Particle Scale Modeling of Material Removal and Surface Roughness in Chemical Mechanical Polishing

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PARTICLE SCALE MODELING OF MATERIAL REMOVAL AND SURFACE
ROUGHNESS IN CHEMICAL MECHANICAL POLISHING















By

SURESH BABU YERUVA


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2005

































Copyright 2005

by

Suresh Babu Yeruva

































This document is dedicated to Sri Paramahansa Yogananda, my parents and sister.














ACKNOWLEDGMENTS

I would like to express my gratitude and appreciation to my advisor, Dr. Brij

Moudgil, for his valuable guidance and support throughout this study. His sincere

dedication towards his students encouraged me to perform my best and expand my

potential. Sincere thanks are also due to Dr. Chang-Won Park, for his valuable guidance

and support throughout the study. I would also like to acknowledge the other members of

my advisory committee, Dr. Rajiv Singh, Dr. Wolfgang Sigmund, Dr. Hassan El-Shall,

Dr. Susan Sinnott and Dr. Dinesh Shah, for their time, helpful discussions and guidance.

I would like to thank Dr. Yakov Rabinovich for help with atomic force microscope

(AFM) and Fourier transform infrared spectroscopy (FTIR) analysis, and Gerald Bourne

from Major Analytical Instrumentation Center (MAIC) for help with focused ion beam

(FIB) and nanoindentation data. Furthermore, I sincerely acknowledge the guidance and

support given by Kuide Qin at Praxair Inc.

I gratefully acknowledge the National Science Foundation's Particle Engineering

Research Center (PERC) for financially supporting this research. Special thanks are due

to PERC staff members, Gary Schieffele, Gill Brubaker, Mike Beasley, and John

Henderson who made this work possible.

My colleagues, Bahar Basim, Jeremiah Abiade, Su-Ho Jung, Vijay Krishna,

Madhavan Esayanur, Scott Brown, Parvesh Sharma, Kyoung-Ho Bu, Pankaj Singh,

Debamitra Dutta and Ivan Vakarelski, who have contributed to this research by their

valuable discussions and friendship, are also gratefully acknowledged.
















TABLE OF CONTENTS

Page

L IS T O F T A B L E S .............................................. ................................... .................. v ii

LIST OF FIGURES ................... ...................... .. ................... viii

ABSTRACT xi

CHAPTER

1 IN TR OD U CTION ............................................... .. ......................... ..

M ultilevel M etallization ................................................................ ...................... 2
N eed fo r P lan arizatio n ............................................ ................................ ................. ........ 4
Planarization Techniques.................... ......... ............... ........ .......................
Overview of the Chemical Mechanical Polishing Process............... ..................7
H history ................... .. .. ..... .. ... ................ ... ... ............................ . 7
Advantages and Disadvantages of Chemical Mechanical Planarization............8
G general C M P applications.......................................................... ............... 9
C m p O utput Param eters ............................................................................ 9
R em ov al rate .............................................................10
Global planarization ............... .. .................... ........ .............. .. 12
S ele ctiv ity ................................ ...................1.........3
M easurem ent T techniques .......................................... ................. ... ............ 14
End Point D election ............................... .............. ......... ........ .... 15
CMP Consumables ............................... .......... ...... ............... 16
C M P S lu rry ............... ............................ ............................... 1 8
R ate of surface reaction ..................................................... ..................... 18
Slurry agglomeration...................... ....... ............................ 19
Chemical M echanical Polishing Pads ...................................... ............... 20
Effect of pad grooves ................................................. .......... .................. 23
Physical and chemical changes in pad during polishing ............................23
Effect of temperature change on polishing pad ..........................................26
Non-uniformity of the polishing pad............................ .................27
C M P process in the future ............................................................... .....................27
S cop e of D issertation ......................................................................... ...................2 8

2 CMP MODELING: OVERVIEW OF PERC I................................... ...............30

L iteratu re R ev iew ....................... ........................................ ........................ .. .3 1


v









Preston Equation ............................................. ........ ... .......... .... 31
Modifications to Preston Equation ........................................ ...............34
Slurry Erosion............................................. 36
Pad Considerations in CM P M odels......................................... ............... 39
Slurry Considerations in CM P M odels..................................... ............... 42
PER C I CM P M odel ........................ .......... ....... .............................44
M odel D evelopm ent ........... ................ .................... .................. 45
Estimation of the Overall Removal Rate.................................54

3 PER C II CM P M O D EL ............... ................................................... ............... 59

A ssum option V alidation ......... ........... ............... ....................... ...............59
P ad-w afer C contact A rea ........................................................... .....................59
Optical m icroscopy ................. .......................................... 61
Fourier transform infrared spectroscopy (FTIR).........................................64
Pad Asperity Height Distribution ................... .................... ...............73
Abrasive Particle Size D distribution .......................................... ............... 74
PER C II M odel D evelopm ent.......................................................... ............... 75
Plastic Deformation of Wafer Surface .......................................... ..........79
Slurry Characteristics Particle Size Distribution.................. ..................79
M material Rem oval by Single Particle........................................ ............... 79
Number of Active Abrasive Particles ................... .....................82
Estimation of the Overall Removal Rate ..................................... ...............83

4 M O D E L A SSE SSM E N T ......................................... .............................................85

M odel Validation .............................. ....... .................................85
Silica C M P : M icron Sized Slurries ........................................ .....................86
Silica CM P: N anosilica slurries...................................... ......................... 87
Copper CMP ............. .. ........ ............. ......... 91
Tungsten CM P ......... ... .............. .. ....................... .... ........92
M odel P reductions ......... .. ............. .................. ............... .. .. ............ ......... ..........94
Removal Rate as a Function of Particle Size for a Given Solids Loading:.........95
Effect of Modified Layer Thickness ............... ......................................96
Effect of M odified Layer Hardness .............. .............................................. 99

5 SUMMARY AND SUGGESTIONS FOR FUTURE WORK ........... .....................101

L IST O F R E F E R E N C E S ...................................................................... ..................... 106

BIOGRAPHICAL SKETCH ........................................................................118















LIST OF TABLES
Table p

1-1. Interconnection delay (RC) in silicon VLSI chip............................................ ............ 3

1-2. Chemical mechanical polishing applications. ................................. .................10

4-1. Parameters included in the revised PERC model................................................. 85

4-2. Parameter values used for comparing PERC I and II models. ..................................95

5-1. Process parameter ranges used in sensitivity analysis ................ ......... ..........103
















LIST OF FIGURES

Figure pge

1-1. Future trends in interconnects .................................. ...................................... 4

1-2. Schematic of a device fabricated using multilevel metallization. ..............................5

1-3. Different degrees of local and global surface planarity..................... .....................6

1-4. Schematic of chemical mechanical polishing process.............. ................................. 7

1-5. Surface layer formation on Cu with various slurry chemistries. ...........................11

1-6. M icro and nanoscale phenomena during CM P ....................................................13

1-7. Parameters involved in CMP process................................ ...............17

1-8. Chronoamperometry measurements for tungsten ............................................... 19

1-9. Type I C M P pad.. ................. ...... .......................... .. ...... .. ............. 22

1-10. Type II CM P pad. ............................................. .. .... ........ ......... 22

1-11 The absorbance spectra of used and dry IC 1000 pad along with dried silica
slu rry ................................................... ...................... ................ 2 5

2-1. Polished wafer surfaces showing nanoscratch surfaces. .........................................33

2-2 Pad consideration in PER C I. ........................................................... .....................46

2-3. Schematic of single particle abrasion showing the removal of chemically
m modified surface layer............ .. .................. ........ ...... .. .. ........ .... 51

2-4. Schematic of PERC I predictions for increasing particle size..............................57

2-5. Polishing of silica by nanoslurry showing optimal particle size.. ............................57

2-6. Polishing of silica at various pressure, velocity and particle sizes showing optimal
p article siz e .........................................................................5 8

3-1. Schematic of the fixture used in measuring pad-wafer (dry) contact area. ................62









3-2. Pad asperity contact spots seen through optical microscope................... ................63

3-3. Pad asperity contact area dependence on applied load. Each legend represents a
selected asperity contact .................. ........................... ....... .... ........ .... 63

3-4. Pad contact area as a function of applied load................................. ............... 64

3-5 Schematic of the FTIR-ATR technique used to measure pad-wafer contact area.......65

3-6. Analysis of the FTIR-A TR spectra................................................. ....... ........ 67

3-7. Absorbance spectra of pad (in pH 4) at different applied pressures...........................67

3-8. Contact area variation with applied load in dry and wet conditions ........................68

3-9. Contact area in dry and wet systems in various pH conditions................................68

3-10. C olloidal probe A FM tip ................................................ .............................. 70

3-11. Force-distance curve indicating softer "modified layer" on the pad surface. ..........71

3-12. Force-indentation curves from AFM for different conditions...............................72

3-13. Schematic of pad surface as deduced from AFM data. ............. ..............72

3-14. Schem atic of polishing pads. ........................................ ......................................73

3-15. Particle size distribution of silica slurry. ...................................... ............... 75

3-16. Schematic of pad, slurry and wafer in PERC I model.................... ..................76

3-17. Schematic of pad, slurry and wafer in PERC II model. ........................................77

4-1. Slurries used in oxide polishing................. ........................................ 87

4-2. Silica polishing by slurries in the micron range. .............................. ......... ...... .88

4-3. Silica polishing by colloidal nanosilica. .............................................................. 89

4-4. Silica polishing by nanosized slurries ...................................................................90

4-5 Copper CMP as a function of particle size...............................................................92

4-6. Alumina slurry size distributions..................... ...... ............................. 93

4-7. Effect of particle size on tungsten CMP .............. ......... ......... ...............94

4-8. Comparison between PERC I and PERC II models with constant solids loading of
different particle sizes.. ....................................... ................. ......... 96









4-9. Model comparison with varying modified layer thickness.. ...................................98

4-10. CMP performance comparison with varying modified layer hardness ................100

5-1. Sensitivity analysis of silica CM P system.............. .............................................. 103














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


PARTICLE SCALE MODELING OF MATERIAL REMOVAL AND SURFACE
ROUGHNESS IN CHEMICAL MECHANICAL POLISHING


By

Suresh Babu Yeruva

December 2005

Chair: Brij M. Moudgil
Cochair: Chang-Won Park
Major Department: Materials Science and Engineering

Chemical mechanical polishing (CMP) is widely adopted in producing excellent

local and global planarization of microelectronic devices. It has been demonstrated

experimentally that the polishing performance is a result of the synergistic effect of both

the chemicals and the particles involved in CMP. However, the fundamental mechanisms

of material removal and the interactions of the chemical and mechanical effects are not

well understood. A comprehensive model for CMP was developed taking into account

both the chemical and mechanical effects for slurries with a given particle size

distribution. The model developed (PERC II) is based on a previously developed model

(PERC I). The chemical aspect is attributed to the chemical modification of the surface

layer due to slurry chemistry, whereas the mechanical aspect is incorporated by

indentation of particles into the modified layer and the substrate depending on the









operating conditions. In this study, the effects of particle size and pad asperity

distributions are included in the model.

The contact area of pad with wafer was measured in dry and wet conditions in

different pH solutions using optical microscopy and Fourier transform infrared

spectroscopy respectively. Pad surface mechanical properties in dry and wet states were

also investigated using atomic force microscopy. The contact area results obtained were

utilized in modeling to estimate the pad modulus leading to pad-wafer contact stress

distribution.

