Simulation and Fabrication of Piezoelectric mems Inkjet Print head

Simulation and Fabrication of Piezoelectric mems Inkjet Print head

MASTER OF SCIENCE

SUPERVISOR LEE JAICHAN

MASTER OF SCIENCE

SUPERVISOR LEE JAICHAN

SIMULATION AND FABRICATION OF PIEZOELECTRIC

MEMS INKJET PRINT HEAD

A Thesis Presented

by

PHAM VAN SO

Submitted to the Graduate School of SungKynKwan University

in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

in Materials Science and Engineering

June 2007 Department of Materials Science and Engineering Graduate School of SungKynKwan University

SIMULATION AND F ABRICATION OF PIEZOELECTRIC MEMS

INKJET PRINT HEAD

Based on the primary design and fabrication of piezoelectric MEMS inkjet (1st

version-InkjetVer1) done in our STD Lab, the computer simulation and validation of

inkjet have been investigated, and then the 2nd version (InkjetVer2) with the modified

nozzle shape was fabricated and characterized

In details, firstly the simulation of piezoelectric MEMS inkjet with the mechanical-fluid interaction has been performed In order to verify the simulation results, a fabrication and characterization of actuator part consisting of PZT-based actuating membrane and ink chamber was carried out These treatments are to determine how much “dynamic force”, in terms of membrane’s maximum displacement, maximum force and driving frequency, can be produced by the actuator membrane Secondly, a simulation of microdroplet generation in inkjet has also been done This work gives an understanding about the droplet generation process, and the effects of driving characteristics, fluid properties and geometrical parameters on droplet generation Especially, this simulation helps to predict how much “dynamic force” is required to generate mirodroplets The combination of both results (i.e., how much

electro-“dynamic force” produced and required) gives an effective guideline in designing inkjet

structure Thirdly, in the experimental work, the fabrication of InkjetVer2 was carried

out based on MEMS techniques And then its electrical, mechanical characteristics as well as possibility of ink ejection were also tested

Finally, the feedback information from these simulation and experimental work helps to suggest a new design (3rd version - InkjetVer3) which is expected to produce

enough “dynamic force” and possibly generate microdroplets Then, mask design and

fabrication of InkjetVer3 have also been proceeding

ACKNOWLEDGMENTS

First, I would like to thank my supervisors, Prof Dr Jaichan Lee and Assoc.Prof.Dr Dang Mau Chien for their professional guidance, constructive criticism and, last but not least, for giving me a good opportunity to study at the Semiconductor and thin film devices Lab, Department of Materials Science and Engineering, SungKyunKwan University

I would also like to thank PhD candidate Sanghun Shin and MSc Jangkwen Lee for sharing their knowledge on MEMS processing with me as well as for their useful discussions

Furthermore, I would like to thank Prof Minchan Kim and Dr Dongwon Lee in Jeju National University for their generous assistance on my simulation work And I’m

so grateful to KIST, KITECH and other labs for sharing all the equipments available for

Finally, I want to thank my parents and relatives for their constant encouragement

and support

DEDICATION

To my parents

Mr Pham Van Vinh and Mrs Le Thi Anh

Table of contents

A BSTRACT i

A CKNOWLEDGMENTS ii

Table of contents iv

List of figures vi

List of tables viii

C HAPTER 1 I NTRODUCTION 1

1.1 Piezoelectricity 2

1.1.1 Piezoelectric effect 2

1.1.2 Lead zirconate titanate (PZT) 3

1.2 Piezoelectric MEMS inkjet print head 5

1.3 Numerical simulation 7

1.3.1 Role of numerical simulation 7

1.3.2 General principle of numerical simulation 8

1.3.3 Numerical simulations of piezoelectric MEMS inkjet with CFD-ACE+ 9

1.4 References 10

C HAPTER 2 N UMERICAL A ND E XPERIMENTAL S TUDY O N A CTUATOR PERFORMANCE O F P IEZOELECTRIC M EMS I NKJET P RINT H EAD 11

2.1 Introduction 12

2.2 Modeling and simulation settings 13

2.3 Experimental procedure 16

2.4 Results and discussion 17

2.4.1 Performance characteristics of PIPH actuator in air 17

2.4.2 Performance characteristics of PIPH actuator in liquid 18

2.5 Conclusion 20

2.6 References 21

C HAPTER 3 S IMULATION O F M ICRODROP G ENERATION I N P IEZOELETRIC M EMS I NKJET P RINT H EAD 26

3.1 Introduction 27

3.2 Modeling and simulation settings 27

3.3 Results and discussion 29

3.3.1 Microdrop generation process 29

3.3.2 Effect of actuating characteristics 29

3.3.3 Effect of fluid properties 30

3.3.4 Effect of geometrical parameters 32

3.4 Conclusion 32

3.5 References 34

C HAPTER 4 F ABRICATION A ND C HARACTERIZATION O F P IEZOELECTRIC M EMS I NKJET P RINT H EAD 38

4.1 Introduction 39

4.2 Experiments 39

4.3 Results and discussion 41

4.4 Conclusion 42

4.5 Rerefences 44

C HAPTER 5 C ONCLUSION A ND S UGGESTION 50

5.1 Conclusion 50

5.2 Suggestion (new design) 50

Appendix A Python Source Script for simulation of microdroplet generation (effects of driving characteristics and fluid properties) 52

