon via-hole. From the experiment results shown in Fig. 5, the fractional 3-dB bandwidth remains unchanged 20% and the return loss is greater than 15dB. While the attenuation is greater than 37dB extend to 11 and 13 GHz and beyond. It is nearly improved by 12dB. Furthermore, the insertion loss that is 1.9dB is also improved by 0.2dB. The experiment results make a good agreement with the simulated ones. The chip size is only 9.6mm×4mm. The photograph of the fiter is shown in Fig. 6.

CONCLUSIONS

A micromachined tapped-line interdigital filter is designed, fabricated and measured. The explicit design procedure is described. All the grounded sections of the filter are realized by micromachined via-hole. The filter has two transmission zeros due to its novel structure. Measured results have shown the excellent performance and advantages of this type of filters. And the filter size is much smaller than the conventional one.

This product is protected by PRC patent NO. 200510094411.2.

Zhang Yong, Zhu Jian, Yu Yuanwei, Chen Chen, Jia Shi Xing A Ku-Band Novel Micromachined Bandpass Filter with Two Transmission Zeros

M

  Micromachined via-hole is used for the grounding at the end of the quarter wave microstrip transmission line. The hole shape and size can also affect the filter performance. It should be chosen carefully. The discussion of the via-hole has been reported explicitly in[START_REF] Zhu | Micromachined Silicon Via-hole and Interdigital Bandpass Filters[END_REF]. After optimized by electromagnetic (EM) simulation, the final structure of the is obtained. Fig.1. shows the sketch of the filter. The length of the resonator (L) is 1730 µm.

Fig. 1 .

 1 Fig. 1. Micromachined interdigital bandpass filter with via-hole.

Fig. 2 .Z

 2 shows the micromachined interdigital filter with tapped-line feed. The tap point L l can be calculated from is the characteristic impedance of the input and output line, I Z 0 is the characteristic impedance of the resonators, e Q is the external Q of the resonator, 0 f is the resonator frequency, and °± ∆ 90 f is the bandwidth about the resonant frequency over which the phase varies from -90 o to +90 o [8]. After optimization, the tapping position And the size of the resonators (w 1 , w 2 … w 8 , s 12 , s 23 …s 78 ) is also optimized. Fig.3. shows the simulated and measured results. The filter works in Ku band. It has a fractional 3-dB bandwidth of 20%. The insertion loss is 2.1dB at 13.2GHz, and the return loss is greater than 15dB within the pass band. The attenuation is greater than 25.5dB extend to 11 and 13 GHz and beyond.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Micromachined tapped-line interdigital bandpass filter.

Fig. 4 .

 4 Fig. 4. Simulated results of two types of filters A and B.

Fig. 5 .

 5 Fig.5. Measured and simulated results of micromachined tapped-line interdigital filter with two transmission zeros.

Fig. 6 .

 6 Fig. 6. Photograph of a fabricated filter


Z F Wang

W Noell

M Zickar

N De Rooij

S P Lim

DEVELOPMENT OF SCANNING MEMS MIRROR WITH NEW ASSEMBLY STRUCTURE

This paper introduces the development of a new MEMSbased optical mirror, which performs optical scanning function with discrete reflection angles in an out-of-plane configuration. The device was fabricated through Deep Reactive Ion Etching (DRIE) process on silicon-oninsulator (SOI) wafer, followed by assembly with two metalised glass dies. The optical mirrors can be tilted by electrostatic forces between the opposite electrodes on the SOI and glass dies. The most outstanding performance that can be expected from the device is the discrete and therefore, reliable tilting angle of the mirror, which is guaranteed by its unique mechanical structure and the electrostatic-driven mechanism. In this paper, the working principle of the new MEMS mirror was presented, followed by the introduction of device design, mechanical simulation, microfabrication process, assembly solution, and some testing results. The potential application of this new MEMS mirror is for light beam scanning or optical sensing (detection).

