Lars Geir

Whist Tvedt

Lars-Cyril Julin Blystad

Einar Halvorsen
email: einar.halvorsen@hive.no

Simulation of an Electrostatic Energy Harvester at Large Amplitude Narrow and Wide Band Vibrations

An electrostatic in-plane overlap varying energy harvester is modeled and simulated using a circuit simulator. Both linear and nonlinear models are investigated. The nonlinear model includes mechanical stoppers at the displacement extremes. Large amplitude excitation signals, both narrow and wide band, are used to emulate environmental vibrations. Nonlinear behavior is significant at large displacement due to the impact on mechanical stoppers. For a sinusoidal excitation the mechanical stoppers cause the output power to flatten and weakly decrease. For a wide band excitation, the output power first increases linearly with the power spectral density of the input signal, then grows slower than linearly.

I.

INTRODUCTION

Decreasing power consumption of autonomous sensor systems makes it possible to obtain longer periods of system operation before maintenance is needed. By getting rid of replacement or manual recharging of batteries, maintenance free operation should in principle be possible. As the surrounding environment holds energy in various forms, it can be utilized to provide the system with the needed electrical power. One possible power source that has received considerable attention in recent years is energy harvesting from motion [START_REF] Beeby | Energy harvesting vibration sources for microsystems applications[END_REF].

The possible transduction mechanisms that can be exploited for motion micro energy harvesting are conventionally categorized as piezoelectric, electromagnetic and electrostatic. Of these, the electrostatic principle is the one that relies on the most mature MEMS processes. These devices typically employ the same construction elements as used for MEMS accelerometers, i.e. a proof mass suspended in some beams, and variable capacitors based on one electrode set attached to the moving mass and one set of fixed counter electrodes attached elsewhere in the structure.

How to bias electrostatic harvesters is a challenge. The idea of providing a voltage source to the harvester seems to defeat its purpose, but makes sense if the source is part of the energy storage and power handling electronics associated with the harvester [START_REF] Meninger | Vibration-to-Electric Energy Conversion[END_REF]. In that case the harvester needs to be kick-started at the beginning of its operational life.

A design that employs an electret as an internal bias and therefore avoids the need for external bias was proposed by Sterken et.al. [START_REF] Sterken | A new power MEMS component with variable capacitance[END_REF]. A sketch of this type of electrostatic energy harvester with internal bias is shown in Fig. 1, top and middle drawing. In the equivalent circuit, bottom drawing of Fig. 1, the electret is represented by the voltage source V e in series with the capacitance C e . An advantage of this design is that its transduction is quite insensitive to stray capacitances between the (large) proof mass and the package. This type of design is often referred to as an in-plane overlap converter [START_REF] Roundy | Energy Scavenging for Wireless Sensor Networks[END_REF]. The structure also can be used with an external bias.

The in-plane overlap varying converter was modeled in [START_REF] Sterken | A new power MEMS component with variable capacitance[END_REF] by the use of equivalent circuit models. In [START_REF] Peano | Design and optimization of an electretbased capacitive energy scavenger[END_REF], optimization of this device was studied with emphasis on the effect of nonlinearities for a fixed drive frequency and amplitude. Nonlinearities were further studied under sinusoidal excitation in [START_REF] Peano | Nonlinear oscillations in a MEMS energy scavenger[END_REF]. All these analyses were made for sinusoidal excitations with amplitudes sufficiently small that the capacit- ance is still given by the plate capacitor formula and the effect of mechanical stoppers can be neglected.

In the present work we investigate the effect of the acceleration magnitude on an in-plane overlap varying device by simulation. We consider the full range from the linear regime and well into the nonlinear regime where the driving signal is sufficiently large that the effect of mechanical stoppers must be considered. For simplicity we consider rigid stoppers and elastic impacts only. In addition to a sinusoidal driving signal, we also consider broadband excitations with a flat power spectral density (PSD) from zero frequency up to a frequency well above the harvester resonance frequency. The method is similar to that described in [START_REF] Halvorsen | Simulation of Electromechanical Systems Driven by Large Random Vibrations[END_REF].

The simulations are made using a design that we have targeted for the current Tronics multi project wafer process using silicon on insulator (SOI) wafer technology with a device layer thickness of 60µm [8].

II.

ENERGY HARVESTER MODEL

In order to simulate the energy harvester performance, we have made a lumped element model. The model is based on a single mechanical degree of freedom (position of proof mass) and two electrical degrees of freedom (charge on the variable capacitors). A schematic model of the device in Fig. 1 is shown in Fig. 2 and consists of a moving mass, its suspension in the form of a spring, mechanical damping through a dashpot and two variable capacitors that vary out of phase as indicated. Two parasitic capacitances are also included.

The electromechanical transduction is described by the equations

(1) (2) (3)
where F T is the force exerted on the transducer, V L1 and V L2 are the voltages across the electrical ports, x is the displacement of the proof mass, k is the spring stiffness, V e is the voltage of the electret, C e is the capacitance of the electret, and q 1 (q 2 ) is the charge on the variable capacitor C 1 (C 2 ).

For the in-plane gap overlap converter, the capacitances of the variable capacitors are given by ( 4) [START_REF] Peano | Design and optimization of an electretbased capacitive energy scavenger[END_REF] where N g is the number of fingers of the comb structure, ε is the permittivity of the medium between the two capacitor electrodes, t f is the thickness of the fingers (equal to the device layer of the SOI wafer), x 0 and g 0 are the nominal overlap of and gap between the finger structures of the capacitor electrodes respectively.

Linearization of (1-3) yields the following three equations for the electromechanical transduction (6) ( 7)

| (8)
where ∆q 1 and ∆q 2 are small changes in the charge on the two capacitor electrodes. x is a small value itself since the equilibrium position is x=0. The couplings between the mechanical and electrical domains are given by α 1 and α 2 :

1 x i 1,2. ( 9
)
where q 0 is the equilibrium charge on either capacitor.

In the lumped model, we include elastic stoppers to allow driving the system at large amplitude accelerations. In the model, they are represented by springs that are only in effect at sufficiently large displacements (Fig. 3).

The purpose of the stoppers is to limit the mass displace- ment, as to prevent structural damage, sticking, and avoid short circuiting of the electrodes. Stoppers must obviously be implemented in a real device, and should also be present in the model, as they affect the harvester operation at sufficiently large mass displacements. Stoppers are implemented in several previous designs [START_REF] Sterken | A new power MEMS component with variable capacitance[END_REF][START_REF] Roundy | A study of low level vibrations as a power source for wireless sensor nodes[END_REF][START_REF] Mitcheson | MEMS electrostatic micropower generator for low frequency operation[END_REF][START_REF] Bren | Optimization of Inertial Micropower Generators for Human Walking Motion[END_REF], but little has been reported on how stoppers are modeled.

The elastic stoppers are modeled as opposing spring forces when in contact:

0 , , , (10)
where F s is the force of the stoppers, k s is the spring stiffness of the stoppers and x s is the displacement at which the stoppers starts acting (maximum possible displacement of the energy harvester). We choose k s very large compared to k to mimic hard walls.

To avoid unreasonable capacitance variations at large displacements, the variable capacitances are "cut off" at both ends as in Fig. 4 and can be expressed as

, , , (11) , , , (12)
where C max and C min are the limiting values of the variable capacitances. x c is the displacement of the mass at which the limits are reached. The cut-off on the minimum capacitance is necessary to avoid an unphysical negative value when the overlap goes through zero. We have x c > x s so that the cutoff is rarely in effect.

Motion of the mass inside the cavity will create gas flow along the mass and its finger structures. We assume Couette flow, giving the damping coefficient

2 ( 13
)
where η is the viscosity of the gas, l f is the length of the capacitor fingers, A m is the area of the mass and d is the distance between the mass and the top and bottom cap of the cavity in which the mass is moving. Newton's second law for the mass gives (14

)
where m is the mass and ma is the fictitious force experienced due to the acceleration of the device.

For the electrical degrees of freedom, the equations of motion depend on the load represented by the resistors R L1 and R L2 and stray capacitances in Fig. 2. Since the model is implemented in a circuit simulator in section III, it can be simulated with almost arbitrary power conditioning circuitry, but we have chosen to use simple load resistors to keep focus on the characteristics of the MEMS device.

The dimensions of the energy harvester are given in Table I and derived model parameters are given in Table II.

III.

SPICE IMPLEMENTATION

The model is represented by an equivalent circuit using the e-V convention which we have implemented in a SPICE simulator. For the mechanical part, the forces are represented by voltages, displacements by charges and velocities by currents. Stiffness is then represented by a capacitor of "capacitance" 1/k, mechanical damping by a resistor of "resistance" b, and inertia by an inductor of "inductance" m.

The sinusoidal vibration signal is represented as a sinusoidal voltage source of a given frequency and amplitude. For broadband vibrations a voltage source with input from a source file with a synthetically generated random broadband signal are used.

The mechanical stoppers are implemented using a behavioral voltage source.

A. Linear SPICE Model

Fig. 5 shows the linear lumped model equivalent circuit based on (6-8) and used for the SPICE simulations. We have used behavioral voltage sources to implement the coupling between the mechanical and electrical parts of the model. In the behavioral model, x is found by using the voltage V m across the capacitor and its value.

The main purpose of the linear model is to compare to the more realistic nonlinear model and identify their differences. We therefore do not include stoppers in the linear model.

C 0 is the nominal capacitance of the variable capacitors, and C P models the parasitic capacitances at the output nodes.

B.

Nonlinear SPICE Model Fig. 6 shows the nonlinear lumped model equivalent circuit based on (1-3) used for the SPICE simulations. The variable capacitors, the last element in [START_REF] Meninger | Vibration-to-Electric Energy Conversion[END_REF] and in [START_REF] Sterken | A new power MEMS component with variable capacitance[END_REF], are realized using a behavioral voltage source in series with a fixed capacitor with value C 0 . V 0 is the voltage across the fixed capacitor. The voltage, V S , is then given by:

1 (15) 1 (16)
IV.

