LASER MICROFABRICATION OF THICK-FILM MICROELECTRONICS

A Thesis

Submitted to the Faculty

of

Purdue University

by

Edward C. Kinzel

In Partial Fulfillment of the

Requirements for the Degree

of

Master of Science in Mechanical Engineering

August 2005

ii

ACKNOWLEDGEMENTS

I would like to thank Professor Xianfan Xu for serving as my advisor on this

project and supplying expertise in the field of laser micro-fabrication. He was very

patient with me and is an excellent advisor. I would also like to thank Professors Robert

Lucht and Professor Normand Laurendeau, for serving on my committee and their

willingness to review this thesis on very short notice. I would especially like to thank

Hjalti Sigmarrson who helped taking measurements and provided extremely useful

feedback. All of my lab mates have been very kind to me but Richard (Xi) Zhang, in

particular, was very helpful in initiating this project and offered invaluable assistance in

setting up the finite element simulations. I would also like to thank Professor William

Chappell for supplying expertise in the field of microwave design and analysis as well as

insights into advanced manufacturing for microelectronics. Carl Berlin at Delphi

Automotive Safety Division provided most of the materials for the experiments as well as

useful comments on the demands coming from the microelectronics industry. Dr. Scott

Mathews at The Catholic University of America introduced me to the concept of runaway

heating with regards to laser sintering on polymer substrates. I would also like to thank

Professor Anil Bajaj and Tiffany Bitzel for proofreading this thesis. Brent Lewis also

deserves credit for capturing the micrographs of the MAPLE-DW events. I am very

grateful for the financial support of the Lozar Student Assistantship as well as the Indiana

21st Century Research and Technology Fund which made this work possible. I hope that

this research will prove to have a good return on investment for the state. I would like to

dedicate this thesis to my father who first motivated my interest in mechanical

engineering.

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TABLE OF CONTENTS

Page

LIST OF TABLES...............................................................................................................v

LIST OF FIGURES ........................................................................................................... vi

NOMENCLATURE ............................................................................................................x

ABSTRACT..................................................................................................................... xiii

1. INTRODUCTION ...........................................................................................................1

1.1 Motivation and Problem Definition .........................................................................1 1.2 Review of Patterning Technologies .........................................................................4 1.2.1 Conventional Thick-Film Technology.........................................................6 1.2.2 Direct Gravure Offset Printing.....................................................................8 1.2.3 The Micropen System..................................................................................9 1.2.4 Ink Jet Technologies ..................................................................................10 1.2.5 LIFT ...........................................................................................................12 1.2.6 MAPLE and MAPLE-DW.........................................................................14 1.3 Functionalization Technologies .............................................................................16 1.3.1 The Conventional Sintering Process..........................................................17 1.3.2 Selective Laser Sintering ...........................................................................18 1.4 Overview of Thesis ................................................................................................19

2. MAPLE-DW..................................................................................................................21

2.1 Introduction............................................................................................................21 2.2 Experimental Setup and Procedure........................................................................22 2.2.1 Instrumentation ..........................................................................................23 2.2.2 Experimental Procedure.............................................................................26 2.3 Experimental Results .............................................................................................28 2.4 Discussion..............................................................................................................34 2.5 Summary ................................................................................................................38

3. MODELING OF THE SUB-THRESHOLD MAPLE-DW EVENT.............................40

3.1 Results from Time-Resolved Microscopy .............................................................40 3.2 Development of an Analytical Model of the MAPLE-DW Event.........................48 3.2.1 Laser Ink Interaction ..................................................................................50 3.2.2 Coupling of Laser Energy to the Kinetic Energy of the Ink ......................52

iv

Page

3.2.3 Viscous Forces ...........................................................................................55 3.2.4 Elastic Forces .............................................................................................56 3.2.5 Damped Harmonic Oscillator ....................................................................58 3.3 Experimental Data Analysis ..................................................................................61 3.5 Conclusions............................................................................................................67

4. SELECTIVE LASER SINTERING ..............................................................................68

4.1 Introduction............................................................................................................68 4.2 Experimental Setup................................................................................................71 4.3 Experimental Results .............................................................................................75 4.3.1 DC Conductivity ........................................................................................76 4.3.2 High Frequency Performance ....................................................................80 4.3.3 Feature Size................................................................................................86 4.3.4 Sintering on Polymer Substrates................................................................89 4.3.5 Sintering of Resistive and Dielectric Elements .........................................93 4.3.6 Sintering Copper Inks in an Ambient Air Environment ............................95 4.4 Conclusions............................................................................................................99

5. NUMERICAL MODELING OF SELECTIVE LASER SINTERING .......................100

5.1 Introduction..........................................................................................................100 5.2 Heat Transfer Analysis ........................................................................................102 5.2.1 Thermal Analysis of Selective Laser Sintering .......................................102 5.2.2 Boundary Conditions ...............................................................................105 5.3 Material Properties...............................................................................................107 5.4 Numerical Simulations.........................................................................................111 5.5 Results..................................................................................................................113 5.6 Summary ..............................................................................................................123

6. CONCLUSIONS AND RECOMMENDATIONS ......................................................124

6.1 Summary and Conclusions ..................................................................................124 6.2 Recommendations for Future Work.....................................................................127

LIST OF REFERENCES.................................................................................................130

v

LIST OF TABLES

Table Page

3.1: Model parameters......................................................................................................62

4.1: Quality factor components........................................................................................83

5.1: Temperature at assorted depths from the ink-substrate interface. ..........................121

vi

LIST OF FIGURES

Figure Page

1.1: Example of a hybrid circuit (an engine control module fabricated by Delphi Delco Electronics from www.dupont.com/mcm/appilic/contmodl.html#sol). ........2

1.2: Antenna metallize on a Kevlar helmet (from www.directwriting.org/dwimages.htm). ........................................................3

1.3: Viscosity changes in thick film pastes during screen printing from Licari and Enlow (1998). ..........................................................................................................7

1.4: Direct Gravure Offset Printing process from Kittilä et al. (2004) (a) doctor blading the gravure to apply ink (b) pressing the substrate against gravure to transfer ink and (c) final printed pattern on substrate. .............................................8

1.5: Micropen system in operation from King et al. (1999). ..........................................9

1.6: Human liver cells being transferred from an ink jet device (Calvert, 2001). ........12

1.7: Schematic of LIFT process from Yamada et al. (2002).........................................13

1.8: Schematic of the MAPLE deposition system from Piqué et al. (2002). ................15

1.9: Schematic of the MAPLE-DW process from Piqué et al. (1999)..........................15

1.10: A commercial MAPLE-DW system (from www.mesofab.com)...........................16

1.11: Furnace profile for DuPont thick-film inks, from Licari and Enlow (1998). ........18

2.1: Picture and schematic of MAPLE-DW setup. .......................................................25

2.2: Application of ink with a wire-coater (from Gaurdco website: www.gardco.com/rods.html) .................................................................................27

2.3: Micrographs of different response regimes (a) sub-threshold (b) jetting and (c) plume......................................................................................................................30

2.4: Deposition on alumina substrate for various fluences ...........................................31

2.5: Micrographs of a 20 μm line..................................................................................33

2.6: Profile measurements of the line shown in Figure 2.5...........................................33

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Figure Page

2.7: Micrograph of a 10 μm line. ..................................................................................34

2.8: Schematics of (a) MAPLE-DW process and (b) Flash-MAPLE setup..................36

2.9: Patterns deposited with Flash-MAPLE fabricated with (a) one-to-one and (b) 10X reduction transfer. ..........................................................................................37

2.10: Flashing MAPLE pattern using a DMD array .......................................................38

3.1: Correlation between nominal and measured film thickness. .................................41

3.2: Bubble displacement vs. time for 14.75 μm beam radius and 9.33 μm ink thickness.................................................................................................................43

3.3: Bubble displacement vs. time for 29.95 μm beam radius and 9.33 μm ink thickness.................................................................................................................43

3.4: Bubble displacement vs. time for 14.75 μm beam radius and 18.02 μm ink thickness.................................................................................................................44

3.5: Bubble displacement vs. time for 29.95 μm beam radius and 18.02 μm ink thickness.................................................................................................................44

3.6: Bubble displacement vs. time for 14.75 μm beam radius and 31.84 μm ink thickness.................................................................................................................45

3.7: Bubble displacement vs. time for 29.95 μm beam radius and 31.84 μm ink thickness.................................................................................................................45

3.8: Deformation after 250 μs vs. fluence.....................................................................47

3.9: Maximum event radius as a function of fluence....................................................48

3.10: Laser interaction with the ink ................................................................................50

3.11: Forces acting on ink bubble during its development. ............................................55

3.12: Surface tension force for surface tension constant of 1 N/m for various beam radii...............................................................................................................58

3.13: Damped harmonic oscillator ..................................................................................59

3.14: Under and over-damped harmonic oscillators. ......................................................60

3.15: Fitted response for 31.84 μm ink thickness and 14.75 μm beam radius................63

3.16: Maximum experimental and modeled event displacements. .................................63

3.17: Ratio of maximum bubble radius to the laser beam radius....................................65

3.18: Ratio of the maximum displacement to the maximum event radius......................67

4.1: Schematic of Selective Laser Sintering setup........................................................72

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Figure Page

4.2: Laser control power vs. measured power at the substrate .....................................73

4.3: DC test patterns written at (a) 0.84 W, (b) 1.96 W, (c) 3.92, W (d) 0.84 W - 0.30 m/s, (e) 1.96 W - 0.20 m/s, and (f) 3.92 W - 0.10 m/s...................................77

4.4: Profiles for the cross section for the test patterns shown in Figure 4.3(d-f)..........78

4.5: DC Conductivity in S/m×107 after (a) one layer of metallization and (b) two layers of metallization............................................................................................79

4.6: /2 microstrip resonator on quartz.........................................................................81

4.7: QU versus conductivity for the microstrip resonators ............................................82

4.8: Comparison between simulation and measurement for glass resonator ................84

4.9: Comparison between simulation and measurement for quartz resonator ..............84

4.10: Current distribution in the resonator from HFSS...................................................86

4.11: Profile across DC line written at 0.4 m/s and 1.96 W............................................86

4.12: Cross sectional profiles for lines written at 0.4 m/s...............................................87

4.13: Cross sectional profiles for lines written with 1.40 W...........................................87

4.14: Photograph of 25 μm wide lines on a 100 μm pitch ..............................................88

4.15: DC conductivity for Heraeus C8772 lines on FR4 ................................................90

4.16: Patch antenna fabricated on FR4 substrate using SLS...........................................92

4.17: Patch antenna pattern on flexible Mylar substrate fabricated using SLS ..............92

4.18: Micrograph of two silver conductors electrically isolated from each other with a layer of dielectric.................................................................................................94

4.19: SEM images of silver line passing over dielectric layer shown in Figure 4.16.....95

4.20: Copper wires between silver contacts with fabricated a laser power of 3.1 W at the substrate........................................................................................................97

4.21: Micrographs of copper lines sintered with (a) 1.1 W, (b) 1.7 W, and (c) 2.2 W. ...............................................................................................................97

4.22: Photograph of thin copper lines sintered at various speeds and powers................98

4.23: Profilometer measurements for lines sintered at 3.92 W.......................................99

5.1: Specific heat and thermal conductivity for (a) silver, and (b) soda-lime glass....109

5.2: Effective specific heat and thermal conductivity used for simulating ink...........109

5.3: Mesh used for finite element model of selective laser sintering..........................112

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Figure Page

5.4: Maximum temperature attained for various depths measured from the interface using 2.0 W of laser power and a scan speed of 0.10 m/s ....................114

5.5: Maximum temperature attained for various depths measured from the interface using 2.0 W of laser power and a scan speed of 0.40 m/s ....................115

5.6: Maximum temperature attained along the centerline of the ink-substrate interface for 2.0 W of laser power .......................................................................115

5.7: Thermal profile for a laser power of 2.0 W and a scan speed of 0.10 m/s. (a) surface xy plane – z=3 μm, (b) cross section of central xz plane – y=0 μm, and (c) cross section of yz plane – x=90 μm...............................................................116

5.8: Temperature profile for a laser power of 2.0 W and a scan speed of 0.10 m/s plotted vs. depth ...................................................................................................118

5.9: Temperature profile for a laser power of 2.0 W and a scan speed of 0.10 m/s plotted vs. time.....................................................................................................118

5.10: Temperature profile for a laser power of 2.0 W and a scan speed of 0.40 m/s plotted vs. depth ...................................................................................................119

5.11: Temperature profile for a laser power of 2.0 W and a scan speed of 0.40 m/s plotted vs. time.....................................................................................................119

5.12: Thermal profile for different scan speeds at the surface of the ink and at 4.85 μm into the substrate for a laser power of 2.0 W and different laser scan speeds...................................................................................................................120

5.13: Maximum thermal profile attained for a laser power of 2.0 W using different scan speeds...........................................................................................................121

5.14: Maximum thermal profile attained using a scan speed of 0.10 m/s for different laser powers .........................................................................................................122

5.15: Maximum temperature attained as a function of power for scan speeds of 0.10 m/s and 0.40 m/s ..................................................................................................122

x

NOMENCLATURE

Symbols

A laser beam cross-sectional area (m2)

a optical absorption coefficient (m-1)

1c laser-ink interaction constant (m2/J)

2c laser-ink interaction constant

3c laser-ink interaction constant (J/m2)

4c viscosity constant

5c viscosity constant

pc specific heat (J/kg·K)

pc effective specific heat (J/kg·K)

d ink thickness (m)

thd thermal penetration depth (m)

E laser pulse energy (J)

vE energy required to vaporize the initial vapor pocket (J)

F laser fluence (J/m2)

dF viscous forces (N)

sF surface tension forces (N)

f frequency (Hz)

h convection coefficient (W/m2·K)

fgh enthalpy of vaporization (J/kg)

I laser irradiance (W/m2)

k thermal conductivity (W/m·K)

ik thermal conductivity of the ink (W/m·K)

sk thermal conductivity of the substrate (W/m·K)

KE kinetic energy of the MAPLE-DW event (J)

An mass flux rate of material leaving the surface (kg/s)

P laser power (W)

abQ heat generation term in the heat conduction equation (W)

xi

Symbols

Qc contributions from the conductor to quality factor

Qd contributions from the dielectric to quality factor

QL loaded quality factor

Qrad contributions from the radiation to quality factor

QU unloaded quality factor

fR optical reflectivity

21S power transmission through the resonator (dB)

T temperature (K)

fT temperature of the air (K)

lT liquidus temperature (K)

sT solidus temperature (K)

surfT temperature of the surface (K)

VT threshold temperature required to vaporize the ink (K)

0R initial radius of the vapor pocket (m)

0r beam radius (m)

vV initial volume of the vapor pocket (m3)

xv velocity in the x direction (m/s)

yv velocity in the x direction (m/s)

0x initial x location of the focal point (m)

0y initial y location of the focal point (m)

0Z initial height of the vapor pocket (m)

0z initial velocity of the MAPLE-DW event (m/s)

thermal diffusivity (m2/s)

s electrical skin depth of the conductor (m)

volume fraction of spherical inclusions in the ink

surface tension coefficient (N/m)

imaginary part of the complex refractive index

laser wavelength (m)

dynamic viscosity (Pa·s)

dynamic viscosity for an infinite shear rate (Pa·s)

0 dynamic viscosity as the shear rate approaches zero (Pa·s)

m electromagnetic permiability (H/m)

density (kg/m3)

xii

Symbols

electrical conductivity (S/m)

laser pulse duration (s)

s shear stress (N/m2)

xiii

ABSTRACT

Kinzel, Edward C., M.S.M.E., Purdue University, August, 2005. Laser Microfabrication of Thick-Film Microelectronics. Major Professors: Dr. Xianfan Xu, Dr. Normand M. Laurendeau, and Dr. Robert P. Lucht, School of Mechanical Engineering.

This work investigates two techniques for fabricating thick-film microelectronics,

Matrix Assisted Pulsed Laser Evaporation – Direct Write (MAPLE-DW) and Selective

Laser Sintering (SLS). There is currently a gap between the size of features that can be

patterned effectively with conventional thick-film techniques (>75 μm) and economically

fabricated using conventional thin-film techniques (<10 μm). MAPLE-DW is a forward

transfer technique that has the potential to fill this gap. The MAPLE-DW approach is

adapted for a system using a pulsed infrared laser and optical x-y scanner with

conventional thick-film inks. This system has the advantage of high writing speeds while

maintaining the potential for rapid prototyping. The ability to deposit patterns with

feature sizes below 25 μm is demonstrated. The fundamentals of the MAPLE-DW

process are studied using results from time-resolved microscopy. A simple analytical

model is developed to investigate the effects of the process parameters. This model is

fitted to experimental results and it is found that the best results are produced for a

minimum ink substrate separation and a minimum ink thickness.

This thesis also investigates the Selective Laser Sintering (SLS) process. The

thick film inks used with MAPLE-DW require firing at 850°C to be functionalized after

patterning. In SLS, a continuous wave infrared laser is focused onto the ink layer and

xiv

heats it locally, which permits the functionalization of thick-film inks on low temperature

substrates such as polymers. The SLS technique can also be used to pattern the substrate

directly or in conjunction with a direct-write technique such as MAPLE-DW. This work

demonstrates that SLS is capable of duplicating the functional performance of the

conventional thick film process at DC and high frequencies on substrates with a damage

threshold 300°C less than the firing temperature. SLS is also demonstrated to be capable

of creating patterns with feature sizes below 25 μm. The temperature profile generated by

SLS is investigated using a finite element simulation. The calculation reveals that the

portion of the substrate closest to the interface with the ink is heated above its damage

threshold. However, if the right scan speed and laser power are used, the depth of the

damaged region is less than 5 μm. The simulation provides insights that help to further

optimize the SLS process.

1

1. INTRODUCTION

1.1 Motivation and Problem Definition

Increases in operational frequency and interconnect density are requiring smaller

feature sizes for microelectronics. New technologies are needed for the fabrication of

inexpensive, highly compact, and lightweight integrated assemblies. While Moore’s Law

has successfully predicted advances in semiconductor Integrated Circuit (IC) fabrication,

the technologies for producing feature sizes in the mesoscopic range (10 μm to 1 mm) is

only recently seeing development. This range falls in between what can be economically

fabricated by conventional thin-film and the practical limits of thick-film technologies.

Many high frequency and medical applications such as radar and biological sensors

require passive electronic components with mesoscopic sized features. The ability to

fabricate these economically will facilitate bringing new devices such as low-cost RFID

tags to market.

In addition to interconnects, passive components, such as resistors, capacitors, and

inductors, are a part of most microelectronic devices. Material and morphological

requirements caused by parasitic losses and mixed feature sizes of RF components limit

the fabrication of passive components on semiconductor dies. Traditionally, high quality

surface mount passive devices are usually soldered to a printed wiring board. It is

desirable to integrate these components into the substrate and packaging for the device.

This is currently being accomplished with the Low Temperature Co-fired Ceramic

(LTCC) process, which is a rapidly maturing technology. The integration of more than

2

one distinct fabrication technology (e.g. semiconductor die and integrated passives)

defines a hybrid microcircuit (Licari and Enlow, 1998). Hybrid microcircuits lead to

more compact devices than printed wiring boards with surface mount components. They

are used in many high-end applications such as space, military or medical for which

weight and size restrictions are important (Licari and Enlow, 1998). An example of a

hybrid microcircuit is shown in Figure 1.1.

Figure 1.1: Example of a hybrid circuit (an engine control module fabricated by Delphi Delco Electronics from www.dupont.com/mcm/appilic/contmodl.html#sol).

The LTCC process has several limitations including high processing temperature

(850°C), morphological/tolerance restrictions as well as a complex fabrication cycle. The

high processing temperature prevents the use of this technology with flexible/conformal

polymer substrates. The patterning technology is currently limited to feature sizes greater

than 75 μm. The complexity of both the fabricated circuits and the fabrication process

limit the effectiveness of computer simulations; moreover, realizing a functional design

may require several iterations of prototypes creating a long development cycle. This

consumes research and development resources, which can cost companies a competitive

edge in the marketplace. The desire is to move directly from Computer Aided Design

(CAD) to Computer Aided Manufacturing (CAM) and produce a device with minimum

operator intervention. The optimum situation will allow a designer to “print” a functional

prototype with little more effort than what is required to produce a paper copy of a

computer document.

3

Thin-film technology involves vacuum evaporation of materials and is typically

used in the fabrication of ICs. These techniques can produce film thicknesses between 3

nm and 2,500 nm (Licari and Enlow, 1998). However, it is generally too expensive to

manufacture most mesoscale devices. There are also limitations in the materials that can

be deposited. For example, resistors with high sheet resistances can not be fabricated

using conventional thin-film technologies (Licari and Enlow, 1998).

Challenges in mesoscale manufacturing were recognized by the Defense

Advanced Research Projects Agency (DARPA) and in 1999 it launched the Mesoscale

Integrated Conformal Electronics (MICE) program. This had the intent of motivating the

development of new technologies to satisfy morphological demands at low temperature

and on nonplanar substrates (Piqué and Chrisey, 2002). Neither the patterning nor

functionalization steps can heat the substrate above its damage threshold, which is much

lower than the processing temperature for conventional thick-film inks (400°C for

Kapton and lower for other polymer substrates, as opposed to 850°C). A typical example

of this type of problem is metallizing a GPS antenna on a soldier’s helmet, as shown in

Figure 1.2.

Figure 1.2: Antenna metallized on a Kevlar helmet (from www.directwriting.org/dwimages.htm).

In addition to conformal and morphological demands, the DARPA MICE

program also had the goal of reducing the development cycle and permitting distributed

just-in-time electronics manufacturing. This requires the fabrication of electronic devices

4

directly from CAD files without the fabrication of a mask, which in turn allows the

economical fabrication of low-batch runs because of minimal capitol costs for new

designs.

Recognizing the challenges described above, the motivation behind this thesis is

to investigate and develop fabrication techniques that have the following capabilities:

The ability to pattern thick-film inks with feature sizes less than 25 μm;

The ability to incorporate multiple materials (both electronic and non-electronic)

to create integrated devices;

Inexpensive in terms of capital, operating, and material costs;

Scalable from rapid prototyping and low-batch production runs to large-batch

sizes for mass manufacturing;

The ability to pattern conformal/flexible substrates with low processing

temperatures;

The ability to be integrated with other microelectronics fabrication operations

such as micromachining.

The remainder of this chapter is organized as follows. Section 1.2 introduces the

conventional thick film process and reviews several new techniques that have been

developed for patterning microelectronics. Section 1.3 discusses the functionalization of

deposited microelectronics using bulk sintering and introduces Selective Laser Sintering.

Finally, Section 1.4 provides an overview of the thesis.

1.2 Review of Patterning Technologies

Most thick-film devices are created by depositing patterns onto the substrate and

then bulk processing the material to functionalize it. The most commonly used patterning

5

technique in the industry is screen printing. This is an additive process and has the

advantage of minimizing material waste. However, the entire component must be fired at

850°C to functionalize the device. The high processing temperature restricts the materials

that can be used for substrates and inks. The screen printing process also struggles to

produce feature sizes below 100 μm.