INTRODUCTION

The electrostatic force is a commonly used actuation method for scanning micromirrors, which is usually generated from a fixed electrode on the substrate and a movable one associated with the scanning mirror. The mirror deflection depends on the voltage applied between the fixed and movable electrodes. A deformation sensor and a control servo are usually required to displace the mirror to the desired position with the required tilting angle. The accuracy of such positional (or angular) control is dependent on the sensitivity of the deformation sensor and the performance of servo circuit. Therefore, the response time and torsional accuracy, which are paramount to the coupling loss and crosstalk of the switching element, are largely dependent on the performance of such sensors and circuits. The mechanical reliability of such scanning mirror is affected by vibration or mechanical shocks due to unstable structures commonly adopted, such as gimbaled rings and fold-up mirrors. [START_REF] Chu | MEMS: The Path to Large Optical Crossconnnects[END_REF][START_REF] Bishop | The Lucent LambdaRouter: MEMS Technology of the Future Here Today[END_REF][START_REF] Wang | Development of 1×4 MEMS-based optical switch[END_REF] In this paper, we present a new scanning mirror based on MEMS technology with precision control of scanning angle without the complexity of position sensing and control servo. Based on the sandwich-like mechanical structure, good reliability under vibration or mechanical shock can be expected. A unique die-to-die assembly structure is also introduced, which is critical in realizing the mirror function. Based on the concept depicted in Fig. 1, a multi-axis torsional mirror can be designed, as illustrated in Fig. 2. It includes one mirror (M), four actuators (A, B, C and D) and hinges that link the mirror, substrates and actuators. Each actuator has two actuation states. The floating plate can be pulled towards the upper or lower substrate. The fixed electrodes are located on the substrates and thin layers of dielectric material are coated on the surface of electrodes to avoid short circuit with floating plate when they are attached. The number of tilting orientations can increase by adding the number of actuators. There are two methods (or modes) of actuation can drive the present mirror system. In the 1 st actuation mode, only two opposite actuators, e.g. A&C or B&D as shown in Fig. 2, are actuated. The other two actuators are kept in idle. Under this mode, the mirror is rotated round one axis (x or y) as depicted in Fig. 2. In the 2 nd actuation mode, all the four actuators are driven simultaneously. Two adjacent actuators, e.g. A&B, are pulling the floating plate upwards, while the other two plates, e.g. C&D, are pulling the floating plate downwards. Therefore the mirror rotates along axis ξ or η, as marked in Fig. 2. In total the mirror has 8 tilting states apart from the original state, and each state contributes one deflection orientation.

DESIGN OF NEW SCANNING MEMS MIRROR

MICROFABRICATION AND ASSEMBLY

Comprehensive modeling and simulation associated with various geometrical design of mirror structure has been done on Coventorware TM . Two different geometrical configurations, type "+"and "Φ", were used for positioning the supporting springs vs. electrodes as shown in Fig. 3 In type "+", the mirror is linked with electrodes by one pair of springs and linked with anchored substrate through another pair of spring. While in type "Φ", each electrode is linked with mirror at one end and linked with anchored substrate at the other end. This "Φ" type structure can significantly save chip space compared with "+" type. This is important for multiple-orientation scanning by using more than big number (more than 4) of actuators.

Through the simulation, the geometrical design of mechanical parts was optimized, especially for the shape Z. F. Wang, W. Noell, M. Zickar, N. de Rooij and S. P. Lim Development Of Scanning MEMS Mirror With New Assembly Structure and dimension of springs. In the final design we used for fabrication, the displacement of actuator (floating electrode) under pull-in condition can be largely (more than 90%) converted into the deflection of mirror plate.

A 3-layer sandwiched structure was employed in device realization, which composed of a SOI structure for making all the moving parts, e.g. mirror, floating electrode and supporting springs, and two metalised glass structure for building upper and bottom electrodes. The three wafers, e.g. one SOI and two glass wafers were fabricated individually through MEMS process in wafer level, and then went to wafer dicing process and assembly. Each micromirror device is made up of 3 dies coming from the 3 wafers. Fig. 4 shows the fabrication process flow. The fabrication started from DRIE process on both sides of SOI wafer, which has top silicon thickness of 110 µm, as illustrated in Fig. 4(a). [START_REF] Marxer | Micro-opto-Mechanical 2×2 Switch for Single-Mode Fiber Based on Plasma-Etched Silicon Mirror and Electrostatic Actuation[END_REF] Through over etching of the buried oxide layer, as shown in Fig. 4(b), the bottom block of silicon was released. On the other hand, wet etching process was taken on two glass wafers to form recess with 10 µm depth, as shown in Fig. 4(c), followed by metallisation, patterning, and deposition of dielectric layer for insulation. Two glass wafers were fabricated under same process flow but with different photomask for metal patterning, as illustrated in Fig. 4(d). The three wafers were then diced into different sizes. The glass die with upper electrodes was diced into identical size of the released back silicon block, so that it could be easily assembled to the SOI die with precise alignment.