Appendix B Pattern conditions for fabrication of Inkjetver2 54

Appendix C Dry etching conditions 55

Rhombohedral (high temp form), RII: Rhombohedral (low temp form), A: rthorhombic, M: MPB, and Tc: Curie temperature 4 Fig 1-5 Deformation mode of piezoelectric inkjet actuator: (a) squeeze, (b) bend, (c)

push and (d) shear mode 6 Fig 1-6 A typical approach to MEMS application from concept to devices 7 Fig 1-7 Steps of overall solution procedure 8 Fig 1-8 Modeling settings for design of piezoelectric MEMS inkjet Computations are

performed using CFD-ACE+ package software 9

Fig 2-1 Model of a piezoelectric inkjet print head (PIPH) structure: (a)

design and (b) CFD-ACE+ symmetric model with meshing grids 23 Fig 2-2 Flowchart of fabrication process (a) and SEM images (b) of PIPH actuator 23 Fig 2-3 Maximum displacement of PIPH actuator membrane (300 um): (a) simulation

and (b) experiment Simulation was extended with membrane width of

500-600 um 24 Fig 2-4 Dependence of actuator performance on geometrical parameters: (a) maximum

displacement vs thickness ratio (PZT/support layer) and (b) maximum force (Fmax) and maximum displacement (δmax) vs membrane width 24 Fig 2-5 Resonance frequency (in air) of PIPH actuator membrane: (a) FEMLAB

simulation and (b) experiment with HP4194A impedance analyzer 24 Fig 2-6 Deflection shape of actuator membrane interacting with liquid: (a) & (b) dome

shape with one peak at low frequencies and (c) & (d) unexpected shape with more than one peak at higher frequencies (above 125 kHz < 379 kHz - resonance frequency in air ) 25 Fig 2-7 Resonance frequency (in liquid) of PIPH actuator membrane: (a) simulation

and (b) experiment 25

Fig 3-1 Inkjet head geometry, (a) Three dimensional (3D) and (b) 2D symmetric

section in CFD-ACE+ 35

Fig 3-2 Microdrop generation process at driving displacement with amplitude of 5 μm and frequency of 30 kHz 35

Fig 3-3 Droplet properties: no-droplet, single droplet and satellite droplets at various driving displacements (2~5um, 50 kHz) 36

Fig 3-4 Time duration for droplet generation at various actuating characteristics: (a) amplitude and (b) frequency Droplets are generated in one cycle or several cycles 36

Fig 3-5 Time duration for droplet generation with fluid properties: (a) surface tension and (b) viscosity High surface tension or viscosity makes cohesive forces predominant 36

Fig 3-6 Geometrical parameters: (a) relative chamber X1/X2, (b) aspect ratio d/h and (c) diffuser 37

Fig 3-7 Time duration for droplet generation vs.: (a) relative chamber size (A-type) and (b) aspect ratio (B-type & C-type) 37

Fig 3-8 Time duration for droplet generation vs driving characteristics of the selected structure (B-type) Microdroplet can be generated at an applied voltage of 9V-21V and frequency above 15 kHz 37

Fig 4-1 Schematic of piezoelectric inkjet print head structure (side view): (a) Inkjet version 1 and (b) Inkjet version 2 with the modified nozzle shape at locations marked 1 &2 45

Fig 4-2 Masks used for fabrication of PIPH : M1-M6 (wafer 1) and M7- M10 (wafer2) 45

Fig.4-3 Fabrication process flow of PIPH: (a) wafer 1-actuator and chamber and (b) wafer 2-channel and nozzle Both wafers are bonded by Eutectic bonding method 46

Fig 4-4 SEM and optical micrographs of the fabricated PIPH structure 47

Fig 4-5 Preparing for ejection test: (a) 4-inkjet heads on 1 cell and (b) PCB-wire bonding and tube attachment 48

Fig 4-6 Ejection testing by high speed digital camera system 49

Fig 4-7 Meniscus vibration under an applied voltage of 10V-40 kHz 49

Fig 5-1 Model of InkjetVer3 (3-silicon wafers) 51

Fig 5-2 Masks used for fabrication of InkjetVer3 51

List of tables

Table 2-1 Fluid properties 22

Table 2-2 Support layer properties 22

Table 2-3 PZT properties (PZT 52/48 ) 22

Table 2-4 The displacement at various driving frequencies (voltage=5V) 22

Table 2-5 Summary of actuator performance characteristics 22

CHAPTER 1 INTRODUCTION

transparencies as well as industrially printing information on cans or bottles Recently

it has been used as free-form fabrication method for building three dimensional parts (maskless fabrication) and is also being used to produce arrays of proteins and nucleic acids