The predictions of the model show a reasonable agreement with the experimental

data. The model is validated for oxide and metal CMP systems. The PERC II model not

only predicts the overall removal rate, but also the surface roughness of the polished

wafer in selected systems. The developed model can be used to optimize the current CMP

systems and provide insights into future CMP endeavors.














CHAPTER 1
INTRODUCTION

The past three decades have witnessed rapid growth of the electronics industry and

its impact on human lifestyle. Ultra-large-scale integrated (ULSI) circuits, with 108 or

more devices on a chip, can now be fabricated on semiconductor wafers, reducing cost

and increasing the performance of electronic products. The number of components on a

memory chip has approximately doubled every two years over the past two decades,

following the famous Moore's law [1]. The advancement in fabrication technology

shrinks the minimum dimension of the device-feature by about 13% per year. This trend

is expected to continue in the future even as 65 and 45 nm processes are set for

production in 2005 [2] and near future.

The relentless competitor and customer driven demand for increased circuit

density, functionality and versatility has led to revolutionary advances in the "front end"

of the chip manufacturing line where the circuit elements are fabricated, and the "back

end" where these elements are appropriately wired within the integrated circuit (IC) [3].

Chip interconnections, or "interconnects," serve as local and global wiring, connecting

circuit elements and distributing power [4]. To incorporate and accommodate the

improvements such as decreased feature size, increased device speed and more intricate

designs, research in the back end of line (BEOL) processes has become equally important

as the development of the front end of line (FEOL) processes to reduce gate oxide

thickness and channel length.









While recent path breaking innovations [5-7] in the field of lithography and

patterning have brought progressive device scaling, the development of a planar BEOL

approach, which incorporates the use of chemical mechanical polishing (CMP) to

planarize inter-level dielectrics and metal stud levels, represents a significant

advancement in BEOL processes. Innovation in BEOL technology is required in each

technology generation, since only part of the density increase could be achieved with

improvements in lithography.

Multilevel Metallization

In earlier stages, the complementary metal oxide semiconductor (CMOS) device

structure had multiple isolated devices connected by a single level of interconnect wiring.

Scaling down of the devices was very effective in achieving the goals of increased device

density, functional complexity and performance. However, device scaling became less

profitable, and speed and complexity were dependant on the characteristics of

interconnects that wired them [8]. With the single level metallization scheme, the total

area occupied by the wiring on the chip significantly increased with the increase in the

active density on the chip.

The interconnect delay is usually measured as RC time delay, which is the total

time taken by the voltage at one end of the metal line to reach 63% of the total value of

the step input applied at the other end. This reduction is due to resistance of the

interconnect wiring metal (R) and the interlayer dielectric capacitance (C) [9]. The

resistance of the line is given by

R =p l/wd (1.1)
where p is the resistivity of the wiring material, 1, w, and d are the length, width, and

thickness of the wiring material respectively. The capacitance of the line is given by









C = s wl/t (1.2)
where s is the relative permittivity and t is the thickness of the insulator. The total RC

delay can be given by

RC= p 1/wd s wl/t =ps 12/td (1.3)
Thus, it can be seen from Eq. (1.3) that RC delay is independent of the line width

and further scaling of line width translates into reduction of IC line thickness which in

turn increases the RC delay. Other factors such as parasitic capacitances and cross-talk

become dominant for sub 0.5 |tm integrated circuits. One approach to decrease the RC

delay is by incorporating metals of low resistivity, and interlayer dielectrics of lower

dielectric constant. Table 1-1 gives the simple RC time constants calculated for a few

metals of given Rs (sheet resistance) and 1 mm length on 1 tm thick SiO2 [9]. The other

approach implemented widely in the industry is forming multilevel metallization schemes

where different levels of metal interconnections are isolated by dielectrics and are

connected by vertical vias.

Table 1-1. Interconnection delay (RC) in silicon VLSI chip.
Metal Bulk Polycrystalline Film Rs Delay'
resistivity film resistivity thickness (Q /square) (ps/mm)
(l2 cm) (S2 cm) (A)
Polysilicon -1000 5000 20 690
CoSi2 10 15 2500 0.6 21
MoSi2 -35 -100 2500 4 138
TaSi2 45 55 2500 2.2 76
TiSi2 13 15 2500 0.6 21
WSi2 -25 70 2500 2.8 97
W 5.65 8-10 2500 0.32-0.4 11-14
Mo 5.2 8-10 2500 0.32-0.4 11-14
Al 2.65 2.7 2500 0.11 4
Cu 1.67 2.0 2500 0.08 3
'Delay=RC=34.5 Rs (ps/mm) for 1 mm length conductor on l[tm thick SiO2 [10].









The increase in the levels of the metallization lines implies that packing density

need not keep pace with the device density and the minimum metal line feature does not

have to scale at the same pace as the gate width. The foremost reason behind the

implementation of multilevel metallization schemes is the reduction in the length of the

metal lines, thereby reducing the RC delay sizably (Eq. 1.3), and allowing direct routing

of the active devices. In places where metal wiring length cannot be reduced, routing can

be done at the upper levels without reducing the metal line width, thus reducing the RC

delay due to the higher surface area. Starting with two levels of metallization, the levels

of metallization have increased up to 8 by 2001 [11]. The future trends in the levels of

metallization can be seen in Fig. 1-1 [12].




--III ..."














Fig. 1-1. Future trends in interconnects [12]

Need for Planarization

Deposition of multiple layers leads to conformation of deposited layer on the

substrate features or already deposited pattern. When multilevel metallization is carried

out without any planarization step, non-planarized surface topography (Fig. 1-2a) results









in several processing difficulties. The irregular surface causes a hindrance in conformal

coating of the photoresist and efficient pattern transfer with contact lithography. The

anomalies in the surface cause the variation of the thickness in fine line widths (sub 0.5

[tm) depending on photoresist thickness. Fig. 1-2 shows a comparison between planarized

and non-planarized surface topography. Effectively planarized surfaces have a number of

benefits such as (a) higher photolithography and dry etch yields, (b) elimination of step

coverage concerns, (c) minimization of prior level defects, (d) elimination of contact

interruption, undesired contacts and electro-migration effects, (e) reduction of high

contact resistance and inhomogeneous metallization layer thickness, and (f) limitation in

the stacking height of metallization layers. Thus the demand for developing devices with

enhanced performance necessitates planarization.














Fig. 1-2. Schematic of a device fabricated using multilevel metallization. (a) Non-
planarized structure. (b) Planarized structure [8, 13]

Planarization Techniques

Techniques such a spin on deposition (SOD), reflow of boron phosphorous silicate

glass (BPSG), spin etch planarization (SEP), reactive ion etching and etch back (RIE

EB), SOD + EB and chemical mechanical polishing (or chemical mechanical

planarization) (CMP) are the most prominent of several competing technologies available









to achieve local and global planarization (Fig. 1-3). The plasma enhanced chemical vapor

deposited oxides have limited capability of gap filling and are restricted in their gap

filling ability below patterns having 0.3-|jm feature size. High-density plasma deposited

oxides have acceptable gap filling capabilities; however, they produce variation in

surface topography at local as well as global level. Even though spin-on deposited (SOD)

doped and undoped oxides and polymeric materials have acceptable ability for gap

filling, CMP is the only technique which produces excellent local and global

planarization of microelectronic materials.

(a) 1.nplanarizecd Gap Fill
-- IJ t YC D | 1








b1 Sur'ace Smoathig SOD (FSGTPSG)




(c) Locallianarizadtni SODWEB (BPSG)
Resist Eth Back




(d) GIobal PH uizatiou CMP




s 10pm


Fig. 1-3. Different degrees of local and global surface planarity [14].









Overview of the Chemical Mechanical Polishing Process

Current semiconductor fabrication technology for logic and memory devices

requires CMP to achieve the required multilevel interconnection densities. Indeed, each

silicon wafer can be exposed to 15 or more CMP steps before final device assembly. A

schematic diagram of the CMP process is shown in Fig. 1-4. In CMP, the wafer is

pressed face down against a rotating polishing pad, while a chemical and physically

abrasive slurry fed between pad and wafer planarizes the wafer. The material removal in

simplest terms takes place by synergistic mechanism between chemical reaction on the

wafer surface due to the slurry, and physical removal of the reacted material by the slurry

abrasives. The various mechanisms between pad, slurry and wafer are tailored to enhance

material removal, planarization, surface finish and higher selectivity compared to the

underneath layer.




Wafer Carrier Slrry,-"


..... Polish Pad


Platen



Fig. 1-4. Schematic of chemical mechanical polishing process.

History

The modern day application of the CMP process in the semiconductor industry was

for polishing the raw silicon wafers to achieve a global flatness. One of the most

widespread applications of CMP outside the semiconductor industry is in optical lens









polishing. In fact, the first semiconductor CMP machine was an innovation of the lens

polishing industry. The first wafers polished using CMP were commercially available in

the early 1960s [15]. There was wide spread industrial implementation of the different

variants of the CMP by companies such as NEC, National Semiconductor, Hitachi, etc.

[10]. This led to the introduction of the first commercial polisher designed specifically for

CMP by Cybeg, Japan in 1988. Later, International Sematech identified CMP as a

technology critical for the future of IC manufacturing and launched a project to develop

competitive and advanced CMP tools in the US [16]. Once the technology and required

equipment were available, CMP was used beyond polishing of inter-level dielectric layers

to polishing of tungsten, which was deposited in via openings between metal layers.

Copper was not used for interconnects until the availability of CMP even though it has

lower resistivity than aluminum [17], as it could not easily be etched by reactive ion

etching. This enabling polishing technology has spread to several other applications, the

significant one being in shallow trench isolation (STI) [18].

Advantages and Disadvantages of Chemical Mechanical Planarization

The advantages of CMP are (a) it achieves global planarization, (b) a wide range of

materials can be planarized, sometimes in the same polishing step, (c) it reduces severe

topography to allow fabrication with tighter design rules, (d) it provides an alternate

means of patterning metal, eliminating the need to plasma etch, (e) it improves metal step

coverage due to reduction in topography and (f) it does not use hazardous gasses common

in dry etch processes.

Conversely, the disadvantages of the CMP process are (a) poor control over the

process with narrow latitude in process variables, (b) new types of defects introduced by

the CMP process itself (scratches, particle residue, etc.), (c) difficult end-point detection









for desired thickness and (d) expensive to operate because of costly equipment and

consumables.

General CMP applications

The process of CMP was initially developed and implemented for planarization of

SiO2 which is used as an interlayer dielectric in a multilevel metallization scheme.

Tungsten is used as an interconnect plug to the source, drain, and gates of transistors in Si

microprocessor chips. Initially Ti and TiN barrier layers are deposited, followed by

chemical vapor deposition of W to fill the contact vias. Proceeding from achieving local

and global planarization of SiO2, removal of excessive tungsten from the horizontal

surfaces on the wafer pattern proved to be an asset for subsequent Al metallization.

Hence CMP was developed with a two-fold approach of (a) planarizing oxide and (b)

removing the via fill metal from the horizontal surfaces. Along with its successful

implementation for the achievement of the above-mentioned objectives, CMP is now

extended to (a) polishing of different metals like Al, Cu, Pt, Au, Ti, Ta, etc., (b) polishing

of different insulators like SiO2, Si3N4, various low-k dielectrics, doped and undoped

oxides of silicon, (c) polysilicon, (d) ceramics like SiC, TiN, TaN, etc., (e) multichip

modules, (f) packaging; (g) optoelectronic components, (h) flat panel displays, (i)

microelectromechanical systems (MEMS), and (j) magnetic recording heads and CD read

write drives [19]. The major applications of CMP are summarized in Table 1-2.