As shown in Fig. 4 (d), the floating electrodes on SOI were seating between their corresponding fixed electrodes on top and bottom glass dies with dielectric layer in between. In practical, the top glass wafer will be preperforated so that the optical beam can go in, be reflected by the tilting mirror and go out. For better optical reflectivity, the mirror surface can be coated with gold or aluminum through evaporation process.

Fig. 5 Stacking contact scheme for electrical wiring

The electrical wiring of the electrodes from the SOI die and the two glass dies was realized by the stacking contact applied during die assembly. In order to apply voltage to the electrodes on top glass, the SOI die serves as interconnection media between top and bottom glass through the conductive silicon substrate. The top silicon block of SOI was divided into several electrically-isolated zones by through etching, as shown in Fig. 5. The electrode on top glass is linked with certain separated zones on SOI through direct contact with metal pads outside the recess area, as labeled "T" in Fig. 4(d). Through proper layout design, such zones eventually contact with electrodes E t on bottom glass, which acts as the control pads of the electrodes on the top glass die. Meanwhile, the connected zone with floating electrode and mirrors are linked with other electrodes on bottom glass, E f , through direct contact, which acts as the control pad of the silicon parts. The contact pad of bottom electrode, labeled as E b , is directly wired out from the bottom recess. In practice, conductive paste can be applied on the contact areas before assembly to achieve better connection.

After fabrication, different device designs have been realized. The size of SOI dies is about 4×4 mm 2 , which include all the moving structures and also serve as the electrical contact media for top and bottom glass dies. In all the designs, mirror is in round shape with diameter of 100 µm and thickness of 110 µm, which is identical with Z. F. Wang, W. Noell, M. Zickar, N. de Rooij and S. P. Lim Development Of Scanning MEMS Mirror With New Assembly Structure that of the top silicon layer of SOI wafer. The top glass die is in size of 2×2 mm 2 , which is equal to the size of the released block of back silicon layer of SOI wafer. This arrangement is for the self-alignment during the assembly with top glass die and SOI die. The bottom glass die, where located the control pads for all the electrodes on the three dies, is 5×5 mm 2 , which equals to the final size of micromirror device after assembly.

Fig. 6 shows the optical microscopy image of SOI dies under different designs after microfabrication process. In device (a), the floating electrodes are with size of 100×100 µm 2 and allocated 80 µm away from the nearest edge of the mirror. The width of spring between floating electrode and mirror is 5 µm. The narrowest part of supporting spring between mirror and anchored substrate has a width of 2-3 µm. In device (b), which represents the "Φ" type design illustrated in Fig. 3 Electrical test has been done on the assembled devices with all the nine designs by applying DC voltage. The mirror can be successfully driven upon the pull-in of the floating electrode under electrostatic force generated between opposite electrodes. The pull-in voltages measured out are in general among 50-100 volts. The tilting angle for device A and B shown in Fig. 6 is approximately 6º and 12º, respectively.

CONCLUSION

In this paper, we present the development of a unique structure for micromirror based on MEMS technology. Accurate control of mirror orientation can be expected due to the structural design. The mirror is always driven into a pre-determined tilting position upon actuation. No sensor or control servo is required for position (or angle) tuning. The mirror can perform good anti-vibration property because that the mirror is constrained by at least two complimentary actuators. It is less susceptible to external vibration in comparison with conventional torsional mirrors. The micromirror device can be extended into larger scale scanning by adding on more actuators, which means more deflection orientations can be realized through multi-axis mechanism.

Other than serving as the switching element in telecommunications, applications in chemical/bio-medical measurement and scanning laser system can also be expected with the integration of this 3D MEMS mirror, which shows good potential in terms of mechanical stability and reliability.