Alternatively, functional material can be applied to the substrate and the pattern

created by removing a negative of the pattern by etching or ablation. This is how

standard Printed Circuit Boards (PCB)s are manufactured. A thin layer of metal is

laminated to an epoxy glass board such as FR4. Next, it is coated with a photoresist and

patterned using lithographic techniques. The metal can then be etched away to leave the

desired pattern. This patterning step is similar to conventional thin-film processing. It is

time consuming, requires the waste and disposal of large amounts of material, as well as

the use of environmentally hazardous chemicals. An alternative to lithography is to

remove the unwanted metal using laser ablation or a CNC milling machine. These

techniques allow the rapid prototyping of printed circuit boards. Passive components

must be surface mounted because these techniques do not lend themselves to circuits with

multiple materials (a resistive layer can not placed on top of a conductive layer because

the upper layer cannot be patterned without damaging the lower layer).

A number of processes can be combined to create a direct write/erase type system.

The materials can be deposited and then trimmed to generate better pattern morphology.

This is commonly done with thick-film resistors that are deposited by screen printing,

fired, and then laser trimmed to obtain a specific resistance. The ability to remove

material is important because the substrate must often be modified by punching vias for

layer interconnects. In the next several sections, a number of patterning technologies are

reviewed in detail.

6

1.2.1 Conventional Thick-film Technology

Conventional thick-film technology or screen printing involves forcing a viscous

paste through apertures in the screen. This technique produces patterns with thicknesses

greater than 2.5 μm and up to 50 μm (Licari and Enlow, 1998). Patterns are generated by

sealing the apertures in the mesh except where ink can be passed through. After the ink

has been patterned onto the substrate, it is dried and fired in a furnace. The firing

temperature (850°C for most inks) restricts acceptable substrates to ceramics such as

alumina. Multiple layer devices can be built using the Low-Temperature Co-fired

Ceramic (LTCC) process. LTCC is distinguished from the High-Temperature Co-fired

Ceramic (HTCC) process by a lower firing temperature (850°C as opposed to 1600°C)

and the ability to fire the package in an ambient atmosphere. The LTCC process involves

screen printing onto green (alumina mixed with organics and binders) substrates. Vias

are punched mechanically and these layers are stacked and aligned before being pressed

and fired together. This approach allows the design of high-density devices with buried

passive components.

Because of the popularity of screen printing for patterning microelectronics, much

work has gone into producing thick-film inks specifically for this process. The rheology

of the ink is very important for producing small and repeatable features. Screen printing

inks are designed to be thixotropic. The viscosity of the ink is high when it is at rest;

however, when a shear force is applied the ink flows easily because the viscosity drops

(Hoornstra et al., 1997; Licari and Enlow, 1998; Kay et al., 2003). This property allows

the ink to be easily forced through the apertures in the screen. After it has been deposited

on the substrate, there is no shear force acting on the ink, and the viscosity of the ink

increases to reduce further flow. This property is illustrated in Figure 1.3. The fluid

properties of conventional thick-film inks are attractive for several other patterning

7

techniques. Because of the wide use of conventional thick-film inks, they are mass

produced, making them economical and available.

Screen printing is a very mature technology and capable of very high throughputs.

However, even with a high mesh number, 325-400 openings per linear inch, the finest

lines and spacings that can be consistently produced are 3-5 mil (75-100 μm) (Licari and

Enlow, 1998). This prevents screen printing from being used for applications, like high-

density interconnects and high-frequency devices. Additionaly, screen printing does not

lend itself to rapid prototyping. While the screens are not as complicated to produce as

the masks for manufacturing semiconductors, they still are expensive and require some

turnaround. This causes many microelectronics manufactures not to fabricate their

screens in-house.

Figure 1.3: Viscosity changes in thick film pastes during screen printing, from Licari and Enlow (1998).

Lithography can also be used to pattern thick-film inks to produce smaller feature

sizes. DuPont’s Fodel system uses photo-imagable inks with a positive mask.

Collimated UV light is used to drive a photo-polymerization reaction in the ink. Both

conductors and dielectrics can be fabricated using this method and feature sizes down to

8

25 μm with 50 μm spacings and 75 μm vias are obtainable (Licari and Enlow, 1998).

However, the inks still must be fired and there are issues with shrinkage. In addition, the

un-solidified ink is wasted and potentially toxic chemicals must be used.

1.2.2 Direct Gravure Offset Printing

Direct Gravure Offset printing is an innovative technique for depositing fine

features (Kittilä et al., 2004). The gravure is formed by pouring silicone polymer into a

mold formed by patterning a photoresist on a glass or metal plate. The silicone polymer

is allowed to harden in the mold, then removed. The gravure is kept rigid by fastening it

to a smooth metal plate. A doctor blade is passed over the gravure to fill the grooves in

the silicone formed by the mold with microelectronic ink as shown in Figure 1.4(a).

Figure 1.4(b) shows the substrate as it is pressed against the gravure to transfer the ink

from the grooves.

(a) (b) (c)

Figure 1.4: Direct Gravure Offset Printing process from Kittilä et al. (2004) (a) doctor

blading the gravure to apply ink (b) pressing the substrate against gravure to transfer ink and (c) final printed pattern on substrate.

The direct gravure offset printing process depends on the adherence of the ink to

the silicone polymer; furthermore the process parameters and ink must be carefully

selected to release 100% of the material onto the substrate to produce fine patterns.

Kittilä et al. (2004) report the ability to produce conductive lines with feature sizes below

20 μm and nearly 1:1 aspect ratios on standard LTCC substrates.

The direct gravure offset printing technique has similar advantages and limitations

to screen printing. It is a parallel process and has the potential for high throughputs. In

9

addition, it is capable of much smaller feature sizes because it is not limited by a mesh.

However, it is not applicable to conformal substrates because the ink requires firing after

it is deposited. The fabrication of the gravure does not lend itself to rapid prototyping or

low-production runs and there may also be problems with selecting arbitrary

conventional thick-film materials because of adherence to the gravure.

1.2.3 The Micropen System

The Micropen system was developed by Ohmcraft Inc. (Honeoye Falls, NY). It

consists of a small nozzle that is kept in contact with the substrate as it traces the pattern.

The smallest nozzles have an inner diameter of 25 μm and outer diameter of 50 μm,

although outer diameters ranging from 100 to 250 μm are more typical (King et al.,

1999). Ink is pumped through the aperture and patterns are created by translating the

substrate relative to the nozzle using a Computer Numerically Controlled (CNC) x-y

table. This direct-write approach has been demonstrated to be capable of producing

feature sizes down to 50 μm. Figure 1.5 shows a picture of the Micropen system.

Figure 1.5: Micropen system in operation from King et al. (1999).

10

The same thick-film pastes that are used for screen printing can be used as the

base ink for the Micropen system. Almost any electronic material can be deposited,

including dielectrics and resistive inks with multiple sheet resistances, as well as

biological and polymer sensing materials. To maintain pattern consistency, the pressure

through the nozzle must be carefully controlled along with the rheological properties of

the ink. Three-dimensional topographies can be patterned with the Micropen if it is

integrated with a force feedback system to adjust the height of the nozzle (Pique and

Chrisey, 2002).

Because standard thick-film inks/substrates can be used with a CAD/CAM

system, the Micropen is an ideal system for low-production runs or rapid prototyping

devices that will later be produced using conventional methods. However, experimental

systems show that particles need to be less than one percent of the size of the interior

diameter of the dispensing system to produce stable flow and prevent clogging of the

nozzle (Pique and Chrisey, 2002). This requires the use of nanoparticles in order to

obtain feature sizes below 25 μm. The advantage of depositing multilayer devices on

three-dimensional substrates is somewhat offset by the need to functionalize these inks

after deposition. This may not be a concern if nanoinks are to be used, but would make

the Micropen cost prohibitive for large-scale production applications.

1.2.4 Ink-Jet Technologies

Most people are familiar with the home and small office desktop ink-jet printers

that dominate the low-end color printing market. This is one of the most common direct

write approaches and has been employed for several innovative fabrication technologies

for rapid prototyping and production of microelectronics. Ink-jet technologies can

reproducibly dispense spheres of fluid with diameters of 15-200 μm at rates of 0-25 kHz

11

and up to 1 MHz for continuous droplets (Piqué and Chrisey, 2002). One of the principle

advantages of ink-jets is the ability of the droplets to free-fly over a millimeter. This

allows the deposition of droplets without contact with the substrate. Like the Micropen,

ink-jet technologies are data driven and additive, removing the need for etchants and

other environmentally unfriendly chemicals.

There are two main types of ink jet printing technologies; Continuous Mode and

Demand Mode. Continuous Mode involves forcing a stream of liquid through an orifice.

This liquid jet is passed through an electrostatic field and breaks into droplets owing to

Rayleigh instability (Pique and Chrisey, 2002). The droplets acquire a charge and can be

steered with deflection plates similar to the electron beam in a cathode ray tube. Unused

droplets are guided into a dump and can be recirculated through the system. This process

allows very high deposition rates but only one type of ink can be used at a time.

Demand Mode involves the electromechanical generation of individual droplets

via forcing ink through an orifice by a volumetric change. This can be produced by a

piezoelectric actuator or with an electrical micro-heater. In the latter case, a small portion

of the ink is vaporized to produce a bubble. Demand Mode has also been used without an

orifice to generate jets from a free surface using a phased array of acoustic sources (Pique

and Chrisey, 2002).

Ink-jet technologies have been successfully applied for many different rapid

prototyping applications including 3D printing, deposition of small quantities of solder

for flip-chip applications, fabrication of micro-lenses on the ends of fiber-optic sensors,

and dispensing of biological materials. Figure 1.6 shows human liver cells being

dispensed from the orifice of an ink jet printer.

12

Figure 1.6: Human liver cells being transferred from an ink jet device (Calvert, 2001).

Redinger et al. (2004) investigated the use of a demand mode printer for the

fabrication of passive microelectronic components for use with RFID type applications.

They were able to produce 160 μm lines using gold nanoparticals. The applications for

large-batch production with ink jet technology are limited because it is fundamentally a

serial process and subject to the same constraints as the Micropen technology.

The main drawback of ink-jet technologies is the rheological requirements of the

fluid. Ideally the fluid should be a Newtonian fluid with a viscosity less than 0.02 N·s/m.

Very low viscosities can lead to problems such as satellite formation and lack of acoustic

damping. The surface tension should be greater than 35 mN/m and the size of any

particles suspended in the liquid should be less than 5% of the orifice diameter (Calvert,

2001). Any viscoelestic behavior will also cause problems with the jet detaching from

the orifice. Problems with the ink arise when it interacts with the substrate, including a

tradeoff between low enough viscosity not to clog the orifice but high enough that it does

not spread on the substrate (Calvert, 2001).

1.2.5 LIFT

Laser Induced Forward Transfer (LIFT) was developed in 1986 by Bohandy et al.,

and is similar to pulsed laser deposition. It involves selective ablation and deposition of

material using a pulsed laser and forms patterns directly on the substrate. A transparent

13

substrate is coated with the material by sputtering or other thin-film deposition

technology to form a ribbon. The procedure is similar to a conventional typewriter with

the exception that the driving force putting the ink in contact with the substrate is

produced by a laser rather than by a mechanical force. The ribbon is positioned with the

material to be transferred in close proximity to the substrate. The laser is focused onto the

interface between the thin film and the transparent support to vaporize the thin film. The

vaporized material then expands and pushes the surrounding material out balistically to

come in contact with the substrate (Yamada et al., 2002). Figure 1.7 shows a basic

schematic for the LIFT process.

Figure 1.7: Schematic of LIFT process from Yamada et al. (2002).

Submicron features have been created using this the LIFT process (Piqué and

Chrisey, 2002). The deposited pattern has the same composition as the material on the

ribbon, allowing functional patterns to be transferred without the need for post

processing. However, this tactic also limits the LIFT process to metals and other

materials that can withstand vaporization and condensation without loosing their

functionality. In addition, very high laser irradiances are required to vaporize metals and

ceramics. The vaporized material must have sufficient pressure to cause the non-

vaporized surface of the film to fail locally and to be detached from the support. This

limits the thickness of the transferred material to very thin films, usually less than 500

14

nm. This constraint prevents LIFT from being used for most thick-film microelectronic

applications.

1.2.6 MAPLE and MAPLE-DW

Matrix-Assisted Pulsed Laser Evaporation (MAPLE) and MAPLE – Direct Write

(MAPLE-DW) are laser-based processes developed at the U.S. Naval Research

Laboratory and patented by Auyeung et al. (2004). These two processes are capable of

depositing almost any material that can be formulated into a rheological fluid (Piqué and

Chrisey, 2002). Both MAPLE and MAPLE-DW use inks formed by dissolving the

material to be deposited in an organic matrix. In MAPLE, the ink is coated onto a

support to form a 1-20 μm layer and frozen (Piqué et al., 2002). The support is separated

from the substrate by ~5 cm and the entire process takes place in a vacuum as shown in

Figure 1.8. The laser energy causes the material to be desorbed from the organic matrix

and transferred onto the substrate. A pattern can be generated by placing a shadow mask

over the substrate. The MAPLE process is similar to thin-film deposition processes with

the exception that it can deposit any material because the matrix is evaporated.

In MAPLE-DW, the ribbon is placed in close proximity to the substrate (25-100

μm) in the forward transfer configuration. A UV laser is focused through the support

onto the ink-support interface. The organic material absorbs the UV radiation and is

rapidly heated and vaporized. This provides a pressure pulse which pushes the material

out and deposits it onto the substrate. The substrate can be translated relative to the laser

to create very precise patterns. The entire process takes place in ambient conditions and

does not heat the substrate. Figure 1.9 shows a schematic of this process. MAPLE-DW is

very similar to LIFT with the exception that the transfer is much softer (lower velocity)

and requires less laser fluence. In addition, the ink can be selected so that the organic

15

matrix preferentially absorbs the laser energy and the heating of the active material is

minimized. This allows the direct writing of polymer, organic and chemical materials

that would be damaged by heating during the LIFT process.

Figure 1.8: Schematic of the MAPLE deposition system from Piqué et al. (2002).

Figure 1.9: Schematic of the MAPLE-DW process from Piqué et al. (1999).

The MAPLE-DW process is analogous to thick-film technology where LIFT is a

direct-write form of thin-film technology. MAPLE-DW has been previously

demonstrated with the LTCC process (Zhang et al., 2003). For these experiments, the

16

ribbons were dried so that the ink would be put directly into contact with the substrate.

This is also necessary for conformal applications. MAPLE-DW is currently being

commercialized by Potomac Phontonics Inc. (Lanham, MD). Chapters 2 and 3 will

investigate this process in more detail.

Figure 1.10: A commercial MAPLE-DW system (from www.mesofab.com).

1.3 Functionalization Techniques

For thick-film fabrication the ink is patterned when it is still wet. In this form, the

film is not functional. The organic material in the ink must be driven off and the

conductive/dielectric/resistive particles fused together by sintering. Both of these

processes are accomplished by applying heat to the system. As mentioned previously, the

functionalization temperature for most thick-film inks is 850°C, which is well in excess

of polymers and most glass-based substrates. Two options for overcoming this problem

are to use inks with a lower functionalization temperature or to locally heat the ink to

minimize the exposure of the substrate to damaging temperatures. Ceramic-metal thick-

film inks with lower firing temperatures (500°C) have been developed for use with glass

substrates. In addition, air-dry polymer based inks that cure at 150°C can also be used but

the lower functionalization temperatures correspond to significantly higher sheet

17

resistances. Nanosized particles have very high surface energies that reduce the thermal

processing requirements without reducing electrical conductivity, but they are generally

too expensive for use with mass manufacturing.

1.3.1 The Conventional Sintering Process

The conventional thick-film sintering process usually takes place in a belt-fed

furnace. There are several steps required to convert the ink from its wet printed form to a

final functional circuit. The first step after a pattern has been deposited onto the substrate

is to dry the ink. This allows the volatile organic solvents to evaporate. Often this first

takes place in air while the pattern is allowed to settle. The process continues inside the

drying portion of the oven at 120-150°C. If the solvents are not removed prior to

exposing the substrate to higher temperatures, the solvents can become trapped below the

surface and when they expand cause blistering or other damaging effects on the pattern.

After the volatile organic solvents have been driven off, the substrate is slowly

heated (35-55°C/min) to 500°C. The temporary organic binder is decomposed by

oxidation. This process requires sufficient air flow to ensure that no carbon deposits are

left in the final pattern that could diminish performance (Licari and Enlow, 1998).

After the completion of the burn out stage the ink is heated to 700°C. This allows

the glass frit and other permanent binders to wet both the surface of the substrate and the

functional material inside the ink. Any glass constituents of the substrate will also be

softened and fuse with the glass frit in the ink. As the ink is heated between 700°C and

850°C, the functional particles in the ink are sintered. This interlocks them with the glass

frit and the substrate to form the functional component. The substrate is usually allowed

to dwell at about 850° for approximately 10 minutes. The sintering temperature is

typically about 100°C below the melting temperature of the main metal ingredient of the

18

ink. The 850°C cycle corresponds to the 960°C melting point of silver (Licari and

Enlow, 1998).

After the sintering process is completed, the substrate and ink are allowed to cool

back to room temperature. This process should be slow enough to avoid thermally

shocking the material. DuPont recommends a 27-33°C/min decent from 800°C to 600°C

and a 40-60°C/min decent from 700°C to 300°C. The entire firing process takes

approximately one hour using a conventional convection-conduction furnace. Figure

1.11 shows a typical firing profile for a belt-fed furnace.

Figure 1.11: Furnace profile for DuPont thick-film inks, from Licari and Enlow (1998).

1.3.2 Selective Laser Sintering

Selective Laser Sintering (SLS) is widely used for the fabrication of three-

dimensional prototypes (Kruth et al., 2003). The advantage of SLS for this application

over other techniques such as Sterolithography or Fused Deposition Modeling is its

ability to fabricate functional metal prototypes. Using a laser to functionalize deposited

microelectronic patterns is very attractive because the sintering temperatures can be

confined to the ink layer and the portion of the substrate in close proximity to the

19

interface with the pattern. This facilitates the use of low-temperature substrates. Chrisey

et al. (2000) proposed using a pulsed IR laser to locally anneal material deposited by

MAPLE-DW. Using a pulsed laser is very difficult because the thermal penetration depth

during the duration of the laser pulse is very short which limits the pattern to submicron

thicknesses. Choppra et al. (1998) propose the fabrication of entire microelectronic

devices using SLS, although no literature demonstrating this approach is available. Other

investigators have demonstrated the use of laser sintering to functionalize the chemical

precursors of electronic components (Marinov, 2004). The use of SLS with

microelectronics will be investigated in detail in Chapters 4 and 5.

1.4 Overview of the Thesis

The goal of this thesis is to fabricate thick-film microelectronics with feature sizes

less than 25 μm. The majority of the work is focused on writing conductors for

applications such as interconnects and antennas, although resistive and dielectric

elements are also demonstrated. One of the primary objectives is to develop technologies

that can be scaled from low to high batch production for the fabrication of devices such

as RFID tags. The economic viability of this type of application requires emphasis on

low-temperature polymer substrates such as Mylar and the use of conventional

microelectronic inks as opposed to inks based on nanoparticles.

The remainder of the work is organized as follows. Chapter 2 investigates the

MAPLE-DW approach to patterning microelectronic circuits. A pulsed Nd:YLF laser is

used with a x-y optical scanner to obtain very high write speeds. Experimental work and

results are discussed with implications for the practicality of this configuration for

manufacturing.

20

Chapter 3 investigates the MAPLE-DW event in detail. The time-history of the

event development was captured using time-resolved microscopy. This information is

used to develop a model for one regime of the MAPLE-DW process. A scaling analysis

is also used to further understand the technique and the effects of the process parameters.

Chapter 4 discusses Selective Laser Sintering. Experimental results using this

process for fabrication of high quality thick-film components is described and the process

parameters are optimized. Fabrication of high-frequency electronics are also discussed,

along with the patterning and functionalization of low-temperature substrates.

Chapter 5 studies Selective Laser Sintering using a finite-element method. The

process is simulated to determine the temperature profile inside the ink layer and

substrate. This provides further insight into the process and how it can be further

optimized.

In Chapter 6, the work presented in this thesis is summarized and

recommendations for further research are discussed.

21

2. MATRIX ASSISTED PULSED LASER EVAPORATION – DIRECT WRITE

Matrix Assisted Pulsed Laser Evaporation – Direct Write (MAPLE-DW) was

investigated using conventional thick-film (screen-printable) inks. The intent of these

experiments was to improve the throughput of the MAPLE-DW technique to expand its

applicability for mid- to high-volume manufacturing applications such as patterning

passive microelectronics as part of the LTCC process.

2.1 Introduction

Chapter 1 introduced Matrix Assisted Pulsed Laser Evaporation – Direct Write

(MAPLE-DW). The ability to integrate MAPLE-DW with tools such as laser ablation,

laser sintering, and laser welding makes it very attractive as a patterning technology.

Previous investigations have reported that this technique is capable of depositing feature

sizes less than 10 μm and is compatible with virtually any material, including polymer

and biological samples (Piqué and Chrisey, 2002). MAPLE-DW has been demonstrated

for several key applications such as patterning passive electronics (Piqué et al., 1999;

Chrisey et al., 2000), LTCC substrate patterning (Zhang et al., 2003), antennas (Piqué et

al., 2003), chemical sensors (Piqué et al., 2003), power sources such as microbatteries

(Piqué et al., 2004; Wartena et al., 2004), microultracapacitors (Arnold et al., 2003), and

even biological materials including DNA (Colina et al., 2004; Fernández-Pradas et al.,

2004).

22

The goal of this chapter is to examine MAPLE-DW as part of a suite of laser tools

for the fabrication of microelectronics. This chapter uses a different apparatus from

previous investigations of MAPLE-DW with the intent of increasing the throughput of

the process to the point where it would be acceptable for large volume manufacturing.

The experimental setup and procedure are described in Section 2.2. Section 2.3 presents

key experimental results. Section 2.4 discusses MAPLE-DW and proposes an alternative

approach using the MAPLE paradigm. The chapter is summarized in Section 2.5.

2.2 Experimental Setup and Procedure

This chapter investigates the implementation of MAPLE-DW using conventional

microelectronic inks with an IR laser and an x-y scanner for high-speed writing. Previous

investigations have used either Excimer or frequency-tripled Nd:YAG lasers which both

produce UV wavelengths. Using IR wavelengths is more convenient because glass and

polymer supports can be employed. In addition, if an IR laser is to be used to sinter the

material after deposition, as will be described in the laser sintering work in Chapter 4, the

same optical system can be employed for both the patterning and functionalization

processes.