Cmp Output Parameters

The critical output parameters of CMP are described below. Depending on the

application, different output parameters are optimized.









Table 1-2. Chemical mechanical polishing applications.
Materials Application
Metal
Al Interconnection
Cu Interconnection
Ta Diffusion barrier/adhesion promoter
Ti Diffusion barrier/adhesion promoter
TiN, TiNxCy Diffusion barrier/adhesion promoter
W Interconnection e-emitter
Dielectric
Cu-alloys Interconnection
Al-alloys Interconnection
Polysilicon Gate/interconnect
SiO2 ILD
BPSG ILD
PSG ILD
Polymers ILD
Si3N4 or SiOxNy Passivation layer, hard mask
Other
Aerogels ILD
ITO Flat panel
High k dielectrics Packaging
High To superconductors Interconnection/packaging
Optoelectronic materials Optoelectronics
Plastics, ceramics Packaging
Silicon on Insulator (SOI) Advanced device/circuits
Ref [19]

Removal rate

The polishing steps involving CMP of STI and metal mainly emphasize removing

an overburden of one material and stop on another material leaving a planar surface. A

high material removal rate is one of the key outputs desired from such CMP processes.

The removal rate of the material being polished is strongly influenced by slurry chemistry

and pressure distribution, i.e., chemical action of the slurry chemicals on the material,

interplay of the different completing agents, oxidizers and corrosion inhibitors and the

mechanical abrasion of the particles on the wafer. Chemicals such as oxidizers and

corrosion inhibitors vastly affect the reaction rate of the slurry with similar particle

nature, size and distributions.











1 0 5% H202, lOn1 M 0n

S8 BTA %

DI Water

2-
0 10mM BTA

0.00 0.01 0.03 0.05 0.07
Time (sec)

Fig. 1-5. Surface layer formation on Cu with various slurry chemistries. [20]
Fig. 1-5 shows the variation of the reaction rate of the different slurry components

on Cu when the reaction kinetics were studied using electrochemical chronoamperometry

[20]. It can be seen from the figure that the surface rate kinetics reach approximately 60

A/s when Cu is immersed in distilled water. The reaction rate increases to around 120 A/s

when 5% H202 is added. However upon addition of 10 mM BTA, the reaction rate

decreased considerably. Therefore, the chemical contribution is very important in the

CMP process. The other important factor is the down pressure used. However, for

effective CMP of materials, the enhancement of removal rate by increasing the down

force should not be at the cost of surface quality (for example, increase in wafer to wafer

and within wafer non-uniformity, delamination, dishing, erosion, etc.) [21, 22] of the

wafer. For this reason, the process throughput is compromised to polish the wafers at

lower applied load, thereby achieving global planarization and better surface quality.









Global planarization

In contrast to glass or silicon wafer polishing, the objective of the CMP process in

interlayer dielectric (ILD) polishing is to planarize the topography created by previous

semiconductor processing steps. The pad and slurry play key roles in achieving global

planarization, concurrently maintaining the removal rate and producing a defect free

wafer surface.

If mechanical removal predominates, high frictional forces are produced which

result in surface defectivity. Also variation in local polishing pressure leads to variable

removal rates within the wafer, which seriously compromises global planarization [20],

whereas, if chemical removal dominates, etching and corrosion [23] can occur. The key

to a good polishing process is dependent on synergy between chemical etching and

mechanical planarization. For this purpose, a passivation layer is created on the wafer

surface by reaction with slurry and removal of this passivation (or modified) layer occurs

due to mechanical abrasion of slurry particles (Fig. 1-6). For example, in Cu polishing,

the formation of the passivation layer is achieved by oxidizers such as hydrogen

peroxide, potassium ferricynate, ferric chloride, and ferric iodate. Corrosion damage to

the surface is prevented by adding corrosion inhibitors such as benzotriazole (BTA). In

tungsten polishing, a rapid formation of surface passivation layer is due to the use of

peroxygen compounds and stabilizing agents [24]. The purpose of the passivation layer in

the case of silica polishing is to soften the surface, which is inherently hard resulting in

minimal material removal. For this purpose, maintenance of alkaline pH is sufficient in

most cases [25, 26]. During Ta polishing, formation of stable Ta205 helps in uniform

removal of material from the surface [27]. To achieve optimal CMP performance, the

time to form the passivation layer of desired thickness should be minimized.






























Abrasive partsic

Fig. 1-6. Micro and nanoscale phenomena during CMP [20]

Selectivity

The difference in the removal rate of one material versus another in a given system

represents the measure of the slurry selectivity for these two materials. The higher the

slurry selectivity, the more effective the end point detection is for the given CMP process.

This is due to a marked change between the tribological properties of the material being

polished, and the underlayer. The difference in tribological properties can be monitored

in-situ using techniques such as motor current, force or acoustic emission for better end

point detection. Selectivity is a very important criterion in designing any slurry for

multilevel metallization. For STI, the slurry must affect the oxide that is being planarized,

and not the underlying nitride layer. For polishing Cu, the slurry needs to react selectively

on Cu and spare the barrier layer Ta and underlying layers of silica or low-k dielectric

material. Typically slurry selectivity of 10-25 has been reported for Cu polishing [20].









The selectivity could be considerably improved up to 1000 by introducing a particle free

slurry [28, 29]. The reduction in mechanical component due to lack of abrasive implies

that the majority of material removal occurs due to the solution chemistry which can be

made highly selective.

Addition of specialized chemicals that can act as catalysts in the chemical

interaction between slurry and the polished material thereby increasing the rate of the

chemical reaction considerably is a common approach for improving the slurry

selectivity. Tetramethyl ammonium hydrate can be added to Cu slurries to considerably

decrease the silica polishing rate [30]. An increase in the polishing rate of TaN with

addition of phosphoric acid in alumina and colloidal silica slurry is also observed. Mixed

abrasive slurries (MAS) containing alumina/silica and alumina/ceria particles have been

developed to improve the selectivity of the CMP slurry. The details of the experiments

with these novel mixed abrasive slurries have been published by Jindal et al. [31, 32].

Though highly selective slurries might help in avoiding defects such as erosion of sub

layers, planar defects such as dishing still exist causing wafer-to-wafer nonuniformity

(WTWNU) due to the differential polishing pressures in the process.

Measurement Techniques

The outputs of the CMP process are quantified by a host of metrics. Material

removal rate (e.g., nm/min) is commonly measured in terms of thickness loss per time or

weight loss per time. In terms of global planarization at the wafer scale, film thickness is

measured at points across the wafer surface and used to calculate within-wafer-non-

uniformity (WIWNU). Most commonly, a 49-point measurement grid is used to

determine the WIWNU, which is the variation of those measurements with respect to the

average thickness. Similarly, a within-die non-uniformity (WIDNU) calculates a similar









variation but just across the area of one die. At the feature-scale of the process, metrics

such as step height reduction are used to indicate efficiency of the CMP process.

Selectivity of the slurry is more often characterized by estimating the erosion or polishing

of the underneath layer.

End Point Detection

Theoretically, the end of a polishing step can be realized by setting a time limit to

the process. However, this is only a rough estimate because variations of polishing pad

surface property, fluctuations in slurry chemistry, particle size distribution, feeding rate,

pad conditioning issues, and other potential variables can cause over- or under-polishing.

Therefore, in-line monitoring or automatic end-point detection of CMP is needed. Initial

oxide CMP relied on process times and control of removal rate stability to achieve target

thicknesses. As the CMP environment is hostile for in-situ metrology, the earlier endpoint

techniques relied on indirect methods. One of the commercialized indirect methods

monitors the motor current change [33] while driving the carrier or platen rotation. This

technique measures changes in friction forces between the pad and the wafer surface. It is

mostly successful for tungsten CMP than for copper or STI CMP processes, because the

frictional forces between the polishing pad and exposed films do not differ significantly

in the case of copper or STI scenarios. The method sufficiently sensitive for STI,

dielectric and metal CMP processes is the vibration monitoring method [34]. Vibrations

during the CMP process are detected using an accelerometer on the carrier behind the

wafer. This method is used to detect delamination of low-k dielectric films in copper dual

damascene process [35].

Optical reflectometry is the preferred method for endpoint detection. But, the

method is highly intrusive, requiring extensive polisher modifications. Various other









endpoint techniques have been developed in recent years, many of which are currently

adapted to the high volume production stage [35].

CMP Consumables

The CMP market in the year 2003 was $1.7B with slurry (24%) and pad (15%)

amounting to 40%. The CMP equipment was estimated to comprise 55% with the

remaining 6% accounting for conditioner and other consumables. The market is expected

to grow to $3.3B in the year 2008. The rapid growth of CMP and its application for

polishing various materials, necessitated development of a variety of slurries, pads,

complex process recipes, more complex slurry mixing and distribution systems. Polishing

of different materials and customized needs of the various semiconductor industries

resulted in more complex CMP equipment with different process dynamics such as

linear, orbital and fixed head machines [35]. The process of CMP has gone through a lot

of evolution from first being used just for silicon dioxide planarization to the present day

planarization applications in pre-metal dielectric (PMD), ILD, STI, metal and gate oxide,

etc.

While the CMP process seems fundamentally easy to understand, there are a

staggering number of process variables (Fig. 1-7) that complicate the underlying

interaction between the pad, slurry and wafer, preventing full comprehension of the

process. The most widely accepted mechanism for the material removal is that the

chemicals in the slurry react with the surface of the wafer (e.g., oxide, copper, etc.) and

create a "modified" layer that can be removed easily. The mechanical action of the

abrasives trapped in pad asperities then physically abrade and remove the modified

material [24, 36, 37].









In terms of the CMP input parameters, the process variables are generally

categorized into chemical and mechanical parameters. The chemical nature of the CMP

process typically relates to the constituent makeup of the slurry and how those chemicals

react with the wafer surface to create a passivated or modified layer, keeping the particles

well suspended in the slurry. The chemicals in the slurry are highly dependent upon the

type of CMP being used. For example, in oxide polishing, an alkaline solution is used

along with various buffering and oxidizing agents, whereas for metal CMP as in Cu

CMP, acidic slurry can be used. The mechanical aspects of CMP largely depend on the

polishing pad, wafer pattern, and process conditions like pressure and relative pad-wafer

velocity.


Slury

" Slurry chemistry
Oddizers

Compi exing agents

pH stabilizers

SPar licl e features

Size distribution

Mechanical strength

Slurry stabilizers

Shape

Slurry agglomeration

*Slurry theology


Wafer
* Wafex material properties

* Feature characteristics


Pad

* Padroughness

* Mechanical properties

* Conditioning technique


Tool

* Load distribution

* Platen rotation

* Wafer rotation

* Slurry flow rate


Fig. 1-7. Parameters involved in CMP process.


C









Polishing in its simplest sense is controlled chemo-mechanical material removal to

produce a globally flat, defect free surface. The main components of CMP are the CMP

slurry and the pad. The complexity of these CMP components and their interactions are

discussed further in the following sections.

CMP Slurry

CMP slurry consists of two major components: abrasives and chemicals.