SIMULATION RESULTS AND DISCUSSION

To investigate the effect of increasing excitation strength both for sinusoidal and for wide band excitation, we first found the optimum load in the linear regime for these two cases. Using this as a starting point, we have performed simulations at various excitation levels.

Results from the simulations on the linear model for a sinusoidal input signal and with increasing frequency and load resistance are shown in Fig. 7. An optimum driving frequency of 1190 Hz and a load resistance of 28 MΩ have been found. In Fig. 8, for the same model with a broadband input signal and increasing load resistance, the same optimum load resistance of 28 MΩ was found. In general they will differ [START_REF] Halvorsen | Broadband excitation of resonant energy harvesters[END_REF]. Due to the small electromechanical coupling they coincide here.

Fig. 9 shows a close-up of phase space plots for the proof mass when driving with a sinusoidal signal. In the simulations the stopper is set to act at displacements larger than 14 µm. The action of the stoppers at displacements larger than this is visible at both 5 g and 10 g. At 3.7 g the displacements are at the limit of the maximum displacement before the stoppers begin to act. For small amplitude vibrations we have an elliptic looking trajectory, which becomes distorted as the stopper comes into effect. Fig. 10 shows a phase space plot for the same model driven by a broadband random acceleration with a PSD of 0.015 g 2 /Hz. Due to the random character of the motion, the trajectory is not cyclic. Nevertheless, since the harvester is quite narrow band it has some cyclic like behavior. When the excitation is increased to 0.045 g 2 /Hz, we get the trajectory shown in Fig. 11. Here the effect of stoppers is clearly seen. Fig. 12 shows the output power of the linear versus the nonlinear model under sinusoidal excitation of fixed frequency. For the nonlinear model at low nonlinearity (before stoppers come into effect) the transduction is more effective and gives a larger output power than what is the case for the linear model. At larger displacements, where the stoppers act more frequently, the output of the nonlinear model flattens and starts to decrease weakly at increasing input vibration amplitude. As the stoppers come into effect, the frequency at which the motion is in phase with the excitation will start to increase; therefore transduction is much less effective at the fixed drive frequency which was optimal in the linear regime.

Fig. 13 shows the average output power and mean square displacement of the mass versus PSD of the input wideband signal for the nonlinear model. The output power increases linearly with the PSD for low level excitations, as it should according to theory [START_REF] Halvorsen | Broadband excitation of resonant energy harvesters[END_REF]. For larger excitations the output power continues to increase, but at a lower rate. The reason why the stoppers have considerably less dramatic effect in the broad band case is that even if the harvester's sensitive frequency drifts as a function of drive level, there are always frequency components at this frequency in the excitation signal. This is true until the sensitive frequency drifts out of the excitation bandwidth.

V.

CONCLUSIONS

We have made a lumped model of an electrostatic in-plane overlap varying energy harvester. The model includes both nonlinearities in the transduction mechanism and the effect of mechanical stoppers for large displacements.

We have demonstrated simulations of the energy harvester for both narrow and wide band excitations using a SPICE implementation of the lumped model.

For a sinusoidal input signal the nonlinear model has a more effective transduction than the linear model at low nonlinearity, but increasing the input signal strength beyond the point where the mechanical stoppers starts acting causes the output power to flatten and weakly decrease. For a wide band excitation, the output power increases linearly with the PSD of the input signal for low signal strength. As the excitation strength increases, the output power continues to increase, but grows slower than linearly with respect to the power spectral density. At a PSD of 0.05 g 2 /Hz the output power is approximately 400nW.

ACKNOWLEDGMENT

We thank E. Westby and S. Husa for useful discussions.

Fig. 1 :

 1 Fig. 1: Schematic view of an electrostatic energy harvester. The harvester has one ground electrode (0), a moving electrode (m), and two static electrodes (1 and 2). Top: Top view. Middle: Side view. Bottom: Equivalent circuit.

Fig. 2 :

 2 Fig. 2: Model of the energy harvester including both the mechanical and electrical subsystems.

Fig. 3 :

 3 Fig. 3: Representation of elastic stopper model.

Fig. 4 :

 4 Fig. 4: Representation of the limitations done to the variable capacitances and their derivatives.

Fig. 6 :

 6 Fig. 6: Equivalent circuit used for simulations on the nonlinear energy harvester model in SPICE. Top: The mechanical part. Bottom: The electrical part.

Fig. 5 :

 5 Fig. 5: Equivalent circuit used for simulations on the linear energy harvester model in SPICE. Top: The mechanical part. Bottom: The electrical part.

Fig. 7 :

 7 Fig. 7: Linear model, average power versus driving frequency and load resistance at a sinusoidal input signal of 1 g acceleration. Filled square:Optimum power output at 1190 Hz and a load resistance of 28 MΩ.

Fig. 8 :

 8 Fig.8: Linear model, average power versus load resistance for a wideband input signal. Optimum output power is found with a load resistance of 28 MΩ.

Fig. 9 :

 9 Fig. 9: Phase space plots for nonlinear model with sinusoidal excitations.

Fig. 10 :Fig. 11 :

 1011 Fig. 10: Phase space plot for nonlinear model at wideband excitation with a PSD of 0.015 g 2 /Hz

Fig. 12 :

 12 Fig. 12: Linear model versus nonlinear model. The nonlinear model has a more effective transduction than the linear model at low nonlinearity.

Fig. 13 :

 13 Fig. 13: Nonlinear model. Left: Average output power versus PSD. Right: Mean square mass displacement versus PSD.

TABLE I

 I

	DIMENSIONS OF THE ENERGY HARVESTER
	Length of capacitor fingers, l f	30 µm
	Width of capacitor fingers, w f	4 µm
	Thickness of capacitor fingers, t f	60 µm
	Gap between capacitor fingers, g 0	3 µm
	Number of capacitor finger pairs, N g	524
	TABLE II
	MODEL PARAMETERS OF THE ENERGY HARVESTER
	Mass, m	5.78 mg
	Spring constant, k	326 N/m
	Damping constant, b	8.45×10 -4 N-s/m
	Electret voltage, V e	20 V
	Electret capacitance, C e	5 pF
	Parasitic capacitance, C p	1,94 pF
	Initial finger overlap, X 0	15 µm
	Displacement limit of stoppers, X s	14 µm
	Spring constant of stoppers, k s	326×10

3

N/m Displacement limit of variable capacitors, X c 14.5 µm


Hela Boussetta
email: hela.boussetta@imag.fr

Skandar Basrour

Marcin Marzencki

Top-Down Behavioral Modeling Methodology Of A Piezoelectric Microgenerator For Integrated Power Harvesting Systems

In this study, we developed a top/down methodology for behavioral and structural modeling of multi-domain microsystems. Then, we validated this methodology through a study case: a piezoelectric microgenerator. We also proved the effectiveness of VHDL-AMS language not only for modeling in behavioral and structural levels but also in writing physical models that can predict the experimental results. Finally, we validated these models by presenting and discussing simulations results.

I. INTRODUCTION AND MOTIVATION

The importance of wireless sensor networks is highlighted by the increasing number of applications, including disaster relief applications, intelligent building, facility management, environment control, machine monitoring and preventive maintenance.... Realizing such wireless sensor networks is a crucial step toward a deeply penetrating ambient intelligent concept. The power supply is a crucial system component since once the energy supply is exhausted; the node fails (Ref. [START_REF] Karl | Protocols and Architectures for Wireless Sensor Networks[END_REF]). To ensure truly long-lasting nodes, limited energy storage is unacceptable. Rather, Self Powered Micro Systems (SPMS) with their extended autonomy represent a promising answer. The challenge while designing such systems is to deal with the diversity of subsystems containing complex MEMS and different physical domains (mechanical and electrical). Since it is not possible to comprehend such complex systems in their entirety, we need to find methods of dealing with this complexity. In this work, we adopted a top/down methodology for behavioral and structural modeling of multi-domain microsystems. Then, we verified the efficiency of such a methodology by modeling and simulating an integrated power harvesting circuit.

II. MODELING MULTI-DOMAINS SYSTEMS

Several definitions of a model can be found in the literature. One possible definition is the following: "A model represents that information which is relevant and abstracts away irrelevant detail" (Ref. [START_REF] Ashenden | The System Designer's Guide To Vhdlams[END_REF]). A direct consequence of this definition is that a system can be represented by several models depending on aspects the designer focus on. Usually, three aspects of modeling are considered: function, structure and geometry. The most abstract model considered in this work is the functional level where the system is described by is function but information about the implementation of this function is not considered. The structural model describes a system as a composition of subsystems connected together. Details about the geometrical and physical parameters of the system are only considered in the physical layer.

The chosen modeling language in this work is VHDL-AMS. Actually, this language offers facilities for describing structure and function of systems in physical domains.

III. PIEZOELECTRIC MICROGENERATOR MODELING

The purpose of this section is to establish a generic library of piezoelectric microgenerators in different abstraction levels. Depending on the wanted compromise time/precision, the user can make its choice.

A. A functional transducer model

The simplest and probably the most abstract model of a transducer is an equivalent electrical circuit composed of an ideal sinusoidal current source, in parallel with a capacitor Cp. This model represents electrical characteristics of the microgenerator. The current amplitude ip depends of the amount of mechanical vibrations but still relatively insensitive to external charge. However, it is not suitable to our study case since the coupling effect is considerable.

B.

A structural piezoelectric microgenerator model . by a simple connection of basic components (current source, inductor, resistance, capacitor and transformer). However, physical aspects of the system are not considered.

The same model can be described by analytical equations obtained from constitutive piezoelectric and circuit equations. The comparison between these two models is done in section IV.

C. Physical piezoelectric microgenerator model

Piezoelectric microgenerator 1D model The target of this simple model is to validate our approach for transduction modeling. The whole system is subjected to mechanical vibrations y(t). The system is represented in Fig. 2. where: w(t) is the displacement of the seismic mass M.

-The stiffness K is calculated from the material stiffness c33 and device dimensions. Considering that this coupled electromechanical structure can be modeled as a damped harmonic oscillator, the analytical model is directly deduced from the Newton's second law of motion and the constitutive piezoelectricity equations.