Fig. 1

 1 Fig. 1 Basic Working Principle of Scanning Mirror An optical mirror system with multi-axis deflection is designed to perform light beam scanning with discrete deflection orientation. Fig. 1 depicts the basic working principle of the optical mirror system. The mirror (M) and two actuators are shown in Fig. 1 (a). Each actuator includes a floating plate (electrode) and two fixed electrodes. The opposite electrodes, A1/A2, C1/C2, are anchored on two parallel planar substrates. Two floating plates, A/C, which are made of conductive material, are used as electrodes under actuation and linked with the mirror through hinges (H1, H2). Without applying voltage, the actuators are in their idle state; A/C are seating in the middle of the gap between A1/A2 and C1/C2, respectively. Upon actuation, one electrode of the actuator is charged by DC voltage, thus electrostatic force is generated and pulls the floating plate. When the two actuators are actuated in a complementary way, as shown in Fig. 1 (b), the mirror is rotated through the pivot

Fig. 2

 2 Fig. 2 Multi-Axis Torsional Mirror, Exclusive of the Upper Substrate

  Fig. 3 COVENTOR simulation: 2 configurations of spring vs. electrode

Fig. 4

 4 Fig. 4 Fabrication process flow

Fig. 6

 6 Fig. 6 Optical microscopy images of fabricated mirror devices (close-up view of the SOI part)

ACKNOWLEDGEMENTS

This research is financially supported by the Agency for Science, Technology and Research (A*Star), Singapore.


Terence O'donnell

Chitta Saha

Steve Beeby

John Tudor

SCALING EFFECTS FOR ELECTROMAGNETIC VIBRATIONAL POWER GENERATORS

This paper investigates how the power generated by electromagnetic based vibrational power generators scales with the dimension of the generator. The effects of scaling on the magnetic fields, the coil parameters and the electromagnetic damping are presented. An analysis is presented for both wire-wound coil technology and micro-fabricated coils.

INTRODUCTION

Electromagnetic principles are one means by which power can be harvested from ambient vibrations. This generally consists of using the vibrations to move a magnet relative to a coil, thus inducing a voltage in the coil defined by Faraday's law. In recent years there have been several reports of vibrational power generators based on the electromagnetic principle [1 -3]. The sizes and structure of these generators have varied and various different power levels have been produced. However it is not clear what the limits are in terms of the power levels which can be generated from ambient vibrations using electromagnetic principles. Vibration based generators are generally aimed at the provision of power to wireless sensor systems. In such systems size is an important consideration and it is generally important that the system be miniaturised. From the application perspective it is therefore useful to understand the relationship between the size of the energy harvesting device and the power which can be generated.

This paper presents a study of how the power which can be generated by an electromagnetic based vibrational energy harvesting device, scales with the size of the device. In order to study the scaling effects there are two factors to be considered. The first is the mechanical energy in the system, which provides an upper limit on the power which can be generated. The second factor to be considered is the efficiency with which the mechanical energy can be transformed to electrical energy.

In a vibrational power generator the available mechanical energy is associated with the movement of a mass through a certain distance. Clearly the available mechanical energy will decrease with the dimensions as both the mass of the moving object and the distance moved is decreased. The electrical energy is extracted from the system by electromagnetic damping. The electromagnetic damping factor depends on flux linkage gradient, the number of coil turns, coil impedance and load impedance. Therefore the efficiency with which the electrical energy can be extracted will also decrease with size (as the magnitude of the magnetic fields decrease with size and the quality of the coils decrease). This study will investigate both effects.

GENERATOR STRUCTURE

The analysis is presented for the electromagnetic generator structure shown in figure 1 below. This structure consists of a coil sandwiched between magnets. The upper and lower magnets consist of two pairs of oppositely polarised magnets. This opposite polarity creates a flux gradient for the coil in the direction of movement, which in this case, is in the x-direction. This is a schematic representation of the type of electromagnetic generator presented in [START_REF] Roundy | A study of low level vibrations as a power source for wireless sensor nodes[END_REF] and [START_REF] Beeby | Power MEMS 2004 conference[END_REF].

Terence O'Donnell, Chitta Saha, Steve Beeby, John Tudor Scaling Effects for Electromagnetic Vibrational Power Generators

In this structure it is assumed that the coil remains fixed while the magnets move in response to the vibration. Since the magnets generally have greater mass, m, than the coil, movement of the magnets is more beneficial than movement of the coil. By placing the coil is the gap between the magnets this structure has the advantage of creating a relatively large magnetic field in the area of the coil. The use of the two pairs of oppositely polarized magnets ensures that the coil is placed in an area of high magnetic field gradient.