Depending on the material of the wafer, the chemistry of the slurry, and the synergy

between them, each kind of slurry behaves differently [38]. CMP is influenced to a great

extent by numerous slurry parameters such as pH, solution chemistry, particle charge

type, concentration and particle size distribution of abrasives, completing agents,

oxidizers, buffering agents, surfactants, corrosion inhibitors, etc.[19, 39]. An ideal CMP

slurry should be well suspended with good slurry stability, and be able to achieve high

removal rate, excellent global planarization, prevent corrosion (in case of metal,

especially Cu), and result in good surface finish, low defectivity and high selectivity.

Rate of surface reaction

The reaction between the wafer and slurry chemicals to form a modified layer of

desired thickness should be fast enough to avoid material removal by mechanical

indentation of the bare wafer. The time scale in which the passivation layer is formed

should be less than the average time of successive particle indentations into the wafer for

abrasion to achieve optimal CMP performance. Fig. 1-8 shows the electrochemical

chronoamperometry (potentiostatic) analysis of Tungsten by first keeping the samples at

cathodic potential to avoid surface oxidation and then anodizingg" them. The generation

of current, which corresponds to surface reaction rate, is monitored on a millisecond scale









as shown. It can be seen form the figure that Tungsten surface quickly passivates which is

conducive for mechanical removal of the material.


r 10,000
+L.7V


1.v



I A
10 -0.2


0.Q0[ 0,001 0,01 0.1 1
Time (s)

Fig. 1-8. Chronoamperometry measurements for tungsten [20]

For selectivity purposes, the reaction of slurry chemicals with the underneath layer

should be significantly low compared to the surface layer. In terms of operational hazard,

the chemicals used in the slurry should not make it hostile for the operators performing

CMP and the post-CMP chemicals should be treated to avoid environmental damage.

Slurry agglomeration

The ideal slurry will have abrasives behaving as discrete single particles during the

CMP process. However, particles in a real CMP slurry apart from being discrete can also

exist in the form of agglomerates [38, 40]. An agglomerate is a collection of particles that

come together into packed clumps due to physical or chemical interactions and act as a

single entity. Although CMP slurries are composed of very fine particles up to 200 nm

(0.2 [tm), "large" particles of 1-3 |jm and greater are often observed during the process.

Such particles can be due to agglomeration or contamination from foreign material.

These are not desirable for CMP as they can cause micro scratches and pits due to deep









indentation or non-uniformity due to varying polishing pressure. Even minimal and

undetectable concentration of larger sized particles are shown to produce surface defects

in CMP [41]. The agglomeration of slurry can be prevented by proper slurry design,

which includes appropriate use of chemicals, and/or surfactants and the suitable order of

their addition to design the slurry [42]. Other than adding chemicals, the particle surfaces

can also be altered to make the suspension stable during the CMP process [42, 43].

In order to prevent the particle agglomeration during the distribution stage,

dispense filters are used which filter out the agglomerated particles before slurry delivery.

Care is taken so that the filtration of the agglomerated particles does not change the

particle distribution and slurry composition. The drop in slurry pressure and flow due to

filtration is minimized by using a series of filters instead of a single filter.

Chemical Mechanical Polishing Pads

The pad traps the slurry particles on its asperities, and executes the polishing action

by transmitting the normal and shear forces for polishing, thereby playing a very crucial

role in process optimization [19]. The polymeric polishing pad must have sufficient

mechanical integrity and chemical resistance to be effective for numerous polishing runs

through its life. The pad must be able to withstand the aggressive slurry chemistries used

in CMP without degrading, delaminating, warping or blistering. Slurry chemistries range

from highly alkaline near pH 11 used for polishing of inter-layer dielectric to highly

acidic near pH 2 used for metal polishing. Slurries also contain oxidizing agents such as

hydrogen peroxide and potassium iodate. The pad material should be resistant to such

environments. As the polishing slurries are aqueous based, pad should be hydrophilic to

allow circulation of slurry to whole wafer during polishing.









The polishing pad is made up of a matrix of cast polyurethane foam with filler

material to tailor the hardness of the polyurethane impregnated felts for the specific CMP

process. Polyurethanes have a unique property of combining high strength to resist

tearing during polishing and, an acceptable level of hardness and good abrasion

resistance to prevent excessive pad wear during polishing. The CMP pads can be

categorized into four types differentiated by their microstructure [44]. They are: Polymer

impregnated felts (type 1), Poromerics (type 2), Filled polymer sheets (type 3), and

Unfilled textured polymer sheets (type 4). Pads of type 1 and 2 are shown in Figs. 1-9

and 1-10. The figures indicate the variety of pad surface textures or asperities involved in

CMP. The polyurethane polymer consists of two major components/blocks of alternating

hard organic isocyanates and soft polyols. Each of these segments has different

properties, the characteristic properties of a given pad depend on the relative ratios of

these hard and soft segments. Isocyanates, the more rigid blocks, influence the hardness,

modulus, tear strength and stability, specifically at elevated temperatures. Polyols on the

other hand tend to affect the elasticity, toughness, abrasion resistance and the low

temperature stability of polymer.

For uniform polishing, the pad needs to be in contact with the whole wafer surface

with the same contact pressure and relative velocity between pad and wafer in all contact

regions. But wafers are not flat and typically have some degree of curvature due to

stresses induced during manufacture process or differing coefficients of thermal

expansion of the various deposited oxide and metal layers on the substrate. This

necessitates the polishing pad to be flexible enough to conform to the wafer-scale

flatness. This is achieved by laminating a stiff polishing pad to a flexible underlying base









pad, which is typically a more compressible material. This improves polishing uniformity

across the wafer without unduly compromising the stiffness of the top polishing pad. A

stacked pad consisting of an IC 1000 top layer on a Suba IV sub-pad (Rodel Inc.,

Newark, DE) is currently the pad system of choice to obtain both good global wafer

uniformity and high removal rate for various CMP systems.

















(a) (b)
Fig. 1-9. Type I CMP pad. (a) Surface. (b) Cross-section [44].


(a) (b)
Fig. 1-10. Type II CMP pad. (a) Surface. (b) Cross-section [44].









Effect of pad grooves

Polishing pads have macrostructure, which can be either perforations through the

pad thickness or surface groove designs. The motivation behind designing pad grooves is

to prevent hydroplaning of the wafer, ensure uniform distribution of slurry over the

wafer, and to remove the polishing debris from the pad surface through these chemicals

[44]. The groove designs can be circular with either concentric or spiral grooves, cross-

hatched patterns arranged as an X-Y grid across the pad surface, other regular design

such as hexagons, triangles and tire-tread type patterns, or irregular designs such as

fractal patterns, or their combinations. The effect of pad texture on tribological and

kinetic properties of polishing pad has been studied by Philipossian and Olsen [45]. Real

time monitoring of coefficient of friction (COF) was done to estimate the normal shear

forces originating during a particular CMP processes for a given pad. Frictional and

removal rate data were taken on Rodel IC 1000 flat, perforated, XY- and K-grooved

pads. The Somerfeld number, COF, a new parameter called tribological mechanism

indicator (TMI) and materials removal rate were some of the parameters monitored

during the experiments. Philipossian and Olsen [45] reported that flat and XY-grooved

pads begin in boundary lubrication and migrate to partial lubrication as Sommerfeld

numbers increase. Thus different pad surface textures showed different material removal

mechanisms. However, the variation of the mechanical properties need to be studied

further on a microscale to gage its impact on the CMP process and material removal

mechanism.

Physical and chemical changes in pad during polishing

Since polishing is a wet process, the mechanical properties of the pad must not vary

considerably when the pad is wet during CMP. However, the hydrophilic pad material









looses modulus and hardness and gains ductility because water acts as a plasticizer. These

changes are reversible [44] and pad properties revert to the dry values, when the pad is in

dry state, indicating that the chemical attack is minimal [46]. The surface of the

polyurethane pad has been studied and reported in literature [47]. The quantitative

analysis of the physical and chemical changes that occur in the polishing pad during

polishing was performed by Lu et al. [48]. In their research, Lu et al. studied the effect of

polishing cycles on the pore size and shape of the commercially available IC 1000/Suba

IV polishing pad. It was reported that the pore size and shape distribution were modified

by polishing cycles. Polishing induced a permanent distortion in the radial direction due

to the oscillatory motion of the wafer, while no change was seen in pad pore size in the

transverse direction (direction of pad motion). The change was attributed to pore closure

by surface reflow of the polymer during polishing or conditioning and not due to debris

filling. The surface profiles generated using white light interferomery showed that the

overall micro roughness of the pad decreases with polishing and there is a smoothening

effect over a period of time due to polishing cycles. Along with physical changes, the pad

undergoes surface chemical modification and degradation due to polishing slurry

chemicals. No pad degradation of the bulk material of the polishing pad was observed.

The change in spectrum (Fig. 1-11) and shifting of the peaks of the used pad as compared

to the new one has been attributed to the realignment of the molecules of the damaged

pad surface layer.

The porous structure of the polishing pad encourages water seepage. The presence

of water in the polymer pore significantly affects the mechanical properties of the

polishing pad. Li et al. [47] studied the effect of pad soaking time on the mechanical









properties of the polishing pad using dynamic mechanical analysis (DMA). The dynamic

shear modulus decreased to two thirds of its original value when the pad is soaked for 5

h. Further, the rate of decrease in dynamic shear modulus decreases at around 14 h but

does not reach a steady state. No significant change in the removal rate was observed

when pads with different soaking time are used in oxide polishing. This shows that

removal rate is more of a surface characteristic of the pad and is not affected by the bulk

material.
















slurry. [48]

Modification of the pad-wafer contact mechanics can directly impact the CMP

process performance. The modified surface can even change the mechanism of material

removal during a polishing process [49]. During polishing, the pad surface layer degrades

decreasing the pad surface roughness. The pad surface which is flattened or "glazed"

needs to be rejuvenated to bring the polishing performance back to the original value.
131)1.1) 12511 12(11 I 1 ) IlflO I [| ) I{H) W, I









Fig. 1-11 Troughening absorbancf the spectrad by a diamof used nditioner is known to result in pad revival.
slurry. [48]

Modification of the pad-wafer contact mechanics can directly impact the CMP

process performance. The modified surface can even change the mechanism of material

removal during a polishing process [49]. During polishing, the pad surface layer degrades

decreasing the pad surface roughness. The pad surface which is flattened or "glazed"

needs to be rejuvenated to bring the polishing performance back to the original value.

The roughening of the pad by a diamond conditioner is known to result in pad revival.

Along with wafer polishing, the conditioner made of diamond grit considerably alters the

surface of the polishing pad. The process of conditioning essentially removes some

amount of top pad surface and is performed either in-situ (during the polishing run) or ex-









situ in between two polishing runs. The pad damage due to insufficient conditioning is

termed as "glazing". Experiments were performed on the CMP pad by Lawing [49] at

different conditioning levels of aggressiveness (expressed as low, medium and high). The

change in polishing rate correlated better with the predicted surface contact area rather

than the average surface roughness.

Effect of temperature change on polishing pad

The polishing pad might be subjected to elevated temperatures during the course of

the CMP process [19]. The heating is due to the frictional forces generated by solid-solid

contact between pad and wafer during polishing. There is some alleviation of heating

when the polishing is done in hydrodynamic contact mode [48]. However, there is an

overall increase in the pad temperature irrespective of the mechanism of polishing. The

effects of pad heating are compounded if the chemical reaction between slurry and pad is

exothermic [38]. The mechanical, physical and chemical properties of the polyurethane

material can be permanently or temporarily altered if the pad is heated beyond a

particular temperature [50]. DMA, thermomechanical analysis (TMA) and

thermogravimeteric analysis have been used for material characterization of the polishing

pad [47, 48].