The deduced differential equations are then correctly incorporated into a VHDL-AMS architecture.

This model was kept intentionally simple to focus on the functionality of the piezoelectric transduction. It is simple enough to have fast simulations as will be proven in section 5. This model is perfect for a first validation but it is neither accurate nor predictive.

Piezoelectric microgenerator 3D model

The micropower generator is based on the structure illustrated in Fig. 3. It is based on a cantilever beam of length Lp, width Bp and the thickness HP on which a thin piezoelectric layer is deposited. A big seismic mass of length LM, width BM and thickness HM is attached at the end of the beam. This seismic mass is used to decrease the resonance frequency and increase the harvested energy. An applied acceleration induces the displacement of the mass and the deformation of the beam. Therefore, the beam apply constraints on the piezoelectric layer whose generate electric charges. Thanks to the proposed dimensions of this mass, we can tune the resonant frequency of the generator. Several important considerations are taken into account especially the important size of the mass compared to the one of the beam, the rigidity of the mass and its rotational inertia. It is also important to consider that the acceleration is applied to the mass and not to the end of the beam. The impact of the electrical and mechanical properties of materials was introduced in the expression of the effective parameters deduced from boundary conditions. Additional information about the description of the model can be found in reference Ref. [START_REF] Marzencki | Basrour Enhanced Models For Power Output Prediction from Resonant Piezoelectric Micro Power Generators[END_REF].

IV. SIMULATIONS RESULTS

A. Comparison between analytical and structural model results

B. Impact of physical properties study

First, we have studied the impact of the piezoelectric properties of the material used on the model by keeping the same dimensions of both devices and just changing the piezoelectric material layer.

The used piezoelectric To do so, we just had to substitute the generic parameters responsible of physical properties of the used material (PZT) in the entity declaration of the previous of the VHDL-AMS model by AlN ones. The used stimulus is 1g acceleration.

As shown in For the AlN material, we have noted lower amplitude and higher resonant frequency. This result was expected because of the poor coupling coefficient of AlN material compared to PZT one.

However, microfabrication process in case of AlN by sputtering techniques is easier than for PZT ones. The deposition of AlN is relatively simple, compatible with CMOS process and does not require post process polarization. For that reasons, we decided to investigate structures based on this material.

We have changed the dimensions of the structure and analyzed the output voltage produced. We used twice the dimensions for the mass (800µm by 800µm) with a SOI wafer (525 µm thick). For acceleration stimuli of 1g amplitude, we obtained the output voltage versus time reported in Fig. 6. We can successfully harvest 1.8V across the electrodes in open circuit. Fig. 6. Output voltage at resonance at micropower generator (with ALN as piezoelectric layer and modified dimensions of the mass) versus time

V. DISCUSSION

The various models of the piezoelectric microgenerator developed in this paper demonstrate clearly that the choice of the degree of abstraction is closely related to the wanted performance: behavior virtual IP for a functional verification early in the design process which is very useful for simulation of complex and big designs or a predictive model comparable to experimental results.

Since all models are generic interfaces lists, several analysis possibilities can be performed just by changing geometric and physical parameters. This kind of tests is very important in the design process since it offers to the designer the opportunity to optimize his model early in the design process. In section C, we studied the impact of geometric properties of the device. We demonstrate by changing the dimensions of the structure and the piezoelectric material, we can harvest a great voltage with easier micro fabrication process. The user still has the possibility to experiment other materials and other geometric dimensions in order to optimize his design without dealing with complicated details of the model. Finally, we had performed global simulations using the MEMS model connected to an electrical circuit based on ultra low threshold voltage diodes used to boost and rectify the weak amplitudes AC signals delivered by such generators (voltages often inferior to 200 mV) (Ref.

[5]).

VI. CONCLUSION AND FUTURE WORK

The reusable aspect of our models offers to designers the possibility to select and use their suitable configurations without having to understand the details of blocks just by changing some parameters. Indeed, the piezoelectric generator model remains valid for other materials and the voltage multiplier circuit is extensible to other technologies. We also proved the effectiveness of VHDL-AMS for modeling behavioral, structural and physical level that can predict the experimental results. Thus, because the models respect energy conservation laws, we had performed global simulations using the MEMS model connected to an electrical circuit used to manage power delivered by the microgenerator. Further work must be done to take into account the damping effect not considered in this work; only viscous damping was considered.

Fig. 1 .

 1 Fig. 1. Structural bimorph piezoelectric microgenerator modelThe structural model described in Fig.11. is developed by Ref.[START_REF] Roundy | Energy Scavenging for Wireless Sensor Networks with Special Focus in Vibrations[END_REF]. As shown in the left side of Fig.11., the structure is a two layer bender mounted as a cantilever beam. The equivalent inductance represents the generator inertia. The mechanical stiffness is represented by the equivalent capacitance CK and σin represents the stress resulting of input vibrations. The transformation ratio n represents the coupling effect, Cb is the piezoelectricity capacitance and v(t) is the output voltage. The VHDL-AMS model is simple, doesn't require a lot of time to be written since it's obtained

Fig. 2 .

 2 Fig. 2. Piezoelectric transducer model

Fig. 3 .

 3 Fig. 3. Schematic of the structure modeled for the physical model

Fig. 4 .Fig. 4 .

 44 Fig. 4. comparison between structural and analytical model of bimorph piezoelectric model Fig. 4. shows a comparison between analytical and structural models. The two curves are similar. The difference between the two models become from the abstraction done in the analytical model. In fact, the analytical model takes into account only the steady state while structural model consider both transient and steady state.

Fig. 5 .

 5 Fig. 5. Comparison between the piezoelectric microgenerator model based on PZT material and the one based on AlN material keeping the same mass dimensions

ACKNOWLEDGMENT

The " Region Rhônes Alpes" and the University Agency for Francophony (AUF) are gratefully acknowledged for their financial support.


Y C Liu

Xuechuan Shan
email: xcshan@simtech.a-star.edu.sg

Study of Mechanical Response in Embossing of Ceramic Green Substrate by Micro-Indentation

Study of mechanical response in embossing of ceramic green substrate by micro-indentation

Y. C. Liu, X.-C.

INTRODUCTION

Low temperature co-fired ceramic (LTCC) has been used for many years in the microelectronics packaging industry. One of the important advantages of LTCC technology is that it can be used to generate 3D structures using multi-layers of tapes and it is a way to create multi-layer circuits with the help of single tapes and applying conductive, dielectric and resistive materials. It can be used for various applications such as telecommunication devices, microwave components, sensors, actuators, microfluidics, meso-system module, biomedical devices, etc [START_REF] Rabe | Hot embossing: an alternative method to produce cavities in ceramic multilayer[END_REF]. The green ceramic tapes are glassceramic composite materials. They include ceramic filler that is usually alumina, glass frit binder and organic vehicle for binding and viscosity control of the tape before sintering. Green ceramic tapes can be manipulated for fabricating 3D structures. The traditional techniques for structuring green ceramic tapes are micro punching, milling and laser machining, etc [START_REF] Gongora-Rubio | Overview of low temperature co-fired ceramics tape technology for meso-system technology (MsST)[END_REF][START_REF] Nowak | Cold processing of green state LTCC with a CO2 laser[END_REF].

Recently micro embossing technique has been applied to create 3D structures in ceramic multi-layers [START_REF] Rabe | Hot embossing: an alternative method to produce cavities in ceramic multilayer[END_REF][START_REF] Andrijasevic | Aspects of micro structuring low temperature co-fired ceramic (LTCC) for realisation complex 3D objects by embossing[END_REF][START_REF] Shan | Microstructure formation on LTCC green substrates using micro embossing[END_REF]. This opened a new possibility of patterning features with micrometer scales on green tapes. Micro embossing or imprinting is usually used for patterning microstructures on a polymeric substrate [START_REF] Becker | Hot embossing as a method for the fabrication of polymer high aspect ratio structures[END_REF][START_REF] Guo | Recent progress in nanoimprint technology and its applications[END_REF][START_REF] He | Research on optimization of the hot embossing process[END_REF]. It uses a master mold to press onto a substrate material under a certain pressure and a temperature, which is usually above the glass transition temperature of the material, to transfer the mold patterns onto the substrate. After the temperature returns below its glass transition temperature, the mold is separated from the substrate, and the substrate material retains the shape of the mold patterns. In this process, temperature plays an important role to both the local-area fidelity and global uniformity of the structure formation. Higher embossing temperature could improve the fidelity of the structures but could cause serious thermal stress during demolding, which results in poor global flatness after demolding. With lower embossing temperature, the global flatness could be improved significantly [START_REF] Shan | Studies of polymer deformation and recovery in micro hot embossing[END_REF]. Hence, a compromise between local fidelity of the embossed patterns and global flatness of the substrate has to be considered. Therefore, study of micro embossing at low temperature for green ceramic tapes is necessary.

The recent development in micro-indentation instrument, i.e., depth-sensing indentation at elevated temperature, offers the capability to preciously control and monitor the load and penetration depth during the indentation process at the desired temperatures [START_REF] Beake | High-temperature nanoindentation testing of fused silica and other materials[END_REF][START_REF] Smith | High temperature nanoscale mechanical property measurements[END_REF][START_REF] Liu | High-temperature creep and hardness of eutectic 80Au/20Sn solder[END_REF]. It is expected that the microindentation test can act as a convenient way to simulate micro embossing process and to study the mechanical response of the embossing materials at process temperature and applied pressure.

In this paper, micro-indentation tests using a micro flatend cone indenter at various temperatures have been performed on green ceramic tapes to simulate imprinting process and investigate the mechanical response during imprinting. The correlation of indentation depth versus applied force at different temperatures was studied. The temperature and load-dependent creep and creep strain rate during holding period were obtained and discussed. The instantaneous recovery and retarded recovery after indentation were investigated as well. EXPERIMENTAL METHODOLOGY

A. Substrate materials

Substrates laminated from low temperature co-fired ceramic (LTCC) green tapes were used in this study. The ceramic green tapes were HL2000 supplied by Heraeus. The ingredients of this ceramic green tape comprise ceramicglass based powders, pores and polymeric additives. The thermogravimetric analysis (TGA) revealed that the amount of polymeric additives was approximately 16 wt%; the porosity factor was affected by the lamination parameters as well as casting process of the green tape. The thickness of a single layer green tape was 127 µm, and six layers of such green tapes were laminated under the pressure of 100 kg/cm 2 at the temperature of 70 °C for 10 minutes. Subsequently the laminated substrate with the total thickness being about 0.7 mm were cut into pieces of 4 mm x 7 mm for microindentation test.