A disadvantage of using IR is that the organic matrix does not directly absorb the

laser energy. Rather, the functional material in the matrix is heated by the laser and this

energy is thermally coupled to the organic material via conduction. An IR laser may not

be acceptable if temperature sensitive materials such as polymers or biological samples

are being deposited because they will be directly heated. However, most passive

microelectronic materials, particularly thick-film inks, are not adversely affected by

heating.

23

In this work, an x-y scanner was used to direct the laser beam onto the sample

surface instead of moving the substrate using CNC translation stages. The x-y scanner

can move the laser beam at a speed of up to 1 m/s. The hope was that this approach

would lend itself better to higher throughputs while maintaining the performance of the

translation stages.

Conventional thick-film inks were used for all the work presented in this thesis.

Employing inks that are already being mass produced, as opposed to specially designed

inks offers cost savings as well as exploiting the features of the inks designed for screen

printing. Our work focuses on printing conductors primarily using QS300, a

silver/platinum conductive ink manufactured by Dupont and specifically developed for

the thick-film industry. This ink is widely available and has been designed for producing

fine-lines down to 75 μm via screen-printing. QS300 has a specified sheet resistance of

4.5 mΩ/ for a fired film thickness of 10 μm after processing at 850°C.

The rheological properties of screen printing inks are specifically designed so that

the viscosity varies with the shear rate of the ink. In the absence of a shear force, the ink

is very viscous which helps the pattern set after it has been deposited on the substrate. To

enable the ink to be forced through the small apertures in the mesh during screen printing,

the viscosity of the ink is much lower when a shear force is applied to it. A more detailed

discussion of rheological properties of thick-film inks are given by Hoornstra et al.

(1997) and Kay et al. (2003).

2.2.1 Instrumentation

Figure 2.1 shows a photograph and a schematic of the experimental setup used for

investigating MAPLE-DW. The apparatus is fixed on a vibration isolation table and the

entire process takes place in an ambient, non-clean room environment. The laser used for

24

the MAPLE-DW experiments is a Spectra Physics 7300 Nd:YLF laser. This is a diode-

pumped laser and produces near IR light (λ=1047 nm) with a pulse duration of 20 ns. The

laser has a pulse repetition frequency that is selectable from 1 Hz to 10 kHz. The power

level of the laser is adjusted using a polarizer rather than the laser power directly. This is

because the temporal shape of the laser pulse may fluctuate depending on the laser

control power. Maintaining a constant temporal shape helps to minimize inconsistencies

between laser pulses. The beam expanders increase the diameter of the laser beam. Two

beam expanders are used in the setup and the second one is fixed to a flip mount. This

allows it to be easily removed from the laser beam path to produce a larger laser spot size

on the substrate.

The optical x-y scanner consists of two mirrors each of which is attached to a

servo motor. The scanner is aligned with the laser beam and a large aperture lens (Ø=100

mm) and the focal length of the lens is 163 mm. This arrangement maps the laser beam

over the substrate. In the setup used for this thesis, the focal point of the laser can be

moved at speeds greater than 1 m/s with a nominal resolution of 1.5 μm and a beam waist

of 16 μm. The x-y scanner is controlled by a digital signal interface. Both the scanner and

the interface are manufactured by GSI Lumonics (Billerica, MA). A digital output card

(SP-ICE, Nutfield Technologies) numerically controls the interface and patterns are

generated with ScanWare, a laser control software also from Nutfield Technologies

(Windham, NH). The software allows the user to draw patterns within a graphical user

interface or import dxf formatted files. The ScanWare/SP-ICE control system also allows

the laser can be switched on and off in coordination with the pattern being traced by the

x-y scanner. This allows non-continuous patterns to be traced without a shutter.

25

Figure 2.1: Picture and schematic of MAPLE-DW setup.

Computer

Nd:YLF Laser Mirror

Polarizer

Beam Expanders

X-Y Scanner

TV Monitor

CCD Camera

Hot Mirror

IR Filter

StageSubstrate

Ribbon

Fiber Laser

Mirror Flip Mirror

(b)

(a)

26

A hot mirror reflects the laser beam while transmitting visible light. This allows

the process to be monitored in-situ with a CCD camera. An IR filter is placed in front of

the camera lens to help protect the CCD. In addition to monitoring the process, the

camera is used for aligning existing patterns with the laser. A continuous wave (CW)

JDSU fiber laser (λ=1100 nm) can be used to sinter the patterns deposited by MAPLE-

DW. The two lasers are aligned so that they have the same optical path through the

scanner and are both focused on the substrate. The use of the fiber laser for sintering will

be discussed in Chapter 4.

2.2.2 Experimental Procedure

Ordinary soda-lime glass microscope slides were used for the support in the

ribbon. Glass slides are inexpensive, transparent to 1047 nm light, and provide a flat,

rigid surface for coating the ink. The ability to use glass slides is one of the advantages

of using visible or near IR light for the MAPLE process.

Applying a consistent ink film is critical for the process, as will be shown in

Chapter 3. There are several ways of coating the support with ink to form a ribbon. Thin

layers of low viscosity ink can be applied using a spin coater. However, this approach is

not applicable for most thick-film inks because of their shear thinning properties. The

ink film will experience a gradient in the shear stress during spin coating because the

regions on the substrate farther from the axis of rotation are moving faster than those

nearer to the center. The shear stress gradient will translate into a viscosity gradient

which will affect the uniformity of the final thickness of the film.

A wire coater can also be used for inks with lower viscosities. The thickness of

the ink film will be proportional to the gauge of wire on the wire coater and several

different gauges of wire are available. The wire coaters used in this thesis were purchased

27

from Paul N. Gardner Inc. (Pompano Beach, FL). A drawing showing the application of

ink using a wire coater is shown in Figure 2.2. The wire coater leaves furrows in the ink

as it is drawn through the film. If the viscosity of the ink is sufficiently low, surface

tension will smooth these furrows out to produce a film of uniform thickness. This

approach is very convenient and was preferred for applying thick-film inks with thinner

added to them. However, consistent films could not be produced for the inks without

thinner when using the wire coater because the viscosity is too high.

Figure 2.2: Application of ink with a wire-coater (from Gardco website: www.gardco.com/rods.html).

A third approach is to “doctor blade” the ink. The ink is applied to the support

using a spatula. Steel shims are placed in contact with the glass slide and a round glass

rod is dragged over the shims to smooth out the ink layer. The height of the ink film is

controlled by the thickness of the steel shims and films with heights up 100 μm can be

created using this method. A round glass rod was used instead of a metal blade because

the angle at which it is held does not affect the ink thickness. This approach proved to be

the most effective for coating thick-film inks without thinner.

The substrate is positioned on the stages under the laser. The ribbon is separated

from the substrate using shims. Employing shims helps to minimize the errors caused by

variance in the thickness of the glass slides. However, shims cannot be used for very

28

short separations. A fixture was also constructed to provide a separation between the ink

and substrate. To maintain consistent rheological properties, the ribbons were used within

several minutes of being coated because the ink begins to dry when it is exposed to air,

The laser can be triggered by the SP-ICE card and ScanWare directly. However,

the laser was set to a constant pulse repetition frequency in the interest of maintaining as

consistent a pulse energy as possible. The laser continued to pulse even between

patterns. Between patterns, the mirrors move the focal point of the laser fast enough (1.25

m/s) to separate the pulses completely.

After patterning the substrate, the ribbon was removed and the substrate was

placed in a convection oven for drying at 150°C for 20 minutes to an hour to drive off the

volatile organics in the ink. After drying, the substrate was placed in a conventional

furnace and heated to 850°C. The substrates were allowed to dwell at this temperature

for 10 minutes before removal from the furnace. Because the ink is deposited at

relatively low velocities in the MAPLE-DW process, additional layers can be added after

drying and then co-fired together in the furnace.

2.3 Experimental Results

The MAPLE-DW process was previously investigated with time-resolved

microscopy by Young et al. (2002). The ink investigated in their study consisted of

BaTiO3 nanopowder in a -terpineol matrix with a small amount of surfactants. Young et

al. (2002) identified three distinct operational regimes for the MAPLE-DW process: sub-

threshold, jetting, and plume, in order of increasing laser fluence. The regimes are

distinguished by the geometry of the MAPLE-DW event and how it evolves. All three

responses begin with the formation of a bubble protruding from the ink surface. In the

sub-threshold regime, this bubble expands to a point but never ruptures. If the bubble

29

does not come into contact with the substrate, it will eventually collapses back into the

ink layer because the kinetic energy of the event is insufficient to overcome viscous and

surface tension forces. The failure of any material to detach from the ink layer

distinguishes the sub-threshold event from the jetting and plume regimes.

The jetting regime is characterized by the collapse of the bubble in the radial

direction so that the front of the event is more slender than the initial radius. The front

velocity is greater than that of a sub-threshold event but less than that of a plume event.

The plume regime is characterized by the rapid expansion of the event and the almost

immediate break-up of the bubble into small droplets. The front of the plume expands

radially as well as normal to the surface of the ink layer. Young et al. (2002) reported that

the front velocity of plume events is linearly proportional to the pulse energy. This

indicates that the process is more complicated than a simple conversion of laser energy to

the kinetic energy of the ink.

Experiments were conducted in conjunction with the Flame Diagnostics

Laboratory at Purdue University to investigate the behavior of conventional thick-film

inks when using the apparatus in Figure 2.1. These experiments are described in detail by

Lewis (2005) and are covered in Chapter 3. Figure 2.3 shows examples of the three

regimes captured in these experiments with the laser fluence used to generate the event.

The ink used for Figure 2.3 was QS300 mixed with 11% (by mass) -terpineol. In

experiments without thinner, the jetting regime was not present.

30

(a) 0.79 J/cm2 (b) 1.02 J/cm2 (c) 1.27 J/cm2

Figure 2.3: Micrographs of different response regimes (a) sub-threshold (b) jetting and (c) plume.

Working in the jetting regime was initially thought to be appealing because the

area the ink collapses to would have a smaller diameter than the laser spot. However,

considerable instability was observed in the jets and the ink splatters when it comes in

contact with the substrate due to the higher front velocity of the jet. Both of these effects

ultimately limit the feature size obtainable when working in the jetting regime.

Additionally, because of the radial collapse of the jet, an isolated event may deposit a

droplet on the substrate that is smaller than the beam radius. However, most electrical

devices require continuous features. When the laser is scanned over the ink layer, the

pulse-to-pulse separation distance cannot be so small that the pulses interfere with each

other on the ribbon. This factor prevents the jetting regime from being used with a

stationary ribbon and substrate.

In a process similar to Laser Induced Forward Transfer (LIFT), Zhang et al.

(2003) used the plume regime with a dried ribbon in contact with the substrate. Because

the ribbon is dried, it is more suitable for storage and more applicable for printing on

conformal substrates. Since the ribbon is in contact with the substrate, the radial

spreading is minimized when a laser with a small spot size is used with a thin-ink layer.

However, there can be problems with producing dense unbroken patterns because the

100 μm

31

dried ink lacks surface tension which helps form coherent patterns. This problem caused

Zhang et al. (2003) to use wet ribbons for depositing dielectrics to avoid pinholing. Both

problems, isolated droplets due to converging jets and the break up of dried discontinuous

patterns, can be overcome by tracing the pattern multiple times after moving the ribbon.

However, this creates additional alignment issues as well as inconsistencies in the

morphology of the final feature because the different areas may not receive the same

number of coatings if the ribbon itself is not recoated.

Figure 2.4 shows micrographs of the deposited patterns with respect to laser

fluence. QS300 without any thinner was used for the experiment shown in this figure to

write lines at 0.07 m/s. The separation between the ink and the substrate is ~12.5 μm.

The figure shows the transition from continuous lines with poor morphology to discrete

droplets. This corresponds to the transition between the plume and sub-threshold regimes

shown in Figures 2.3(a) and 2.3(d), respectively. The sub-threshold regime shown in

Figures 2.4(d-f) was selected because the only possibility of creating small features when

using the plume regime was to post trim the lines using laser ablation. However, the sub-

threshold regime requires multiple passes to create continuous small features.

The sub-threshold regime was selected for further investigation and QS300

without the addition of thinner was used for the remainder of work on MAPLE-DW.

However, because of shear thinning of the ink, effective plastic deformation of the bubble

occurs and the bubble cannot return to the surface for all but the lowest laser fluences.

This can be a great impediment to writing thin lines because the ribbon is not moving in

this work. The laser generated pressure bubble can escape through the hole in the ink film

caused by the previous shots interaction with the substrate. The best experimental results

are obtained when the ribbon is positioned as close to the substrate as possible (<12.7

μm) and the majority of the displaced ink is deposited. The interaction between the ink

and the substrate is also important and how well the ink wets the substrate can play a

32

critical role in the morphology of the final pattern. Alumina coated with a dielectric

(Dupont QM44) was used in this work as the substrate. This substrate has some surface

roughness (~1 μm) and appears to draw the ink down and hold it to form fine patterns.

(a) 2.99 J/cm2 (~140 μm) (b) 2.71 J/cm2 (~100 μm) (c) 2.54 J/cm2 (~70 μm)

(d) 2.35 J/cm2 (~50 μm) (e) 2.13 J/cm2 (~40 μm) (f) 1.65 J/cm2 (~20 μm)

Figure 2.4: Deposition on alumina substrate for various fluences (approximate line widths are in parenthesis).

Figure 2.5 shows a portion of a 20-μm wide, 5-mm long wire printed with a laser

fluence of 1.26 J/cm2. This line was patterned twice before drying and firing in a furnace

at 850°C. After it was fired the conductivity of the wire was measured to be 1.6 × 107

1/Ω·m, which is ~75% of the specified value for QS300. This discrepancy is most likely

due to inconsistencies in the line dimensions and porosity in the fired material. Figure 2.6

shows the cross sectional profile for the wire. The pattern has a consistent profile,

especially in comparison with the surrounding substrate.

33

Figure 2.5: Micrographs of a 20 μm line.

-4

-2

0

2

4

6

8

-40 -30 -20 -10 0 10 20 30 40

z [

m]

x [m]

Figure 2.6: Profile measurements of the line shown in Figure 2.5.

The MAPLE-DW process is very sensitive to the thickness of the ink layer and

the separation between the substrate and the ink layer. Using shims to coat the ribbons

and separate the substrates makes it difficult to control these parameters precisely across

the entire surface of the substrate. The narrowest line obtained in this work is about 10

34

m wide, as shown in Figure 2.7; however these lines cannot be consistently produced.

Smaller lines with smother edges can be obtained by ablating the edges of the lines. The

separation between the substrate and the ink film was maintained using a fixture with a

nominal separation distance of 12.7 μm. However, for both the patterns in Figures 2.5

and 2.7, portions of the substrate were in direct contact with the ink.

Figure 2.7: Micrograph of a 10 μm line.

When the lines are deposited onto the substrate, the material still has the same

properties as the ink on the ribbon. Because there is a substantial amount of organic

material in the deposited pattern, it is difficult to sinter the pattern in-situ. If the organic

material is vaporized too rapidly, it will damage the pattern. One option is to incorporate

a block heater into the fixture. This would allow the substrate to be dried in-situ after the

ribbon had been removed.

2.4 Discussion

In the previous section, the laser beam was scanned relative to a stationary ribbon

and substrate. Producing continuous features with well defined edges is very difficult

using this approach. The spacing between laser pulses must be on the same order as the

diameter of the laser pulse if the pattern is to be deposited by only tracing over it once

with the laser, and at this spacing the shots appear to interfere with each other. This

10 μm

35

phenomenon can be explained by the escape of the pressure pulse generated by the laser

through the hole left by a previous shot. However, experiments such as those shown in

Figures 2.5-2.7 demonstrate that if the substrate was positioned close enough to the ink

layer, very fine features could be produced. Maintaining this separation proved to be

very difficult experimentally and producing patterns with the resolution shown in Figures

2.4 and 2.5 were only the result of running many different tests with the same nominal

process parameters. This variance would be unacceptable for a manufacturing process.

One alternative is to keep the ribbon continuously moving while leaving the

substrate stationary, as demonstrated in the literature. This can be accomplished by

rotating the ribbon or feeding it reel-to-reel underneath the laser. However, neither is

compatible with a stationary substrate and moving laser beam. To keep the laser from

hitting the same spot (or near the same spot) twice, the movement of the ribbon needs to

be coordinated with the movement of the laser beam and translating the ribbon in this

manner would negate the benefits of using the x-y scanner.

Another concept that offers the advantages of MAPLE-DW along with high

throughputs is to use a mask-based approach. Figure 2.8 shows schematics of the

conventional MAPLE-DW process and a parallel MAPLE process using a mask. Using a

mask requires a large incident beam with a spatially uniform profile. The laser passes

through the apertures in the mask and generates sub-threshold events simultaneously

throughout the pattern.

36

(a)

(b)

Figure 2.8: Schematics of (a) MAPLE-DW process and (b) Flash-MAPLE setup.

Because the entire pattern is transferred at one time, the problem of pulse-to-pulse

interference is avoided. However, as will be shown in the next chapter, different size

apertures will produce different sized events for a given laser fluence. It may therefore

be necessary to either use a grayscale mask (pattern a semi-absorbent layer over areas of

the mask) or use a mask that has a modified pattern which is not identical to the desired

pattern.

An Excimer laser (λ=248 nm) was used to test the mask-based approach to

transfer thick film patterns onto alumina substrates. The pulse width of this laser was

also ~20 ns. A quartz slide was coated with thick-film ink and a metal stencil was taped

to the side of the slide opposite the ink. The ink side was positioned facing an alumina

Stages

Quartz Slide

Ink Substrate

Laser PulseGold Mask

Laser Pulse

Support Ink

Substrate

Stages

Ink Heated by Laser

Deposited Pattern

37

substrate. The separation between the ink and the substrate was 20 μm. The laser

provided ~80 mJ of pulse energy over an area ~2.5 cm2. This successfully transferred the

pattern onto the alumina substrate as shown in Figure 2.9(a). The laser beam can also

pass through an imaging system with a 10X demagnification. This was also successful

and the transferred pattern is shown in Figure 2.9(b).

(a) (b) Figure 2.9: Patterns deposited with Flash-MAPLE fabricated with (a) one-to-one and (b)

10X reduction transfer.

This concept of parallel writing can also be applied with the Digital Micromirror

Device (DMD) technology from Texas Instruments (Dallas, TX). This is an array of

micromirrors that are individually digitally addressable. A dynamic mask can be created

by reflecting the laser beam off the DMD and through the support onto the ribbon as

shown in Figure 2.10. An area larger than the DMD can be patterned by breaking the

pattern into areas the same size as the DMD and translating the substrate and ribbon

between predetermined set points. At each set point the pattern on the DMD can be

5 mm

500 μm

38

changed. This process offers all the advantages of MAPLE-DW with much higher

throughputs. The most significant limitation to this approach is the need for a laser with

a large diameter and sufficient pulse energy to deposit the pattern. In addition, the DMD

must be sufficiently reflective so that it is not damaged by the laser itself. For this

reason, it is unlikely that an LCD dynamic mask would be able to absorb this energy

without being damaged.

Figure 2.10: Flashing MAPLE pattern using a DMD array.

2.5 Summary

This chapter has demonstrated that conventional screen printable inks can be used

with MAPLE-DW when using an infrared pulsed laser and x-y scanner. The main

emphasis of the study was to demonstrate the potential of this approach to deposit

functional patterns with feature sizes below 25 μm for applications such as interconnects.

This was successful; however, much better fixturing and coating techniques are required

39

to maintain a consistent film thickness and ink-substrate separation. Eliminating variance

in these process parameters will be critical if this MAPLE-DW approach is to be applied

in industry.

The best lines were all obtained in the sub-threshold regime, where the bubbles

would collapse to the ink film if they did not impinge on the substrate. The deposited ink

does not spread because the interaction between the substrate and the MAPLE-DW event

occurs at lower velocity than in the jetting or plume regimes. The sub-threshold regime

is investigated in further detail in Chapter 3.

An alternative MAPLE approach was also presented. Using a shadow mask

offers many of the advantages demonstrated previously with MAPLE. Because this

approach is a parallel process it may be more applicable for high volume manufacturing.

The advent of DLP offers the potential of a parallel process while maintaining the direct-

write capabilities required for rapid prototyping and low-volume manufacturing. This

approach deserves further investigation in the future.

40

3. MODELING OF THE SUB-THRESHOLD MAPLE-DW EVENT

In this chapter an analytical model of the bubble displacement is developed to

study the MAPLE-DW process operating in the sub-threshold regime using a commercial

thick-film ink and the experimental setup described in Chapter 2. Understanding the

development of the bubble displacement is important for predicting the effect of the

process parameters on the printed pattern. For example, in Chapter 2, a parallel approach

to the MAPLE-DW process using either a fixed or a dynamic mask was introduced.

Using a mask to determine the pattern exposes the ribbon to multiple irregularly shaped

apertures simultaneously as opposed to the standard Gaussian laser spot when the laser is

scanned across the ribbon. The mapping for a given pattern to its mask may not be one-

to-one. For example, a feature with a larger area may require lower laser fluence than a

feature with a smaller area. The model developed in this work is fitted to the

experimental data and the results are discussed using a scaling analysis.

3.1 Results from Time-Resolved Microscopy

Chapter 2 presented the experimental investigation of MAPLE-DW. It was

concluded that the sub-threshold regime produced the best results. This chapter further

describes the sub-threshold regime using results from time-resolved microscopy. The

experimental work of capturing the sub-threshold event was carried out at the Flame

Diagnostics Laboratory at Purdue University using time-resolved microscopy, as

described by Lewis (2005). Images of ink displacement were captured at different time

41

delays between the MAPLE-DW laser pulse and an imaging laser pulse. Each data point

of ink displacement in time-history was generated by averaging 15 different pictures

taken at a given time delay. The experiment was performed for three different ink

thicknesses (nominally 0.0005”, 0.0010” and 0.0020”), and two different laser spot sizes

(14.75 μm and 29.95 μm radii measured at the 10-90% points). The beam radius was

taken as the beam waist at the 1/e2 points. This is an error which contributes to the

inaccuracy of the model. Ordinary glass slides were coated by a technique similar to

“doctor blading”. A small quantity of ink was placed on the slide in between two steel

shims. This ink was spread by drawing a glass rod over the ink to uniformly distribute it,

as described in Chapter 2. However, when the ink film was measured using the

microscope, its thickness was found to be less than the nominal thickness of the steel

shims, as shown in Figure 3.1. A correlation between the nominal thickness and the

measured thickness was developed and the measured thickness was used for modeling the

MAPLE-DW process. The measured film thickness, d, is used when referring to the ink

thickness throughout the remainder of this chapter.

0

10

20

30

40

50

0 20 40 60 80 100

Mea

sure

d T

hick

ness

[m

]

Nominal Thickness [m]

Figure 3.1: Correlation between nominal and measured film thickness.

42

DuPont QS300, a commercial screen-printable silver-based conductive ink was

used for these experiments. No thinner was added to the ink for the experiments in this

section. Three different laser fluences were used for each experiment. The fluence was

selected so that the resulting MAPLE-DW event was in the sub-threshold regime with the

upper fluence for each experiment just below the onset of the plume regime. Because of

the rheological properties, no combination of process parameters (ink thickness, beam

radius and laser fluence) successfully produced events in the jetting regime for this ink.