For the purpose of the analysis the system is assumed to be well represented by the equations of motion of a resonant mass-spring-damper system [START_REF] Mitcheson | Architectures for Vibration-Driven Micropower Generators[END_REF]. For the purpose of this study we will assume a cubic volume, i.e. x = y = z = d where d is the dimension of the device. Note that only the magnet and coil dimensions are included in the volume. Any practical generator must also include the volume of the housing and the spring. Since the housing and the spring can be implemented in many different ways these are neglected for the present analysis. It is assumed that the spring can be implemented so as to allow the required movement of the mass at the frequency of interest.

The available mechanical energy will depend on the level of vibrations and acceleration to which the device is subjected. However the maximum displacement will be constrained by the volume of any self-contained device, i.e. the peak displacement, x m , is given by the difference between the external dimension, d, and dimension of the mass, x mass . Therefore a choice can be made to have a thin mass with a large displacement or a wide mass with a small displacement. It is of interest to find the optimum ratio of peak displacement, x m , to mass dimension, x mass , which maximises the mechanical energy. Assuming a sinusoidal vibration, and expressing the peak displacement of the mass as x m = (x -x mass )/2, the kinetic energy of the mass can be expressed in terms of the mass dimensions and its displacement; 8

) ( 2 . 2 2 2 mass mass x x yzx mV E K - = = ω ρ (1)
where V is the velocity of the mass, m, ρ is the density of the mass material, x mass , y and z are the dimension of the mass and ω is the angular frequency. By taking the derivative of this with respect to x mass and equating to zero it can be found that the kinetic energy is maximized when x m = x/3. Thus a single magnet x-dimension is taken to be 1/6 of the overall dimension. The magnets are assumed to extend for the full y-dimension. The zdimension of the magnet is taken as 0.4 times the overall dimension. This leaves the gap between the magnets as one fifth of the overall dimension. The coil thickness is assumed to occupy half of the gap. The next section presents the basic equations which are used to describe the behavior of the generator.

ANALYSIS OF GENERATOR

Since the generator is assumed to be describe well by a mass-spring damper system, the basic equation of motion is given by;

o e p F kx dt dx D D dt x d m = + + + ) ( 2 2 (2)
where D p represent parasitic damping, D e represents electromagnetic damping, k is the spring constant, and F o is the driving force, which is given by the mass times the acceleration, a. The parasitic damping represents loss mechanisms such as air damping, squeeze film effects, thermoelastic damping, and friction in the clamping. The electromagnetic damping represents the mechanism by which the electrical power is extracted from the system, i.e. the current flowing in the coil.

The typical solution for displacement given by;

2 2 2 2 ) ( ) ( ) ( ω ω e p o D D m k F t z + + - = (3)
The average electrical power from the generator can be expressed as;

] ) ( ) [( 2 2 2 2 2 2 2 0 ω ω ω e p e avg D D m k F D P + + - = (4)
At resonance with ω = ω n this reduces to; The power at resonance is maximized if D e = D p and this maximum power, P max , is given by;

p D ma P 8 ) ( 2 max = (6)
Alternatively this can be expressed using the damping ratio, ζ p = D p /(2mω n ) and open circuit quality factor of the system, Q oc = 1/ (2ζ p ) , as;

oc n Q ma P ω 8 2 max = (7)
This maximum power can only be achieved if the electromagnetic damping can be made large enough to match the parasitic damping. The electromagnetic damping factor is given by;

Terence O'Donnell, Chitta Saha, Steve Beeby, John Tudor Scaling Effects for Electromagnetic Vibrational Power Generators

) ( 1 2 2 c l c e L j R R dx d N D ω φ + +       = (8)
where N is the number of coil turns, dφ/dx is the average flux linkage per turn for the coil, R c is the coil resistance, L c is the coil inductance and R l is the load resistance.

The flux linkage gradient dφ/dx can be assumed to be a constant only if flux linkage varies linearly with displacement of the magnet relative to the coil. The linearity of the flux linkage can be investigated using Finite Element Analysis (FEA). Figure 2 shows the fluxlinkage vs. displacement curve obtained from a 3D FEA model of a generator with a 6 mm dimension. The magnets are assumed to be made from bulk sintered, NdFeB. As can be seen the flux linkage varies linearly over most of the displacement, but flattens out towards the end. The corresponding flux linkage and voltage vs. time plots (for an arbitrary 100 turn coil and a 100 Hz frequency). The flattening of the flux linkage at the outer limits of the displacement results in a distortion of the voltage waveform, which depends on the gradient of the flux linkage. The voltage is no longer perfectly sinusoidal. For the present analysis we will ignore the non-linearity and approximate the flux linkage gradient by a line fit. If the magnet size were increased relative to the coil then the flux linkage could be made linear over the displacement range, although this would deviate from the optimum dimensions for maximising kinetic energy as outlined earlier.