The objective of this thesis is to investigate the piezoelectric MEMS inkjet print head from design to fabrication Therefore, this chapter will briefly summarize the background of piezoelectricity, types of piezoelectric MEMS inkjet head and general principle of numerical simulation

1.1 Piezoelectricity

1.1.1 Piezoelectric effect

All polar crystals show piezoelectricity, since any mechanical stress T will result in strain because of the elastic properties of the materials And the strain will affect the polarization since the polarization is caused by a displacement of the charge centers of the anions and cations For small changes of the stress T, the relation

P=d.T

is called the direct piezoelectric effect, where d denotes the piezoelectric coefficient

Once a force (mechanical stress) is applied to a piezoelectric material, surface charge is induced by the dielectric displacement and therefore an electric field is built up On applied electrodes this field can be tapped as electrical voltage (Fig 1-1 (a)) If the electrodes are shorted, the surface charge balances out by a current ((Fig 1-1 (b)) The direct piezoelectric effect is employed for mechanical sensors

Fig.1-1 Direct piezoelectric effect in open circuit (a) and in shorted circuit (b)

Because of the piezoelectric property of polar materials, a converse effect is

observed If an external electrical field, E is applied, a strain

S=d.E

is observed If this strain is prevented (blocking totally or partially the material), an elastic tension T occurs A force F is thereby applied to the device, which prevent to the distortion of the piezoelectric body (Fig 1-2.(a)) In practice, the converse piezoelectric effect is used in static as well as dynamic operation (Fig 1-2 (b)) and it is used for

mechanical actuators The first experimental work on piezoelectricity was performed by Pierre and Jacques Curie in 1880

Fig 1-2 Converse piezoelectric effect: (a) free displacement and blocking force and (b)

static and dynamic operation

The piezoelectric effect is exhibited by a number of naturally and synthetically

single crystals under two different behaviors Materials such as quartz exhibited a zero

polarization when the external electric or mechanical field is removed Other single crystal materials such as Rochelle salt, barium titanate, and others show a remanent polarization without external stress Moreover, the direction of the polarization could be reversed by application of an inverse electric field In this case, a hysteresis field appears and the material is called ferroelectric The origin of the piezoelectric effect in both types of crystal is common and related to an asymmetry in the cell unit and the resultant generation of electric dipoles due to the mechanical distortion leading to a net polarization at the crystal surface [2,3]

1.1.2 Lead zirconate titanate (PZT)

Lead zirconate titanate (PZT) is a kind of perovskite oxide which has a stably cubic structure at temperature above its Curie temperature (Tc) as seen in Fig 1-3(a) When the temperature decreases and falls below Tc the structure changes The O2- and the Pb2+ions are moved from their cubic positions and the Ti4+ and Zr4+ ions are moved from the center of the cube (Fig.1-3(b)) This results in a dipole and a structure that is no longer cubic but rather than tetragonal

The significant feature of PZT is its phase diagram, which is characterized by a

boundary, known as the morphotropic phase boundary (MPB, i.e the boundary between

rhombohedral and tetragonal phases at PbZr0.52Ti0.48O3) Figure 1-4 shows the phase diagram for the PbZrO3-PbTiO3 system PZT compositions were developed for moderate power applications PZT compositions have a low loss tangent resulting in low power losses as well as high distortion constant and high Curie point Compositions near MPB have the largest piezoelectric constants and dielectric constants This enhancement is a result of enhanced polarizability arising from the coupling between two equivalent energy states, i.e the tetragonal and rhombohedral phases, allowing optimum domain reorientation during the poling process In other word, it is due to the greater ease of polarization near MPB

Fig 1-3 Structure of PZT unit cell: (a) Cubic (T≥Tc) an (b) tetragonal (T< Tc)

Fig 1-4 Phase diagram for the PbZrO3-PbTiO3 system C: Cubic, T: Tetragonal, RI: Rhombohedral (high temp form), RII: Rhombohedral (low temp form), A: rthorhombic, M: MPB, and Tc: Curie temperature

Among the important material parameters, electromechanical coupling, dielectric constant, and associated piezoelectric coefficient are the key parameters to be compositionally engineered In general, the piezoelectric properties of a ferroelectric ceramic can be expressed using the simplistic term,

d ij ~ 2 kε o Q ij P i

where dij is the piezoelectric coefficient, Pi the remnant polarization on poling, k the dielectric constant, Qij the electrostriction coefficient Since both Qij and Pi exhibit little dependence on composition at temperature below Tc in ferroelectric ceramics such as PZT, the dij and k are interrelated, i.e a ceramic with high piezoelectric coefficient also exhibits a large dielectric constant To achieve a high dielectric constant or piezoelectric coefficient, MPB based ceramics can be further engineered by compositionally adjusting the Tc downward relative low temperatures The lower the Tc, the higher the dielectric constant is [4,5]