However, as mentioned in Chapter 2, MAPLE-DW events were not as consistent in the

jetting regime as they were in the sub-threshold regime in addition to the other problems

of using jetting with a stationary ribbon and substrate described in Chapter 2.

Figures 3.2-3.7 show the time history of the mean bubble displacement at each

delay time for the MAPLE-DW event plotted on a logarithmic time scale. The error bars

show the maximum and minimum bubble displacements at each time step. The resolution

of the imaging system was 1.6 μm. At first glance, these figures resemble the response

from an over-damped simple harmonic oscillator, particularly for the smaller bubbles.

This indicates the presence of both conservative and non-conservative forces which are

attributable to surface tension and viscous effects, respectively.

43

0

10

20

30

40

50

60

70

0.01 0.1 1 10 100 1000

175556991

Bub

ble

Dis

plac

emen

t [m

]

Time [s]

mJ/cm2mJ/cm2mJ/cm2

Fluence d = 9.33 mr = 14.75 m

Figure 3.2: Bubble displacement vs. time for 14.75 μm beam radius and 9.33 μm ink thickness.

0

10

20

30

40

50

60

70

0.01 0.1 1 10 100 1000

185410728

Bub

ble

Dis

plac

emen

t [m

]

Time [s]

mJ/cm2mJ/cm2mJ/cm2

Fluence d = 9.33 mr = 29.95 m

Figure 3.3: Bubble displacement vs. time for 29.95 μm beam radius and 9.33 μm thickness.

44

0

10

20

30

40

50

60

70

0.01 0.1 1 10 100 1000

76511601691

Bub

ble

Dis

plac

emen

t [m

]

Time [s]

mJ/cm2mJ/cm2

mJ/cm2Fluence d = 18.02 m

r = 14.75 m

Figure 3.4: Bubble displacement vs. time for 14.75 μm beam radius and 18.02 μm thickness.

0

10

20

30

40

50

60

70

0.01 0.1 1 10 100 1000

3456401017

Bub

ble

Dis

plac

emen

t [m

]

Time [s]

mJ/cm2mJ/cm2mJ/cm2

Fluence d = 18.02 mr = 29.95 m

Figure 3.5: Bubble displacement vs. time for 29.95 μm beam radius and 18.02 μm thickness.

45

0

10

20

30

40

50

60

70

0.01 0.1 1 10 100 1000

1422200923423418

Bub

ble

Dis

plac

emen

t [m

]

Time [s]

mJ/cm2mJ/cm2mJ/cm2

Fluence

mJ/cm2

d = 31.84 mr = 14.75 m

Figure 3.6: Bubble displacement vs. time for 14.75 μm beam radius and 31.84 μm thickness.

0

10

20

30

40

50

60

70

0.01 0.1 1 10 100 1000

64011051581

Bub

ble

Dis

plac

emen

t [m

]

Time [s]

mJ/cm2mJ/cm2

mJ/cm2Fluence d = 31.84 m

r = 29.95 m

Figure 3.7: Bubble displacement vs. time for 29.95 μm beam radius and 31.84 μm thickness.

For MAPLE-DW, the best results are obtained when the bubble is pushed out to

the point that it just comes in contact with the substrate so that the velocity at the time of

46

impact is minimal. Figures 3.2-3.7 show that for a given ink thickness and laser radius the

bubble displacement is affected by the laser fluence. This is advantageous because the

laser fluence is easily adjusted and for a given pattern there may be a range of feature

sizes. For example, the inductor portion of an LC resonator may require a line width

below 50 μm (printed with just enough fluence for the bubble to interfere with the

substrate) while the capacitor portion of the same LC resonator may be a filled region 1

mm2 (printed with higher fluence corresponding to a larger bubble). Ultimately the

bubble interaction with the substrate needs to be further investigated because it was

observed experimentally that the substrate material has a large effect as far as the quality

of the deposition. The surface tension between the ink and the substrate appears to play a

large role, with the ink forming higher features with higher aspect ratios on glass than on

uncoated alumina substrates.

Figures 3.2-3.7 also show that less fluence is required to push the bubble out to a

given distance for a larger laser spot size. This may be attributed to the fact that the

surface tension is inversely proportional to the radius of curvature. It is also seen that the

maximum bubble displacement is proportional to the laser fluence, and that the fluence

required to displace the bubble a given distance is proportional to the ink layer thickness

since more mass is accelerated. The figures all show that a lag in time occurs after the

laser pulse for the ink layer to begin to deform. This time lag is shorter for higher laser

fluences.

There also appears to be some plastic deformation of the ink layer (the bubble

never returns to its un-deformed shape). This is particularly true for the bubbles with

larger maximum deformations. Figure 3.8 shows the displacement of the bubble after 250

μs. The figure shows that the displacement at this time is a function of fluence. Figure

3.2-3.7 showed that at 250 μs the displacement is constant with respect to time for most

of the bubbles. As discussed in Chapter 2, the bubble’s failure to return to its undeformed

47

shape causes interference with adjacent sub-threshold events. This is the largest limiting

factor for implementing MAPLE-DW when using a stationary ribbon and substrate with a

moving laser beam.

0

10

20

30

40

0 1000 2000 3000 4000

BFJNRV

Dis

plac

emen

t aft

er 2

50s

[m

]

Fluence [mJ/cm2]

r = 14.75 mr = 29.95 mr = 14.75 mr = 29.95 mr = 14.75 mr = 29.95 m

d = 9.33 md = 9.33 md = 18.02 md = 18.02 md = 31.84 md = 31.84 m

Figure 3.8: Deformation after 250 μs vs. fluence.

The ratio of the maximum displacement to the final displacement is larger for

events generated with smaller laser beam radii. This may be attributable to the fact that

the curvature of these bubbles is much larger than for bubbles generated with the larger

beam radius. As a result, the stress and strain are both higher for the smaller bubbles,

causing them to yield sooner than the bubbles with the larger transverse radius.

Figure 3.9 shows the maximum radius (measured at the base of the bubble)

attained by the sub-threshold event. The maximum radius occurs when the bubble has its

largest displacement, however, this does not change much over time and is assumed to be

constant. For the smaller bubbles, the radius has a large relative uncertainty because the

radius is on the same order as the resolution of the imaging system (1.6 μm).

48

0

10

20

30

40

50

60

70

0 500 1000 1500 2000 2500 3000 3500

ARBRCRDRERFR

Max

imum

Eve

nt R

adiu

s [

m]

Fluence [mJ/cm2]

r = 14.75 mr = 29.95 mr = 14.75 mr = 29.95 mr = 14.75 mr = 29.95 m

d = 9.33 md = 9.33 md = 18.02 md = 18.02 md = 31.84 md = 31.84 m

Figure 3.9: Maximum event radius as a function of fluence.

The remainder of the chapter develops a model for the displacement in the sub-

threshold regime. Section 3.2 describes the physical model underlying the MAPLE-DW

process. This model is linearized to form a 2nd order ordinary differential equation.

Section 3.3 describes comparisons between model predictions and the experimental data.

Section 3.4 examines the model further to determine what effects the process parameters

have on the MAPLE-DW process. Finally, Section 3.5 summarizes the chapter.

3.2 Development of an Analytical Model of the MAPLE-DW Event

Insight into the MAPLE-DW process can be obtained from a rudimentary model

describing key parameters of the process. This section develops a model of the sub-

threshold event. Physically, the development of the event is very complicated with

multiple coupled phenomena. The time histories show the presence of conservative and

non-conservative forces and resemble the response from a damped harmonic oscillator.

The goal is to synthesize a model that captures the basic behavior of the bubble.

49

The laser pulse irradiates the ink through the glass slide (support) for ~20 ns. The

ink is rapidly heated locally and a small portion of the organic material in the ink will be

vaporized. The vapor expands away from the interface with the support displacing the

ink. The vapor will also dissipate energy by transferring heat across the interface with the

un-vaporized ink and the glass support. Because glass has a low thermal conductivity, it

can be assumed that the un-vaporized ink and with the support slide are adiabatic. This

assumption is probably more valid for thinner ink layers because there is less mass to

displace.

A portion of the laser energy transferred to the ink will be consumed in the

vaporization process. The remainder is available for providing the kinetic energy to the

bubble. It is assumed that after the vapor supplies this initial impulse to the ink, no further

interaction results in energy transfer. This is more plausible in the jet or plume regimes

because the vapor bubble can escape through the breach in the ink surface. A more

accurate model should consider interaction with the vapor bubble from its rapid

expansion to its eventual condensation.

As the bubble expands there are dissipative forces due to the viscous motion of

the ink. It is assumed that there is negligible flow in the radial direction and that the

unaffected ink forms channel walls that allow the bubble to expand only in the direction

normal to the ink. Conservative forces due to surface tension also oppose the expansion

of the ink bubble because the surface area is being increased. Throughout this model the

ink is assumed to be incompressible and the effects of gravity are considered to be

negligible because the mass of the ink involved in the MAPLE event is very small.

50

3.2.1 Laser Ink Interaction

The first step occurring in MAPLE-DW is the interaction between the laser and

the ink. The goal is to develop an approximation that computes the initial temperature

rise generated by the laser pulse. Figure 3.10 shows an annotated diagram of the model.

R0

2r0

P

d

p k c

Z0

Figure 3.10: Laser interaction with the ink.

Because the pulse length of the laser is short, the center of the laser beam can be

assumed to be effectively stationary. For example, at a scan speed of 1 m/s the center of

the laser beam translates only 20 nm over a 20 ns pulse. The laser beam is also assumed

to have a Gaussian profile. The irradiance is a function of the radius, r, and given by

2

2 20 0

2, exp 2

P t rI r t

r r

(3.1)

where 0r is the laser beam waist and P is the laser power. Some of the radiation will be

reflected by the glass slide and the remainder will be absorbed by the ink. The laser flux

is absorbed inside the ink layer according to Lambert’s law

, , 1 , exp fq r z t R I r t az (3.2)

where fR is the optical reflectivity and a is the optical absorption coefficient given by 4a (3.3)

51

where is the imaginary part of the complex refractive index and is the wavelength

of the incident laser pulse. The value of for silver is 7.09 at the wavelength of the

Nd:YLF laser, 1047 nm, which corresponds to an absorption coefficient of 8.51 x 107 m-1.

It is assumed that the ink is homogenous. In reality, the ink consists of silver

particles distributed in a transparent organic matrix. The reflectivity and absorption

coefficients of these materials will be different; the silver will absorb much more of the

laser energy and transfer it to the organic material by conduction. A more rigorous model

would be to use a ray tracing approach and consider the heat transfer between the media.

However, for this model, the reflectivity and imaginary dielectric constant of silver are

assumed to be representative of the effective values.

The volumetric distribution of the absorbed laser energy is

, ,, , 1 , exp ab f

dq r z tQ r z t a R I r t z

dz (3.4)

This equation maps the laser irradiance to a heat generation term in the heat conduction

equation. The transient three dimensional heat transfer equation governing the thermal

profile in the ink is p abc T Q k T (3.5)

where , pc and k are the density, specific heat and thermal conductivity of the ink.

Because the heat generation is localized at the interface between the support and ink

layer, it can be assumed that the convection and radiation terms are negligible. An

estimate of the thermal penetration depth, thd , is given by

4thd (3.6)

52

where is the thermal diffusivity which ranges from 1.74×10-4 m2/s for silver to

8.59×10-8 m2/s for organic material, and is the pulse duration which is on the order of

20 ns. These correspond to a thermal penetration depth of 2.89 μm for a mass weighted

composition of 60% silver and 40% organic. Because a large portion of the ink is organic

and the silver particles cannot interact directly with each other, the heat transfer due to

conduction during the duration of the pulse is assumed to be negligible. Combining Eq.

(3.4) with Eq. (3.5) and assuming a constant specific heat permits T to be integrated over

time to provide an expression for the temperature of the ink prior to its expansion. Thus,

2

2 20 0

2, , 1 exp exp 2f

p

a P rT r z R az

c r r

(3.7)

3.2.2 Coupling of Laser Energy to the Kinetic Energy of Ink

It is useful to consider the laser radiation in terms of fluence. For a laser pulse

with a uniform circular profile, the fluence is given by

20

0

1E PF P t dt

A A r

(3.8)

where E is the laser pulse energy and A is the cross-sectional area of the laser beam.

The laser fluence for the experimental results presented in Section 3.1 was caclulated by

measuring the pulse energy and the radius at the 10-90% points to obtain the spot area.

Given the temperature profile from Eq. (3.7), the region of the ink with a

temperature at the threshold temperature required to vaporize the ink, VT , marks the

boundary of the vapor bubble at the end of the laser pulse. Its initial profile is given by

2

1 20

1ln 2

rz r c F

a ar (3.9a)

where

53

1

21 f

p v

ac R

c T (3.9b)

The initial vapor bubble has a parabolic shape. The maximum initial radius, 0R , is

at the interface with the support and the maximum initial height, 0Z , is at the centerline.

These parameters are given by

0 1

1lnZ c F

a and 2 2

0 0 1

1ln

2R r c F (3.10)

The threshold temperature used in Eq. (3.9) is not the equilibrium vaporization

temperature because some energy will be absorbed by the latent heat when the ink is

vaporized. The amount of energy required to vaporize the initial vapor bubble is

v fg vE h V (3.11)

where fgh is the enthalpy of vaporization and vV is the volume of the vapor pocket. The

upper limit for the initial velocity is when all the internal energy is converted instantly to

kinetic energy. Accordingly, the energy balance can be expressed as:

22 0 02 fgKE c E R Z h

(3.12)

where c2 accounts for the percentage of laser energy transferred to the vapor (the rest is

transferred to the glass support).

To simplify the analysis, the bubble is assumed to have a parabolic profile with a

constant radius. The displacement, velocity and acceleration of the bubble can be written

as

2

20

1,

rz r t z t

R (3.13a)

54

2

20

,1

rdz r tz t

Rdt (3.13b)

22

220

,1

rd z r tz t

Rdt (3.13c)

where 0R is the width of the bubble, which is assumed to be the initial vapor bubble

radius calculated in Eq. (3.10). Because the thickness of the ink is not great and there will

be much larger pressure gradients in the normal direction compared to the radial

direction, it is assumed that the ink expands by displacing the ink normal to the interface

and does not expand radially.

Using Eq. (3.13), the kinetic energy in Eq. (3.12) can be rewritten as

0

22

2 2 2020

0

11

2 6

R r dKE mV d z t r dr z R

R

(3.14)

Using Eqs. (3.8), (3.10), and (3.11) with Eq. (3.14) the initial velocity is found to be

0 2 3 1

1

6 2ln

ln

Fz c c c F

d c F

where 3 2fgh

ca

(3.15)

For this model it is assumed that the pressure pulse provides an initial kinetic

energy to the ink but has no further interaction. A more accurate model could be obtained

by considering the expansion of the vapor bubble over the entire time history. The

remainder of the analysis assumes that the bubble is being pushed though a cylindrical

channel because the radial expansion of the vapor bubble has been neglected. After the

pressure pulse is over, there are viscous, dF , and surface tension forces, sF , acting on the

ink as shown in Figure 3.11.

55

z(t)

R0

Fd

Fs

Figure 3.11: Forces acting on ink bubble during its development.

3.2.3 Viscous Forces

As the vapor expands, the ink undergoes viscous flow which dissipates energy.

Thick-film inks are designed to have a viscosity that varies with the shear rate z r .

Kay et al. (2003) discuss this property in more detail and present the Cross model, which

gives a relationship between the viscosity and shear rate. This relation is

5

04

1

1c

zc

r

(3.16)

where is the dynamic viscosity for an infinite shear rate, 0 is the limit of the

dynamic viscosity as the shear rate approaches 0, and 4c and 5c are constants. For a

Newtonian liquid, 5c approaches 0 and is greater than 0 for a shear thinning fluid. The

shear stress is related to the dynamic viscosity and shear rate by

s

z

r (3.17)

The ink has zero velocity along the boundary with the un-affected ink due to the

non-slip boundary condition. The shear stress at the boundary is

56

0 0

0 0 20

22 2 4

dr R r R

rzzF R d R d d z

Rr (3.18)

To linearize the model, the dependance of the viscosity on the shear rate is

neglected (the ink is assumed to be a Newtonian fluid). This introduces error into the

analysis but greatly simplifies the modeling.

3.2.4 Elastic Forces

The surface tension acts to minimize the surface area of the protruded ink. The

time histories in Figures 3.2-3.7 demonstrate that an elastic term is present because after

the bubbles reach their maximum displacement they begin to collapse. Additionally, the

presence of the jetting regime, shown in Figure 2.3, shows the effects of surface tension

which causes the plume to collapse in the radial direction to form a slender jet. This force

is very nonlinear.

The work dW required to increase the surface area a differential amount sdA is

s sdW F dz dA so that

ss

dAF

dz (3.19)

where is the surface tension coefficient. The bubble is assumed to have a parabolic

geometry given by Eq. (3.13). The surface area of the bubble is given by

0 02 2 2

3 20 32 24 2 0000 0

42 1 2 1 4

6

R R

s

Rz r zA r dr r dr Rz R

r R z (3.20)

which has a limit of 20R as z approaches 0 and agrees with the undeformed surface area.

From Eqs. (3.19) and (3.20), the force due to surface tension is

57

1 2 3 22 20 0 3 2 20 3 0 0

24 4

3

s

s

dA R RF z R R z R

dz z z (3.21)

Figure 3.7 shows the surface tension force for several different radii of the

parabola with a surface tension constant of 1 N/m. The equation is non-linear and as the

bubble displacement grows to infinity the surface tension force approaches a limit of

0

4lim

3

sz

F R (3.22)

The derivative of the surface tension force with respect to displacement is

1 22 2 2 20 0 03

0 1 24 2 20

8 16

4 16

s

z R R z RdFR

dz z z R (3.23)

which has a limit of 2 as the displacement approaches 0. The force from Eq. (3.22)

can be linearized using a first order Taylor series approximation

0

lim 2

s

sz

FF z z

z (3.24)

Figure 3.12 also shows the linearized surface tension force, which is used in the model.

For larger bubble displacements, large errors are introduced by the linearization.

Experimental results showed that the ink appears to plastically deform if the

displacement grows large enough. This phenomenon is not captured by the surface

tension model and the ink film is treated as being perfectly elastic. As the bubble grows

beyond the elastic limit the ink layer begins to yield until it eventually ruptures. Surface

tension can collapse the bubble in the radial direction to produce a jet after the bubble

walls fail. However this only occurs if enough if the expansion is great enough to detach

ink from the support but slow enough that the surface tension forces can overcome the

radial expansion. The addition of thinner lowers the viscosity which lowers the velocity

58

of the ink necessary for the event to escape the support. It may also raise the surface

tension of the ink.

0

50

100

150

200

250

0 20 40 60 80 100

Sur

face

Ten

sion

For

ce [

]

Displacement [m]

Parabola Radius N/m5 m10 m25 m50 m

Figure 3.12: Surface tension force for surface tension constant of 1 N/m for various beam radii.

3.2.5 Damped Harmonic Oscillator

From Newton’s Second Law, the sum of the forces acting on the ink bubble (see

Figure 3.11) is related to acceleration as

z d sF mz F F (3.25)

From Eq. (3.13), the mass of the moving ink bubble is

0

20

0

22

R

mz d zr dr dR z (3.26)

59

combining Eq. (3.26) with Eqs. (3.18) and (3.25) gives 2

0 8 4 0 dR z d z z (3.27)

This governing equation corresponds to the damped harmonic oscillator shown in

Figure 3.13, where

20m dR 8c d and 4k (3.28)

m

k cz(t)

Figure 3.13: Damped harmonic oscillator.

Equation (3.27) is a second order ordinary differential equation and requires two

initial conditions, the initial displacement and the initial velocity. The initial displacement

can be assumed to zero and the initial velocity is obtained from Eq. (3.15). For

2 202 d R the system is over-damped. If 2 2

02 d R the system is critically

damped, and for 2 202 d R , the system is under-damped. When the system is under-

damped, it will oscillate multiple times. Figure 3.14 shows the typical behavior of the

damped harmonic oscillator for the over and under-damped systems.

60

-0.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7 8D

ista

nce

Time

Underdamped(m=1 c=1 k=1 z

0=4)

.

Overdamped(m=1 c=4 k=1 z

0=4)

.

Figure 3.14: Under and over-damped harmonic oscillators.

Because of the effects of shear thinning and plastic deformation the response of

the under-damped system may not be evident in the time history. The closed form

solution to the damped harmonic oscillator is given below in Eqs. (3.29) and (3.30). For

2 4c mk (over-damped case), with an initial position of 0z and initial velocity of 0z :

1 20

1 2

r t r tz

z t e er r

and 1 201 2

1 2

r t r tz

z t r e r er r

(3.29a)

where

2

1

4

2

c c mkr

m and

2

2

4

2

c c mkr

m (3.29b)

The maximum displacement will occur when the velocity is zero. Solving Eq.

(3.29) for 0z t gives the time when the ink has reached its maximum displacement,

maxt , and the maximum displacement maxz t

1 2max

2 1

ln ln

r r

tr r

and (3.29c)

0 1 2 1 2max 1 2

1 2 2 1 2 1

ln ln ln lnexp exp

z r r r rz t r r

r r r r r r

(3.29d)

For 2 4c mk (under-damped case)

0 sin atz

z t e btb

and 0 sin cos atz

z t e a bt b btb

(3.30a)

61

where

2

ca

m and

24

2

mk cb

m (3.30b)

Solving 3.30(a) for 0z t gives:

1max

1tan

b

tb a

and (3.30c)

10max 2 2

exp tanz a b

z tb aa b

(3.30d)

3.3. Experimental Data Analysis

The model for the bubble development described in Eq. (3.27) depends on six

total parameters. There are three material properties: density, , dynamic viscosity, ,

and the surface tension constant, , as well as three coupling coefficients: 1c , 2c , and 3c

from Eqs. (3.9b), (3.12) and (3.15), respectively. The density of the ink was measured

experimentally to be ~3800 kg/m3, but the other five parameters must be curve fit to the

time histories shown in Figures 3.2-3.7. Substituting Eqs. (3.15), (3.28) and (3.29b) into

Eq. (3.29a) gives the displacement of the MAPLE-DW event with respect to time for the

over-damped case

2 2 2

022 3 12010

2 2 22 2 20

020

4 2 42 explnln

64 16 4 2 4

exp

d d dRF tc c c FdRc FR

z td R d d dR

tdR

(3.31)

A similar equation can be developed for the under-damped case. However it was

found that the over-damped case fit the data better than the over-damped case. Eq. (3.31)

is highly nonlinear and difficult to curve-fit. The measured density was used and the

remaining parameters, , , , 1c , 2c , and 3c , were found by minimizing the sum of

62

the squared differences between the displacement predicted by Eq. (3.31) and the

experimental data. Because the linear model cannot capture the plastic deformation, the

parameters were curve fit only to experimental data prior to and including the maximum

displacement. Table 3.1 shows the parameters that were generated from this fit.