The applicability for DMA for polishing pads has been elaborately studied by Lu et

al. [48]. Based on the results of previous experiments performed by Li et al., [47], DMA

was performed to evaluate the structure-property relationship of polyurethane pads. The

glass transition temperature is the temperature at which the macromolecules of the

polyurethane break away from entanglements and undergo micro-Brownian motion.

Investigation of glass transition temperature of the polyurethane pad is important as it









corresponds to a sharp decrease in the hardness and modulus of the pad which in turn

affects the removal rate and global planarization.

Non-uniformity of the polishing pad

The pad might be directly responsible for several process defects like WTWNU

where there is non-homogeneity of polishing when one wafer is compared to another or

WIWNU where there is non-homogeneity of polishing at different areas of the same

wafer. The scanning ultrasound transmission (UST) is a nondestructive technique

developed that works on the principle of ultrasound permeability through absorbing

visco-elastic medium [51, 52]. The difference in the ultrasound absorption in the areas of

varying density and viscoelasticity is used to determine the non-uniformity within a

single pad there by giving an in-depth idea of the physical characteristics of the given

pad. In order to improve the yield of the CMP process and, to get a highly planar, defect

free uniform wafer surface with reduced overall manufacturing costs involved, there is a

need to extensively study the fundamental properties of the CMP pads on the whole.

CMP process in the future

The semiconductor industry has effectively adapted its CMP technology for the 300

mm wafer [53]. Beyond the adoption of copper interconnects, several technologies are

necessary to continue the shrinkage of device dimensions and the increase of packing

density in ULSI manufacturing. The use of ultra low-k materials as interlayer dielectrics

has been at the forefront for decreasing the "C" part of the "RC delay". However,

polishing of ultra low-k dielectrics which are mechanically weak (soft) is a daunting task.

The single and dual damascene structures comprising of ultra low-k porous or polymeric

materials are more prone to buckling and crushing failures due to significantly lower

hardness and Young's modulus as compared to silicon dioxide. According to the ITRS









roadmap [12] materials with dielectric constant 2.2 will be integrated in the IC by year

2007.

Also, there needs to be a marked improvement in slurry selectivity for accurate end

point detection when the constituent layers of the damascene structure namely, metal,

hard mask, cap layer, barrier layer and dielectric are polished. Furthermore, it is

necessary to explore the niche of the CMP process in STI and other applications such as

backside polishing and the fabrication of micro-electro-mechanical systems (MEMS).

Here, the CMP process must be integrated horizontally and vertically to achieve high

throughput and performance. In MEMS applications, horizontal integration ensures

reliability and good performance of a specific CMP process run. The development of new

polishing pads and pad architectures, novel slurries, new metrology techniques, etc.

comes within the scope of horizontal CMP integration. Vertical integration ensures

success of every successive CMP operation. This includes the integration of the upstream

processes such as Cu/barrier deposition, etching and downstream processes such as ILD

deposition and lithography. This opens a wide scope of research for further optimization

and development in Cu CMP process. Due to intricate interactions of the processes

involved in any CMP process, modeling efforts are needed to get a systematic

understanding of the process and predictability of the CMP outputs.

Scope of Dissertation

The importance of polishing and the various available planarization techniques

with emphasis on CMP have been discussed in Chapter 1. A general overview of the

parameters involved in CMP are discussed with prominent interactions between them.

Chapter 2 gives an overview of the CMP modeling efforts and the framework of the

PERC I CMP model. The model's challenges are described, which necessitated the






29


development of the PERC II model. The assumptions of the PERC I model are refined as

necessary in chapter 3. Model development is also delineated with critical differences

between PERC I and II models. Chapter 4 validates the PERC II model comparing to

experimental literature data and comments on the predictive capability of the model.

Chapter 5 summarizes the findings of the study along with the suggestions for future

work.














CHAPTER 2
CMP MODELING: OVERVIEW OF PERC I

Like most semiconductor manufacturing processes, simultaneous tuning of

process variables is a formidable task due to many varying parameters. Unfortunately,

much of the commercial CMP process development cycle is based on nearly blind

design-of-experiment (DOE) testing. While these empirical tests help to optimize

parameters in a very small range, the overall approach does not necessarily facilitate a

deeper understanding of the process. Thus, CMP research has focused on developing

process models in order to gain further insight on the process mechanics for better control

over the CMP outputs.

The ultimate goal is to model at three scales of CMP, namely, the particle, die and

wafer scales. The models at the particle scale are needed to understand the mechanisms

involved in interactions between slurry particles, chemicals, polishing pad and wafer

during blanket wafer polishing. The models at the feature or die scale are needed to

address the topography evolution of integrated circuit (IC) chips as a function of pattern

density, line width, pitch width and polishing time. The wafer-scale models also need to

address the issues related to the material removal non-uniformity over the entire wafer

surface. To satisfy the manufacturability requirements in the sub-micron IC fabrication,

the margin of the profile non-uniformity is usually limited in the range of several hundred

nanometers. The material removal non-uniformity across the wafer is rooted in the non-

uniform distributions of pressure and velocity over the wafer surface, which in a large









degree, are determined by the configurations of CMP equipment. A model at this scale,

therefore, needs to consider the equipment configurations appropriately.

Literature Review

In the last decade, various kinds of models have been proposed by researchers,

concentrating on different aspects of CMP covering the particle, die and wafer scales. But

the effectiveness of die and wafer scale models depends strongly on the robustness of the

particle scale models, as the die and wafer-scale models are developed based on the

particle scale models. Therefore, in order to understand and predict the performance of

CMP in wafer scale, the current study aims to understand the behavior of CMP at particle

scale. As the current work focuses mainly on particle scale modeling, only related models

will be reviewed here.

Preston Equation

The Preston equation [54] as an empirical relation for optical glass polishing was

substantiated by Cook [24] who considered that the interaction between abrasive particles

and wafer surface leads to removal of atomic clusters due to bond breakage. Preston

provided a simple model of material removal in glass polishing tools which is often

adopted for CMP processes also. But, experimental results have shown that slurry and

pad properties also significantly influence the process along with down pressure and

platen speed [55, 56]. In order to explain the non-Prestonian behavior, many modeling

efforts have been carried out in the past decade and is still a topic of considerable interest.

The three most important elements in the CMP material removal process are the

wafer being polished, slurry and polishing pad. Researchers adopted two main

approaches in modeling the CMP process. One approach is based on fluid

hydrodynamics, where material removal is considered to be caused mainly by slurry









erosion. Slurry film thickness, hydrodynamic pressure and removal rate are generally

calculated by solving Reynolds or Navier-Stokes equation [57-62]. The other approach

uses the theory of contact mechanics, which assumes that the material removal occurs by

particle indentation into the wafer surface. Pad surface roughness and hardness are

generally used to calculate the particle indentation into the wafer thereby calculating the

removal rate [27, 63-67]. Finite element modeling (FEM) has also been used to determine

the pad asperity mechanical properties recently [68, 69].

It is generally agreed that the typical CMP process conditions lead to major

material removal by particle abrasion rather than by slurry erosion [70]. Experimental

observations of polished surfaces have revealed that material removal in CMP occurs as a

consequence of a combination of chemical reaction of the slurry chemicals with the wafer

surface and ploughing (repeated sliding, rolling, or indentation) of the abrasive particles

against the wafer surface that is already modified. The chemical reaction results in

formation of a thin layer on surface which is of different modulus than the

substrate/wafer, aiding in material removal [71].

When particles are introduced between wearing surfaces, the wear is due to the

particles embedded in one of the sliding surfaces. This process is referred to as three-

body abrasion. In the CMP process, the particles acting as single point cutting tools, dig

into the wafer and plow a series of grooves in it. Therefore, the CMP process is

essentially a three-body abrasive wear. The analysis of the texture of polished surfaces

also supports this observation. Fig. 2-1 illustrates typical post CMP surfaces as examined

via an optical surface profiler. The surface texture consists of a number of randomly










oriented nano-grooves (Fig. 2-1). The width and depth of the grooves are determined by

the penetration depth of the abrasive particles into the wafer surface.


301


' 75,00


S2,5

f-


5.0 nm



2.5 nrm



0.0 nm


111111111-- -.. -
0 2,50 5.t
C1m
(b)
Fig. 2-1. Polished wafer surfaces showing nanoscratch surfaces. (a) Silica wafer [72]. (b)
Si wafer [73].

The material removal process in CMP can be considered as sliding of the indented

slurry particles over a chemically influenced thin layer over the wafer surface. The









knowledge of critical factors that effect the CMP process and the interactions among

them is critical to select the respective parameters and design an enhanced CMP process,

predicting material removal rate, and surface quality (roughness, defects, etc.). The most

popular material removal equation is the Preston's Equation [54], which was initially

introduced for glass polishing,

MRR= KePV, (2 1)

where MRR is the material removal rate, Ke an all-purpose coefficient, P the down

pressure and V the relative velocity over the wafer-pad inteface. It demonstrates a linear

dependency of material removal rate on the pressure and velocity. Not all experimental

MRR data in CMP, especially in metal CMP, support the linear dependency between

material removal and the product of pressure and velocity.

Modifications to Preston Equation

In order to explain the non-Prestonian behavior of the CMP process, revised

Preston's equations were proposed by several researchers. For example, considering that

the material removal rate does not extrapolate to zero, Maury et al. [74] introduced a

fitting parameter MRRo into Preston's equation

MRR= KePV + MRRo (2.2)

Later, the nonlinear equation

MRR= KePu VO, (2.3)

where ac and P are two fitting parameters, was proposed by Wrschka et al. [75] to get a

better fit for the experimental data.

The major problem with Preston's equation and its revisions are that they are

empirical modeling efforts. Therefore, they do not shed any light on gaining insight into









the process especially regarding other process variables. By extending Brown's model

[76] of the metal polishing to the silicon polishing, Cook [24] developed a physical

model to address this limitation. The interactions between the abrasive particles and the

wafer surface is proposed as a Hertzian elastic penetration [77] of a spherical particle

under uniform pressure P into the wafer surface, sliding along the surface with a velocity

V and removing material volume proportional to the penetration. The MRR formulation

was proposed was

MRR= PV/(2E) (2.4)

where E is the Young's modulus of the wafer material. This model can be taken as a

theoretical equivalent to the Preston's equation since it supports the linear dependency of

MRR on pressure and velocity. The relationship between the wafer surface roughness Ra

the down pressure P, and abrasive size can also be obtained based on this model

Ra=3/4 b (P/2klE)2/3 (2 5)

where kl is the particle concentration, which is unity for a filled close hexagonal packing

[24] and b the diameter of the slurry particles. A similar model was developed by Liu et

al [78] based on the statistical method and Hertzian elastic penetration. Besides the wafer

material properties including wafer hardness Hw and wafer Young's modulus Ew, this

model included pad hardness Hp and abrasive Young's modulus Es resulting in


MRR = C, H,- E, + E PV (2.6)
H +H, P Es Ew

where Ce is a coefficient to account for the effects of slurry chemicals and other

consumable parameters. This model, similar to Cook's model, suggests that the material

removal is proportional to the applied pressure and relative speed









The advantages of Cook's and Liu's models over Preston's equation are that they

provide more insights into the roles of the consumable parameters. The contributions of

the slurry abrasives and pad, for example, have been attributed to their size and hardness.