B. Micro-indentation

The mechanical test was performed with a microindentation system equipped with a high-temperature stage [START_REF] Liu | High-temperature creep and hardness of eutectic 80Au/20Sn solder[END_REF]. The sample stage itself included a heater, a thermocouple and ceramic block. A micro flat-end cone indenter was used in the experiment as shown in Fig. 1. A small heater and a miniature thermocouple were installed around the diamond indenter stub to prevent heat flow upon diamond-specimen contact. A thermal shield was interposed between the loading head and the hot stage to eliminate any thermal interference. The applied force was monitored by electric current applied to a movable coil, and the displacement of the indenter head was measured via a capacitive transducer. A small amount of high-temperature adhesive was used to attach specimen onto the hot stage. Some strips of glass fiber were used to isolate the diamond/specimen with environment to preclude heat flow between diamond/specimen and environment. The stage and the diamond indenter were heated up to the desired 20 µm temperature simultaneously before indentation and the distance between indenter and specimen was 150 µm during the heating process. The loading duration was controlled at 20-30 seconds for all indentations and the holding time at the peak load was 300 seconds for investigating the creep response at various loads and temperatures. The test temperature was set to 25 °C and 75 °C, respectively. In each experiment, a holding period of 100 seconds was introduced after the load was unloaded to 10% of its peak value for the purpose of measuring instantaneous recovery and thermal drift at this unloading point.

C. Charaterization

After indentation, a Veeco atomic force microscope (AFM) was utilized to measure the profile of some shallower indentation cavities for studying the retarded recovery after indentation. The tapping mode was used with a vertical resolution of 0.1 nm. The scan area was set to 70 µm x 70 µm to cover an indentation cavity and the scan rate was 1 Hz.

III. RESULTS AND DISCUSSIONS

A. Indentation at various temperatures Fig. 2 shows the loading-hold-unloading curves of green ceramic tape at various peak loads and various temperatures. For example, curve ABCDEF represents the loading-holdunloading curve at 75 °C under peak load of 8 mN. The portion of AB represents the loading process, the portion of BC represents the holding period at the peak load for 300 seconds, the portion of CDEF represents the unloading process in which the portion of DE represents the holding period of 100 seconds for measurement of the instantaneous recovery after 90% unloading and the thermal drift of the instrument. It was noticed that higher peak force caused deeper depth of penetration at a desired temperature, i.e., created a bigger cavity. It was also observed that similar depth of indentation could be generated with smaller force when working temperature was increased or dwell time at the peak load was longer. It indicated that the depth of indentation, i.e., size of cavity created, was force, temperature and dwell time dependent. It suggested that we could apply higher force at low temperature or apply lower force at higher temperature or apply smaller force at lower temperature but hold the peak load for longer time to create a particular size of cavity or channel. The cavity or channel could be retained after withdrawing the applied load. This was attributed to the plastic deformation of the green tape caused by compression. It implied that permanent feature could be formed by compression at low temperature even at room temperature. Figs. 3 and4 show the applied force versus depth of penetration and the applied stress versus depth curves at 25 °C and 75 °C. There are three curves obtained from three locations for each temperature. The applied stress was calculated based on the following equation:

σ = A P (1)
where σ is the stress, P the force and A is the projected contact area. A is a function of indentation depth, h , and is given below in the present work.

where the unit of h is micrometer.

It was observed that the applied force and stress required for a particular depth of indentation at 75 °C were much smaller than those at 25 °C. It was also found that the indentation resistance was larger at the initial indentation, i.e., the incease of applied force and stress needed for penetrating a unit depth at the initial stage was larger than that at a deeper stage at both 25 °C and 75 °C.

B. Creeps at various loads and temperatures

From Fig. 2, it was noticed that there were significant increase in depth at the holding period under peak load. This implied that the creep occurred in the green tape. Fig. 5 shows the depth increase versus time under various loads and at various temepratures. The increase in depth at the peak load is defined as the creep penetration at the peak load. For micro-indentation, the creep strain rate can be expressed as the equation below [START_REF] Mayo | A micro-indentation study of superplasticity in Pb, Sn, and Sn-38 wt% Pb[END_REF]:

dt dε = h 1 dt dh (3)
where dt dε is the creep strain rate, h the depth of indentation and t is the creep time. Based on the curves of creep penetration depth versus time, as shown in Fig. 5, the creep strain rate can be determined. Figs. 6 and7 indicate the creep strain rate of the ceramic green substrate and all the curves are obtained from the curve fitting of the experimental results. It was noticed that the creep of green substrate was load and temeprtaure dependent. Higher load and higher temperature caused larger creep. It was also found that the creep strain rate at the peak load of 8 mN was the largest for both 25 °C and 75 °C. This suggested that larger peak load would cause larger creep strain rate. In addition, it was observed that green ceramic substrate exhibited higher creep strain rate at higher temperature; the creep strain rate for all temperatues and peak loads had a maximum value at the initial creep and it decreased dramatically and finally approached to zero after a period of load holding.

C. Instantaneous recovery and retarded recovery when unloading

In all unloading processes, we hold 10% of peak load for 100 seconds to monitor the change in depth after 90% unloading. It was observed that there was significant depth decrease at the holding period. For example, the depth of indentation decreased from 18017 nm (point D) to 17766 nm (point E) for the curve ABCDEF in Fig. 2. Fig. 8 shows the depth decrease versus time from point D to point E. It was noticed that the depth decreased significantly in the first 40 seconds and depth fluctuated from 40 seconds to 100 seconds. It could be interpreted as that the depth decrease in the first 40 seconds was due to the instantaneous recovery and the fluctuation of the depth after 40 seconds was caused by the thermal drift of the instrument. When the applied force was fully withdrawn, the depth of penetration approached to point F that is 17383 nm.

After indentation, an atomic force microscope was used to measure the profile of indentation cavities for studying the geometry of the indents and retarded recovery after indentation. The profile measurements were conducted both immediately after the specimen was removed from indentation instrument and a few days after indentation. Fig. 9 shows the three-dimensional images of two indents measured as soon as specimens were removed from the indenter. Fig. 10 shows their cross-sectional profiles. It was observed that less load was required to obtain a deeper cavity at elevated temperature. It was also noticed that there was no obvious pile-up due to material flow near the edge regions of the indented cavities, which were normally observed in polymeric hot embossing. This indicated that, in the process of embossing ceramic green substrate, there was no significate material flow, or the material flow contributed to filling the neighboring porosities. This indicated that plastic deformation and viscoelastic deformation under compression were the main causes of generating micro features on ceramic green material at the temperatures of 25°C and 75 °C. The reason for the little material flow in embossing could be the low amount of polymeric additives in ceramic green tapes. Table 1 indicates the depth change of the cavities after a period of indentation. It was found that the depth of the cavities reduced about 5% in the first day after indentation and the subsequent decrease was less than 1% which is considered as insignificant. It can be concluded that the recovery occured immediate after indentation and there was no significant retarded recovery in the depth of cavity after the first day of indentation.

IV. CONCLUSIONS

Thermo-mechanical behavior of ceramic green substrate has been studied by micro-indentation experiments at 25 °C and 75 °C. Indentation cavity could be formed in the temperature range from 25 °C to 75 °C and the cavity formation was attributed to the plastic deformation and viscoelastic deformation of green ceramic substrate under compression. The size of the cavities created was force, temperature and dwell time dependent. Higher temperature, higher applied force and longer dwell time could generate bigger and deeper indentation cavities. Creep occurred and made a larger contribution to the plastic deformation during the indentation process at elevated temperatures and high peak loads. There was instantaneous recovery during the unloading process and retarded recovery in the first day after indentation. The permanent cavity could be retained after indentation. The results could be used as a guideline for embossing ceramic green substrates.

Fig. 1 .

 1 Fig. 1. The flat end cone indenter used in this study with a diameter of 20 µm and an angle of 39°48'11".

Fig. 2 .

 2 Fig. 2. The loading-hold-unloading curves of green substrate under different loads at 25 °C and 75 °C.

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 11 April 2008 ©EDA Publishing/DTIP 2008 ISBN: 978-2-35500-006-5

Fig. 3 .Fig. 4 .Fig. 5 .

 345 Fig. 3. Curves of applied force versus depth of penetration on ceramic green substrates at various temperatures: (a) at 25 °C; (b) at 75 °C.

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 11 April 2008 ©EDA Publishing/DTIP 2008 ISBN: 978-2-35500-006-5

Fig. 7 .Fig. 8 .Fig. 9 .

 789 Fig. 7. Creep strain rate of the ceramic green substrate under various loads when heated up to 75 °C.

Fig. 10 .

 10 Fig. 10. The cross-sectional profiles of indents obtained at different temperatures and applied loads

TABLE I DEPTH

 I CHANGE OF THE INDENTATION CAVITIES VERSUS TIME

		Depth (µm)	Depth (µm)	Depth (µm)
		as -prepared	after indentation	after indentation
			for 1 day	for 5 days
	Cavity 1	2.29	2.14	2.13
	Cavity 2	2.27	2.17	2.18
	Cavity 3	2.26	2.15	2.07
	Ave.	2.27	2.15	2.13

9-11 April 2008 ©EDA Publishing/DTIP 2008 ISBN: 978-2-35500-006-5 ACKNOWLEDGMENT The authors would like to thank Ms. Hla Phone Maw for sample preparation. This work is supported by Agency for Science, Technology and Research (A*STAR) of Singapore for Singapore-Poland Cooperation.