The other parameters which contribute to the electromagnetic damping such as coil resistance and inductance will be dependant on the number of turns in the coil. In order to maximize the power the electromagnetic damping should be chosen to be equal to the parasitic damping by choosing the number of turns for the coil and the load resistance. The next section presents an analysis of how the electromagnetic damping will scale with the dimension of the generator for the structure shown in figure 1.

SCALING

For the scaling analysis, it is assumed that as the dimension is reduced, all of the relative dimensions are retained. Thus for example at a dimension of 10 mm the magnets are 4 mm in height, with a 2 mm gap between them. At a dimension of 1 mm the magnets are 0.4 mm in height with a gap of 0.2 mm between them. The scaling of the kinetic energy and the maximum power with dimension is relatively easy to determine using equations ( 1) and ( 6). However the maximum power can only be extracted if the electromagnetic damping can be controlled. As equation [START_REF]Transformer and Inductor Desing Handbook[END_REF] shows, the magnitude of the electromagnetic damping depends on the magnet parameters and the coil parameters. Obviously the magnetic fields will decrease with dimension and the resistance of coils tends to increase. These effects are investigated in the following sections. Another critically important aspect of the generator is the parasitic damping.

A detailed analysis of how this scales with dimension is beyond the scope of this paper, however parasitic damping is discussed in section 4.4.

Magnetic fields

For the electromagnetic generator the important parameter for the magnets is not the flux density but

Terence O'Donnell, Chitta Saha, Steve Beeby, John Tudor Scaling Effects for Electromagnetic Vibrational Power Generators rather the flux linkage gradient. As can be seen from equation [START_REF]Transformer and Inductor Desing Handbook[END_REF] the flux gradient must be maximized in order to maximize the electromagnetic damping. It would be expected that the magnitude of the field remains constant with scale reduction and that the gradient of the field would actually increase [START_REF] Cugat | Magnetic Micro-Actuators and Systems (MAGMAS)[END_REF]. However in the present case the parameter of importance is the gradient of the flux linkage with the coil, which of course depends on the area of the coil. Therefore if the dimension of the generator is reduced by a factor, b, the flux density gradient will increase by a factor, b, and the area of the coil will decrease by a factor, b 2 . Thus the overall effect is for the flux linkage gradient to decrease by a factor, b. This reduction can be verified by finite element analysis (FEA). The graph in figure 4 plots the flux linkage gradient obtained from 3D FEA on various generator structures with dimensions, d, varied from 1 mm to 10 mm. The graph shows a linear dependence of the gradient on the dimension.

Coil Parameters

The coil parameters such as number of turns, resistance and inductance are not independent. If the coil volume is fixed then the coil resistance and inductance depends on the number of turns. If certain technology specific parameters for the coils are fixed then the resistance and inductance can be expressed in terms of the number of turns. Generally coils can be fabricated using either wirewinding or using micro-fabrication techniques. For a wire-wound coil we assume a multilayer, circular coil with a given inner radius, r i , and outer radius, r o , and thickness, t . The resistance of the coil can be expressed as

wire MT cu c A NL R ρ = (9)
where ρ is the conductor resistivity, assumed to be the resistivity of copper, N is the number of turns, L MT is the length of the mean turn, and A wire is the cross sectional area of the wire. The area of the wire can be related to the overall cross sectional area of the coil, A coil , by assuming a certain copper fill factor, k cu , i.e. A wire = k cu A coil /N. The copper fill factor depends on tightness of winding, variations in insulation thickness and winding shape. In wire wound transformers copper fill factors in the range of 0.5 to 0.6 can be achieved [START_REF]Transformer and Inductor Desing Handbook[END_REF]. For a given inner and outer coil radius the coil resistance can therefore be expressed as;

t r r k r r N R i o cu i o cu c ) ( ) ( 2 - + = π ρ (10)
The coil inductance can also be expressed as a function of the number of turns and the coil geometry however for the present analysis the inductance is neglected as the resistive impedance of the coil is always significantly larger than the inductive impedance at 1 kHz. It can be seen from ( 10) that for a constant number of turns the coil resistance is proportional to the inverse of the scaling factor provided that the copper fill factor does not depend on the scaling, (an assumption which would merit further investigation).