An additional benefit is that not only material removal rate, but also surface quality issues

such as roughness (Eq. 2.5) can be addressed using these models.

Slurry Erosion

In Cook's and Liu's models, the mechanical removal by abrasive particles was

assumed to be the dominant mechanism. However, some researchers instead assumed the

material removal to be by "slurry erosion" approach, i.e., due to mechanical-enhanced

erosion. Runnels et al. [79-81] developed an erosion-based model for CMP. They

assumed that a fluid film exists between the wafer and pad interface, which affects the

erosion/material removal rates at each single point through the fluid stress tensors.

Motivated by observations at feature scale, modification to Preston's equation was

proposed, with relative velocity V, replaced by the tangential stress on the wafer surface;

MRR=Ceoton (2.7)

where Ce is an all purpose coefficient, ot is the shear stress due to the slurry flow and on

the normal stress.

The model uses a steady state incompressible Navier-Stokes equation to model the

slurry flow at the wafer-polishing pad interface. The wafer surface is assumed to be

smooth and spherical with a large radius of curvature. The fluid layer thickness and the

angle of attack between the pad and the wafer are obtained through an iterative procedure

satisfying force and momentum balance. Runnels' model has been integrated into several

particle-scale models by researchers including Tseng and Wang [82] and Zhang and









Busnaina [83]. Tseng and Wang attributed the normal stress at the particle-wafer contact

to the elastic indentation of the particle into the wafer surface, which is similar to that

proposed by Cook and calculated the normal stress over the wafer-particle interface as

F
n (2.8)


where F is the force acting on the spherical particles, which is proportional to the pressure

P. The radius of particle-wafer contact, re is given by

r3 3d 1 2 1 v '2
r 8 F+ Er- (2.9)
8 E E'

where d is the diameter of particles, v and v' the Poisson's ratios of wafer surface and the

particle and E and E' the elastic modulii of the wafer and particles, respectively. The

shear stress due to the slurry flow can be approximated as

t =CeIVPA, (2.10)

where |t is the dynamic viscosity of the slurry and Ao the area of wafer surface

respectively. Substitution of equations (2 8) and (2 10) into (2 7) yields

MRR=KeP5/6V1/2 (211)

where Ke is the parameter to account for material properties, slurry abrasive

concentration and chemical processes. This model demonstrated a nonlinear relationship

between the material removal and the product of pressure and velocity. Tseng's model

attempted to connect the elastic indentation to the erosion rate, whereas Cook's and Liu's

models connect it to the mechanical abrasion. While the down pressure dependency (P5/6)

is quite close to linear dependency, the velocity dependency (V2) however, is quite

nonlinear. This is because the contribution of velocity has been attributed to the slurry









flow instead of abrasive sliding. Due to pad porosity and surface asperities, such a slurry

film is bound to be interrupted by solid-solid contact. Thus hydrodynamic lubrication

may be responsible for distributing the slurry, while the material removal occurs mainly

through solid-solid contact.

Cook's, Liu's and Tseng and Wang's models attributed the penetration of the

abrasive particles to Hertzian elastic contact. Zhang and Busnaina [83] estimated the

contact pressure between the particle and the contact surface in their model and found

that it is larger than the yield stress of the polished materials. Therefore, they proposed

that plastic deformation is a more likely deformation mechanism in polishing. The

contact pressure over the particle-wafer interfaces is suggested to be equal to the hardness

Hw of the wafer materials. Replacing the normal stress (Eq 2 8) in Tseng and Wang's

model with the hardness Hw yields the following material removal rate formulation

MRR= Ke(PV)1/2 (2.12)

where Ke is the parameter to account for materials properties, slurry abrasive

concentration and chemical processes. Both Tseng and Wang; and Zhang and Busnama's

models suggest a nonlinear pressure times velocity dependency of material removal rate.

Moreover, it is noted that besides the external force applied on the particles from the pad,

Zhang and Busnaina also proposed that an adhesion force, either van der Waals force or

electrostatic force depending on the separation distance between the particle and the

wafer, contributes to the indentation. This has been integrated into another particle-scale

model by Zhang et al. [84]. In a series of articles by Ahmadi and Xia [85], and Mazaheri

and Ahmadi [86, 87], a thermodynamic work parameter Wa of adhesion was added to

account for its effects on the indentation of abrasive particles. Mazaheri and Ahmadi [86]









introduced a double layer (dl) force into the indentation force, whose magnitude is a

function of the zeta potential of the abrasives and the wafer. Beside the abrasive wear,

Ahmadi and Xia [85] also considered the adhesion wear of the wafer in their model.

Moreover, while most of the models treated the abrasives as having a spherical shape,

Mazaheri and Ahmadi represented them as spheres with a number of hemispherical

bumps around their surface. The penetrations of slurry abrasives are modeled using the

penetrations of the bumps.

The above models imply that the abrasives are embedded in the pad and indent into

the wafer surface. It should be noted that some modeling efforts also assume that the

abrasive particles float in the slurry and impact the wafer surface from time to time

causing material removal [88].

Pad Considerations in CMP Models

The pad is assumed to be smooth in the earlier particle-wafer interaction models. It

has been observed that the pad topography and pad material play an important role in

material removal processes. For example, the material removal rate has been reported to

increase with the pad surface roughness [55]. Without conditioning of the polishing pad

surface, the material removal rate decreases exponentially with polishing time [89]. In

consideration of this, Yu et al. [63] developed a pad-based model. They approximated the

peaks on the pad surface by hemispherical asperities with constant radius and the asperity

heights to follow Gaussian distribution. Based on the model, the real contact area is

smaller than the nominal (apparent) contact area and linearly proportional to the down

pressure. Steigerwald et al. [19] proposed that the material removal rate is proportional to

the number of abrasive particles over the contact area. Combining this argument with









Yu's model yields a linear dependency of the material removal rate on the down pressure,

which agrees with Preston's equation.

Zhao and Shi [90] also proposed a model based on the wafer-asperity contact.

Unlike Yu's model [63], this model does not consider the Gaussian distribution of the

asperity heights. The contact area between an asperity and the wafer is given by Aa Ua P2/3

based on Hertz elastic contact theory. By combining Steigerwald's argument, the material

removal rate formulation can be obtained as

MRR= K(V)P(2/3) (2.13)

where K(V) is a function of the relative velocity V and other CMP parameters. It is

further considered by Zhao and Shi [90] that when the particles are rolling against the

wafer surface, their contribution to material removal will be negligible. They argued that

whether the particle is rolling or not is determined by the surface friction between the

particles and the wafer, and only when the down pressure P is larger than a threshold

down pressure Pth, the pure rolling can be avoided. The material removal rate is given as:

MRR = K(V)(P2/3 Pth2/3) for P > Pth (2.14a)

and

MRR = 0 for P< Pth (2.14b)

The fundamental difference between the above pad-based models and the particle-

based models by Cook and others is that pad-based models attribute the material removal

rate to the number of abrasive particles captured by the polishing pad while the later

attributes the material removal rate to the interaction between a single abrasive and the

wafer.









A particle-pad interaction is critical to the particle scale models considering that the

function of the pad is to trap the abrasive particles and transmit load to the particle-wafer

interface. Cook's model [24]suggested a close-packing of spherical abrasives onto the

pad. It is assumed that the wafer and pad are separated completely by the abrasives and

no direct pad-wafer contact exists. The force applied on a single abrasive under these

assumptions is given by


F = Pr2 (2 15)
ki

where P is the polishing pressure, r the abrasive size and kl the particle fill fraction on the

pad. This particle-pad interaction model has been integrated into the material removal

model of Cook. It is also used by Ahmadi and Xia [85] to evaluate the force on a particle

in their case of a hard-pad and a larger concentration of abrasive particles. Later, Zhao

and Shi [90] proposed that when the pad is soft enough, the abrasive particles will be

embedded deeply into the pad and the force from the wafer is supported by the pad and

abrasives together. This idea has been applied by Luo and Domfeld [27, 91, 92] and Fu et

al. [93] in their model. Luo and Dornfeld's model [27, 91, 92] suggested that this force is

proportional to the contact pressure multiplied by the abrasive size by assuming that the

abrasives are closely packed to each other and these closely packed abrasives are

enclosed by the pads so that the effective contact area between wafer and pad is equal to

that without abrasives. Moreover, the size of the abrasives that may be captured by the

pad is assumed to be a function of abrasive size distribution and pad properties. Their

model, however, neglects the lower sizes of the particle size distribution in material

removal calculation. Fu et al. [93] later assumed that the abrasives are dispersed evenly

over the pad surface and used a beam model to evaluate the wafer-pad direct contact









between two single abrasives. The force supported by a single abrasive can be obtained

from the beam model and is a function of abrasive size, down pressure and pad material

properties [93].

Besides the force, the second purpose of an abrasive-pad interaction model is to

evaluate the number of abrasives involved in the material removal process. Fu et al. [93]

considered the number of trapped particles as an independent parameter in their model.

This may be misleading considering that various parameters, for example, the abrasive

weight concentration and abrasive size, have an influence on the number [27, 72, 91, 92].

Luo and Dornleld considered more complex scenarios and suggested that only a portion

of abrasives are involved in the material removal process, which is not reasonable.

Slurry Considerations in CMP Models

The contribution of slurry chemicals to the material removal is either neglected in

earlier models or represented by an all-purpose coefficient. Cook [24] suggested a

complete but complicated scenario of the chemical effects. Besides the mechanical

removal, it is proposed that the surface removal during polishing include the following

five chemical processes (i) the slurry chemical diffusion into the wafer surface, (ii) the

subsequent wafer material dissolution under the load imposed by the abrasive particles,

(iii) the adsorption of the dissolution product onto the surface of the polishing grain, (iv)

the re-deposition of the polishing materials back onto the wafer surface, and (v) the

corrosion rate between particle impacts. These steps are not considered in most of the

early models as they are complex to model quantitatively.

The major contribution of slurry chemicals on the material removal process has

been attributed to the formation of a surface layer. This idea is well demonstrated by

Kaufman et al. in their Tungsten CMP model [37].









Kaufman et al. proposed that this passivation layer is removed by slurry abrasives

and the fresh tungsten surface is exposed, which is subsequently passivated and removed.

This mechanism of continued passivation and removal can be used to explain the copper,

aluminum and other metal CMP systems as well. A similar mechanism is supposed to

work in silicon, silica and low-k CMP systems. Paul [94] and Zhao et al. [95] have

proposed detailed surface kinetics models to connect the slurry chemical concentrations

and fresh metal surface sites available to the formation rate of the surface layer. Their

models can explain the material removal rate as a function of chemical and abrasive

weight concentration. Borst et al. [62] have proposed a five-step model for CMP of SiLK

dielectrics (i) mass transport of reactant from the slurry to the slurry/wafer interface, (ii)

adsorption of reactant to available surface site, (iii) reaction between adsorbed reactant

and specific wafer surface to form an altered wafer surface layers, (iv). mechanical

removal of the altered wafer surface layer, and (v) mass transport of removed material to

the bulk slurry. In their work, the mass transportation, slurry chemical concentration and

reaction rate to the formation of the surface layer were incorporated. This detailed model

was suggested to be able to be extended to the CMP of other materials.