R F Shyu

Feng-Tsai Weng
email: ftweng@nfu.edu.tw

Chi-Ting Ho

Manufacturing of A micro probe using supersonic aided electrolysis process

Keywords: Micromachining, Micro probe, Electrode, Electrolysis, Supersonic

In this paper, a practical micromachining technology was applied for the fabrication of a micro probe using a complex nontraditional machining process. A series process was combined to machine tungsten carbide rods from original dimension. The original dimension of tungsten carbide rods was 3mm; the rods were ground to a fixed-dimension of 50µm using precision grinding machine in first step. And then, the rod could be machined to a middle-dimension of 20µm by electrolysis. A final desired micro dimension can be achieved using supersonic aided electrolysis. High-aspect-ratio of micro tungsten carbide rod was easily obtained by this process. Surface roughness of the sample with supersonic aided agitation was compared with that with no agitation in electrolysis. The machined surface of the sample is very smooth due to ionized particles of anode could be removed by supersonic aided agitation during electrolysis. Deep micro holes can also be achieved by the machined high-aspect-ratio tungsten carbide rod using EDM process. A micro probe of a ball shape at the end was processed by proposed supersonic aided electrolysis machining process.

I. INTRODUCTION

Micro-electrical-mechanical-system (MEMS) technology becomes important due to the growing electro-optical industry. The cost amount of products is very significant in the industry fields of semi-conductor, precision fabrication, optical, and biotechnology in recent years. Electrical discharge machining (EDM) process which can be used for micromachining usually uses graphite or a metal tool to generate high frequency sparks between electrode and the work piece in a dielectric fluid. A rapid methodology has been proposed to form 3D electrode using the electroplating of EDM [START_REF] Dimla | Investigation of complex rapid EDM electrodes for rapid tooling applications[END_REF]. However the machining time of the process is too long. Since wire electrical discharge grinding (WEDG) system was developed to process microelectrode [START_REF] Masuzawa | Wire Electro-Discharge Grinding for micro machining[END_REF], the potential micromachining in EDM process is noticed from then on. Researchers used the same idea of WEDG to machine a 4.3µm microelectrode with a aspect ratio of 10 [3]. The electrode can be used to drill micro hole in EDM process, and to machine the silicon wafer. However, the wear of tungsten carbide is large, the aspect-ratio is still low, and the bending of micro electrode can occasionally happen due to the machining stress. Copper can be etched by FeCl 3 or CuCl 2 enchant [START_REF] Chang | Studies on Cupric Chloride Etching Solution[END_REF][START_REF] Datta | Electrochemical Micromachining: An Environmentally Friendly, High Speed Processing Technology[END_REF][START_REF] Cai Jian | Effects on etching rates of copper in ferric chloride solutions[END_REF], and the thickness of the TiNi foil could be etched to about 10µm by a proper volume ratio of HF/HNO 3 /H 2 O etching solution [START_REF] Chen | Chemicl Machined Thin Foils of TiNi Shape Memory Alloy[END_REF]. Although chemical machining (CHM) can be used to machine a metal rod to a small size, but the surface of the work piece is uneven [START_REF] Weng | Fabrication of microelectrodes for EDM machining by a combined etching process[END_REF]. Electrochemical machining (ECM) is a well known for the non-traditional machining process. Electroplating, electro grinding, and electrolysis are all part of applications of ECM. Nano electrode of the tungsten with a tip of about 500-800 nm could be achieved by the anodic etching [START_REF] Bhattacharyya | Electrochemical micro-machining: new possibilities for micro-manufacturing[END_REF][START_REF] Yamamoto | Solid-state pH ultramicrosensor based on a tungstic oxide film fabricated on a tungsten nanoelectrode and its application to the study of endothelial cells[END_REF]. Although the result of experiment shows this process has capability to produce the nanometer scale electrode, but the aspect-ratio of the electrode is still not large enough, and their wire materials are too soft that can not be widely adapted in the industry. Applications of Supersonic aided machining combined with other machining processes, such as turning, milling [START_REF] Pei | Rotary ultrasonic machining for face milling of ceramics[END_REF], EDM [START_REF] Guo | A Study of Ultrasonic-aided Wire Electrical Discharge Machining[END_REF], ECM, CHM, grinding, and polishing, can provides better performance, where the removal rate is higher, the cutting force and the tool wear are reduced [START_REF] Zhang | Material Removal-Rate analysis in the ultrasonic machining of engineering ceramics[END_REF], the tool life and the machined surface roughness are improved, better fluid diffusion and propagation can be obtained by the disturbance of the supersonic [START_REF] Roetzel | Propagation of the third sound wave in fluid: hypothesis and theoretical foundation[END_REF].

Tungsten carbide has the good stiffness and the heat resistance, and it can be machined to less than 10µm by precision grinding process. It can provide excellent electrode for the micro-EDM, but the aspect ratio is still not large enough. In this study, a composite processing technology includes precision grinding, super sonic agitation, and electrolysis were combined to process the tungsten carbide material. Tungsten carbide alloy rods of diameter 3.0 mm could be machined to the desired micro size by this process.

II. EXPERIMENTAL EQUIPMENTS AND PROCEDURE

The electrolysis system for machining micro electrodes contained a D.C. power supply and a container for electrolyte. The power supply used in the experiment is a model CT-3032D, which has an output voltage of 0-30 volt, and an output current range of 20mA -2A. It is made in Taiwan by The experimental procedures include: 1) 3mm tungsten carbide electrodes were processed by the precision grinding to two different sizes, one of a ball of diameter 150µm at the end, and another of rod 50µm at the end. 2) Machined microelectrodes were diverged separately into the electrolyte, and were connected as an anode; pure copper was connected as a cathode for electrolysis. The electrolyte was copper sulfate hydrate solution. The concentrate of electrolyte for electrolysis in experiments is CuSO 4 , 5H 2 O (50 g/l), CuCl 2 , 2H 2 O (0.4 g/l), H 2 SO 4 (15 g/l). Initial. In the machining of electrolysis, the anode electrode is eroded in accordance with the Faradays' law. Reaction of anode is metal ionized in the electrolyte from electrode, and cathode is iron deposited to the electrode.

III. RESULTS AND DISCUSSION

Table1 shows the comparison of the surface roughness of the samples that were processed by electrolysis with supersonic aided agitation and that with no agitation. Initial voltage was 10V, Initial current was 15mA. Tungsten carbide electrodes were machined from 50µm to 20µm. From results, the surface roughness with no agitation is much higher than that with agitation, and the machined time with agitation is also quicker than that with no agitation. The reason may be that electrolysis generated particles on anode can be automatically separated from the electrode with agitation of supersonic. From Fig. 1 to Fig. 4, SEM photographs show different machined diameters with different machined voltage, current, and time. Tungsten carbide microelectrode was first machined from 3mm to 50µm by precision grinding (Fig. 1). Electrode length is about 150µm. Fig. 2 and Fig. 4 shows the different diameter of the tungsten carbide microelectrode from 20µm to 2µm, and they show good quality machining results by supersonic agitation. Fig. 2 and Fig. 3 shows the SEM photograph of a micro electrode with no agitation during machining, the particles around the electrode can be effectively removed by supersonic agitation. High aspect ratio of the micro tungsten carbide rod can be obtained by this process. Fig. 5 shows the SEM photograph of a micro hole of a copper plate machined by a fine electrode of 10µm by EDM machining. The thickness of the copper plate is 50µm. The current is 0.3A, the voltage is 35V, and the machining time is about 1min. Fig. 6 shows SEM photo of a micro probe by supersonic aided electrolysis. The machined current is 0.2mA, Voltage is 10V. The machine time is about 20min. Fig. 7 shows SEM photo of a micro probe by supersonic aided electrolysis. Dimension of micro probe with a tip of about 20nm. The machined current is 0.2mA, Voltage is 10V. The machine time is about 20min. The diameter before machining was 20µm. Fig. 8 shows SEM photo of Deep micro hole machined by a 20µm tungsten carbide electrode using EDM process. Material is a 0.2mm stainless plate. The machined current is 0.3A, Voltage is 35V. The machine time is about 5min.

IV. CONCLUSIONS

Micro electrodes can be processed to a desired micron size by varies machining time in a fixed small voltage and current. Electrodes can be processed to a very small size with no bending. This technology has potential in the nano scale electrode machining. Deep micro holes can also be achieved by the machined high-aspect-ratio tungsten carbide rod using EDM process. A micro probe of ball diameter was processed to be 80µm at the end by proposed supersonic aided electrolysis machining process. The micro probe can be used as a sensor for measurement equipments. Dimension of micro probe with a tip of about 20nm could be obtained at the tip of the end by this process.

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 11 April 2008 ©EDA Publishing/DTIP 2008 ISBN: 978-2-35500-006-5 the Sampo Corporation. A supersonic cleaner was used for cleaning the work piece during electrolysis. This machine offers an output of 50-60Hz, at max 235W power, and an output of 100W, at an operating frequency of 42 KHz. This machine is manufactured by Branson sonic Corporation, USA. (Model 2501R-DTH). The vibration amplitude of this machine is about 30µm. A precision grinding machine was used for the machining in first step. The grinding machine is manufactured in Germany. It provides highly automatic NC machining capability in micro machining.

Fig. 1

 1 Fig.1 SEM photo of tungsten carbide microelectrode machined by precision grinding. The diameter is 50µm. The length is 150µm.

Fig. 2

 2 Fig.2 SEM photo of 20µm tungsten carbide microelectrode. This electrode is obtained by 0.5mA and 10V for 1/2hr. The original diameter before machining was 50µm.

Fig. 4

 4 Fig.4 SEM photo of 2µm tungsten carbide. This electrode is obtained by 0.1mA and 10V for 1hr. The original diameter before machining was 20µm.

Fig. 6

 6 Fig.6 SEM photo of a micro probe by electrolysis. The machined current is 0.2mA, Voltage is 10V. The machine time is about 20min.

Fig. 7

 7 Fig.7 SEM photo of a micro probe by electrolysis. Dimension of micro probe with a tip of about 20nm. The machined current is 0.2mA, Voltage is 10V. The machine time is about 20min. The diameter before machining was 20µm.