Table 3.1: Model parameters.

ρ 3800 kg/m3

μ 0.92 Pa·s

γ 1.97 N/m

c1 0.0006 m2/J

c2 0.82

c3 0.00 m-2

Figure 3.15 shows a time history predicted by the model using the parameters in

Table 3.1 plotted with the experimental data for the 18.02 μm thick ribbon and a beam

radius of 29.95 μm. Because the model does not include any plastic deformation, the

collapse of the bubble cannot be adequately captured. Ideally the model should be able to

fit all six experiment data. In reality even after extensive trial and error, no one set of

parameters was found to satisfy this requirement.

Figure 3.16 shows the value of the maximum displacement predicted by Eq.

(3.29d) using the parameters in Table 3.1 plotted with the experimental values for all 19

time histories. The solid lines are calculated values and the dots are experimental data.

Although the model cannot predict the exact value of the maximum displacement, it does

capture the general trends observed in the experimental data. The maximum

displacement increases with the laser fluence and beam radius while it decreases with ink

thickness.

63

0

10

20

30

40

50

60

70

0.01 0.1 1 10 100 1000

3456401017LMN

Bub

ble

Dis

plac

emen

t [m

]

Time [s]

d = 18.02 mr = 29.95 m

Fluence

mJ/cm2mJ/cm2

mJ/cm2 = 1.97 N/m = 0.92 Pa s = 3800 kg/m3

c3 = 0.00 m-2

c2 = 0.82

c1 = 0.0006 m2/J

Figure 3.15: Fitted response for 31.84 μm ink thickness and 14.75 μm beam radius.

0

10

20

30

40

50

60

70

0 1000 2000 3000 4000 5000

m1m2m3m4m5m6

Max

imum

Eve

nt D

ispl

acem

ent [m

]

Fluence [mJ/cm2]

r = 14.75 mr = 29.95 mr = 14.75 mr = 29.95 mr = 14.75 mr = 29.95 m

d = 9.33 md = 9.33 md = 18.02 md = 18.02 md = 31.84 md = 31.84 m

c3

= 0.00 m-2c

2 = 0.82

c1 = 0.0006 m2/J = 1.97 N/m = 0.92 Pa s = 3800 kg/m3

Figure 3.16: Maximum experimental and modeled event displacements (points are experimental data and lines represent the displacement predicted by the model).

The dynamic viscosity for QS300 is given in a specifications sheet for the ink to

be 200-300 Pa·s. However, as mentioned in Section 3.2.3 this will vary with shear stress

and the shear rates during the bubble expansion process are very high. The surface

64

tension constant for water at room temperature is 0.075 N/m. The high surface tension

constant shown in Table 3.1 may indicate an effective property. A negative gauge

pressure may develop within the vapor pocket during the bubble development. This will

promote the bubble collapse similar to forces from surface tension. This effect was

neglected in the model because it was assumed that after the ink was provided with an

initial momentum impulse by the vapor but after t=0, the vapor did not interact with the

system. Using thermal properties of water, 1c should be on the order of 10-1 and 3c

should be on the order of 101. The constant, 2c , is the amount of energy that is coupled

to the system from the laser so it must fall between 0 and 1.

It is important to observe that the difference between the fitted viscosity and the

value specified for the ink is likely a result of the shear-thinning discussed in Section

3.2.3 which could not be considered using a linear model. Neglecting the energy

consumed by vaporizing the ink 3 0c provided the best fit to the data. This could be

due to the fact that the amount of material turn to vapor is very small. The curve fit found

that c2 = 0.82, that is 82% of laser energy was coupled to kinetic energy.

Figure 3.17 shows how the maximum bubble radius varies with fluence

normalized by the beam radius. Figure 3.9 showed that there are two branches of the

maximum event radius corresponding to the two different laser spot sizes. These two

branches collapse onto one curve when the maximum radius is divided by the beam

radius as predicted by Eq. (3.10). This is plotted in Figure 3.17, along with relationship

predicted by Eq. (3.10), using a value of c1 = 0.0006 m2/J from Table 3.1. Figure 3.17

shows that the functional relationship between the maximum bubble radius is closer to

being linearly proportional to the fluence and beam radius than the modeled value. This is

due to expansion in the radial direction for larger laser fluences, which was assumed to be

negligible in the model.

65

0

1

2

3

4

5

0 500 1000 1500 2000 2500 3000 3500

1m2m3m4m5m6m

R0/r

Fluence [mJ/cm2]

r = 14.75 mr = 29.95 mr = 14.75 mr = 29.95 mr = 14.75 mr = 29.95 m

d = 9.33 md = 9.33 md = 18.02 md = 18.02 md = 31.84 md = 31.84 m

R0/r = (0.001359 cm2/mJ) F + 0.04894

R0/r = [ 0.5 ln(c

1F)]

0.5

Figure 3.17: Ratio of maximum bubble radius to the laser beam radius as a function of fluence.

As shown in Figure 3.8, the larger bubbles will have an effective plastic

deformation and not return completely to the undeformed ink layer. This effect causes

pulse-to-pulse interference. A figure of merit for the sub-threshold MAPLE-DW event is

the ratio between the maximum displacement of the bubble and the radius of the bubble

at its base. This aspect ratio will help to determine the quality of features that can be

produced with a given set of process parameters. In addition to minimizing the pulse-to-

pulse interference, a slender (larger ratio of the maximum displacement to the base

radius) bubble will produce more consistent results because there will be less variance in

the bubble radius at the plane where the bubble interacts with the substrate. This quality

factor is plotted in Figure 3.18. The dashed lines in the figure represent the ratio predicted

by the model (Eq. (3.29d) divided by Eq. (3.10)) using the coefficients from Table 3.1.

The model predicts that the ratio of maximum displacement to bubble radius increases as

the fluence increases. However, for larger laser fluence the bubble radius will be also be

larger so gains from a higher aspect ratio will not be realized at very high fluences. The

66

model also predicts that thinner ink layers will create the highest aspect ratios. This

agrees with experimental results.

0

0.5

1

1.5

2

0 500 1000 1500 2000 2500 3000 3500

1m2m3m4m5m6m

z max

/R0

Fluence [mJ/cm2]

d = 9.33 md = 9.33 md = 18.02 md = 18.02 md = 31.84 md = 31.84 m

r = 14.75 mr = 29.95 mr = 14.75 mr = 29.95 mr = 14.75 mr = 29.95 m

c3

= 0.00 m-2c2 = 0.82c

1 = 0.0006 m2/J

= 1.97 N/m = 0.92 Pa s = 3800 kg/m3

Figure 3.18: Ratio of the maximum displacement to the maximum event radius vs. fluence (the dashed lines represent the value predicted by the model using parameters

from Table 3.1).

As shown in Figure 3.17 and predicted by Eq. (3.10) the event radius will be

proportional to the laser mean radius and does not have a strong dependence on the

thickness of the ink. The maximum displacement varies inversely with ink thickness;

therefore, the thin-ink films with small beam radii will produce the best results. This

agrees with experimental parameters that produced the smallest feature sizes in Chapter

2. However, the maximum displacement for these bubbles will still be relatively small

relative to those created with greater ink thicknesses and larger beam radii. This requires

the substrate to be positioned as close as possible to the ink on the ribbon and the ability

to control this parameter will limit the feature sizes that can be fabricated using MAPLE-

DW in the sub-threshold regime.

67

3.5 Conclusions

This chapter developed an analytical model for the expansion of the sub-threshold

MAPLE-DW event. The model incorporates the three process parameters, laser fluence,

beam radius, and ink thickness to find the time history of the bubble’s displacement. The

model predicts that the maximum displacement will increase with laser fluence and beam

radius but decrease with the ink film thickness. The model also predicts that the event

radius will be proportionate to the beam radius. Although these trends agree with the

experimental data, several assumptions and the linearization limit its ability to completely

capture the development of the expansion process. This includes the fact that pressure

pulse is encapsulated by the ink layer and its expansion accelerates the surrounding ink

layer rather than providing a discrete momentum impulse. The linearization of the model

prevented this from being considered. Because the shear rate inside the ink will vary

during expansion so will the viscosity because of the shear thinning property of the ink.

This will cause the ink to set before returning to the undeformed profile and may answer

some of the nonlinearity observed in the experimental time histories. The model predicts

that the highest quality bubbles should be produced for a minimum ink thickness and

beam radius. Because the maximum displacement of these bubbles will be small, this

will require a minimum ink-substrate separation.

68

4. SELECTIVE LASER SINTERING

This chapter presents an experimental investigation of a Selective Laser Sintering

process for fabricating passive thick-film microelectronic devices. The patterning and

functionalization steps in this procedure are integrated. The experimental apparatus and

procedure is described in detail along with a summary of the testing procedure. These

experiments established optimum process parameters and demonstrated the applicability

of the process for microwave components, small feature sizes, low-temperature

substrates, and sintering thick-film copper in ambient conditions.

4.1 Introduction

Chapters 2 and 3 investigated MAPLE-DW. This process and other direct-write

patterning technologies such as those described in Chapter 1 still require the ink to be

functionalized after its deposition. This can be accomplished by bulk firing the entire

package in a furnace similar to the conventional screen printing process. However, most

conventional screen printing inks have been designed to be sintered at 850C. Using

conventional inks is attractive because of their performance and low cost; however, the

high firing temperature is well in excess of the damage threshold for polymer and glass

substrates. Limiting the choice of substrates to materials such as alumina and quartz

makes the integration of passive microcircuits into the packaging of a device difficult.

Using polymer-based substrates is attractive for disposable microelectronic

devices such as RFID type tags and sensors. The flexibility of polymer substrates permits

69

reel-to-reel fabrication and simplifies packaging. Flexibility also allows conformal (3D)

designs to be fabricated using 2D patterning and then folded/formed to their final shape.

In addition to extending the range of possible substrates to glass and polymers

while maintaining the performance and cost effectiveness of conventional thick films, a

demand exists to further reduce feature sizes for high-frequency devices and high-density

interconnects. Thin-film lithography can produce submicron feature sizes but is not

economic for either low-volume manufacturing such as rapid prototyping or high-

volume, very low–unit-cost devices such as RFID tags. The morphological gap between

thick- and thin-film technologies is satisfied by several of the technologies mentioned in

Chapter 1. However, the challenge of functionalization on low-temperature substrates is

not intrinsically answered. Several research groups (Piqué et al.; 1999 and Redinger et

al., 2004) have demonstrated the use of innovative new materials, such as solutions based

on nanoparticles, as a partial solution to this problem. While the use of nanoparticles

dramatically lowers the functionalization temperature, it is not clear that it will be

economically viable for low cost applications.

One solution to both the problem of low-temperature substrates and mesoscopic

feature sizes is to use a laser to locally sinter the ink while minimizing the heating of the

substrate. Selective Laser Sintering (SLS) has been demonstrated previously for 3D

metallic mechanical parts (Kruth et al., 2003), including microscale objects (Kathuria,

1997, 1998), and proposed for the fabrication of electronic circuitry (Chopra et al., 1998).

Marinov (2004) investigated the DC resistance of components fabricated using a

combination of deposition of chemical precursors followed by laser sintering. Laser

sintering has also been proposed for use with other direct write techniques (Chrisey et al.,

2000; Piqué et al., 2003; Bieri, 2004).

This chapter investigates a different approach from pervious direct techniques

because the same laser is used to simultaneously functionalize and pattern the device. To

70

our knowledge no work demonstrating this concept has been attempted with thick-film

inks even though it is considerably simpler than using a direct-write technology to

deposit the pattern and a second technology to functionalize the device.

SLS does have the disadvantage that it cannot be used to pattern unsinterable

materials such as biological or chemical elements that may be required for some sensors

or power sources. However, this chapter demonstrates that it can be used to create

complete passive devices using conventional thick-film inks. If unsinterable materials are

required, they can be fabricated using MAPLE-DW or another direct-write technique

(Wu et al., 2001; Wartena et al., 2004).

Advantages of the process investigated in this chapter include:

Patterns on low-temperature substrates such as Mylar;

Feature sizes below 25 μm;

Conductive, resistive, and dielectric materials can be patterned and

functionalized;

Resistor values can be tuned by varying the laser power and speed without

modifying the geometry of the pattern;

High-frequency performance agrees with conventional thick-film

specifications;

Non-equilibrium nature of process allows processing of thick-film copper

in ambient environment and is compatible with conventional dielectric and

resistive ink processing.

This chapter is organized as follows. Section 4.2 discusses the experimental setup

used for investigation of SLS. Section 4.3 covers the experimental work. The DC

conductivity of patterns created on glass with SLS is studied in Section 4.3.1 and these

results are used to investigate the performance of conductors at microwave frequencies in

71

Section 4.3.2. Section 4.3.3 investigates the minimum feature size obtainable without

subsequent laser trimming using SLS and Section 4.3.4 demonstrates the applicability of

the process to polymer substrates. The ability to sinter copper thick-film inks in ambient

conditions is demonstrated in Section 4.3.5. Finally, Section 4.4 presents a summary of

this chapter. The heat transfer process during SLS is further analyzed in Chapter 5.

4.2 Experimental Setup

A schematic of the setup used for Selective Laser Sintering is shown in Figure

4.1. As with MAPLE-DW, the entire process takes place in an ambient non-clean room

environment, and by rotating a flip-mirror both the fiber and Nd:YLF lasers share the

same optical path through the scanner. This allows the same system described in Chapter

2 to also be used to control the fiber laser. The combination of high speed, accuracy and

flexibility makes this setup attractive for both rapid-prototyping applications as well as

higher-volume production. The laser used for the Selective Laser Sintering experiments

was a JDS Uniphase IFL9 fiber laser which produces a wavelength at 1.10 μm. The beam

is focused to a spot size of 20 μm on the substrate and the laser provides up to 9.0 W of

continuous wave power. However, because of reflections throughout the optical setup,

only 56% of this power is available at the substrate. A calibration curve for the laser

power at the substrate is shown in Figure 4.2.

The CCD camera and monitor allow the process to be monitored in-situ. This is

useful for aligning the sample for sintering multiple layers and identifying defects in the

pattern caused by inhomogeneity of the ink or inconsistencies in film thickness. The

substrate is positioned against hard-stops on top of a set of x-, y- and z-translational

stages. This allows the substrate to be positioned relative to the origin of the pattern in the

computer by adjusting the x and y stages. The ability to align existing designs allows the

72

system to be used for modifying existing designs and repairing circuits. The depth of

focus of the camera is small enough (~20 μm) that it can also be used to position the

surface of the substrate in the focal plane of the laser by adjusting the z-stage.

Figure 4.1: Schematic of Selective Laser Sintering setup.

Laser Beam

Unsintered ink

Ink Heated by Laser Path of laser

Sintered ink

Substrate

Nd:YLF Laser Mirror

Polarizer

Beam Expanders

X-Y Scanner

Computer

TV Monitor

CCD Camera

Hot Mirror

IR Filter

Stages Substrate

Fiber Laser

Mirror Flip Mirror

73

0

1

2

3

4

5

0 2 4 6 8 10

Mea

sure

d P

ower

[W

]

Control Power [W]

0.5604 PC

Figure 4.2: Laser control power vs. measured power at the substrate.

Commercial thick-film inks were used for all the experiments presented in this

thesis. These included conductors, DuPont QS300, QM22 and 6002F, and Heraeus

C8772 and C7257; resistors, DuPont 100 Ω/ and 10 kΩ/, and dielectrics, DuPont

QM44 and Heraeus IP9029 and IP9035. All the DuPont inks were designed for the

standard 850°C firing cycle. Heraeus C8772, IP9029 and IP9035 are designed to be fired

at 500°C. For the copper ink (DuPont 6002F), specifications call for firing at 900°C in a

nitrogen environment to prevent oxidation.

The ink is first diluted with thinner (α-terpineol based) to lower its viscosity. The

ratio of unadulterated ink to thinner is 10:1. This permits the ink to be applied to the

substrate using a wire-coater. Wire-coaters from Paul N. Gardner Inc. (Pompano Beach,

FL) with different gauges of wire are available and the film thickness can be controlled

by selection of the wire coater. The results presented in this thesis were all fabricated

using a #4 wire roller. The nominal wet ink thickness for this roller is 7.7 μm and it was

found to produce consistent films between 5 and 10 μm thick. Figure 2.2 showed a

cartoon of the application of ink with a wire coater from the supplier’s website. After

coating, the substrate is allowed to level in ambient air for 10 minutes. Allowing the ink

to settle after coating is important because the wire coater creates furrows in the ink film.

74

These furrows level out due to surface tension to form a uniform coating. An alternative

for the creation of thinner films would be to use a spin coater. However, this requires the

ink to be diluted to a low viscosity which lowers the density of the functional particles

within the ink. Using a wire coater or spin coater requires the substrate to be planer.

Nonplanar substrates can be coated by spraying the component with ink or dipping it into

a vat full of ink.

After coating the substrate and leveling, the substrate is dried in a convection

oven. Heating the ink expedites the evaporation of the volatile organic material from the

ink. The temperature of the convection oven is selected so as not to damage the substrate.

Typically the ink was left in the oven for 20 minutes at a temperature of 150°C. During

the drying process the thickness of the film can shrink by more than 50% due to the

driving off of organic components in the ink. The amount of shrinkage depends on the

concentration of thinner, which provides additional control on the thickness of the ink

layer prior to sintering. After drying, the ink film is not bonded to the substrate. This is

crucial because the ability to easily remove the dry unsintered material is important for

fabricating patterns with small feature sizes and consistent edges.

If the ink is not dried prior to the SLS process, then the laser will vaporize the

volatile organics causing them to expand so rapidly that the pattern is damaged. Further

experiments should be undertaken to investigate the feasibility of depositing a film of dry

particles onto the substrate, similar to conventional SLS.

After drying, the ink coated substrate is positioned in the processing fixture. The

laser scans the pattern up to a speed of 1 m/s. To create thick lines, the laser beam is

rastered back and forth. A 20 μm pitch was used for most experiments because that is the

diameter of the laser beam. For scanning longer lines (large length/width ratios), the

temperature profile will be different depending on whether the laser is rastered in the

length or width direction. The laser is also turned off when it reverses directions.

75

Otherwise, the laser beam will dwell at the edges, heating this region to a higher

temperature.

Once the entire pattern has been sintered, the material that was not sintered is

removed using a solvent such as methanol or acetone. This can be accomplished by

rubbing the pattern with a moist rag or by placing the entire substrate in an ultrasonic

cleaner. For several experiments, the removed ink was purposely rubbed into the sintered

pattern and the pattern sintered again. This appeared to improve the conductivity and

further work should be done to investigate the effect of infiltrating dried ink particles into

porosity formed in the original sintered ink layer. For very fine lines the ultrasonic

cleaner proved less destructive to the patterns themselves when removing unsintered

material than cleaning with a rag.

Sometimes it is desirable to add one or more layers of ink to a pattern to either

build up its thickness and or repair defects. This is particularly true if the ink has been

heated to the point that it is completely melted. The molten ink coalesces to form voids

in the pattern. Because the feature height is on the order of micrometers, subsequent

layers can also applied using the wire coater. Other materials can also be patterned on top

of previously sintered layers to form structures such as capacitors and resistor networks.

Because of the hard stops and the in-situ monitoring system, complete devices can be

fabricated. After the final layer is sintered and the unsintered material removed, the

circuit is fully functional without the need for any additional post-processing.

4.3 Experimental Results

The Selective Laser Sintering process was investigated using several experimental

studies. The DC and high-frequency conductivity of the sintered patterns was measured.

This work was conducted with Hjalti Sigmarrson from the School of Electrical and

76

Computer Engineering at Purdue University. Fabrication of resistive and dielectric

components on low-temperature substrates was also studied. Finally, the potential of

applying the technique to sinter copper thick-film inks was investigated in an ambient

environment compatible with other thick-film inks.

4.3.1 DC Conductivity

A parametric study of the process parameters was performed to characterize the

DC conductivity of sintered material. DuPont QS300, a standard silver-based thick-film

ink, conductors were written on soda-lime glass. QS300 has a specified sheet resistance

of 4.5 mΩ/ for a 10 μm fired thickness (at 850°C) which corresponds to a conductivity

of 2.22×107 S/m. Soda-lime glass has a glass transition temperature of ~550°C, which is

about 300°C lower then the specified sintering temperature of QS300. The laser power

and scan speed were swept over a range from 0.56 W to 3.92 W (measured at the

substrate) and 0.1 m/s to 1.0 m/s, respectively. The DC resistance was measured using an

Agilent 34401A digital multimeter and then the substrates recoated with a fresh layer of

ink, dried, and patterned again using the same parameters. The DC resistance was also

measured after the second layer. Figure 4.3 shows three of the test patterns written on

soda-lime glass. The wire between the connectors is 10 mm × 0.4125 mm. The test

patterns in the figure all have two layers of metallization. The number above the test

patterns shows the control power (Figure 4.2 shows the relationship between control

power and the power measured at the substrate).

Cross-sections of the test patterns shown in Figure 4.3(d-e) are plotted in Figure

4.4. For low laser powers and high scan speeds, the temperature of the ink is insufficient

to sinter it to the substrate and parts or whole areas of the pattern are removed during the

cleaning step as shown in Figure 4.3(a,d). For a range of laser powers and scan speeds,

77

the patterns are successfully sintered to the substrate, producing a relatively uniform

cross-sectional profile, as shown in Figure 4.3(b,e). Finally, for high laser powers and

low scan speeds, the temperature at the interface is high enough to melt the ink and

damage the substrate, as shown in Figure 4.3(c,f).

(a) (b) (c)

(d) (e) (f)

Figure 4.3: DC test patterns written at (a) 0.84 W, (b) 1.96 W, (c) 3.92 W (d) 0.84 W – 0.30 m/s, (e) 1.96 W – 0.20 m/s, and (f) 3.92 W – 0.10 m/s.

78

-5

0

5

10

15

20

-300 -200 -100 0 100 200 300

0.8406 W - 0.3 m/s1.9614 W - 0.2 m/s3.9228 W - 0.1 m/s

Hei

ght [m

]

Lateral Distance [m]

Power - Scan Speed

1 Layer

Melting and reflow

2 Layers

Damage to glass

Figure 4.4: Cross sectional profiles of the test patterns shown in Figure 4.3(d-f).

The DC conductivity for one and two layers of metallization is plotted in Figures

4.5(a) and 4.5(b), respectively. The figure shows that adding the second coat helps to

repair voids in the ink, particularly for high power and speeds where the ink has

coalesced due to melting. The average thickness of the patterns after two layers of

metallization measured by a depth-of-focus method using a microscope is 3 μm. This

gives the highest measured conductivity of 2.27×107 S/m and occurred for a laser power

of 2.24 W and a scan speed of 0.10 m/s. This value agrees with the specified value

produced by bulk sintering. Figure 4.5 shows that an optimum band exists, where

sintering is possible with high scan speeds combined with slightly higher laser powers to

produce acceptable conductivity.