The idea of continuous surface modification and removal has been applied in the

model developed by Qin and co-workers [96]. A similar approach has also been used in

Luo and Dornfeld's model [91]. They extended Kaufman's model by proposing that the

surface layer is a bi-layer structure, though in reality there might be a gradual transition

between the layers. They did not cover the details on how the formation rate of the

surface layer is affected by the slurry chemicals. But Luo's model assumes that all the









asperities contact the wafer and that the particles fill the asperity-wafer contact spots,

which is not necessarily true.

The slurry chemicals affect not only the wafer but also the slurry abrasives and

polishing pad. Their contribution to material removal is therefore not only reflected

through surface kinetics, but also through alteration of the abrasive and pad properties

such as the abrasive shape, abrasive size and pad Young's modulus. There are not many

modeling efforts on these two interactions yet. A recent model by Castillo-Mejia et al.

[97] tried to explain the effect of water-pad interaction in CMP. The water is proposed to

plasticize the polishing pad and reduce its elastic modulus. A formulation on the ratio of

the Young's modulus of wet pad to the dry pad is suggested. This Young's modulus is

then used in a wafer-pad contact model to evaluate the material removal.

Many of these models were also extended to patterned wafers along with other

modeling concepts including combination of the solid-solid contact and slurry erosion

approaches [98-109]. Polishing mechanisms were also based on surface reaction kinetics

[95, 110, 111] and modeled using molecular dynamics simulations [112-115].

PERC I CMP Model

Most of the earlier models have concentrated on one or two interactions of the

CMP process parameters. They are useful for identifying the input parameters. However,

they may not be sufficient for understanding the whole material removal process. The

effects of the same input parameters may be contrary to each other when acting in

different conditions. A comprehensive model of CMP integrating the main interactions

together is therefore needed. For this purpose, a model was developed by Qin et al.[72],

taking into consideration most critical CMP parameters. This section discusses the









assumptions on which the model is built, its effectiveness in predicting the CMP process

variables and the model limitations.

Model Development

The chemicals in a slurry alter the properties of the wafer surface that is in contact

with them. Since the chemical influence is restricted to a thin region near the wafer

surface, a thin surface layer whose mechanical properties are different from those of the

bulk wafer is assumed. This surface layer can be formed by chemical reactions at the

surface or by the diffusion of slurry ionic species into the wafer. The surface layer is then

removed by mechanical action of the slurry particles and/or by dissolution into the slurry

through a convective diffusion process. Although there may be a few exceptional cases

[Luo98], material removal by the dissolution is small compared to that by the mechanical

action of the slurry particles, and it is not considered in this model. Fig. 2-2 describes

schematically the physical situation that is considered in the present analysis. The pad

asperities that are in contact with the wafer surface act as the anchoring sites for the

slurry particles. The anchored particles then gouge the chemically altered wafer surface

or the bulk wafer depending on the indentation depth resulting in material removal. In the

following section, various parameters considered in the present analysis and the

underlying assumptions are described followed by the details of the model development.

Topology of a pad surface has been characterized and described statistically by

various researchers [63, 116] Their measurements indicated that pad asperity heights

were in the order of tens of microns and appeared to have a normal (or Gaussian)

distribution. In Fig. 2-2, the topology of the pad surface is shown schematically along

with a statistical description characterizing the pad asperities. In this figure, 3 is the









mean radius of curvature of the tip of the pad asperities, 4 is the distribution function for

the height of the asperities, and cy the standard deviation of the pad asperity heights,

respectively.


Asperity Height, z


(b)


Fig. 2-2 Pad consideration in PERC I. (a) Schematic of the pad surface that is in contact
with the chemically modified layer formed on the wafer surface; (b)
Distribution of the pad asperity heights (When the height of an asperity is
greater than the average gap h between the pad and the wafer, that asperity is
in contact with the wafer surface.) [72]









Since the characteristic length scale for the roughness of the pad surface (e.g., 3) is

much larger than the feature sizes on the wafer, it was assumed that the wafer surface is

smooth and flat compared to the pad surface. This assumption makes it possible to use

the Greenwood-Williamson model [117] that describes the contact area, Areal, between a

flat surface and a randomly rough surface under a normal force (or load), L:


A ,real = TNA z h) (z)dz (2.16)

L = NAE12(z h)3/2 ()dz (2.17)

where N is the number density of the pad asperities (i.e., number of asperities per unit

area), Ao is the total area of the flat wafer surface, and h is the average gap between the

smooth wafer and the rough pad under the given conditions. Then, the down-pressure, P,

applied to the wafer with an area Ao is L/Ao whereas the actual mean contact pressure, Pr,

is L/Areal if the normal force applied to the wafer is entirely supported by the pad

asperities in contact with the wafer. That is

L =PA,= PrAreal (2.18)
E* is the composite modulus between the two surfaces in contact, that is defined as

1 1-v2 _V2
1 ~ (2.19)
E* Ep E

where E and v are the Young's modulus and the Poisson's ratio, and the subscripts p and

w represent the pad and the wafer, respectively.

Equations 2.16, 2.17 and 2.18 provide an explicit relationship between the contact

area (Ar) and the down pressure (P) that is needed in modeling the CMP process. From

Eqs. 2.16 and 2.17,










AL 4E* 3 h h)/2(z Jz (2.20)
L 4E (z -h)3/( Z


Following Yu et al.[63], the normal distribution function may be used for the


distribution of the asperity height, ). When )(z) = exp -z-- is substituted into
Cy [27j 2CY2 2

Equation 2.20, the integral cannot be obtained in an explicit form. Instead, a numerical

integration should be preformed. Johnson showed that the ratio of the two integrals in Eq.

2.20 is nearly a constant for a broad range of h/o [77]. Thus,

rea =-C 1 =C-1, PA, 22
A-C C (2.21)


where C is a constant whose value is between 0.3 and 0.4 when h/l is in the range of 0.5

and 3.0. Recalling that o is the standard deviation of the asperity height distribution,

h/o=3.0 represents a situation where only 0.13% of the pad asperities are in contact with

the wafer whereas about 30.85% is in contact when h/o=0.5. Practical situation in a

typical CMP process is well within this range ofh/l value. From Eqs. 2.18 and 2.21,


Pr = C E (2.22)


It should be noted that the contact area (Ar) increases linearly with the down-

pressure whereas the contact pressure (Pr) remains constant due to the linear increase of

Ar with P.

The underlying assumption for Eq. 2.18 is that the applied normal force on the

wafer is supported entirely by the pad asperities. As is mentioned previously,

experimental measurement on the friction coefficient indicates that the hydrodynamic









pressure is negligible under typical CMP operational conditions. Furthermore,

commercial pads often have grooves or perforations to prevent hydroplaning (i.e., to

prevent a large pressure development due to a lubrication flow) and to ensure uniform

slurry distribution. Thus, the assumption that the hydrodynamic pressure is negligible is

justifiable.

Small Plastic Deformation of the Thin Layer on the Wafer Surface

Considering the fact that the deformation of the surface layer by the slurry particles

under the contact pressure is very small in the order of several nanometers, the mode of

deformation can be assumed to be plastic deformation. In the case of oxide CMP, it is

known that the silica surface is softened when it is in contact with an aqueous solution. A

surface layer (or so-called gel layer) is formed due to the diffusion of water molecules

into the silica surface altering the surface properties.

The situation may be different in the case of metal CMP. Since an oxidizer is added

in most metal CMP processes, metal oxide is formed on the wafer surface creating a

structure mismatch at the interface between the oxide layer and the bulk wafer

underneath. Thus, delamination or microcracking of the oxide layer may occur at the

interface during the metal CMP process. However, as evidenced in previous sections, it is

likely that plastic deformation is still the dominant mode of deformation because the

indentation depth by the slurry particles is small (e.g., less than several nanometers).

Furthermore, the oxide layer may be soft due to hydration in an aqueous environment.

Thus, the assumption that the chemically altered thin surface layer on the wafer exhibits

plastic deformation is plausible. This assumption enables us to apply the abrasive wear

theory in deriving the expression for the material removal rate. When the indentation

depth is beyond the surface layer, the deformation of the unaltered wafer material may be









either plastic or elastic depending on the hardness of the wafer material and the slurry

particles.

Material Removal by a Single Particle

In the present analysis, it is assumed that the slurry particles are monosized and of

radius 'R'. The overall material removal rate is assumed to be the multiple of the removal

rate by a single particle and the number of particles in contact with the wafer:

(RR) = n (RR)v/Ao (2.23)

where n is the number of slurry particles anchored in the region of the pad that is in

contact with the wafer, and (RR)v is the volumetric removal rate by a single particle. The

overall removal rate, (RR), is typically described in terms of the thickness removed per

unit time; hence the division by the nominal wafer area Ao.

Schematic illustration of single particle abrasion is given in Fig. 2-3. The material

removal is viewed as a sliding-indentation process in which the volumetric removal rate

by a particle is given as

(RR)v = AiV (2.24)

where Ai is the cross-sectional area of the particle immersed in the wafer under pressure

(hashed area in Fig. 2-3a), and V is the relative velocity of the pad to the wafer.

Assuming that the hard particle maintains its spherical shape,


A, = -a(R o)+ R2 arcsin a
R (2.25)

where co is the indentation depth and a the radius of the circular indentation on the wafer

surface by the particle of radius R,

Because co is very small compared to R, a/R is also very small and Equation 2.25

can be linearized about a/R to give









A, = ac +
3 I R]) (2.26)

Thus the volumetric removal rate is


(RR), = ao V
3 (2.27)


WaferWafer
t
a Co t '"


b Pad
PPad t

tFa P Fa


(a) (b)
Fig. 2-3. Schematic of single particle abrasion showing the removal of chemically
modified surface layer. (a). o < t. (b). o > t with soft wafer materials.

Because a2=(2Rco-o2) and co is much smaller than R, Equation 2.27 can be

rewritten as

2a3V
(RR) 2aV
3R (2.28)

Once the indentation depth co (or a) is known, the volumetric removal rate by a

single particle can be readily calculated from Eq. 2.28.

Depending on the relative magnitude of the indentation depth (co) to the surface

layer thickness (t), the material removal may be classified into two different regimes as

depicted in Fig. 2-3; (a) o < t and (b) co > t.









Indentation depth smaller than the surface layer thickness (i.e., o _< t)

When the chemically modified surface layer is thick enough, the indentation depth

co will be no greater than the surface layer thickness and only plastic deformation within

the surface layer occurs. In this case, o) (or a) can be obtained from the force balance

imposed on the particle by the pad and the wafer that depends on the indentation depth of

the particle into the wafer surface. The force imposed on a particle by the pad is given as

F = 7rb' (2.29)


where b is the radius of the circular indentation into the pad as described in Fig. 2-3a, and

P, is the contact pressure given by Eq. 2.22. The force on the particle by the deforming

wafer can be given as


F = Ta 2B (2.30)


where Be is the effective Brinell hardness of the chemically modified surface layer. The

term "effective" is used because its value is influenced by the thickness of the chemically

modified surface layer and the material property of the underlying substrate. The pad is

supposed to hold the particles in place thereby transmitting the normal force to the

particles that cause indentation of the wafer surface. The pad should be soft enough to

provide stable anchoring of the particles on its surface. However, if it is too soft, the

particles will be embedded too deeply into the pad diminishing the material removal

capability of the particles. Thus, the pad should be sufficiently hard to make the value of

b in Fig. 2-3 to be close to the particle radius R. Then, from equations 2.29 and 2.30 with

b R,








1/2
a=R (2.31)


This equation along with equations 2.22 and 2.28 gives the following expression for the

volumetric removal rate by a single particle of radius R.