Fig. 8

 8 Fig.8 SEM photo of Deep micro hole machined by a 20µm tungsten carbide electrode using EDM process. Material is a 0.2mm stainless plate. The machined current is 0.3A, Voltage is 35V. The machine time is about 5min.

Table 1

 1 Comparison of copper surface roughness which the samples were processed by electrolysis and electroplating of supersonic aided agitation and no agitation.The voltage was 10V, and the current was 15mA.

		no agitation	supersonic aided agitation
	Surface roughness of electrolysis	2.51µm Ra	1.67µm Ra
	Machining time	140min	92min

ACKNOWLEDGMENT The authors are grateful to the National Science Council of Republic of China for the support of this research grant No 93-2622-E-150-051-CC3. 9-11 April 2008 ©EDA Publishing/DTIP 2008 ISBN: 978-2-35500-006-5


Kai Axel Hals

Einar Halvorsen

Xuyuan Chen

Measurement of Large Forces and Deflections in Microstructures

HAL is

INTRODUCTION

The direct wafer level measurement of force versus deflection of MEMS structural elements is not available in conventional probe stations, but is highly desired. Verification of the elastic stiffness at specific points could be useful as design verification and possibly also in process control. Furthermore, if sufficiently large deflections could be made, it would allow for strength assessment at wafer level. For accelerometers this would be an alternative to shock testing of packaged devices or could serve as a complementary test.

Measurement of displacement versus force can be done by atomic force microscopy, but is limited with respect to displacement and scan range. Surface profilometers could in principle also be used for this purpose [START_REF] Denhoff | A measurement of Young's modulus and residual stress in MEMS bridges using a surface profiler[END_REF][START_REF] Hopcroft | Micromechanical testing of SU-8 cantilevers[END_REF], but are limited with respect to force range and are not suitable for measurements at a point. There are nano-indenters that have both the displacement and the scan range necessary to make them useful for this kind of measurements [START_REF] Kraft | Mechanical testing of thin films and small structures[END_REF][START_REF] Pharr | Measurement of thin film mechanical properties using nanoindentation[END_REF]. These expensive instruments are optimized towards characterization of thin films and surfaces, not for test of MEMS structural elements. In particular they have much finer spatial resolution and different tip geometry than needed for measurement of large deflections of a structural element such as a beam or a suspended proof mass.

From the above, it is clear that there is a need to investigate methods for mechanical test of MEMS structural elements directly on wafer. It is therefore worthwhile to investigate if a simple and affordable approach for mechanical testing of MEMS can be found. In particular it is interesting to investigate large deflection for potential fracture test on wafer.

We have built a simple and affordable measurement setup for probing mechanical properties of MEMS structures at wafer level. In the following we give a detail description of our setup and analyze its behaviour over a wide range of loads based on measurements on micromachined silicon accelerometers.

I I. MEASUREMENT SETUP

The basic principle of the apparatus is shown in Fig. 1. A probe tip is attached to a load cell which measures the vertical force on the probe tip. The load cell is attached to a linear zactuator which is computer controlled with known displacement. The above equipment is mounted on a fixture that is attached to a manual xy-actuator (a small xy-table). Since the z-displacement is known and the force is measured, we can obtain the force versus deflection response at any point of choice on a device.

The measurement setup is depicted in Fig. 2a. The load cell was a Honeywell 25g Minigram beam load cell, the linear actuator was a Zaber CE Linear actuator. The actuator and the load cell were connected to a PC. The actuator was connected through the RS-232 interface and the load cell was read by a Texas Instruments USB 6009 ADC, both controlled by a LabView program. In addition a laboratory microscope was used for visual inspection and probe tip positioning. The whole setup was placed on an anti-vibration table. The probe tip is a very critical element. In our initial design considerations for the setup, we analyzed the maximum stress in the tip based on the Hertz contact problem. For a tip radius of 10um, a silicon substrate and 10mN tip force, the maximum stress is several GPa for several choices of tip material. We therefore opted for a diamond tip. The probe was made by removing the cantilever from a Shure SS35C-Q stylus and gluing the cantilever into an alignment groove in a copper plate. The copper plate was fixed to the load cell by a screw as depicted in Fig. 2b. The SS35C-Q stylus needle is made from polished natural diamond and has a tip spherical radius of 18um [START_REF]User Guide Shure SS35C-Q[END_REF]. A close-up of the probe tip is shown in Fig. 2c.

The accuracy in the vertical displacement is given by the precision of the linear actuator. Even though the step-size is about 0.1um, there is a systematic cyclic error in the positioning of +/-1um according to the manufacturer. For large displacements, we can safely neglect this error. For stiffness estimates the systematic error can be cancelled by sampling at the spatial period of the systematic error. This is sufficient for our purpose.

Without any precautions, the dominating error in the force measurements comes from the electrical noise in the load cell. By estimating the power spectral density of the electrical signal from the load cell, we have verified that it is essentially flat so that the correlation time is correspondingly very short. The standard deviation in the readout is about 1mN when estimated from a long time series. This is far too much for our requirements. To increase accuracy we have adopted a sampling frequency of 20kHz and used the average readout over 3 seconds at this sampling rate for the estimate of the force. This procedure reduces the standard deviation in the estimates to 4.4uN which is sufficient.

The mounting of the probe tip explained above, gives a slightly different loading of the load cell than what it is calibrated for. In order to account for this, we have verified and calibrated the setup by measuring the force when pushing the tip onto the scale pan of a precision micro scale and comparing to the readout of the scale. This test shows that the mounting

ISBN: 978-2-35500-006-5
gives a systematic overestimate of the force of about 2.5% which we correct for.

The scale pan is based on a force restoration principle so that it does not deflect when loaded. By assuming that the displacement that is set for the actuator is completely accounted for by the deformation of the apparatus itself, we can estimate the stiffness of our measurement system. We find 4635N/m. This is one to two orders of magnitude stiffer than the structures that we have measured.

III. MEASUREMENTS

To investigate the capabilities of our setup, we have performed measurements on an accelerometer design that were fabricated in a silicon bulk micromachining process with beam and proof mass thicknesses defined by etch stop on pnjunction, a cantilever type design. This design had a symmetrically placed single beam and the nominal stiffness when loaded by a point force at the centre of mass is about 10N/m. All measurements reported here, were made by placing the probe tip on top of the proof mass such that the forces act in the plane of symmetry of the device.

Measurements were made by placing the probe tip initially at the symmetry centre of the top surface of the proof mass, see Fig 3a . Then the probe tip was displaced vertically (orthogonal to the wafer plane) in controlled steps over a range of deflections from 0 to about 300um. At each displacement the force was measured. The load cell is sensitive in the vertical direction. Hence it is only that component of the force that is read out from the apparatus. The resulting force versus deflection curve is shown in Fig. 4.

Roughly we can divide the force readout into three characteristic regimes as indicated in the Fig. 4: 1) a linear regime for deflections up to about 50um, 2) a regime of geometric nonlinearities from about 50um to 230um, and 3) a regime with contact nonlinearities from about 230um to fracture.

A. Stiffness in the linear regime

When the proof mass deflection is sufficiently small that the loading conditions are not substantially altered, we have the linear regime. The measured force then equals the actual force between the tip and structure and is directed in the vertical direction as indicated in Fig. 3a. In this case the force readout is well described by Hookes law F z =kz, where k is the stiffness of the structure at the point where the load is applied and z is the vertical displacement of the point. This stiffness will vary with the position of the load. We measured it as a function of position for various probing positions along the proof mass from one edge to the other. For each probing position, 3-4 measurements of force versus deflection over a small range of deflections well within the linear range were made. The stiffness was then estimated by a linear fit to the force versus deflection measurement at each position. The range of deflections in this experiment was from about 5um to 50um and the forces were in the range from 20uN to 1.3mN.

The resulting stiffness versus position trace is shown in Fig. 5 together with corresponding data obtained from analytical calculations (rigid mass and Euler-Bernoulli theory for the beam). In the figure position 0µm is at the support of the beam. The calculated results are in good qualitative agreement with the measurement, but systematically overestimate the value of the stiffness. We attribute this to the neglect of support compliance in the calculated results.

B. Geometric nonlinearities

When the proof mass is sufficiently displaced and rotated the loading conditions are significantly altered and we have the regime of geometric nonlinearities. This situation is shown in proof mass, the force F on the proof mass must be orthogonal to the surface. This force can be decomposed into a component in the vertical direction F z and a component in the horisontal direction F x . The sensitive direction of the load cell is in the vertical direction, so it is only F z that is measured. As the deflection increases, so does the rotation of the proof mass and F z becomes a correspondingly smaller fraction of the total force. The point of contact slides towards the outer edge of the proof mass as the deflection grows. Therefore, for a given total force F, the bending moment in the beam will be larger than it would have been if the point load had stayed fixed with respect to the surface. Due to the larger bending moment in the beam, the F necessary to sustain a certain rotation of the proof mass is then smaller than it otherwise would have been.

The net result is that the measured force component F z initially increases, reaches a maximum, and then decreases from a deflection of 140um onwards, even though total force F increases.

There is a small effect that acts against this effect. The stylus is not perfectly sharp, but has a tip radius of 18 µm. This will cause a rolling effect that moves the point of the applied force inwards. This effect is limited from above by the tip radius which is small compared to the length that the tip slides on the mass.

C. Contact nonlinearities and destructive tests

We refer to regime no. 3 in Fig. 4 as the regime of contact nonlinearities. Here, the way that the probe tip makes contact with the proof mass changes. When the initial position is at the centre of symmetry, the main sequences of events are as depicted in Fig. 6. First the probe tip slides along the proof mass (top panel), then it slides off the proof mass edge (middle panel), then it slides on the edge until finally the proof mass surface becomes parallel to the tip surface and there is distributed contact between the tip and the proof mass surface (bottom panel).