79

Power [W]

Spe

ed [

m/s

]

1 1.5 2 2.5 3 3.50.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

10.0-0.30.3-0.60.6-0.90.9-1.21.2-1.51.5-1.81.8-2.12.1-2.4

Power [W]

Spe

ed [

m/s

]

1 1.5 2 2.5 3 3.50.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

10.0-0.30.3-0.60.6-0.90.9-1.21.2-1.51.5-1.81.8-2.12.1-2.4

Figure 4.5: DC Conductivity in S/m×107 after (a) one layer of metallization, (b) two layers of metallization.

(a)

(b)

80

4.3.2 High Frequency Performance

To evaluate the conductivity at microwave frequencies, /2 microstrip resonators

were fabricated using SLS along with their ground planes, using parameters from the

parametric study of the DC values. Two substrates were used, soda-lime glass and quartz,

with the geometry shown in Figure 4.6. Quartz was used because it has a lower loss

tangent, tan, than soda-lime glass (the loss tangent is the ratio of the imaginary to the

real portion of the complex dielectric constant, and determines the losses in the subtrate).

Quartz is not a low-temperature substrate, because its damage threshold is in excess of

850°C; however its thermal properties are similar to soda-lime glass (ρ=2200 kg/m3,

cp=670 J/kg·K, k=1.4 W/m·K for quartz and ρ=2470 kg/m3, cp=770 J/kg·K, k=1.05

W/m·K for soda lime glass). It is therefore assumed that the quality of the metallization

on quartz will be similar to that on soda-lime glass for a given set of process parameters.

Figure 4.6. /2 microstrip resonator on quartz.

The physical length of the resonator was chosen to be 15 mm on both substrates.

The microstrip widths were chosen to match a 50 Ω characteristic impedance using

Advanced Design System (ADS), an Electronic Design Automation software package

from Agilent (Palo Alto, CA) to be 2.130 mm and 1.365 mm for quartz and glass,

respectively. The gap between the resonator and the feed lines was tuned using High-

15.00 mm

1.175 mm

2.13 mm

81

Frequency Structure Simulation (HFSS), an electromagnetic finite element package from

Ansoft (Pittsburgh, PA) and was selected to be 1.175 mm for both designs. This provides

weak external coupling which enables accurate determination of the quality factor for the

resonators (Liu et al., 2004). The resonant frequencies from simulation were 4.308 GHz

and 5.423 GHz for glass and quartz, respectively.

The energy dissipation due to conductive losses lowers the unloaded quality

factor, QU, of the resonator (Pozar, 1998),

average energy stored

2energy lost/secondUQ f (4.1)

where f is the frequency. Because QU can be easily obtained from measurements with a

network analyzer, it provides a convenient way of characterizing the high-frequency

conductivity of the patterns produced by SLS. The resonator was simulated in Ansoft

HFSS for a range of conductivity values. For each simulation, the loaded quality factor,

QL, and the power transmission through the resonator, 21S , were extracted in order to

calculate the unloaded quality factor QU. QL is inversely proportionate to the 3 dB

bandwidth measured from the normalized resonant peak (Pozar, 1998). If the resonator

coupling is symmetric, the relationship between QU and QL is given by (Liu, 2004)

211

LU

QQ

S

(4.2)

The relationship between QU and the conductivity is plotted in Figure 4.7. A

curve fit of the simulated data produced the following equations 7 7.991.44 10 UQ (Glass) (4.3a)

7 6.678.51 10 UQ (Quartz) (4.3b)

where is the effective conductivity of the resonator.

82

40 50 60 70 80 90 100 110 1200

1

2

3

4 Simulated Quartz

Simulated Glass

Experimental Quartz

Experimental Glass

QU

[S

/m x

107 ]

3.9W 0.8 m/s (Quartz)

2.2W 0.5 m/s (Glass)

1.4W 0.1 m/s (Quartz)

2.2W 0.1 m/s (Quartz)

2.0W 0.1 m/s (Quartz)

Figure 4.7: QU versus conductivity for the microstrip resonators.

The fabricated resonators were measured using an Agilent 8720ES network

analyzer and QU was calculated. Using Eqs. (4.3a) and (4.3b), the conductivity was

extracted and plotted in Figure 4.7. The average measured resonant frequencies were

4.305 GHz and 5.486 GHz for the glass and quartz resonators, respectively. Figures 4.8

and 4.9 show a comparison between the measured and simulated values of the power

transmission through the resonators 21S .

The glass resonator is in close agreement with simulation, with less then a 0.1%

shift in the resonant frequency. For the quartz resonators, the shift is 1.26%. One

explanation for this is that the dielectric constant of quartz was acquired from Ramo et al.

(1993), because the supplier did not directly state the dielectric constant.

The metallization at microwave frequencies is comparable and in some cases

slightly higher than the conductivity from DC measurements. For the quartz resonators,

the relative difference ranged from 2.77% to 15.4%, for laser powers from 1.40 W to 3.92

W. The conductivity of the best resonator (1.96 W, 0.1 m/s) was 15.4% higher than the

83

corresponding value extracted from the parametric study and 5% higher than the quoted

value for DuPont QS300. The glass resonator written with 2.24 W had 92.7% of the DC

pattern conductivity.

The unloaded quality factor, QU, is made of contributions from the radiation, Qrad,

the dielectric, Qd, and the conductor, Qc, according to Pozar (1998)

1 1 1 1

U rad d cQ Q Q Q (4.4)

The metallization on both substrates can be compared by finding Qrad and Qd so that Qc

can be isolated. Qd is directly related to the loss tangent by Qd=1/tan. Figure 4.7 shows

that as the conductivity approaches infinity, the unloaded Q approaches an asymptote of

11rad dQ Q

. This value will be higher for quartz than for soda-lime glass and the QU

will be more sensitive to changes in metal conductivity.

For quartz, tan is well known to be ~0.0002. However the loss tangent for soda

lime glass is given as the range 0.01-0.05. For this reason a waveguide cavity

perturbation technique was used to find a more accurate value for the substrates used in

these experiments. The dielectric is placed in a waveguide cavity, this excites a resonance

in the dielectric, which change the resonant frequency and quality factor of the cavity.

Comparing the measured results with HFSS simulations gives the loss tangent of the

glass to be tanδ=0.011±0.001. The radiation loss was found from the HFSS simulations.

Table 4.1 summarizes these components for resonators written using optimal process

parameters.

Table 4.1: Quality factor components.

Qu Qrad Qd=1/tanδ Qc

Glass 56.54 439 90.91 226.75

Quartz 103.87 182 5000 254.26

84

-55

-50

-45

-40

-35

4.1 4.2 4.3 4.4 4.5

HFSSHFSS2.24 W - 0.5 m/s

S21

[dB

]

Frequency [GHz]

=2.25x107

=2.5x107

Figure 4.8: Comparison between simulation and measurement for glass resonator.

-40

-35

-30

-25

-20

5.3 5.4 5.5 5.6 5.7

HFSSHFSS1.40 W - 0.10 m/s1.96 W - 0.10 m/s2.24 W - 0.10 m/s

S21

[dB

]

Frequency [GHz]

=2.0x107

=2.5x107

Figure 4.9: Comparison between simulation and measurement for quartz resonator.

The values of Qc for both substrates are similar. The difference is partially

attributable to the large relative uncertainty of tan and the other material properties.

However, this experiment indicated that the quality of the metallization was of the same

85

quality for both quartz and soda-lime glass, even though the glass substrate could not

withstand the sintering temperature of the ink.

At DC or low frequencies the current is carried throughout the cross-section of the

conductor. However, at high frequencies, the current is carried predominantly along the

interface with the substrate and the edges of the pattern. Figure 4.10 shows the current

distribution inside the resonators obtained from the HFSS simulation. The skin-depth for

a conductor is given by Pozar (1998)

1

s

mf

(4.5)

where μm is the permiability. For a conductor with the specified conductivity of QS300

(2.27×107 S/m) the skin depth is only 1.49 μm at 5 GHz. This means that δs from the

interface and boundaries, the fields within the conductor will have decayed by 1/e (Pozar,

1998). From the perspective of SLS, this poses a significant challenge. The temperature is

lowest at the interface where the majority of the current is carried. An additional factor is

any roughness defining pattern edges will increase losses in the resonator and lower the

quality factor. Figure 4.7 shows that the best resonators were created using slower write

speeds. Figure 4.11 shows a profile for the DC test pattern written using 1.96 W and 0.40

m/s. It shows that the surface has significant roughness attributable to melting and

resolidification. There will always be a trade-off between generating sufficient sintering

temperatures at the interface and damaging the surface of the pattern with melting and

resolidification for the inks investigated in this work. However, for microstrip

transmission lines, the effects of additional roughness on the top surface appear to be

minimized because the current density is lower than at the interface. The thermal profile

inside the sintered pattern during sintering will be further explored in Chapter 5.

86

Figure 4.10: Current distribution in the resonator from HFSS.

0

0.5

1

1.5

2

2.5

3

3.5

4

-200 -100 0 100 200

Hei

ght [m

]

Lateral Distance [m]

Power: 1.96 WSpeed: 0.4 m/s

Figure 4.11: Profile across DC line written at 0.4 m/s and 1.96 W.

4.3.3 Feature Size

As previously mentioned, there is considerable motivation to fabricate small

feature sizes. The minimum feature size producible, with the setup described in Section

4.2, was investigated using several thick film inks on glass substrates. The smallest

features are created when the laser is passed once along a line without any rastering.

Figure 4.12 shows the cross-sectional profiles for lines created by sintering DuPont

QS300 on a glass substrate. The lines in Figure 4.13 were created by moving the laser at

87

0.4 m/s for different laser powers and the lines in Figure 4.14 were created by exposing

the substrate to 1.40 W of laser power and different scanning speeds.

0

0.5

1

1.5

2

2.5

3

3.5

4

-40 -20 0 20 40

1.40 W2.24 W3.08 W3.92 W

Hei

ght [m

]

Lateral Distance [m]

Power

Figure 4.12: Cross sectional profiles for lines written at 0.4 m/s.

0

0.5

1

1.5

2

2.5

-40 -20 0 20 40

0.1 m/s0.2 m/s0.3 m/s0.4 m/s

Hei

ght [m

]

Lateral Distance [m]

Speed

Figure 4.13: Cross sectional profiles for lines written with 1.40 W.

88

When the laser was only passed along the line once, two bumps are formed on

either side of the centerline of the laser. This indicates that where the irradiance of the

laser and therefore the temperature is highest, the ink is melted and flows laterally due to

Marangoni effects. In addition, the sintered lines are wider because the intensity at a

given point lateral to the center point is greater for higher power. For low enough power

(or fast enough speed), the temperature developed on the ink is not sufficient to melt

down to the surface of the glass.

The best feature sized produced was continuous lines with widths less than 25

μm. Figure 4.14 shows these lines on a 100 μm pitch. The lines were created by moving

the laser across the ink layer once at a speed of 0.4 m/s and a power of 1.12 W on the

substrate. The unsintered ink was removed by placing the substrate in a methanol bath in

an ultrasonic cleaner.

Figure 4.14: Photograph of 25 μm wide lines on a 100 μm pitch.

For the proper power and speed, the feature size is on the same order as the laser

spot diameter. Smaller features can be created by further reducing the laser spot size.

Additionally, if the substrate is recoated in-situ, it is believed that features with higher

100 μm

89

aspect ratios can be created by printing multiple layers. An additional option for further

reducing feature size is to use a pulsed laser (for example the Nd:YLF laser used for the

MAPLE-DW investigation) to ablate lines immediately adjacent to the pattern. Then the

fiber laser can be used to trace along the pattern to produce features sizes smaller than the

spot size of the sintering laser. However, this technique may be difficult to implement on

low-temperature substrates that are not laser transparent because the regions of the

substrate where the ink has been ablated will be directly exposed to the sintering laser.

4.3.4 Sintering on Polymer Substrates

Selective Laser Sintering has exciting potential for fabricating functional

microelectronic components on polymer substrates. However, as will be shown in the

next chapter, temperatures well in excess of the damage threshold of most polymers

extend several μm into the substrate. Several inks, such as Heraeus C8772, have been

designed to be sintered at 475-525°C. This is lower than the standard thick-film sintering

temperature but still considerably higher than glass transition temperature, Tg=140°C, of

FR4, a standard glass-epoxy substrate used with microelectronics.

Because of its lower firing temperature, Heraeus C8772 was used in the

experiments on polymer substrates. This is a commercial thick-film fritted silver

conductive paste. The quoted sheet resistance for this ink is 5.0 m/ at 14 μm fired film

thickness which corresponds to a conductivity σ of 1.43107 S/m. To investigate the laser

sintering process on low temperature substrates, another DC conductivity study was

performed using Heraeus C8772 on an FR4 substrate. Because of its wide use, low cost

and low damage threshold, FR4 is a good material to demonstrate the technique on.

When drying the ink in a convection oven, it was found that if FR4 is exposed to 150°C

for longer than 10 minutes, its color begins to change indicating the onset of damage.

90

Because the samples are not dried for as long as those on glass substrates, more

organics are left in the ink. This causes problems because of the rapid phase change of

the organics when superheated by the laser. However, it was found that this effect was

somewhat mitigated when the laser was moved at slower speeds and lower power.

Because heat is transferred via conduction ahead of the laser beam, the organics can be

driven off in-situ. This produces visible smoke and a small fan was added to the setup to

help blow away the vaporized organics and prevent them from scattering the laser light.

A series of lines 15 mm long and 500 μm wide were written between contacts

similarly to the parametric sweep for QS300 on glass. These lines were written with a

single coat of ink and sintered at speeds ranging from 0.05 to 0.8 m/s. The undamaged

patterns had a thickness of ~2 μm measured with the depth of focus method using the

100X microscope objective. Figure 4.15 shows the conductivity as a function of laser

scan speed. The best conductivity was produced when the power of the laser was set to

1.121 W and the laser scanned at 0.4 m/s. These settings produced a line with 57% of the

conductivity specified for the ink sintered using the standard procedure.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.2 0.4 0.6 0.8 1

0.56040.84061.1211.4011.681

[S

/m x

107 ]

Speed [m/s]

Power [W]

Figure 4.15: DC conductivity for Heraeus C8772 lines on FR4.

91

When the power of the laser was set to 1.62 W, all the patterns were measured to

be open. This is largely due to the onset of runaway heating. The runaway heating occurs

when the opaque substrate is heated to the point that it combusts. The oxidation causes

the substrate to be visibly charred and turn black, causing its absorptivity to dramatically

increase which increases the temperature in the surrounding material. The condition often

occurs when the laser slows down to change directions when rastering to fill in a solid

area. After the onset of damage the charred area propagates along the laser path even

though the thermal profile would not be sufficient to cause damage if the absorptivity had

not changed. This effect can be avoided by turning off the laser during the period when it

is decelerating and accelerating. Using a laser transparent substrate helps because the

material will not directly absorb the laser; hence if there is a hole in the ink film it will

not lead to the initiation of the runaway heating event. A third option is to measure the

temperature on the surface of the ink in-situ and construct a feedback loop to control the

power of the laser.

One of the primary uses of metallizing low-temperature substrates is fabricating

microwave components such as antennas. To demonstrate the suitability of SLS for this

application, a 4.9-GHz microstrip fed patch antenna was designed and fabricated. Figure

4.16 shows a photograph of the patch antenna. It was tested and compared with

simulation and patch antennas fabricated using conventional techniques. The results were

in good agreement and are covered in more detail in Sigmarsson et al. (2005).

The SLS technique can also be applied to thin-film substrates such as Mylar.

Mylar is attractive because it is transparent, flexible and widely available. Flexibility will

permit it to be fed in a reel-to-reel setup for higher throughputs. It also permits conformal

(3D) devices to be fabricated by folding or forming a 2D substrate. A two-dimensional

pattern is much easier from a manufacturing standpoint. However, using the setup

92

described in this thesis, the flexibility of this substrate poses a challenge for coating it

with ink and positioning it in the fixture. For this reason, the Mylar was fixed to a glass

slide with double sided tape. This helped hold the Mylar flat during coating, drying and

sintering, and removed when the process was completed. Figure 4.17 shows a microstrip

patch antenna pattern fabricated on a flexible Mylar substrate.

Figure 4.16: Patch antenna fabricated on FR4 substrate using SLS.

Figure 4.17: Patch antenna pattern on flexible Mylar substrate fabricated using SLS.

93

Because of the low thermal damage threshold of polymer substrates, lower laser

powers must be used for sintering them. This produces poorer electrical properties than

can be produced using higher temperature substrates such as glass. The poorer electrical

properties can be overcome by using the SLS process to pattern the flexible substrate and

then electroplating this pattern which produces conductivity close to bulk copper. Before

it is electroplated, the patterned substrate can be conformed/folded to form a 3D shape

which is a useful feature for the manufacturing of several devices, including antennas.

Electroplating is commonly used in industry for metallizing flexible electronics;

however, the standard approach is to use photolithography to either etch a laminated

pattern, or thin film processes to provide a seed layer (Gilleo, 1992).

4.3.5 Sintering of Resistive and Dielectric Elements

Although most of this work is dedicated to work on conductors, some preliminary

investigations were undertaken to investigate the SLS technique for fabricating resistive

and dielectric elements. These components are integral parts in most microelectronic

devices. Resistive and dielectric thick-film inks are well established for fabrication using

the conventional screen printing process. The ability to pattern and process dielectric and

resistive components using thick-film technology allows the passive components to be

integrated into the substrate or into a device to form a hybrid circuit. This offers

advantages over soldering surface mount components to the substrate, both in terms of

size, performance, and reliability in applications subject to vibrations and mechanical

shock (Licari and Enlow, 1998).

The procedures described in Section 4.2 can be applied with resistive and

dielectric inks. The optical absorptivity of resistive inks is much greater than silver-based

inks, which allows much lower powers to be used to pattern resistors. An additional

94

benefit of the using the laser to sinter these devices is that their properties can be tuned

with the laser. The conductivity of the resistive inks is a function of the laser parameters,

just as it is for the silver based conductors.

Another advantage of Selective Laser Sintering is that complete passive designs

can be realized using a simple manufacturing setup. Resistive, dielectric and conductive

layers can be fabricated without the need for multiple masks. For example, Figure 4.18

shows two silver conductors electrically isolated from each other with a layer of

dielectric (DuPont QM44) fabricated on glass using this procedure. The silver patterns

were patterned using Heraeus C8772 with 2.24 W of laser power and a scan speed of 0.2

m/s. The dielectric was processed with 3.36 W of laser power and a scan speed of 0.04

m/s. The higher power and slower speed are required to pattern the dielectric because it

does not absorb the laser irradiance as well as the silver ink.

Figure 4.18: Micrograph of two silver conductors electrically isolated from each other with a layer of dielectric.

As with conventional screen printing, the presence of pinholes in dielectric films

presents a non-trivial challenge. This can be overcome by sintering multiple layers of

Dielectric

Silver

95

dielectric to help repair any gaps in previous layers. The dielectric layer in Figure 4.18

was formed by coating and sintering the pattern 4 times. This was necessary because

dielectric was melted and resolidified. Figure 4.19 shows Scanning Electron Microscope

(SEM) images of the component shown in Figure 4.18.

Figure 4.19: SEM images of silver line passing over dielectric layer shown in Figure 4.18.

4.3.6 Sintering Copper Inks in an Ambient Air Environment

Copper has a conductivity similar to silver but is much less expensive. This factor

is very attractive because its price does not fluctuate and secure facilities are not required

for manufacturing. It also adheres better to ceramic substrates than gold does and has

better solderability and solder leach resistance. However, it rapidly oxidizes when

exposed to oxygen at high temperatures and must be fired in nitrogen. This causes

100 μm

Dielectric

Silver

Glass

Glass

Silver

Dielectric

10 μm

96

problems because the organic binders require burnout by oxidation, which makes thick-

film copper pastes incompatible with standard dielectric and resistive pastes.

Additionally, even after firing, copper is susceptible to corrosion and must be protected.

The additional cost of nitrogen and specialized inks offset much of the cost savings

(relative to the total cost of the device) generated by the lower cost of copper (Licari and

Enlow, 1998).

Because both heating and cooling are very rapid in Selective Laser Sintering, it

can be used to sinter copper while minimizing the amount of oxidation. The same

procedure that was used for sintering the silver-based inks was used with the exception

that the drying process was shortened. Thick-film copper inks begin to oxidize above

120°C. The substrates were coated with wet ink and placed in the oven at 150°C, but

were removed as soon as the solvent was visibly driven off (between 30 and 60 seconds).

This leaves some volatile organic material in the solvent but prevents oxidation. It was

found that if the wet substrate was dried at 150°C for 10 minutes or more, a thick oxide

layer was formed and the substrate was unusable.

The presence of organic material prevents the laser from being moved at high

speeds because of the need for in-situ drying by the laser. As mentioned previously, if the

laser is moved too quickly the organic material undergoes an explosive phase change

which damages the pattern. Because of melting of the ink and damage by the

vaporization of the solvent, a noticeable porosity occurs in the sintered pattern. A dry rag

was used to clean the substrate. The intention of this was to infiltrate any pores or

discontinuities with unsintered dry ink. The pattern was traced a second time with the

laser to sinter the added material before being finally cleaned with methanol.

Figure 4.20 shows a DC test pattern for copper wires between silver contacts.

There are two layers of metallization on the wires and Figure 4.21 shows micrographs of

copper wires written at 0.1 m/s at several different laser powers. Figure 4.21(c) shows

97

how the ink coalesces after it has been melted by the laser. The maximum conductivity

was found to be 1.43 × 107 S/m for a power of 2.24 W and 0.01 m/s. This is 24% of the

conductivity of bulk copper.

Figure 4.20: Copper wires between silver contacts with fabricated a laser power of 3.1 W at the substrate.

(a) (b) (c)

Figure 4.21: Micrographs of copper lines sintered with (a) 1.1 W, (b) 1.7 W, and

(c) 2.2 W.

98

Small features can also be created using this technique. Figure 4.22 shows an

array of thin lines written at several different speeds. Profilometer measurements are

shown in Figure 4.23 for a laser power of 3.92 W. Some of these lines have widths less

then 20 μm; however, considerable variation exists in the line thickness and line height,

particularly for slower speeds. This is attributable to melting and coalescing during

resolidificaiton. 3.92 W 3.08 W 2.24 W 1.40 W

Figure 4.22: Photograph of thin copper lines sintered at various speeds and powers.

0.1 m/s 0.2 m/s 0.3 m/s 0.4 m/s 0.5 m/s 0.6 m/s 0.7 m/s 0.8 m/s 0.9 m/s 1.0 m/s

99

0

2

4

6

8

10

12

0 200 400 600 800 1000

0.2 m/s0.4 m/s0.6 m/s0.8 m/s1.0 m/s

Hei

ght [m

]

Lateral Distance [m]

Speed Power: 3.92 W

Figure 4.23: Profilometer measurements for lines sintered at 3.92 W.