For a micro-fabricated coil, the resistance is more conveniently expressed in terms of the number of turns, the turn width, w, spacing, s, and thickness, t, and the coil outer, d o , and inner dimensions, d i . If it is assumed that the tracking spacing, track width and thickness are equal, then the coil resistance for a single layer, microfabricated coil can be expressed as;

) 4 4 ( ) ( ) ( 8 2 3 2 N N N d d d d R i o i o cu c + - - + = ρ (11)
For large N, the N 2 and N terms can be neglected. The dependence of the coil resistance on the cube of the number of turns arises in this case, from the fact that the turn cross-sectional area decreases with the number of turns squared, i.e. both track width and thickness decrease with N. Again we can see from [START_REF] Pourkamali | High-Q single crystal silicon HARPSS capacitive beam resonators with self aligned sub-100-nm Terence O'Donnell[END_REF] that for a constant number of turns the coil resistance is proportional to the inverse of the scaling factor.

The number of turns in any given area can be increased only to the extent which the particular technology allows. Thus in the case of wire winding the main constraint is the minimum wire diameter, which may be as low as 12 µm. For a microfabricated coil the limitation is the minimum turn width or spacing. With advanced processes this can be submicron, although 1 µm is a reasonable practical limit for relatively standard photolithography.

Electromagnetic damping

Terence O'Donnell, Chitta Saha, Steve Beeby, John Tudor Scaling Effects for Electromagnetic Vibrational Power Generators In section 4.1 it was shown that the flux linkage gradient scales linearly with dimension. Equation ( 10) and ( 11) also show that the coil resistance has an inverse dependence on scaling factor. This would therefore suggest that the EM damping would have a dependence on the cube of the scale factor. However this can be compensated for to some extent, by increasing the number of turns and decreasing the load resistance as the EM damping also depends on these. However the extent to which this can be done depends on the relationship between the coil resistance and the number of turns. If the relationship in equation ( 10) holds for a wire wound coil then the EM damping factor can be increased by increasing the number of turns, because the coil resistance only increases at the same rate as the number of turns squared (R c ∝ N 2 ) . However if the relationship in [START_REF] Pourkamali | High-Q single crystal silicon HARPSS capacitive beam resonators with self aligned sub-100-nm Terence O'Donnell[END_REF] holds for a micro-fabricated coil then the coil resistance increases at a faster rate than the number of turns squared (i.e. R c ∝ N 3 ) so that in this case an increase in the number of turns actually reduces the EM damping.

It is therefore the case that the EM damping scales differently with dimension depending on the relationship between coil resistance and number of turns. For a wire wound coil the EM damping can depend on scale factor squared, but for a micro fabricated coil it can depend on the scale factor cubed.

Parasitic damping

The parasitic damping occurs due to effects such as air damping, squeeze film damping, clamping friction for the beam, and thermoelastic damping. There have been considerable efforts to find analytical expressions for these various damping mechanisms particularly for Silicon based MEMS devices such as resonators [START_REF] Hosaka | Evaluation of energy dissipation mechanisms in vibrational Microactuators[END_REF] [START_REF] Zhang | Viscous air damping in laterally driven microresonators[END_REF]. These damping effects cannot be estimated without defining the beam dimensions and material which has not been addressed in this paper. However as will be shown in the next section unloaded (no EM damping) quality factors of tens of thousands are required in order to get the maximum energy from the structures considered here. Quality factors of this magnitude have been reported for Silicon based beam structures [START_REF] Pourkamali | High-Q single crystal silicon HARPSS capacitive beam resonators with self aligned sub-100-nm Terence O'Donnell[END_REF], however the quality factor obtained for fabricated generators have only been of the order of several hundreds [START_REF] Beeby | Macro and Micro Scale Electromagnetic Kinetic Energy Harvesting Generators[END_REF]. In the analysis presented in the next section both levels of parasitic damping are considered. It is clear that a more thorough understanding of the sources of parasitic damping is required in order to fully optimize the generators.