The small "bump" seen in the leftmost part of the contact nonlinearity regime in Fig. 4, is due to the tip sliding off the edge. The following irregular behavior is due to the tip sliding on the edge, then making distributed contact with proof mass and finally, for sufficiently large deflections, the region of contact extends onto the beam. In the latter case, the force distribution becomes very difficult to analyze. It is clear that the structure is substantially stiffer when loaded in this region. This is the reason why there is an increase in the measured force values in the end of the curve. When the structure is deflected further, it fractures.

It is possible to avoid that the tip slides off the mass by placing the probe tip further from the outer edge. We therefore did another experiment where the stylus is placed 50 µm closer to the spring than the centre of symmetry (COSYM). In Fig. 7 the result of this measurement is shown together with the original measurement for comparison.

The second measurement shows both a linear and a geometrically nonlinear regime similar to the first. The differences are due to the much higher stiffness which results in larger forces and a smaller range of deflections. In the second measurement, the stylus does not slide off the mass. Also, for sufficiently large deflections, distributed contact is achieved, but extends onto the beam immediately. Hence, the irregular behavior of the first measurement is absent in the second. The sharp rise in force at large deflection is due to the tip being in distributed contact with beam in both cases.

Due to the rigidity of the proof mass, the distributed contact between the probe tip and proof mass is entirely dictated by the probe tip angle regardless of the initial probe tip position. It is possible to avoid the distributed contact by tilting the probe or using a probe tip with one vertical side, but unfortunately that is not an option in our current setup. In order to estimate fracture strength, we need to have a well defined loading of the device. The distributed contact prohibits that for the tested design because it is compliant enough to reach a slope equal to the probe tip angle before fracture.

To investigate a situation without the distributed contact, we measured samples of a stiffer accelerometer design. This design had two beams placed widely apart and a nominal stiffness at the centre of mass of about 60N/m. It is described in [START_REF] Lowrie | Piezoresistive threeaxis accelerometer for monitoring heart wall motions[END_REF], and the measurement is shown in Fig. 8. In this case fracture arises before the distributed contact took place, but the probe tip just barely slid off the edge prior to fracture of the beam. Both devices fractured at about 4.5mN vertical force and about 110um deflection. The last point on the curve before the tip slid off was 4.0mN at 90um deflection.

D. Sample to sample variations

To further investigate the capabilities of the measurement setup, we have made a series of measurements on wafer. Fig. 9 shows the test results measured at the centre of the mass of six accelerometers located at different sites on the wafer. As seen from Fig. 9, there exist some variations in the six measurements.

From the setup characterization processes, we found that the standard deviation of one point in a measurement was found to be 4.4µN. In addition the accuracy of the placement of the stylus will play a significant role in determining the accuracy of the measurement. With the current measurement setup, where the stylus is placed optically through a microscope, it is difficult to place the stylus on the exact same place on each structure. By placing the stylus in a line prolonging the cantilever, it was found that a deviation of placement of the stylus of +/10µm would cause a variation of up to +/-60µN in the force versus deflection curve. Though above mentioned factors contribute to the uncertainty in the measurements, the deviation in placement of the stylus dominates. The variations presented in Fig. 9 are well within the range caused by the placement inaccuracy. The variation from accelerometer to accelerometer across the wafer are simply too small to detect with this measurement setup. With the possibility to place the stylus more accurately, the main reason for the measurement variations would disappear. This could be done with a more precise x-y-table, or a more suitable optical instrument for placement.

IV. CONCLUSIONS

In conclusion, we have designed, built and characterized a system for wafer level force versus deflection measurements on microsystems. With an accuracy of 1um in displacement and 4.4uN resolution in force up to a range of 250mN, we have sufficient precision to measure stiffness at chosen points on the device. The mechanical behavior of the test accelerometer measured with the system, from small to large deflections of the cantilever beam, all the way up to the fracture of the beam, was analyzed and understood. Measurements on two types of accelerometers provide a solid basis for future development.

ACKNOWLEDGMENT

Infineon Technologies SensoNor AS is acknowledged for supplying test structures and financial support. We appreciate Dr. Trond Inge Westgaard for his initiative of building this setup and discussions during realization of the setup.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Basic principle of measurement setup.

Fig. 3 .Fig. 4 .

 34 Fig. 3. Load, a) linear regime b) geometrically nonlinear regime.

Fig. 3b .Fig. 5 .

 3b5 Fig. 5. Spring constant versus position along proof mass.

Fig. 6 .

 6 Fig. 6. Stylus at different loading conditions.

Fig. 7 .

 7 Fig. 7. Force readout for different initial placements of stylus.

Fig. 8 .Fig. 9 .

 89 Fig. 8. Force versus deflection readouts from a stiffer accelerometer design.

9-11 April 2008 ©EDA Publishing/DTIP 2008 ISBN: 978-2-35500-006-5


C W Lu

Y C Lam

Xuechuan Shan
email: xcshan@simtech.a-star.edu.sg

S H Ling

H P Maw

Micro Embossing of Ceramic Green Substrates for Micro Devices

Micro Embossing of Ceramic Green Substrates for

Micro Devices

INTRODUCTION

Multilayered ceramic substrates with embedded micro patterns are becoming increasingly important, for example, in harsh environment electronics and microfluidic devices [START_REF] Gongora-Rubio | Overview of low temperature co-fired ceramics tape technology for meso-system technology (MsST)[END_REF]. These micro patterns, which include micro channels, cavities and vias, as well as an assembly of them, are the constituent parts for microfluidic devices; they can also be filled with conductive or dielectric materials to form high aspect interconnections or passive components for multifunctional substrates. The embedded micro patterns are conventionally fabricated by mechanical punching or laser machining on ceramic green sheets, followed by lamination and sintering [START_REF] Wang | Fabrication of microvias for multilayer LTCC substrates[END_REF][START_REF] Hagen | Fabrication of smallest vias in LTCC Tape[END_REF]. These conventional fabrication methods, however, have unavoidable limitations, for instance, the minimum features are limited by the size of the machining tools, and the minimum depth is restricted by the layer thickness of a ceramic green tape.

Micro hot embossing is a cost-effective technique for manufacturing micro structures on polymeric materials [START_REF] Becker | Hot embossing as a method for the fabrication of polymer high aspect ratio structures[END_REF]. The mechanisms for cavity filling and process optimizations in polymer embossing have been widely investigated and reported by many research groups [START_REF] Guo | Recent progress in nanoimprint technology and its applications[END_REF][6][START_REF] He | Research on optimization of the hot embossing process[END_REF], and it has been successfully used for manufacturing micro components for fluidic devices and systems.

We proposed to utilize micro embossing for patterning micro structures on ceramic green substrates, followed by lamination and sintering to manufacture embedded micro patterns [START_REF] Shan | Microstructure formation on LTCC green substrates using micro embossing[END_REF]. In this paper, we present our study on the process issues of embossing ceramic green substrates. A ceramic green substrate composes of ceramic-based powders and polymeric additives; the proportion of polymeric additives is approximately 20 wt%. This makes the embossing of ceramic green substrates different from polymer embossing. The challenges of embossing a ceramic green substrate include the following aspects: (1) material flow during embossing is slow; (2) the embossed substrate will be torn or deformed during demolding due to its low strength. To address these fundamental process issues in ceramic embossing is necessary and important.

In our study, a ceramic green tape that possesses nearzero shrinkage in x-y plane was employed, six layers of which were laminated for micro embossing. The dynamic thermo-mechanical analysis showed that extending the holding time at a certain temperature range would harden the green substrates; this would increase the difficulty in achieving high quality embossing. The process parameters that impact on the embossing fidelity were investigated. Micro patterns with a feature size of several micrometers were formed on ceramic green substrates. The embedded micro channels were obtained by laminating the embossed substrate with green tapes, followed by sintering.

II. EXPERIMENTAL DESIGNS

A. Micro Embosser and Embossing Mold

A desk-top hot embosser was used, which utilized a hydraulic pressing mechanism for supplying pressure with a maximum working force of 150,000 kN. It possessed two pressing platens -the top and bottom platens; each of which was 100 mm in diameter and equipped with an embedded heater. Both the top and bottom heaters could be preset to a 9-11 April 2008 ©EDA Publishing/DTIP 2008 ISBN: 978-2-35500-006-5 maximum temperature of 250 °C with a tolerance of ± 2°C. After embossing, cooling was achieved by means of watercooling blocks attached to the platen as well as natural air convection. A nickel template with micrometer-scaled cavities and channels was employed as the mold for embossing. The mold was replicated from a silicon master via electroplating; the plated mold was about 1 mm thick and was coated with a thin anti-sticking layer (100 nm thick) to improve the ease in demolding.

B. Preparation of Ceramic Green Substrate

Most of the ceramic green tapes will suffer shrinkage in all directions upon sintering; the tolerance control of the shrinkage in each direction will affect the final dimension and location of the components and features fabricated on the tapes. A ceramic green tape, the HeraLock™ HL2000 from Heraeus, was used, which possessed near-zero shrinkage in the x-y plane, densifying itself by shrinking primarily in the z direction. This shrinkage property would simplify designs in feature dimension and component layout. The thickness of a single layer tape was 127 µm. Six layers of the green tapes were precisely aligned and then laminated to form a stack, which was used as the substrate for micro embossing. The lamination was carried out by using an isostatic thermal laminator with a pressure of 100 kgf/cm 2 (9.8 MPa) at 75 °C for 5 minutes.

C. Experimental Methodology

The laminated green substrate was characterized by means of a thermo-gravimetric analyzer (TGA) to determine the weight ratio of polymeric additives; its thermal properties were characterized via dynamic mechanical analyzers (DMA) to determine its glass transition temperature to facilitate the choice of suitable process parameters. Three groups of embossed patterns with regular channel-width (S) and protrusive line-width (L) were targeted.

(1) Group A: the channel-width S and line-width (L) were 50 µm and 100 µm (S/L = 0.5), respectively.

(2) Group B: S and L were 100 µm and 100 µm respectively, and S/L = 1.0;

(3) Group C: S and L were 100 µm and 400 µm respectively, and S/L = 0.25;

The profile of the embossed patterns was measured and observed by means of a profilometer and a microscope.