4.4. Conclusion

This chapter has demonstrated the use of Selective Laser Sintering for the

fabrication of thick-film microelectronics. This technique can be used with conventional

thick-film inks and has several advantages, notably it can be used for rapid prototyping

and low-volume production, it can sinter low-temperature substrates, and it can be used

with multiple materials. Because SLS is a rapid process, it can also be used to sinter

copper and other materials that oxidize at high temperatures.

100

5. NUMERICAL MODELING OF SELECTIVE LASER SINTERING

The selective laser sintering process was modeled using the finite element method

to calculate the thermal profile inside the ink layer and the substrate. This chapter

presents a 3D thermal model of the laser beam scanning over an ink coated substrate.

Effective material properties are used to represent the ink and the effects of the different

process parameters, particularly the laser scan speed and laser power on the profile are

discussed and compared to experimental results.

5.1 Introduction

The finite element method is a valuable way to study the effects that the laser and

other experimental parameters have on the sintering process. It has been used previously

for studying conventional selective laser sintering by Kolossov et al. (2004). However, to

the author’s knowledge, no in-depth investigations have been conducted of laser sintering

for thick-film microelectronics.

The goal of the investigation is to study the influence of the different process

parameters on the thermal profile developed by the laser inside the ink layer and

substrate. In bulk sintering, material densification is a function of the sintering

temperature and the dwell time at this temperature. Electrical properties should

correspond to the density of the functional particles after sintering (Marinov, 2004). For

example, if the silver particles in a conductor are heated to a higher temperature, the final

component should have lower resistivity than a component that was fired at a lower

101

temperature because more junctions will be formed between the silver particles as the

temperature increases.

For selective laser sintering, both the heating and cooling are very rapid compared

to the designed firing profile for thick-film inks shown in Figure 1.11. In addition, the

heating inside the ink layer is not uniform. However, Chapter 4 showed that functional

parts with electrical properties matching those from the ink manufacture for furnace-fired

components can be fabricated by laser sintering. Experimental results showed that the

electrical conductivity of silver conductors fabricated by selective laser sintering is a

function of laser power and laser scan speed. The thermal profile developed inside the

ink and substrate is also a function of these parameters. This chapter helps to identify

what effect the thermal profile has on the functional performance of the electrical

component. The laser parameters also control the morphology of the final component,

including the surface and edge quality of the component and the minimum obtainable

feature sizes.

It is difficult to measure the thermal profile inside the ink layer in-situ. However,

given the material properties and laser parameters, the thermal profile can be modeled

using numerical simulation. This chapter presents a 3D model for the selective laser

sintering process, including interactions between the ink layer and substrate. Because of

uncertainties in the material properties, the results cannot be definitely made to

correspond to a specific experimental case. However, the insight gained into the

selective laser sintering process is valuable for understanding the limitations and

possibilities of the process.

102

5.2 Heat Transfer Analysis

This section describes the model for the laser interaction with the ink, the

coupling of radiative energy to thermal energy, and its dissipation due to thermal

conduction. The purpose of the model is to simulate the experiments described in

Chapter 4. The commercial finite element code ABAQUS (HKS, Inc., Pawtucket, RI) is

used for this investigation.

5.2.1 Thermal Analysis of Selective Laser Sintering

The interaction of the laser with the ink is modeled as a volumetric heat source

moving at a constant velocity. For a laser with Gaussian beam profile, the laser flux at a

point ,x y on the surface can be expressed as

2 2

0 00 2

0

( , ) exp 2x x y y

I x y Ir

(5.1a)

where 0 0,x y is the center of the focal point of the laser, 0r is the beam radius, and 0I is

the laser irradiance at the center of the beam. When the laser is scanned across the

sample, the focal point will change so that 0 0 0 0, ,x yx y x v t y v t (5.1b)

where xv and yv are the velocities in the x and y directions, respectively and 0 0,x y is

the location of the focal point of the laser at 0t . For the simulations considered here,

the beam is scanned along the x direction at a constant velocity.

The laser flux is related to the laser power, P t , by

,A

I x y dA P t (5.2a)

103

For a continuous wave (CW) laser with a Gaussian profile, the laser power is constant

with respect to time. Combining Eqs. (5.1a) and (5.2a) gives

0 20

2PI

r (5.2b)

The laser energy is absorbed by the ink according to Lambert’s law. This provides

an exponential attentuation of the absorbed laser energy. The ink layer is opaque and any

incident laser energy will be either absorbed or reflected. Combining the attentuation and

surface reflection terms gives the laser intensity profile within the ink layer as ( , , , ) (1 ) ( , , ) expfq x y z t R I x y t z (5.3)

where fR is the optical reflectivity of the ink. The absorption coefficient, a , is given by

4

a

(5.4)

where is the imaginary part of the complex index of refraction for the ink. Both

and fR are effective properties because of the composite nature of the ink. As the ink

layer is heated, the composition of the ink changes due to the burn out of the temporary

organic binders, the fusion of the permanent binders with the substrate and the sintering

of the silver particles. The depth of focus of the laser beam is long enough that the beam

radius can be considered constant for the affected region of the ink. There could be some

scattering of incident radiation within the ink layer, but this effect is not considered.

The volumetric distribution of the heat source term generated by the absorbed

laser energy is given by

(1 ) ( , , ) expab f

dqQ a R I x y t z

dz (5.5a)

104

Combining Eq. (5.5a) with Eqs. (5.1a), (5.1b), and (5.2b), the heat source term is

obtained as

2 2

0 02 2

0 0

2(1 ) exp 2 expx

ab f

x x v t y yPQ a R z

r r

(5.5b)

The three-dimensional transient heat conduction equation that governs the heat

transfer within the material is

( )p ab

Tc k T Q

t

(5.6)

where pc is the specific heat, is the density, and k is the thermal conductivity of the

medium (either the ink or the substrate). The laser source is modeled by a discrete source

term, with the center advancing according to Eq. (5.5b). The time step must be small

enough that the continuously moving volumetric term can accurately approximate the

scanned laser beam.

Successful sintering requires that at least some of the ink undergo a phase change.

The glass frit will be heated to the point that it wets the functional particles and fuses

with the substrate. Additionally, the temperature at the surface of the ink may be

sufficient to melt the silver particles themselves. The melting and resolidification of parts

of the ink consumes and releases additional latent energy. These latent heat effects can

be modeled by replacing the specific heat, pc , from Eq. (5.4) with an effective specific

heat, pc , that includes latent heat effects. This parameter is the derivative of specific

enthalpy with respect to temperature. Impure materials begin to melt at a solidus

temperature, sT , and are completely liquid when the temperature is above the liquidus

temperature, lT . The latent heat of fusion, fgh , can be assumed to be linearly distributed

105

from the solidus temperature to the liquidus temperatures (the mushy zone), s lT T T ,

so that

,

p s l

p fgp s l

l s

c T T T T T

c T hc T T T T

T T

(5.7)

Using an effective specific heat in the mushy zone permits the entire ink layer to be

treated as a continuous medium modeled by a single domain without calculating the

phase boundaries explicitly (Zhang, 2004).

5.2.2 Boundary Conditions

During the sintering process, some of the heat will be transferred to the

surroundings via convection and radiation. In the experimental setup, a fan forces

ambient air over the surface of the ink as it is sintered. The air flow removes some heat

via convection although its main purpose is to blow away the temporary organic binders

that evaporate from the ink as it is sintered. The convection heat flux at the surface can

be modeled by Newton’s Law of cooling

convection f surfq h T T (5.8)

where h is the convection coefficient, fT is the temperature of the air, and surfT is the

temperature of the surface. Because the temperature of the surface will always be greater

than that of the surrounding air, the heat transfer will be from the surface of the ink to the

surroundings. Although the formulation in Eq. (5.8) assumes a constant convection

coefficient, a more accurate consideration of convective heat transfer would calculate the

convection coefficient as a function of the geometry of the substrate and test fixture.

However, heat transfer from convection is much smaller than the heat generation from

the laser.

106

The surface of the ink will also exchange radiation with the surroundings

according to the Stefan-Boltzmann law. If the ink is assumed to be a gray body, it will

absorb and radiate energy with the same absorbtivity and emmisivity. The net heat

exchange with the surroundings due to radiation is given by

4 4radiation surfq T T (5.9)

where is the emissivity, is the Stefan-Boltzmann constant which has a value of

5.670×10-8 W/m2·K, and T is the temperature of the surroundings. Both radiation and

convection boundary conditions are modeled in ABAQUS; however, their contribution to

the overall heat transfer is minor in comparison to the laser heat flux.

There will also be evaporative cooling as the temporary organic binders are

heated above their vaporization point during the sintering process. The heat flux due to

evaporative cooling can be approximated by evap A fgq n h (5.10)

where An is the mass flux rate of material leaving the surface, and fgh is the latent heat

for this material. It is very difficult to incorporate this mode of cooling into the

simulation because changing the material properties in a nonreversible manner cannot be

modeled without significantly complicating the simulation. Fortunately, the amount of

heat that is removed through evaporative cooling is negligible with respect to the heat

generated within the ink layer by the laser.

There will be heat transfer via conduction across the interface between the

substrate and ink layer. The ink is assumed to completely wet the substrate, so that the

contact resistance is neglected. Because the heat flux leaving the ink must be equal to

that entering the substrate, the thermal profile at the interface is governed by

107

i s

T Tq k k

z z

(5.12)

where ik and sk are the thermal conductivities of the ink and substrate, respectively.

The z direction is oriented normal to the interface between the substrate and the surface

and the plus and minus signs indicate the side of the discontinuity at the interface where

the gradient is to be measured. A uniform profile in the ink and a sharp decline in

temperature within the substrate is desirable for sintering; therefore, the ratio of the

thermal conductivity of the ink to the thermal conductivity of the substrate should be

maximized.

5.3 Material Properties

The exact material composition of the thick film-inks used in this research is

proprietary and a source of great frustration. However, from the Material Safety Data

Sheet (MSDS) for QS300, the ink is initially more than 60% silver by weight. The silver

is in the form of particles with diameters on the order of 1 μm. The ink also has up to 5%

glass constituents which form a matrix for the silver particles. The volatile organic

constituents and any added thinner are assumed to have been completely driven off

because the ink film is dried in a convection oven prior to laser sintering. The intent of

this model is to analyze the sintering process of thick-film inks in general and not to

simulate the sintering of a specific thick-film ink. The material properties are selected to

represent a typical highly silver loaded thick-film ink.

For the model presented in this thesis, the ink is considered to be 90% silver and

10% soda-lime glass by mass. The two main constituents of a thick-film ink are the

functional particles (silver) embedded in a glass frit matrix that will adhere to the

108

substrate. The substrate is modeled as pure soda-lime glass and intended to represent a

typical glass microscope cover slide.

The density and specific heat of the ink are taken to be the mass weighted

averages of the constituent properties. The density of silver is 10,490 kg/m3 and soda

lime glass is 2500 kg/m3 at 300 K. Because of the unavailability of density data at higher

temperatures, these values are taken as constant with respect to temperature; however,

this in not a good assumption because the sintering process is known to cause

densification. The density of the ink is taken to be 9691 kg/m3. The temperature

dependant thermal conductivities and specific heats of silver and soda lime glass used are

shown in Figures 5.1(a) and 5.1(b). The thermal conductivity and specific heat data for

silver are taken from Incropera and Dewitt (1996), the thermal conductivity data for soda

lime glass is taken from Kiyohashi et al. (2002), and the specific heat data for soda lime

glass is interpolated from Touloukian (1972).

The effective thermal conductivity is calculated using the Maxwell effective

medium theory derived for effective electrical conductivity (Wang et al., 1999). This

approach is valid for a random suspension of spherical particles in a homogeneous

medium. The thermal conductivity has an identical mathematical formulation to the

electrical conductivity

1 00

1 0

31

2ek

k kkk k

(5.13)

where is the volume fraction of the spherical inclusions, and 0k and 1k are the thermal

conductivities of the medium and spherical inclusions, respectively. Maxwell’s formula

is only valid for dilute suspensions because it assumes that the spheres do not interact

thermally. Figure 5.2 shows the specific heat and thermal conductivity used when

simulating the ink.

109

220

230

240

250

260

270

280

290

300

340

360

380

400

420

440

0 500 1000 1500

Specific Heat

Thermal ConductivitySpec

ific

Hea

t [J/

kg K

]

Therm

al Conductivity [W

/m K

]

Temperature [K]

(a) Silver

600

800

1000

1200

1400

1600

1800

0.5

1

1.5

2

2.5

3

3.5

0 500 1000 1500

Specific Heat

Thermal Conductivity

Spec

ific

Hea

t [J/

kg K

]

Therm

al Conductivity [W

/m K

]

Temperature [K]

(b) Soda-lime Glass

Figure 5.1: Specific heat and thermal conductivity for (a) silver, and (b) soda-lime glass.

250

300

350

400

450

500

6

8

10

12

14

16

18

20

22

200 400 600 800 1000 1200 1400 1600

Specific Heat

Thermal Conductivity

Spec

ific

Hea

t [J/

kg K

]

Therm

al Conductivity [W

/m K

]

Temperature [K]

Figure 5.2: Effective specific heat and thermal conductivity used for simulating ink.

110

Pure silver has a melting point of 1235 K and a latent heat of 103 kJ/kg. From Eq.

(5.7), these have a significant effect on the specific heat of the material and must be

included in the model. Glass does not have a definitive latent heat. As the glass frit is

heated, it experiences a glass transition rather than a definitive melting process. Because

there is much more silver by mass, it can be assumed that the effects of the glass

transition are negligible. The latent heat of silver is weighted by the mass fraction of

silver. The solidus temperature is taken to be the melting point of silver and the range of

the mushy zone is taken to be 20 °C. Using a larger mushy zone helps reduce the

magnitude of nonlinearities that cause the numerical solver to have problems converging.

The dried ink reflects the incident laser beam diffusely, and the reflectivity of the

dried ink was measured to be 0.45 using an integrating sphere. This value for reflectivity

is considerably less then 0.99, the normal spectral reflectivity at the wavelength of 1100

nm for pure silver from Touloukian (1972). The transmission through the ink layer was

also measured to be negligible. A possible explanation for the lower reflectivity of the

dried ink layer is that the ink layer is a composite material consisting of ink particles of

the order of 1 μm in diameter. These silver particles scatter the incident laser beam

locally, and some of the reflected light is directed toward other particles instead of

returned to the ambient. This allows the small absorbance of the silver particles to be

compounded so that the effective absorptivity is much higher.

The imaginary portion of the dielectric constant of silver is 7.47 at the wavelength

of 1100 nm at 20°C. The glass frit in the ink may be assumed to be completely

transparent to the laser wavelength. Because of the multiple reflections/absorptions

within the ink layer, the absorption depth may be up to the order of the silver particle size

(about 1 μm). The absorption depth, d, is inversely proportional to the absorption

coefficient, and from Eq. (5.4) an absorption depth of 1 μm corresponds to an effective

imaginary portion of the dielectric constant of 0.088. For the simulations, a value of 3.50

111

was used for the dielectric constant of the ink. This corresponds to an absorption depth

of 25 nm.

Both the reflectivity and the absorption coefficient could be better modeled using

ray tracing. In reality the ink layer has nontrivial porosity after drying due to the small

voids formed when the organic portions of the wet ink are driven off during the drying

process. This will serve to reduce the density, specific heat, and thermal conductivity.

Because of irreversible changes to the composition of the ink during the laser sintering

process, the ideal situation would be to observe the reflectivity and other properties in-

situ. Despite the rudimentary first order estimations for the material properties of the ink

layer, the model is representative of the experimental phenomena and insight into the

effects of the process parameters including changes to material composition of the ink are

still relevant.

5.4 Numerical Simulations

The 3D mesh used in the model is shown in Figure 5.3. The simulation domain is

150 μm wide and 200 μm long. The ink layer and the substrate are 3 μm and 75 μm thick,

respectively. These two regions share a common set of nodes at the interface. The laser

is scanned for 100 μm in the x-direction along the centerline of the sample starting at 50

μm from the edge. The laser beam in normally incident on the surface of the ink and has

a radius of 10 μm. To reduce the simulation time, the symmetry about the center plane is

exploited by assigning an adiabatic boundary condition at this plane.

The model uses a total of 99,200 nodes and 92,070 elements. The mesh is

uniform along the x direction (the direction along which the laser is scanned). However,

it is more densely spaced in the y and z directions near the laser path where the thermal

gradients are high. The symmetric mesh has 100 nodes in the x direction and 32 nodes in

112

the y direction (if the symmetry condition were not used, the full domain would have 63

nodes). In the z direction, the substrate layer has a total of 20 nodes while the ink layer is

12 nodes thick. As mentioned previously, these two layers have the entire xy interface

plane of nodes in common. Both the ink and substrate regions of the mesh are modeled

using DC3D8 elements. These are 3D, 8-node linear brick elements for heat transfer

from the ABAQUS element library.

Figure 5.3: Mesh used for finite element model of selective laser sintering.

The interaction with the laser is modeled by applying a heat source term to the ink

layer. The substrate is assumed to be transparent and not to absorb any energy from the

Symmetry Plane

Ink

Substrate

113

laser directly. The exposed surface of the ink is modeled using convection and radiation

boundary conditions. A constant convection coefficient of 20 W/m2·K is used to account

for the air flow over the surface, and an emissivity of 0.10 is assumed. Both the ambient

surroundings and the air flow are assumed to be at 20°C. The nodes on the exterior

boundaries of the model also have fixed temperatures of 20°C because the substrate is in

contact with a large metallic thermal mass.

The simulations in this chapter each took approximately 74 hours on a

workstation equipped with two 1.8 GHz Intel Xeon processors and 1 GB of RAM. The

standard ABAQUS solver was used for this simulation. The simulations that used more

laser power and produced melting and resolidification took longer. This is because it

takes longer for the numerical solver to converge to a solution when the thermal gradients

are higher, and the phase change causes nonlinearities.

5.5 Results

The depth is measured from the interface between the substrate and the ink film

and oriented so that z=3 μm corresponds to the surface of the ink. The focal point of the

laser starts at x=0 μm (50 μm from the edge) at time t=0. It is scanned across the

substrate at a constant velocity and finishes 100 μm from the starting point and 50 μm

from the opposite edge. Because the heat is conducted away from the focal point, it is

important to know how quickly the ink reaches a consistent thermal profile. This

consideration determines the quality of the lines and features that can be created while

moving the laser with a constant speed and a constant profile.

Figures 5.4 and 5.5 show the maximum temperature reached for nodes along the

central xz plane at different depths for laser scan speeds of 0.1 m/s and 0.4 m/s. All of the

results shown in Figures 5.4, 5.5, and 5.6 used 2.0 W of power incident on the substrate.

114

The dashed lines in the figure show the maximum temperature at each depth for the entire

simulation. The small ripples in the temperature are caused by the fact that the time-

temperature data for the model is recorded only every 10 time steps; for a given location,

the time when the focal point is coincident with the corresponding node may not be

recorded. This is more noticeable for the nodes closer to the surface because the

temperature declines more rapidly with respect to time at these points. For both scan

speeds, the layers farther from the surface reach a consistent thermal profile later than the

surface does. Figure 5.6 shows the maximum temperatures reached for nodes along the

centerline of the interface for different scan speeds. It is observed that the faster the laser

is moving, the smaller the distance necessary for the thermal profile to reach equilibrium.

0

200

400

600

800

1000

1200

1400

-50 0 50 100 150

3.00 0.00 -4.85 -8.95

Tem

pera

ture

[°C

]

Distance [m]

Depth [m]

2.0 W0.10 m/s

Figure 5.4: Maximum temperature attained for various depths measured from the interface using 2.0 W of laser power and a scan speed of 0.10 m/s.

115

0

200

400

600

800

1000

1200

-50 0 50 100 150

3.00 0.00 -4.85 -8.95

Tem

pera

ture

[°C

]

Distance [m]

Depth [m]

2.0 W0.4 m/s

Figure 5.5: Maximum temperature attained for various depths measured from the interface using 2.0 W of laser power and a scan speed of 0.40 m/s.

0

200

400

600

800

1000

1200

-50 0 50 100 150

0.10 m/s 0.20 m/s 0.40 m/s

Inte

rfac

e T

empe

ratu

re [

°C]

Distance [m]

Speed

Power2.0 W

Figure 5.6: Maximum temperature attained along the centerline of the ink-substrate interface for 2.0 W of laser power.

116

Figure 5.7: Thermal profile for a laser power of 2.0 W and a scan speed of 0.10 m/s. (a) surface xy plane – z=3 μm, (b) cross section of central xz plane – y=0 μm, and (c) cross

section of yz plane – x=90 μm.

Figure 5.7 shows a contour plot of the temperature profile in the system for a line

scanned with 2.0 W of power and a scan speed of 0.10 m/s. The center of the laser is

located 90 μm from the start of the line, and from Figure 5.4, it is assumed that the

thermal profile has stabilized so that it will be the same with respect to the time that the

laser passes the point (it will not depend on the distance along the scan path). Figure 5.7

1250

1045

840

635

430

225

20

Temperature [°C]

50 μm

(a)

(c)

117

shows that, for this scenario, the area heated above the sintering threshold will be much

greater than the 20 μm laser spot size. The figure also shows that the thermal profile is

confined near the ink-substrate interface. Although the portion of the substrate near the

interface will be melted, the size of this region will be limited.

The thermal profile inside the ink is plotted with respect to depth and time for a

scan speed of 0.10 m/s and a laser power of 2.0 W in Figures 5.8 and 5.9, respectively.

The time shown in these figures is indexed so that at time t=0 the laser is directly focused

at the point z=3 μm. The same information is plotted for a scan speed of 0.40 m/s and a

laser power of 2.0 W in Figures 5.10 and 5.11. For both cases the temperature profile is

far enough from the starting point of the laser that it has reached steady state (x=67.17

μm and x=57.07 μm for the 0.10 m/s and 0.4 m/s scan speeds, respectively). These

distances were selected because the time steps were recorded to include the time when

the laser was directly over the points.

Both Figures 5.8 and 5.10 show the discontinuity at the interface due to the

difference in thermal conductivities in the ink layer and substrate. This discontinuity

indicates one possibility for optimizing the system. From Eq. (5.12), if the ratio of the

thermal conductivity of the ink to that of the substrate is increased, so will the difference

in the slope of the thermal profile at the interface. This is advantageous because

increasing rate at which the temperature decreases with respect to depth within the

substrate minimizes the portion of the substrate heated above its damage threshold. In

addition, maximizing the specific heat of the substrate will also minimize the temperature

rise for a given heat flux from the ink.

118

0

200

400

600

800

1000

1200

1400

-24-20-16-12-8-40

-0.1656 ms-0.0874 ms-0.0091 ms0.0301 ms0.1475 ms0.3040 ms

Tem

pera

ture

[°C

]

Depth [m]

Time2.0 W0.10 m/s

Figure 5.8: Temperature profile for a laser power of 2.0 W and a scan speed of 0.10 m/s plotted vs. depth.