PZT is one of extremely important materials in mechatronics and MEMS applications In its bulk form, PZT is not readily amenable for integration into silicon micro-mechanical devices However PZT thin films are extremely promising as electro-mechanical elements for use with micro-mechanical structures PZT is a polar dielectric, which exhibits a high degree of piezoelectric activity PZT can be deposited by a number of processing routes onto silicon devices The most common deposition methods are sputtering, sol-gel, metalorganic chemical vapor deposition (MOCVD) and laser ablation [6] In this research, PbZr0.52Ti0.48O3 thin film which is a main component

of actuator membrane of piezoelectric MEMS inkjet print head was formed by spin coating its sol-gel solution

1.2 Piezoelectric MEMS inkjet print head

Piezoelectric actuators convert electrical signals (i.e., voltage, charges) into mechanical displacements or force Depending on the deformation mode of the piezoelectric material, the piezoelectric inkjet technology can be classified into four main types: squeeze, bend, push, and shear (as shown in Fig 1-5) For squeeze mode, radially polarized ceramic tubes are used In both bend- and push-mode design, the

electric field is generated between the electrodes parallel to the polarization of the piezo-material In a shear mode printhead, the electric field is designed to be perpendicular to the polarization of the piezoceramics [4] All of them have the same principle of droplet generation that the deformation of piezoelectric actuator under applied voltage leads to change of volume, causes the destabilization of the ink liquid and generates the droplets if the competition between cohesive and descriptive forces occurs favorably

Fig 1-5 Deformation mode of piezoelectric inkjet actuator: (a) squeeze, (b) bend, (c)

push and (d) shear mode

Piezoelectric MEMS inkjet structures used the piezoelectric thin film as main component of actuator part which has forcing function, and were integrated fluidic components such as ink chamber, channel and ink reservoir In the case of inkjet heads, print resolution is one of the primary measures of product performance When printing with inkjet heads, smaller, more tightly spaced droplets of ink result in sharper print quality However, this produces a smaller print area, resulting in an increased printing time To optimize both print quality and speed, a printer head must deliver an increased number of smaller-sized droplets, droplets; this equates directly to an increase in the density of holes per inch in an inkjet head [7] Therefore, the contribution of MEMS technology in fabricating inkjet heads is not only an integration of multi-components as well as their micro-scales but also an increase of numerous nozzles or array of nozzles (based on deep reactive ion etching (DRIE) technique)

1.3 Numerical simulation

1.3.1 Role of numerical simulation

A typical approach to MEMS application from concept to devices can be shown in Fig 1-6 The approach consists of several steps such as specifications of MEMS device, design, modeling to evaluate performance, fabrication and testing Reviews of the modeling and test results enable optimization of the performance of the MEMS device

Fig 1-6 A typical approach to MEMS application from concept to devices The process of developing a MEMS application starts with determining the specifications for MEMS device (i.e., inkjet print head) The specifications come from the nature of physical phenomenon, mechanism of operating principle and etc With the specifications in place, the next step is design which is the most important step in the flow sheet from concept to prototype Depending on the complexity of the design, it’s often difficult to predict the performance of MEMS devices intuitively In these cases computer simulations may provide a means to study the performance of MEMS devices prior to fabrication Behavior individual components as well as integrated components

of the entire device can be predicted by computer simulations By including the review step after simulation, structures can be optimized their geometrical parameters before fabricating the components or devices Computer simulations can significantly shorten the possibly long process of MEMS design, fabrication and testing Not only can they

provide a more complete understanding of the physical phenomenon but they can also

be used to develop optimal designs and to minimize the risk of wasting expensive production time on a flawed design [8-10]

1.3.2 General principle of numerical simulation

Physical phenomena are generally described by mathematical equations, typically partial differential equations (for example: Navier-Stokes equations are used to characterize the fluid flows) Analytical solutions of partial differential equations involve close-form expressions which give the variation of the dependent variables continuously throughout the domain In contrast, numerical solutions can give answers

at only discrete points in the domain, called grid points Numerical methods become more effective with the aid of computer The numerical solution procedure consists of discretization process (discreting partial differential equations into a system of algebraic equations) and solution process (using iterative methods to get the approximate results) (Fig.1-7) The discretization includes space discretization or grid generation and equation discretization There are three basic grids such as structured grids, unstructured grids and hybrid/mixed grids Equation discretization can be done by boundary methods

or domain methods such as finite difference method (FDM), finite volume method (FVM) and finite element method (FEM) So far, there have been a lot of commercial softwares developed based on these methods such as ANSYS, FEMLAB Intellisuite, CFD-ACE+, etc…