III. EXPERIMENTAL RESULTS

A. Characterizations of Ceramic Green Substrates

Thermo-gravimetric Analysis (TGA), which measures the changes in weight of a sample as a function of temperature, was performed with the purpose of determining the percentage and thermal degradation temperature of organic additives in the green substrate. TGA was carried out with air as the purging gas and the sample size was approximately 8.0 mg. Fig. 1 shows the percentage of weight change of the ceramic green substrate with temperature ranges from 30ºC to 800ºC at a heating rate of 1ºC/min, 5ºC/min, 10ºC/min and 20ºC/min. For all the four different heating rates illustrated in Fig. 1, the thermal degradation of the organic additives showed two obvious regions, although the initiation and completion temperatures of thermal degradation were different for different heating rates. Taking the heating rate of 1ºC/min as an example, the TGA curve shows that the green substrate lost about 0.4 wt% when the temperature reached 110 ºC; this was attributable to the evaporation of plasticizer. The ceramic green substrate continued to lose its weight as temperature increases and it lost about 16.5 % of its weight when the temperature reached 350 ºC. There was not much weight change thereafter up to 800 ºC. This indicated that this particular ceramic green tape consisted of about 16.5 wt% of organic additives and 83.5 wt% of ceramic particles.

The ceramic green tape used in this study was flexible at room temperature, but its thermal behaviour at raised temperature was unknown. Similar to polymer embossing, the glass transition temperature (Tg) of the ceramic green material was an important indicator for determining its embossing temperature. Therefore, the dynamic mechanical analysis (DMA) was conducted to determine both its viscoelastic and thermal properties. Fig. 2 illustrates the results obtained from dynamic mechanical analysis (DMA Q800). The sample was a sixlayer laminate, which was the same as that used for embossing. The temperature varied from room temperature to 130 ºC, with the temperature ramp and frequency being 2ºC /min and 1 Hz, respectively. Both the storage modulus (G′) and loss modulus (G″) decreased as the temperature increased to 130 ºC. The peak of tan δ (tan δ= G″/G′) indicated that the glass transition temperature (Tg) of the green substrate ranged from 35-50 ºC. The increase of temperature above its Tg resulted in further decrease of moduli G' and G″. As a result, the green substrate softened and became more flexible with an increase in temperature, which is advantageous for micro embossing. It was also found that the moduli G″ and G' would not decrease significantly while the temperature was further increased above 60 ºC. Hence, a good embossing temperature would range from 60 ºC to 100 ºC.

B. Effect of Applied Force

The ceramic green tapes consist of solid powders and organic additives. The organic additives are less than 16.5 wt%; this makes the embossing of green substrates more difficult since a lower ratio of polymeric content will limit and slow down the material flow in embossing. Nevertheless, micro embossing of ceramic green substrates was successfully performed using the six-layered lamination. Fig. 3(a) demonstrates the embossed result of a tapered channel; its sharp end was less than 5 µm. This result indicated that micrometer-scaled features can be formed on ceramic green substrate using embossing. Fig. 3(b) shows cross section of the embossed micro channel array with the ratio of channel-width/line-width being 100µm/100µm. The sidewalls of the channels were slightly collapsed on dicing the green substrate for showing the cross section. Hence, the actual fidelity would be better than illustrated in Fig. 3(b).

The impact of the applied forces to the embossed pattern fidelity was investigated when the embossing temperature and holding time were 70 °C and 3 minutes, respectively. Fig. 4 illustrates the embossed depth for group B (channelwidth/line-width = 100µm/ 100µm) when the applied force changed from 10 kN (equivalent to an average pressure of 2.5 MPa) to 20 kN and 25 kN. Fig. 5 shows the effect of the force on the embossed depth of the patterns in Group B and Group C (channel-width/line-width = 100µm/ 400µm). Fig. 5 indicates that the embossed depth depended not only on the applied force but also on the pattern design or pattern density. For the targeted two groups of patterns, it was estimated that a applied force of 20 kN or above was suitable to achieved the required embossing depth.

C. Effect of Embossing Temperature

The impact of embossing temperature was investigated with the applied force kept at 20 kN (equivalent to an average pressure of 5.0 MPa) for 3 minutes before demold. Fig. 6 illustrates the measured depth of the embossed channels in Group A (channel-width/line-width = 50µm /100µm) under different temperatures. The embossed depth increased with an increase in process temperature, and the increase in depth was obvious when the temperature was below 70 °C. However, there was no significant increase when the temperature was above 70 °C. Embossing above 120 °C made it difficult to separate the substrate from the mold; in some cases the embossed patterns were elongated during demolding. Under the same temperature and applied pressure, lower pattern density (lower ratio of channelwidth/line-width) resulted in larger embossed depth of channels. Fig. 7 indicated that the embossed depth of Group C (channel-width/ line-width = 100µm/ 400µm) reached the maximum depth even at 50 °C. Fig. 8 summarized the influence of the embossing temperature to embossing depth. Conclusion could be made for the three targeted groups that stable embossed depths were achieved when the embossing temperature was set above 70 °C.

D. The Effect of Time Factor

The effect of holding time at peak applied-force was investigated. For the three targeted groups of patterns, the effect of holding time was not obvious. It appears that 3 minutes was a suitable and sufficient period of holding time to get the maximum embossed depth. In the case that the pattern was not completely replicated within 3 minutes, extending the holding time increased the depth of macro deformation [START_REF] Shan | Microstructure formation on LTCC green substrates using micro embossing[END_REF] but demonstrated little improvement in embossed depth of tiny patterns, and this was true especially for high-density micro patterns. This is due to the low fluidity of the ceramic green material to fill up the micro patterns especially in the vertical direction.

The force ramp could be defined as the rate of force increment with respect to time. In the cases of 10 kN or 20 kN, the force was increased to its peak value in 5 seconds, 10 minutes and 20 minutes. It was found that a slow force ramp reduced the macro deformation in a certain degree but showed little effect in improving the embossed depth of micro patterns.

Thus, the experimental results indicate that both the holding time and force ramp showed little effect for improving the fidelity of micro pattern formation. This rather "time independent" behaviour of the ceramic green substrate in micro embossing is likely due to the following reasons: (1) The low viscoelasticity and low fluidity of the green material, which were attributed by the amount of polymeric additives in the material, slowed down and/or limited the filling of tiny patterns, thus resulted in incomplete embossing. [START_REF] Wang | Fabrication of microvias for multilayer LTCC substrates[END_REF] The little material flow contributed in filling the porosities in green substrate rather than pattern formation. (3) The thermal properties of the green substrate had changed during the embossing. Further investigations were required to identify the key reasons and solutions for improving embossing fidelity. IV.

DISCUSSIONS

To investigate both the viscoelastic and thermal properties at raised temperature of the green substrate, dynamic mechanical thermal analysis (DMTA) in torsion was conducted by using a rotational rheometer -Physica MCR from Anton Paar with air as the purging gas. The specimens with a rectangular shape of 36 mm× 10mm× 0.7 mm were prepared, which were subjected to a tensile force of 0.2±0.05N (frequency: 1Hz and percentage strain γ: 0.01%) with a heating rate of 1ºC/min. Fig. 9 presents the viscoelasticity behaviors of the green substrate at isothermal condition with holding time of 20 minutes. These tests were conducted with an open hysteresis loop by heating up the specimens at room temperature to the desired process temperature at 1ºC/min, hold the specimens isothermally for 20 minutes, and then cooling down to 30ºC. It was found that both the storage modulus (G′) and the loss modulus (G″) were decreasing with an increase in temperature, which indicated that the green substrate was being softened. At process temperature below 80 ºC, there was a negligible change in G′ and G″ during the holding period. However, when the process temperature increased to or above 100ºC, the value of storage modulus G′ increased with holding time whereas G″ decreased. This indicated that the thermodynamic property of the green substrates had altered at these temperature ranges. The organic additives were believed to have partially decomposed. This led to the increases of G′ with holding time. The increase of G′ implies that the substrate behaves more elastically. The decrease of G″ could mean that the heat supply was not enough to soften the second type of organic additives in the green substrate. In any case, it could be predicted that the embossing process carried out at such temperature would result in poor embossing fidelity, and the fidelity would not be significantly improved by increasing the holding time at peak temperature. These observations are consistent with our embossing results.

V.

CONCLUSIONS

Micro embossing of ceramic green substrates was demonstrated. The process parameters that impact on the embossing fidelity were studied. Micro features with several micrometers and micro channels with channel-width as small as 50 µm were formed. The quality and fidelity of embossed patterns depended not only on the applied force (pressure) and temperature, but also on the pattern density. The influence of holding time and force ramp were more complicated; simply extending the holding time or using low force ramp demonstrated little effect in improving the embossed depth or embossing quality. Nevertheless, the achievements of this study demonstrated that micro embossing is a promising technique for fabricating microstructures on ceramic green substrates.

ACKNOWLEDGMENT

The authors would like to thank Mr. Ricky T. Rjeung for his contribution. This work is supported by Agency for Science, Technology and Research (A*STAR) of Singapore for Singapore-Poland Cooperation.

  Fig.1. TGA curves of green substrate at different heating rates. The weight loss below 110 °C was attributable to evaporation, and the thermal degradation below 400 °C showed two obvious regions.

Fig. 2 .

 2 Fig. 2. DMA curves for analyzing glass transition temperature of ceramic green substrate.

  An embossed tapered channel 200 µm (b) Cross section of the embossed patterns with channelwidth/ line-width being 100µm /100µm.

Fig. 3 .Fig. 4 .Fig. 5 .

 345 Fig. 3. Patterns embossed on ceramic green substrates

Fig. 6 .Fig. 7 .Fig. 8 .

 678 Fig.6. Effect of embossing temperature on patterns in Group A with channel-width/line-width being 50µm/100µm.

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 11 April 2008 ©EDA Publishing/DTIP 2008 ISBN: 978-2-35500-006-5

Fig. 9 .

 9 Fig. 9. Effect on storage modulus G′ and loss modulus G″ at different temperatures (80 ºC, 100 ºC, 120ºC and 140ºC) with a holding time of 20 minutes