0

200

400

600

800

1000

1200

1400

-0.5 0 0.5 1

3.000.00-4.85-8.95-16.77-31.35

Tem

pera

ture

[°C

]

Time [ms]

Depth (z)2.0 W0.10 m/s m

mm

mmm

Figure 5.9: Temperature profile for a laser power of 2.0 W and a scan speed of 0.10 m/s plotted vs. time.

119

0

200

400

600

800

1000

-24-20-16-12-8-40

-0.0334 ms-0.0067 ms0.0022 ms0.0201 ms0.0379 ms0.0557 ms

Tem

pera

ture

[°C

]

Depth [m]

Time2.0 W0.40 m/s

Figure 5.10: Temperature profile for a laser power of 2.0 W and a scan speed of 0.40 m/s plotted vs. depth.

0

200

400

600

800

1000

-0.1 0 0.1 0.2 0.3 0.4

3.000.00-4.85-8.95-16.77-31.35

Tem

pera

ture

[°C

]

Time [ms]

Depth (z)2.0 W0.4 m/s m

mm

mmm

Figure 5.11: Temperature profile for a laser power of 2.0 W and a scan speed of 0.40 m/s plotted vs. time.

120

Figure 5.12 shows how the temperature at the surface, and at 4.85 μm into the

substrate vary with respect to time. The quality of the sintering is not only a function of

the maximum temperature reached by the ink but also how long it is exposed to that

temperature. This figure shows that, although the damage to the substrate in minimized

for higher scan speeds (for 0.4 m/s the temperature 4.85 μm is well below the damage

threshold of glass), the duration of exposure to the high temperature is also much lower.

This may not allow the ink to be functionalized and explains why the conductivity

decreases slightly for higher speeds, as shown in Figure 4.5.

0

200

400

600

800

1000

1200

-0.4 -0.2 0 0.2 0.4 0.6

0.1 m/s - 3.000.1 m/s - -4.850.2 m/s - 3.000.2 m/s - -4.850.4 m/s - 3.000.4 m/s - -4.85

Tem

pera

ture

[°C

]

Time [ms]

Speed - Depth (z)2.0 Wm

m

mm

mm

Figure 5.12: Thermal profile for different scan speeds at the surface of the ink and at 4.85 μm into the substrate for a laser power of 2.0 W and different laser scan speeds.

Table 5.1 shows the maximum temperature attained at several depths and for

different scan speeds and laser powers. The table shows that for all the scenarios, the

temperature at 16.77 μm into the substrate is below the damage threshold of glass. The

temperature at the surface of the ink is well in excess of the melting point of silver for the

higher laser powers. Figures 5.13 and 5.14 show the maximum temperature profiles

121

attained for different laser scan speeds and different laser powers, respectively. Figure

5.15 shows a comparison between the maximum temperature attained at the surface, at

the interface, and at 8.75 μm into the substrate for different laser powers and for scan

speeds of 0.10 m/s and 0.40 m/s.

Table 5.1: Temperature [°C] at assorted depths from the ink-substrate interface.

Depth (z) [μm] Speed [m/s]

Power [W] 3.00 0.00 -4.85 -8.95 -16.77 -31.35 -52.70

0.10 0.50 447.05 388.01 229.21 160.73 95.24 48.80 29.60 0.10 1.00 805.93 704.95 409.87 285.03 165.05 77.05 39.29 0.10 2.00 1244.83 1148.41 731.04 507.26 289.71 135.65 58.57

0.10 3.00 1556.75 1412.01 989.65 704.36 401.39 185.44 77.66 0.20 1.00 705.81 600.78 307.22 199.31 106.49 48.45 28.94 0.20 2.00 1145.99 1020.17 548.56 350.02 186.16 82.73 38.13 0.20 3.00 1409.80 1269.83 753.86 486.76 257.29 112.41 47.15

0.20 4.00 1681.12 1492.10 938.24 612.74 322.28 140.39 59.59 0.40 1.00 586.81 480.51 209.00 126.28 66.03 34.86 24.39 0.40 2.00 1009.41 851.70 368.96 221.84 110.71 52.00 28.93 0.40 3.00 1243.23 1100.94 515.09 306.81 152.07 64.34 33.52

0.40 4.00 1462.94 1284.27 643.22 385.05 177.31 39.89 20.27

0

200

400

600

800

1000

1200

1400

-24-20-16-12-8-40

2.00 W - 0.10 m/s2.00 W - 0.20 m/s2.00 W - 0.40 m/s

Tem

pera

ture

[°C

]

Depth [m]

Laser Power - Scan Speed

Figure 5.13: Maximum thermal profile attained for a laser power of 2.0 W using different scan speeds.

122

0

200

400

600

800

1000

1200

1400

1600

-24-20-16-12-8-40

0.50 W - 0.10 m/s1.00 W - 0.10 m/s2.00 W - 0.10 m/s3.00 W - 0.10 m/s

Tem

pera

ture

[°C

]

Depth [m]

Laser Power - Scan Speed

Figure 5.14: Maximum thermal profile attained using a scan speed of 0.10 m/s for different laser powers.

0

200

400

600

800

1000

1200

1400

1600

0 1 2 3 4 5 6

0.10 m/s0.10 m/s0.10 m/s0.40 m/s0.40 m/s0.40 m/s

Tem

pera

ture

[°C

]

Power [W]

Scan Speed - Depth- 3.00 m- 0.00 m- -8.95 m- 3.00 m- 0.00 m- -8.95 m

Figure 5.15: Maximum temperature attained as a function of power for scan speeds of 0.10 m/s and 0.40 m/s.

123

The thermal profile will vary when different laser power and scan speeds are

used. The effect of changing the laser power is nonlinear because of the melting and

resolidification of the ink. The peak temperature within the ink layer is related to the

power and the duration of the exposure to the sintering temperatures which is dependent

on the laser scan speed. These parameters also determine the thermal profile in the

direction normal to the laser path which governs the feature sizes that can be produced.

5.6 Summary

This chapter presents a model of selective laser sintering. A 3D, finite element

model of the heat transfer during selective laser sintering is developed. This model

includes modeling the thick-film inks’ thermal properties using effective media theory.

The model also simulates phase changes in the ink layer when it is heated above the

melting point of silver.

The trends obtained from the model are in agreement with the trends found in the

experiments. The results show that to heat the interface to the sintering temperature, the

surface of the ink must be heated above its melting temperature. The model also

demonstrates that the heating of the substrate above its damage threshold can be confined

to the first 5 μm.

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6. CONCLUSIONS AND RECOMMENDATIONS

6.1 Summary and Conclusions

Chapter 1 established the requirement and demand for new microfabrication

technologies. It also explained how techniques using lasers are uniquely positioned to

satisfy this need. The two main advantages of laser techniques are:

Integratability – The combination of temporal and spatial precision requires their

use for some operations such as localized sintering. Once the decision to use one

laser process is made (for example laser sintering) it is easy to integrate other

laser processes such as laser direct write or laser micromachining.

Scalability – Unlike competing direct write approaches, those using lasers offer a

direct path from the serial processes used in rapid prototyping to the parallel

processes required for mass manufacturing using lithographic techniques

(masking a pattern).

Chapter 1 also reviews the conventional screen printing process used for

manufacturing most thick-film microelectronics along with several recently developed

techniques such as direct gravure offset printing and ink-jet techniques.

Chapter 2 investigated Matrix Assisted Pulsed Laser Evaporation – Direct Write

(MAPLE-DW). The experiments presented in this chapter differed from those

undertaken in the literature because an IR laser source was used with an x-y optical

scanner and a stationary substrate and ribbon. In addition, conventional thick film inks

were used as opposed to inks that were specifically designed for the MAPLE-DW

125

process. This is important because the thick-film industry is well established and using

existing inks lowers the material costs of MAPLE-DW. An experimental investigation

concluded that the sub-threshold regime produced the best experimental results. It was

found that while use of an x-y scanner facilitates high write speeds, the stationary ribbon

and substrate cause problems because the laser pulses interfere with each other. Despite

these difficulties, MAPLE-DW was demonstrated to be capable of depositing patterns

with feature sizes down to 25 μm.

Chapter 3 investigated the sub-threshold MAPLE-DW event in detail. Time

histories for the event captured by Lewis (2005) were analyzed and an analytical model

was developed. This model was fit to the time histories and successfully predicts some

trends observed experimentally, including that the smallest features will be produced

using a minimum ink thickness, minimum radius, and minimum ink to substrate

separation.

Chapter 4 studied Selective Laser Sintering (SLS). This process can be used to

functionalize and pattern thick-film microelectronic patterns. The effects of the process

parameters were studied on the DC performance. The following features of the SLS

approach were also investigated:

The values of conductivity specified for firing the ink in a furnace can be

duplicated using SLS on substrates with a damage threshold 300°C below the

specified firing temperature.

The high-frequency performance of conductors fabricated using SLS is sufficient

for operating at microwave frequencies.

The fabrication of functional devices on polymer substrates was proven and

functional microwave antennas were patterned on FR4.

126

The SLS process was shown to be capable of patterning feature sizes below 25

μm without the need for additional post-processing.

The functionalization of thick-film copper inks using the SLS technique is

possible in an ambient environment. This is exciting because conventionally

these inks must be fired in a nitrogen environment that is incompatible with other

passive components.

Chapter 5 investigated the SLS approach using the finite element method. These

simulations generated the thermal profile induced by the laser inside the ink-substrate

system. It was shown that the SLS process can develop temperatures inside the ink layer

that exceed the melting temperature of silver while limiting the exposure of the substrate

to temperatures exceeding its damage threshold to the first 5 μm. We conclude that the

SLS approach is more effective than MAPLE-DW for patterning thick-film passive

microelectronics. This conclusion is especially valid on low temperature substrates

because both techniques would have to be used (deposition by MAPLE-DW followed by

SLS to functionalize the pattern). However, MAPLE-DW is still important for patterns

that cannot be sintered such as chemicals and biological materials that are used in power

sources and sensors.

A summary of the original contributions of this work are summarized below

Demonstration of a MAPLE-DW system using an IR laser and x-y scanner with

conventional thick-film materials to fabricate functional patterns with feature

sizes less than 25 μm.

Demonstration of a mask-based MAPLE approach.

Development of an analytical model for the sub-threshold MAPLE-DW event.

Demonstration and development of SLS for microelectronics fabrication using

thick-film materials including resistors and dielectrics.

127

o Demonstration of process parameters on DC conductivity.

o Investigation of high-frequency conductivity of patterns fabricated by

SLS.

o Demonstration of SLS approach on low-temperature substrates and the

ability to directly fabricate functional patterns with feature sizes less than

25 μm.

o Demonstration that the SLS approach can be used to pattern and

functionalize thick-film copper patterns in an ambient environment.

Development of a finite element model to predict thermal profiles generated by

the SLS process.

6.2 Recommendations for Future Work

The parallel MAPLE-DW approach should be further developed and combined

with Digital Micromirror Device technology. The hope is that the parallel MAPLE-DW

approach can deposit the fine feature sizes required by the microelectronics industry with

high enough throughputs to be economically viable. Designing masks for this process (or

alternatively an algorithm for controlling the DMD device) will require a better model for

the MAPLE-DW event. Nonlinear effects such as shear thinning of thick-film inks and

expansion of the vapor pocket need to be taken into consideration, along with non-

parabolic displacement profiles. In addition, beam profiles with distributions other than

Gaussian should be investigated, along with the three-dimensional displacement profiles

that these will produce.

Complete functional microelectronic devices such as RFID transceivers need to

be developed to further demonstrate the SLS process. The ability to fabricate core

components has been shown but they have not been integrated together. The capability

128

of tuning electrical properties of resistive components by controlling the speed and power

of the laser was observed experimentally. This must to be further investigated to identify

what range of values can be produced along with demonstrating the repeatability of the

process. The tuning paradigm should also be extended to dielectric components because

the ability to fabricate periodic patterns with significantly different dielectric constants is

very attractive for several high-frequency applications. The oxidation of copper needs to

be further investigated and the limits of the SLS process should be identified for sintering

thick-film copper patterns in ambient conditions. The use of electroplating to increase

the conductivity of a seed layer deposited by SLS is important for polymer substrates and

deserves to be further investigated.

Better values for the material properties of the thick-film inks need to be obtained

experimentally to improve both the analytical model for the MAPLE-DW process and the

finite element model for the SLS process. This should include how viscosity varies with

shear rate and how density, specific heat, and thermal conductivity vary with

temperature. The finite element model should be expanded to cover the laser rastering for

sintering whole areas. The effects of changing ink thickness and material properties

should be further investigated along with the potential to develop inks specifically for the

SLS process.

The SLS model can be improved by including the densification of the ink layer

during sintering. Because unsintered ink is removed after the pattern has been sintered,

the bonding mechanism and adherence threshold warrant further investigation. A much

better understanding of the absorbance of radiation in mixed media is required to better

model the penetration of the laser into the ink layer. The sintering process entails

irreversible changes in material properties of the ink and the effects that portions of the

pattern that have already been sintered have on the process should be investigated.

129

It may be possible to further limit damage to the substrate by placing an

intermediary thermally resistive thin-film between the substrate and the ink. This layer

should have low thermal conductivity and high specific heat. The potential for this should

be investigated experimentally and numerically. The ideal situation is to measure the

temperature in-situ and use this information as part of a closed control loop. By

controlling the laser power and scan speed, more consistent patterns can be developed.

The goal is to generate a constant thermal profile within the ink layer. This will require

insight gained from finite element simulations of the sintering process.

Finally, both processes investigated in this thesis should be further integrated with

other laser microfabrication tools such as micromachining, laser welding and laser

diagnostics. This may require the addition of visible laser sources and lasers with higher

powers.

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Appendix A: ABAQUS Input Files for Simulation of SLS

The following code was used with ABAQUS for the simulation of SLS. The

format of the code was adapted from the work of Xi Zhang (2004).

A.1 ABAQUS Input File

The model is symmetric about the YZ plane. The origin is centered at the

interface between the ink and the substrate. The following parameters control the

geometry and density of the mesh:

X – Simulated area width

YS – Simulated substrate height YI – Simulated ink height Z – Simulated area length M – Number of nodes in the x-direction (both ink and substrate) NS – Number of substrate nodes in the y-direction NI – Number of ink nodes in the y-direction L – Number of nodes in the z-direction (both ink and substrate)

*HEADING INPUT FILE *.inp IS TO CALCULATE THE 3D TRANSIENT TEMPERTAURE FIELD FOR A SCANNED LASER BEAM SINTERING A THIN LAYER OF INK *PREPRINT, ECHO=NO, MODEL=YES, HISTORY=NO ** [5] DEFINE BASE NODES *NODE 10001, -0.5•X, -YS, -0.5•Z 10000+M, 0, -YS, -0.5•Z 10000+M • (L-1)+1, -0.5•X, -YS, 0.5•Z 10000+M • L, 0, -YS, 0.5•Z ** [11] DEFINE EDGES OF BASE *NGEN, NSET=L_B 10001, 10000+M •(L-1)+1, M *NGEN, NSET=M_B 10000+M, 10000+M•L, M ** [16] FILL BASE NODES BIAS DETERMINES RELATIVE SPACING BETWEEN NODES *NFILL, NSET=N_B, BIAS=1.1 L_B, M_B, M-1, 1 ** [19] COPY BASE NODE PLANES TO INTERFACE AND SURFACE PLANES *NCOPY, OLD SET=N_B, NEW SET=N_I, CHANGE NUMBER=(NS-1)• 10000, SHIFT 0, YS, 0 0, 0, 0, 0, 1, 0, 0 *NCOPY, OLD SET=N_B, NEW SET=N_S, CHANGE NUMBER=(NS+NI-2)• 10000, SHIFT 0, YS+YI, 0 0, 0, 0, 0, 1, 0, 0 ** [26] FILL IN NODES FOR BASE AND INK *NFILL, NSET=N_Sub, BIAS=1.1 N_B,N_I,(NS-1),10000

*NFILL, NSET=N_Ink, BIAS=1.1 N_I,N_S,(NI-1),10000 ** [31] UNIFY ALL NODES INTO SET N_A *NSET, NSET=N_A N_Sub,N_Ink ** [34] CREATE CENTER NODE SET *NSET, NSET=N_C, GENERATE 10000+M, 10000+M·L, M 20000+M, 20000+M·L, M ... (NS+NI-2)· 10000+M, (NS+NI-2)·10000+M·L, M (NS+NI-1)· 10000+M, (NS+NI-1)·10000+M·L, M ** [36+NS+NI-1] CREATE CENTER NODE SET *NSET, NSET=N_E, GENERATE 10001, 10000+M · (L-1)+1, M 20001, 20000+M · (L-1)+1, M ... (NS+NI-2)· 10000+1, (NS+NI-2)·10000+M · (L-1)+1, M (NS+NI-1)· 10000+1, (NS+NI-1)·10000+M · (L-1)+1, M ** [38+2·(NS+NI-1)] CREATE CENTER NODE SET *NSET, NSET=N_RE, GENERATE 10001, 10000+M, 1 20001, 20000+M, 1 ... (NS+NI-2)· 10000+1, (NS+NI-2)· 10000+M, 1 (NS+NI-1)· 10000+1, (NS+NI-1)· 10000+M, 1 ** [40+3·(NS+NI-1)] CREATE CENTER NODE SET *NSET, NSET=N_LE, GENERATE 10000+M · (L-1)+1, 10000+M·L, 1 20000+M · (L-1)+1, 20000+M·L, 1 ... (NS+NI-2)· 10000+M·(L-1)+1, (NS+NI-2)· 10000+M·L, 1 (NS+NI-1)· 10000+M·(L-1)+1, (NS+NI-1)· 10000+M·L, 1 ** [42+4·(NS+NI-1)] GENERATE ELEMENTS AND PROPAGATE TO FORM MESH *ELEMENT, TYPE=DC3D8 10001,10001,20001,20001+M,10001+M,10002,20002,20002+M,10002+M *ELGEN, ELSET=E_A 10001,M-1,1,1,NS+NI-2,10000,10000,L-1,M,M-1 ** [47+4·(NS+NI-1)] GENERATE ELEMENT SETS FOR SUBSTRATE *ELSET, ELSET=EL_S, GENERATE 10001, 10000+(M-1)·(L-1), 1 20001, 20000+(M-1)·(L-1), 1 ... (NS-2)· 10000+1, (NS-2)· 10000+(M-1)·(L-1), 1 (NS-1)· 10000+1, (NS-1)· 10000+(M-1)·(L-1), 1 ** [49+5·NS+4·NI-5] GENERATE ELEMENT SETS FOR INK *ELSET, ELSET=EL_I, GENERATE NS·10000+1, NS·10000+(M-1)·(L-1), 1 NS·20000+1, NS·20000+(M-1)·(L-1), 1 ... (NS+NI-3)· 10000+1, (NS+NI-3)· 10000+(M-1)·(L-1), 1 (NS+NI-2)· 10000+1, (NS+NI-2)· 10000+(M-1)·(L-1), 1 ** [51+5·NS+5·NI-6] GENERATE ELEMENT SETS FOR SURFACE *ELSET, ELSET=EL_Surf, GENERATE (NS+NI-2)· 10000+1, (NS+NI-2)· 10000+(M-1)·(L-1), 1 ** [54+5·NS+5·NI-6] DEFINE SUBSTRATE SECTION AND MATERIAL *SOLID SECTION, MATERIAL=Mylar, ELSET=EL_S *MATERIAL, NAME=Mylar

*SPECIFIC HEAT 1172,300 *DENSITY 1390,300 *CONDUCTIVITY 0.1549,300 ** [63+5·NS+5·NI-6] DEFINE SUBSTRATE SECTION AND MATERIAL *SOLID SECTION, MATERIAL=QS300, ELSET=EL_I *MATERIAL, NAME=QS300 *SPECIFIC HEAT 288.50,300 *DENSITY 9688.0,300 *CONDUCTIVITY 7.58,300 ** [78] DEFINE PHYSICAL CONSTANTS AND BOUNDARY CONDITIONS *PHYSICAL CONSTANTS, ABSOLUTE ZERO=0.0, STEFAN BOLTZMANN=5.669E-8 *INITIAL CONDITIONS, TYPE=TEMPERATURE N_A, 293.15 ** [82] SET UP HEAT TRANSFER ANALYSIS *RESTART, WRITE, FREQUENCY=100 ** [?] INC PARAMETER IS THE MAXIMUM NUMBER OF ITERATIONS PER TIME STEP *STEP, INC=4000 *HEAT TRANSFER, DELTMX=25.0 2.E-12, 0.02 ** [87] SET BOUNDARY CONDITIONS CONVECTION/RADIATION ON SURFACE *BOUNDARY N_B, 11, 11, 293.15 N_E, 11, 11, 293.15 N_LE, 11, 11, 293.15 N_RE, 11, 11, 293.15 ** *FILM USED TO SPECIFY CONVECTION AT SURFACE ** ELEMENT SET, FACE, AMBIENT TEMPERATURE, CONVECTION COEFFICENT *FILM EL_Surf, F2, 293.15, 20.0 *RADIATE EL_Surf, R2, 293.15, .1 ** [94] SET VOLUMETRIC HEAT GENERATION FROM INPUT FILE (*.for) *DFLUX EL_I,BFNU ** [97] SET OUTPUT REQUSTS *OUTPUT, FIELD, VARIABLE=PRESELECT, FREQUENCY=10 *NODE OUTPUT, NSET=N_C NT *NODE PRINT, FREQUENCY=10 NT *PRINT, FREQUENCY=10, SOLVE=YES *NODE FILE, NSET=N_C, FREQUENCY=10 NT *END STEP

SUBROUTINE DFLUX(FLUX,SOL,KSTEP,KINC,TIME,NOEL,NPT, 1 COORDS,JLTYP,TEMP,PRESS,SNAME) INCLUDE 'ABA PARAM.INC' DIMENSION COORDS(3),FLUX(2),TIME(2) CHARACTER*80 SNAME FLUX(1)=0.0 FLUX(2)=0.0 C DEFINE REFLECTIVITY A=0.97 C DEFINE BEAM RADIUS R0=10E-6 C DEFINE SCAN VELOCITY VEL=0.4 IF (TIME(1).GT.0.0 .AND. TIME(1).LE.0.00025) THEN Y_CENT=0. X_CENT=VEL*TIME(1)-50E-6 QR=1 ELSE Y_CENT=0 X_CENT=150E-6 QR=0 ENDIF C DEFINE LASER WAVELENGTH RAMDA=1100.0E-9 C DEFINE SCAN VELOCITY ALPHA=40000000 C DEFINE PI PI=4.*ATAN(1.0) Q0=0.5*12732395447 B1=-2.0*((COORDS(3)-X_CENT)**2+(COORDS(1)-Y CENT)**2)/R0**2 ABSORB=EXP(-ALPHA*((3E-6)-COORDS(2))) FLUX(1)=(1.-A)*Q0*QR*ALPHA*EXP(B1)*ABSORB RETURN END