Fig 1-7 Steps of overall solution procedure

1.3.3 Numerical simulations of piezoelectric MEMS inkjet with CFD-ACE+

Piezoelectric MEMS inkjet print head is a complex device integrated mechanical-fluidic components The modeling, therefore, was performed in a separated way consisting of simulating (1) actuator performance and (2) droplet generation The former concentrates on analyzing the piezoelectric actuator characteristics (i.e., driving force, displacement and frequency) with electro-mechanical-fluidic couplings The fluid flow is driven by the vibration of the thin plate and the flow also imposes a resistance to this vibration Thus, vibrations of the plate and the fluid flow are inherently coupled The vibration characteristics of actuator membrane of piezoelectric MEMS inkjet head highly depend on this fluid-structure coupling Therefore, fluid-structure interaction is one of the primary concerns when studying piezoelectric inkjet head The later considers the generation of microdroplets which is influenced by a strong competition between cohesive and disruptive forces (i.e., driving force, viscous force and surface tension force) The simulations have been performed by CFD-ACE+ package software known as a multiphysics modeling tool The details of simulation settings will be described in chapter 2 and chapter 3 The goals of these simulations are indicated in Fig 1-8

electro-Fig 1-8 Modeling settings for design of piezoelectric MEMS inkjet Computations are

performed using CFD-ACE+ package software

1.4 References

[1] Paul Calvert, Inkjet printing for materials and devices, Chem.Mater.2001,13,

3299-3305

[2] Rainer Waser, Nanoelectronics and Information Technology, Volume.1, Advanced

Electronic Materials and Novel Devices, WILEY-VCH,2003

[3] Alfredo Vázquez Carazo, Novel Piezoelectric Transducers for High Voltage

Measurements, Ph.D Thesis, 2000

[4] Jürgen Brünahl, Physics of Piezoelectric Shear Mode Inkjet Actuators, Universitets

service US AB, Stockholm 2003

[5] Seung-Eek Park and Thomas R Shrout, Characteristics of Relaxor-Based

Piezoelectric Single Crystals for Ultrasonic Transducers, IEEE TRANSACTIONS ON

ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL 44,

NO 5, SEPTEMBER 1997

[6] D.F.L JENKINS, W.W CLEGG, E CATTAN & D REMIENS, PZT Thin Film

Bi-Layer Devices for Phase Controlled Actuation in MEMS, Journal of Electroceramics, 7,

5–11, 2001

[7] Janet Hopkins, DRIE of Silicon for MEMS Inkjet Heads, Surface Technology

Systems Ltd., Newport, UK-11/1/2004, Semiconductor International

[8] Xiaopeng Zhao, Modeling and Simulation of MEMS Devices, PhD dissertation,

Blacksburg, Virginia, 2004

[9] Oliver Geschke, Henning Klank, Pieter Telleman, Microsystem Engineering of

Lab-on-a-chip Devices, WILEY-VCH Verlag GmbH & Co KGaA, 2004

[10] CFD-ACE+ Modules Manual version 2004

CHAPTER 2 NUMERICAL AND EXPERIMENTAL STUDY ON ACTUATOR PERFORMANCE OF PIEZOELECTRIC MEMS

INKJET PRINT HEAD

Abstract

In this study, we focused on considering the actuator performance of a piezoelectrically actuated inkjet print head with the numerical and experimental analysis The actuator part consisting of multi-layer membranes, such as piezoelectric, elastic and other buffer layers, and ink chamber was fabricated by MEMS processing The maximum displacement of the actuator membrane obtained from the simulation and experiment was ca 0.053 um/V and 0.059 um/V, respectively As a result of fluidic damping, both simulation and experimental results show the resonant frequency of membrane in liquid is ca.3 times smaller than its resonant frequency in air These simulation and experimental studies play an important role to predict how much

“dynamic force”, in terms of membrane’s maximum displacement, maximum force and driving frequency, can be produced by a certain actuator membrane interacting with fluid

2.1 Introduction

MEMS technology is inherently multidisciplinary, which has resulted in synergies between previously unrelated fields, such as fluidics and microelectronics For example, piezoelectric MEMS inkjet print head, one of the most important elements in an ink-jet printing system, is a combination of microfluidics and microfabrication (MEMS) and is used to eject small amounts of fluid on target surfaces Compared to conventional electrostatic, thermal or magnetic actuating schemes, piezoelectric MEMS inkjet has the advantages of lower power consumption, lower voltage operation and relatively larger driving force In addition, Piezoelectric inkjet print heads normally offer a greater range

of ink compatibility than thermal ink-jet heads, which are limited to water-based inks or require a new design for each different type of ink solvent [1-7]

Various designs and fabrication techniques of piezoelectric inkjet print head (PIPH) have been reported in the literatures [4-7] In this study, we designed a PIPH structure which could be fabricated from two silicon wafers using MEMS processing However, depending on the complexity of PIPH structure integrating actuator-chamber-reservoir components, it’s difficult to predict the performances of inkjet intuitively One of important parts of a PIPH is actuator component which exhibits the ability of PIPH to work and eject the ink droplets Therefore, a numerical simulation of PIPH to analyze its actuator performance has been performed prior to fabrication In order to verify simulation results, a fabrication of PIPH’s actuator component was also carried out before the whole PIPH structure was fabricated In addition, this treatment helps to understand physical phenomena in interaction between solid and fluid components such