DISCUSSION OF SCALING EFFECTS

In order to investigate the effects of scaling on the power which can be generated from an electromagnetic generator, we assume a vibration frequency of 1 kHz and an acceleration level of 9.81 m/s 2 . The magnets are assumed to consist of sintered NdFeB. Using equation [START_REF] Mitcheson | Architectures for Vibration-Driven Micropower Generators[END_REF] it is relatively straightforward to plot the available the maximum electrical energy vs. the generator dimension assuming an open circuit quality factors. Since the power depends on the square of the mass then the power will scale with the sixth power of the scaling factor for a constant unloaded Q-factor. However the real scaling will depend on how the parasitic damping scales with dimension. However equation [START_REF] Mitcheson | Architectures for Vibration-Driven Micropower Generators[END_REF] assumes that the EM damping can be made equal to the parasitic damping. This can only be achieved if the parasitic damping is low enough. If the parasitic damping is very high then the situation can arise where the EM damping cannot be increased to equal the parasitic damping. This leads to two different strategies for maximizing the electrical power from the generator. Where D p is comparable to D e then power is maximized when load resistance and number of turns are chosen so as that D e is made equal to D p . However when D p >> D e power to the load is maximized when the load and coil resistance are equal (the usual maximum power transfer condition).

Figure 5 below plots the maximum electrical power and the power delivered to the load for generator dimensions from 1 mm to 10 mm for both wire-wound coils and micro-fabricated coils. Curves are plotted for unloaded Q-factors in the range of 2000 -30,000 which allow an unloaded displacement of twice the maximum displacement and for an unloaded Q-factor of 300, which is more typical of what has been measured on generators fabricated to date. For the large unloaded Q-factors, the characteristics of the wire-wound coils allow the EM damping to be made equal to the parasitic damping for all but the smallest dimensions. For small dimensions the number of turns is limited by the minimum wire diameter which is taken to 12 µm. For the micro-fabricated coils the EM damping cannot be made equal to the parasitic damping because of the high coil resistance.

For the unloaded Q-factor of 300 the parasitic damping is typically an order of magnitude larger than the maximum EM damping achievable even with the wire wound coil. In this situation the displacement is much less than the maximum allowed and is controlled by the parasitic damping, i.e. changes in the EM damping have little effect on the displacement. In this case the load resistance is set equal to the coil resistance in order to achieve maximum power transfer to the load.

The graph shows that if high unloaded Q-factors can be obtained then the theoretical maximum power can be Terence O'Donnell, Chitta Saha, Steve Beeby, John Tudor Scaling Effects for Electromagnetic Vibrational Power Generators extracted from the generator using a wire-wound coil. This is because the high EM damping can be achieved and little power is lost in the coil due to the resistance. However only a fraction of the theoretical maximum energy can be extracted using micro-fabricated coil due to the higher resistance which has the effect of limiting the EM damping and also increasing loss in the coil. It is interesting to not that at small dimensions the power extracted using a micro-coil can exceed that extracted using a wire-wound coil due to the limitations in minimum wire diameter. The load voltages for the generators are plotted in figure 6 below. It can be seen from this that the load voltages obtained from the micro-coils are unacceptably low if the open circuit quality factor of the generator is low.

CONCLUSIONS

With high enough mechanical Q factor the performance of the generator is not limited if wire wound coils are used, i.e. the optimum condition for maximum power generation can be achieved. In this case the power scales approximately with the fourth power of the dimension. However the use of micro-fabricated coils tend to limit the generator performance due to the large coil resistance. However micro-fabricated coils will have better performance than wire-wound coils at dimensions less than 2 mm. From measured results on fabricated generators it would appear that the mechanical Q is a limiting factor. The source of is an important area for further investigation.

Figure 1 :

 1 Figure 1: Schematic representation of the electromagnetic generator. In this case the magnets vibrate relative to the coil in the x-direction. The peak displacement, xm = (xxmass)/2.

Figure 2 :

 2 Figure 2: Flux linkage vs. displacement plot for a generator with a 6 mm outer dimension.

Figure 3 .

 3 Figure 3. Flux linkage and voltage vs. time for a generator with a 6 mm outer dimension.

Figure 4 :

 4 Figure 4: Variation of flux linkage gradient with generator dimension.

Figure 5

 5 Figure 5 Maximum power and power delivered to the load for generator dimensions from 1 mm to 10 mm.

Figure 6 .

 6 Figure 6. Load voltages for generator dimensions from 1 mm to 10 mm.

ACKNOWLEDGEMENTS

The authors wish to acknowledge fund for this work under the European Union Framework 6 STEP project VIBES, project reference 507911.