as piezoelectric actuator and ink chamber Fan et al revised that no complete coupling study would lead to that the flow rate increased continuously with increasing the frequency even at extremely high frequencies [4] Therefore, structural-fluidic interaction is one of primary concerns when studying actuator performance of inkjet head structure In simulation work, the finite element method (FEM) and computational fluid dynamics (CFD) with finite volume method (FVM) are employed to study the membrane-fluid coupling In experimental work, the piezoelectric actuator component

was fabricated using MEMS processing Then, its characteristics including displacement and resonance frequency were also monitored using a LK-G10-KEYENCE non-contact laser displacement measurement and a HP4194A impedance analyzer, respectively This paper addresses how the maximum displacement, maximum force and driving frequency affect to the PIPH actuator performance Simulation results

in air and in liquid agree well with experimental ones

2.2 Modeling and simulation settings

The inkjet structure consists of an ink chamber connected directly with a nozzle and

a reservoir This chamber is covered by a multi-layer membrane which consists of a primary piezoelectric actuator layer (PZT) and other secondary layers including an elastic layer (SiNx) and several buffer layers, i.e., SiO2, Ta/Pt Total thickness of secondary layers is 2.3 um In simulation, all secondary layers are modeled by an equivalent layer (called support layer) with effective parameters calculated by ROM (rule of mixtures) model [8] Therefore, the model of PIPH actuator is a bi-layer membrane (called actuator membrane) including PZT film and support layer The relative size (ratio of lateral dimensions) of PZT layer and support layer is 0.8 [our previous report, 9] In order to reduce the backflow from chamber to reservoir but still maintain good recovery of flow from reservoir to chamber, a diffuser is used as an active connector between them The selection of geometrical parameters of diffuser such as divergence angle, aspect ratio and etc is based on standardized data [10] With this model of PIPH, the fluid flow is driven by the vibration of the actuator membrane and the flow also imposes a resistance to this vibration Thus, the vibration of actuator membrane and the fluid flow are inherently coupled The actuator performance characteristics of PIPH highly depend on this fluid-structure coupling The model of PIPH structure is shown in Fig 2-1

For the simulation of PIPH structure, some governing equations on both the fluid side and the solid structure side are needed The governing equations on the fluid side are the Navier-Stokes equation and the mass continuity equation, while the governing equations on the solid structure side are equations for the actuation of piezoelectric

actuator and the motion of the elastic membrane

Because the characteristic length of the PIPH is in micro scale (10-6) and the Reynolds number is very low, the flow can be assumed as an incompressible laminar flow Therefore, the Navier-Stokes equations and the mass continuity equation become [11]

P V g

Dt

V D

0)

Boundary condition at the membrane-fluid interface is given by

k ijk kl E ijkl

P f t

W t

∂

∂+

D denotes flexural rigidity of membranes

)1(

The membrane has a clamped boundary condition at its edges, that is We=0

Equation (3) shows that the boundary condition on the fluid side at the membrane-fluid interface is controlled by the displacement of the membrane, while equation (5) shows that the motion of the membrane is significantly influenced by the pressure of fluid exerted on the membrane This is the key of the fluid-membrane interaction The equations (4) and (5) will be solved by the finite element method (FEM), while equations (1) and (2) are solved by the finite volume method (FVM) Combination of both these solutions at every time step helps to give the final results of the coupled problem

In order to save the calculation memory, a half of the symmetric structure was modeled and first order elements were used for PZT-support layer membrane with the FEM solution The Euler first order was applied to the FVM solution for the transient fluid flow Both FEM and FVM solutions are supported in the CFD-ACE+ package To obtain a high accuracy, grids at the bi-layer membrane and at the corners of the diffuser and nozzle should be denser than elsewhere [4-8] Both structured and unstructured grids were used The total number of the nodes is 61,346 and total number of the cells is 181,116 (Fig 2-1(b))

Because the support layer of PIPH is integrated with the surrounding walls, its edges considered to be clamped The boundary conditions for the fluid model are non-slip at

the fluid-wall The boundary condition at the nozzle outlet is free convection In order to combine the FEM and FVM solutions in the same integrated PIPH, the pressure at the support layer-fluid interface and the deformation at PZT-support layer interface and support layer-fluid interface were set as implicit values Then the electro-mechanical-fluid couplings were performed with the CFD-ACE+ package software [14]

2.3 Experimental procedure

PIPH actuator part was fabricated by MEMS processing Piezoelectric PZT thin film was prepared using sol-gel process The ratio of Zr to Ti in a PZT precursor solution was 0.52:0.48, which corresponds to the morphotropic phase boundary (MPB) The detailed synthesis process for the precursor is described in our earlier reports [15] Figure 2 shows the fabrication steps and SEM images of PIPH actuator Low stress SiNx and low temperature oxide SiO2 (LTO) were prepared by low pressure chemical deposition (LPCVD) Pt (1500Å) metallic layer as bottom electrode with thin Ta (200Å)

as an adhesion layer was deposited at 350°C on the LTO/SiNx/Si substrate by DC magnetron sputtering 0.5 um thick PZT thin film was deposited by sol-gel spin coating with the synthesized precursor solution, followed by fast anneal at 700°C for 5 min in a tube furnace Then the etching of PZT thin film was carried out using reactive ion etching (RIE) in an inductively coupled plasma (ICP) etcher Before the top electrode Pt (1000Å) was deposited by DC magnetron sputtering and patterned by a lift-off process,

an inter-layer dielectric (ILD) polyimide (1.2 um) was deposited by spin-coating and patterned by photolithography The back side silicon was etched by wet chemical etching with a KOH solution (KOH : DI water=6:4) at 80°C

The fundamental frequency and mechanical displacement of PIPH actuator was measured using a HP4194A impedance analyzer and a LK-G10-KEYENCE non-contact laser displacement measurement, respectively The measurement of resonance frequency was carried out both in air and in liquid in order to compare with simulation results

2.4 Results and discussion

2.4.1 Performance characteristics of PIPH actuator in air

PIPH actuators offer a wide variety of performance and operate in many different ways, such as piezoelectric squeeze-, bend-, push- and shear-mode inkjet actuators [16] For our current analysis, a PIPH actuator is a work-producing device operating in bend-mode The maximum actuation displacement, δmax, and the maximum actuation force,

Fmax, are basic characteristics of PIPH actuator The product δmax Fmax is an estimate of the maximum work in a single stroke When considering the dynamic operation (multi-strokes) of PIPH actuator, the performance approaches a limit in form of a maximum power, pmax, which is proportional to the maximum frequency of operation, fmax, (pmax=cfmaxδmaxFmax- c is a dimensionless cyclic work coefficient) The limit fmax is defined by the frequency of first resonance [17] Therefore, performance characteristics

of PIPH actuator were considered in terms of maximum displacement, maximum force and first resonance frequency or fundamental frequency

With membrane size of 300 um, the numerical and experimental values of the maximum displacement rate were ca 0.053 um/V and ca 0.059 um/V, respectively (Fig 2-3) The simulation was also extended for various sizes of PIPH actuator membrane (i.e., 500um, 600um) Fig 2-4(a) indicated the relationship between the maximum displacement of PIPH actuator membrane and thickness ratio of PZT to support layer at

an applied voltage of 5V (thickness of support layer was fixed of 2.3 um) Increasing PZT thickness makes the PZT actuation strain increased and the stiffness of PIPH actuator membrane, thus, also increased, which decreased its displacement Total actuation strain of PIPH actuator membrane finally depends on the competition between them Therefore, maximum displacement of PIPH actuator membrane slightly increased from thickness ratio of 0.2 to 0.5 (corresponding to PZT thickness of 0.5 um to 1.15 um) and then decreased with thicker PZT film According to Gere & Timoshenko, the

maximum displacement of a pure bending membrane (with width a and Young’ s

modulus E) under uniform load, P, can be expressed as [18]

3 4 max

Et Pa

a

Et F

a2) However, the maximum force was enhanced significantly (i.e., 1.75 times) in case

of the PZT thickness of 1 um In addition, the maximum force reached the saturated values at membrane width of ca 600 um This marks a notice in selecting optimized sizes of PIPH actuator membrane which can produce both high maximum displacement and maximum force so that the highest value of the maximum work can be obtained Finally, the fundamental frequency of PIPH actuator membrane (width of 300um) was predicted using FEMLABTM software and compared with an experimental result monitored by HP4194A impedance analyzer Its simulation and experimental values were ca 379 kHz and ca 328 kHz, respectively (Fig.2-5)

2.4.2 Performance characteristics of PIPH actuator in liquid

Amount of the fluid ejected through the nozzle is determined not only by the maximum actuation displacement, maximum actuation force of the membrane and the behavior of the fluid inside the system, but also by the deflection shape of the membrane [4] The displacement of the membrane is due to the shear stress applied by the actuator and by the pressure of the fluid This pressure was solved from Navier-Stokes equations by setting the membrane displacement as one of its boundary conditions Therefore, the behavior of the PIPH is a set of electrical-mechanical-fluid couplings

When the fluid-membrane interaction was considered, the maximum displacement slightly reduced (i.e., 0.049 um/V (in liquid-interaction) vs 0.053 um/V (in air)) The maximum force, thus, also reduced in accordance to equation (8) The maximum displacements of PIPH actuator membrane at various driving frequencies are listed in Table 2-4 And typical deflection shapes are shown in Fig.2-6 At low frequencies (100 Hz-25 kHz), the deflections were not sensitive to the driven frequency The PIPH actuator membrane bends in one direction and it has only one peak (Fig.2-6 (a,b)) The maximum displacements in these cases were 0.245 ~ 0.267 μm At higher frequencies (25 kHz-100 kHz), the deflections increased with the frequency and were different between bend-up and bend down modes Moreover, because of the membrane-fluid interaction, the membrane deflection shape was changed at frequencies above 100 kHz The deflection shape of PIPH actuator membrane was sophisticated and exhibited two

or more peaks (Fig.2-6 (c,d)) The appearance of the deflection peaks becomes one of the disadvantages for the PIPH actuator performance The behavior of fluid inside the chamber, thus, also changed unexpectedly Below 125 kHz, outlet flow rate increased with increasing the frequency The response of fluid and the vibration of membrane were in phase The ratio between backflow and net flow reached the minimum value of

ca 3% at driving frequency of 25 kHz Above 125 kHz, the response of fluid and vibration of membrane were out of phase (Fig.2-7(a)) This frequency is considered as a resonance frequency of the PIPH actuator membrane in liquid And the experimental result showed the resonance frequency of membrane in liquid was ca 90 kHz (Fig.2-7(b)) Both numerical and experimental resonance frequencies of membrane in liquid were about 3 times smaller than those of membrane in air The driving frequency of PIPH actuator must be smaller than this resonance frequency of membrane in liquid Summary of maximum displacement and resonant frequency was shown in Table 2-5 The prediction for actuator membrane with width of 600 um was also given in this table The simulation results agree well with experimental ones This work along with another work studying microdroplet generation of PIPH (will be reported elsewhere) offers an effective guideline in designing the PIPH

2.5 Conclusion

Performance characteristics of PIPH actuator have been investigated numerically and experimentally The maximum actuation displacement and the maximum actuation force are basic performance characteristics of a work-producing PIPH actuator Natural frequency of actuator membrane was known as a limit of PIPH actuator operating at dynamic regime Considering the electro-mechanical-fluid couplings indicated the inter-dependence between PIPH actuator membrane and fluid, which leads to significant changes such as the decrease of resonance frequency or the appear of multi-peak deflection shapes as well as out-of-phase response of ink liquid The numerical results agree well with the experimental ones These results play an important role in selecting the appropriate design parameters so that characteristics of PIPH actuator can be optimized

2.6 References

[1] M Usui, Seiko Epson Corporation, Shiojiri, Nagano, Japan

[2] Hermann Seitz and Joachim Heizl, J.Micromech.Microeng.14(2004) 1140-1147 [3] Steve Temple, Xaar plc, Cambridge

[4] B Fan, G Song and Hussain, Smart Mater.Struct 14 (2005) 400-405

[5] Vishal Singhal and Suresh V.Garimella, IEEE transactions on advanced packaging, VOL.28.N0.2, MAY2005

[6] J KIM, ME608 Final project, Apr.26.2002

[7] J S Yahng and S C Jeoung, D S Choi and D Cho, J H Kim, H M Choi and J

S Paik, J.Korean Phys Soc.Vol 47, No 6, December 2005, pp 977_981

[8] K.Y.Lee, E.D.Case, Journal of Materials Science 31(1996)2253-2264

[9] Jun-Kyu Paik, Sanghun Shin, Sun-Woong Na, Nae-Eung Lee, and Jaichan Lee, Integrated Ferroelectrics, 69:383-390 (2005)

[10] Frank M.White, Fluid Mechanics, 4th ed (Mc Graw Hill, 1998)

[11] Joel h Ferziger et al, Computational Methods for Fluid Dynamics (Springer Verlag, 1999)

[12] IEEE Standard on Piezoelectricity, ANSI/IEEE Std176-1987

[13] Szilard R, Theory and Analysis of Plates, Classical and Numerical Methods (Englewood Cliffs, NJ: Prentice-Hall,1974)

[14] CFD-ACE+ Modules Manual version 2004

[15] J R Ahn, D W Kim, G Y Yeom, J B Yoo, and J Lee, Ferroelectrics, 263, 244

(2001)

[16] Jurgen Brunahl, Physics of Piezoelectric Shear Mode Actuators (Stockholm,2003) [17] J.E.Huber, N.A.Fleck and M.F.Ashby, Proc.Soc.Lond.A (1997)453,2185-2205 [18] Gere & Timoshenko, Mechanics of Materials, 3rd ed (PWS-KENT, 1990)

Table 2-1 Fluid properties

Property Density (ρL) Dynamic viscosity (μ)

Unit kg m-3 x10-3 kg m-1 s-1

Table 2-2 Support layer properties

Property Density (ρ) Young’s Modulus (E) Poisson’s ratio (υ)

Table 2-3 PZT properties (PZT 52/48 )

Piezoelectric coefficients (x10-12 C/N) Density

(kg m-3)

Young’s

Modulus (Pa)

Poisson’s ratio (υ) d13 d23 d33 d42 d51

Table 2-4 The displacement at various driving frequencies (voltage=5V)

Frequency, f (Hz) Max bend up (μm) Max Bend down (μm)

Maximum displacement (in liquid)

Resonance frequency (in air)

Resonance frequency (in liquid) Simulation (300 um) 0.053 um/V 0.049 um/V 379 kHz 125 kHz

Prediction (600 um) 0.240 um/V x ~ 100 kHz ~ 30 kHz