(2 "-3/4 E 3/2
(RR) C3/2R2 ~/2 V (2.32)
S3 P Be

Indentation depth greater than the surface layer thickness (i.e., o > t)

When the bulk wafer material beyond the surface layer is relatively soft (e.g.,

copper) compared to the hardness of the particles, it is possible for the particle to cause

deformation into the wafer beyond the surface layer (Fig. 2-3b). As it was described in

the previous section, the deformation is expected to be plastic for both the surface layer

and the bulk wafer, and the force causing the deformation may be given as

F, = [2tRB, + (a2 2tR)B j (2.33)

where Bw and Be are the Brinell hardness of the bulk wafer material and the chemically

modified surface layer, respectively. Because this force is equivalent to the one imposed

on the particle by the down-pressure, Eq. 2.33 is equated with Eq. 2.29 with b=R to give


R2P, + 2(B, Bj)Rt 12
a R + 2(B (2.34)


Then, Eq. 2.28 for the volumetric removal rate by a single particle is reduced to


(RR) =2C(j R2 +21 Rt (2.35)
3 B BR









While equation 2.35 describes a situation where the deformation reaches into the

bulk wafer beyond the surface layer, deformation of the bulk wafer may not occur if the

bulk wafer material is very hard. This limiting case corresponds to the situation of

infinitely large Bw in equation 2.35 that is reduced to


(RR) =4, R1/2t3/2 (2.36)
3

Equations 2.32, 2.35 and 2.36 indicate that the volumetric removal rate by a single slurry

particle depends on the geometry of the pad and the particle (i.e., 3, C and R), the

material properties (E*, Bw and Be), the thickness of the surface layer (t), and the relative

velocity of the pad (thus the particle) to the wafer (V). It may be interesting to note that

(RR), is independent of the down pressure, P. It is due to the fact that the contact

pressure, Pr, is independent of P. As equation 2.21 indicates, the contact area of the pad

with the wafer (Ar) increases linearly with P. Consequently, the mean contact pressure,

P, which is PAo/Ar, is independent of P. In the following section, the number of particles

in contact with the wafer surface is estimated to determine the overall removal rate.

Estimation of the Overall Removal Rate


When the wafer is pressed against the pad and is in sliding motion relative to the pad, the

particles can be entrapped only in the region where the local distance between the wafer

and the pad asperity is smaller than the particle diameter, 2R. Thus, the number of

particles that can be trapped on the pad asperities is


n = 2R'Areal" Pn


(2.37)









Here A, is the real contact area between the wafer surface and the pad asperities as

it was described in previous section. p, is the number density of the particles in the slurry

(i.e., number of particles per unit slurry volume), that can be calculated from the solid

loading Ca (wt%) of the slurry particles as

3 Cap,
P, (2.38)
4 7R3 pa


where pa and ps are the densities of the particle and the slurry solution, respectively.

Substitute of Eqs. 2.38 into 2.37 gives


3 Cap9
n = A, (2.39)
2 7R2pa


By combining Eqs. 2.39 and 2.18, the number of particles anchored on the pad asperities

becomes


3 Ca s 0 pAA
n- 2C -CR (2.40)
2C 7R2 pa a E


Now that (RR), and n are given in terms of various processing variables and material

properties, the overall material removal rate in a CMP process can be estimated from Eqs.

2.32, 5.27 and 2.40 for the two different cases described above:

Removal Rate: Indentation depth smaller than surface layer thickness (i.e., co

(RR= C P (E)2Be32 PV (2.41)



Removal Rate: Indentation depth larger than surface layer thickness (i.e., co > t),










(RR) = -C1 {c U+ 21 1-1 3/2 PV (2.42)
v zC pA, El ) B B) R


As Eq. 2.23 indicates, the overall removal rate, (RR), is the thickness removal rate which

is the volumetric removal rate divided by the nominal wafer area Ao. We may recall that

C is a constant whose value is about 0.35 when h/o is between 0.5 and 3.0 [Joh85]. The

overall removal rate given above is reminiscent of Preston's equation in that the material

removal rate is proportional to the down-pressure, P, and the relative velocity, V. It

should be noted that the Preston's coefficient Kp, whose value relies on empiricism, is

now given as a function of various processing variables and material properties.

The model predicts the removal rate as a function of pressure and velocity product (PV)

very well [72]. The removal rate is usually only considered as a function of PV in many

modeling efforts, ignoring other processing parameters. But the PERC I model considers

the particle size effect, which is crucial for any CMP system.

Equation 2.41 indicates that the overall removal rate is independent of the particle size R

whereas Eq. 2.42 indicates a decrease in (RR) with increasing particle size. When the

indentation-depth is smaller than the surface layer thickness (i.e., 0)
removal rate by a single particle (RR), is proportional to R2 (Eq. 2.32). The number of

particles in contact, on the other hand, is inversely proportional to R2 as the Eq. 2.40

indicates. Consequently, the particle size effect is negated.

Thus the model predicts as shown in Fig. 2-4 that the removal rate is either

independent of particle size in the modified layer removal regime or decreases with

particle size in the substrate indentation regime. But, the reported literature has shown






57


that removal rate also increases with particle size in a given range, and that there is an

optimal particle size at which enhanced polishing can take place as shown in Figs. 2-5

and 2-6. To overcome these limitations, a (PERC II) model is developed by analyzing the

crucial assumptions in PERC I, and refining them when necessary. The following chapter

deals with assumption validation and PERC II model development.


Modified
layer
removal


Wafer
removal


Partide Size
Fig. 2-4. Schematic ofPERC I predictions for increasing particle size.


0 10 20 30 40 50
Mean Particle Size (nm)


60 70


Fig. 2-5. Polishing of silica by nanoslurry showing optimal particle size [118].


200


150
E

* 100

o
E 50
a-











600
-*- 18 kPa, 0.4 m/s
5500 -- 32 kPa, 0.6 m/s

-0 45 kPa, 0.9 m/s
400

i 300

B~200

100

0
25 60 95 130
Mean Particle Size (nm)

Fig. 2-6. Polishing of silica at various pressure, velocity and particle sizes showing
optimal particle size [116].














CHAPTER 3
PERC II CMP MODEL



The previous chapter highlighted the basic concepts involved in PERC I model

[96] development, along with various challenges faced by it. In this chapter, some of the

critical model assumptions are verified and refined as necessary. The changes are

incorporated into the basic framework of the PERC I model to develop the PERC II CMP

model.

Assumption Validation

The critical components in the CMP process are the wafer, pad and slurry. As the

wafer is fixed in a given CMP process, the contributions from pad and slurry are

investigated to include their most crucial characteristics into the model. The main role of

the pad in CMP is to trap the abrasive particles for material removal and transmit the load

applied onto the trapped particles. In particle scale modeling, the function of the pad in

global planarization need not be considered.

Pad-wafer Contact Area

The pad-wafer contact area strongly influences the number of particles that can be

trapped under each pad asperity. The greater the contact area between pad and wafer, the

higher the number of particles that can be trapped resulting in enhanced material removal.

The changes in pad properties during polishing are important to model the CMP process.

Often dry properties of the pad are investigated [119], rather than the more appropriate

wet properties. The pad characterization investigations are also limited to the bulk [48,









68, 120] of the material rather than the surface. These bulk properties in dry state are

usually employed in conventional CMP modeling efforts [68]. Since, polishing involves

the interfacial behavior of pad, abrasive, and wafer, pad surface properties should be used

rather than the bulk properties. Surface properties of the pad rapidly change due to

immersion in slurry [121, 122], quickly reaching equilibrium values [46].

There is one fundamental question that needs to be answered. What is the real

contact area between pad and wafer? And is the Greenwood-Williamson model [117],

which states that "contact area is linearly proportional to the applied load" applicable in

CMP systems? A basic assumption of the PERC I model is that removal rate is linearly

dependant on the pad-wafer contact area. Abrasive particles trapped between pad

asperities and wafer are considered to be responsible for material removal. As applied

load on the wafer increases, the pressure at the pad asperity-wafer interface is supposed

to remain constant due to elasticity of the pad, while the pad-wafer contact area increases.

This behavior is predicted by the "Greenwood-Williamson" model, which assumes that

the pad asperity tips contact the wafer under Hertz elastic theory conditions. Although a

number of CMP models have employed this concept [63, 109], no systematic attempts

are reported that provide validity of this assumption. Similarly, some researchers have

assumed the contact area to be proportional to the power of two-thirds [90] of pressure

without any experimental basis. In the past, pad-wafer contact area has been generally

derived mathematically [27, 123]based on statistical surface roughness rather than actual

experimental measurements. The pad-wafer contact area reported in literature including

theoretical calculations varies from 0.0005% to 20% [27, 49, 63, 109, 124, 125].

Considering the importance of reliable value of the pad-wafer contact area and its









dependence on applied load in CMP modeling, a systematic attempt was made to

measure it under CMP conditions. Kim et al. [124] have measured the pad-wafer contact

area using optical microscopy and have reported a value of 5%. On the other hand, Basim

[125] has reported the value to be 0.3% in dry state based on FTIR measurements. To

investigate the pad-wafer contact area, a reliable technique is needed. To establish the

reliability of optical microscopy and/or FTIR techniques, contact area measurements

were performed on pad using optical microscopy.

Optical microscopy

The average pad asperity radius is around 30 |jm for a typical CMP pad and the

RMS roughness around 5[im. Therefore, an optical microscope can be used to study the

contact spots, the majority of which can be expected to be over a micron in size. To

simulate the wafer, a microscope coverslip was used. To minimize the bending of the

coverslip under applied load, a fixture was fabricated as shown in Fig. 3-1 which enabled

easy access to the microscope objective lens for translation in "in-plane" direction. The

fixture consists of a base plate with a window hole of 10mm x 5mm to allow optical

observation of the contact spots with minimum bending of the coverslip under applied

load.

Optical measurements were performed in dry environment using Leika microscope

equipped with frame grabber. One inch square coupons were punched out from IC 1000

pad, which was used for polishing. The pad was ex-situ conditioned using a grid-abrade

diamond pad conditioner. Minimal contrast between contact and non-contact regions was

obtained, when the pad specimens were analyzed under the given load. This was not even

sufficient for qualitative analysis. Measurable distinction between contact and non-









contact spots was achieved with coating of the pad surface with a 5-10 nm thick gold-

palladium layer using the Denton sputter coater. The thin coated layer is not expected to

affect the pad-wafer contact area results, as the attempt here is to measure the contact

area under dry conditions.












Cover sl


Metallic Base

Microscope objective
Fig. 3-1. Schematic of the fixture used in measuring pad-wafer (dry) contact area.

Measurements were performed in two modes. Mode I consisted of measuring the

contact area of selected asperities as a function of applied load and mode II consisted of

measuring various contact spots under applied load by translating the microscope

objective to cover the entire specimen in view. The optical micrographs were analyzed

using Spot and Image-Pro software to calculate the percent contact area.

The micrographs obtained in mode I are shown in Fig. 3-2. The regions "P" and

"N" indicate the pad asperities that are of interest in all three figures, though only Fig.3-

2a is labeled for clarity. In "P" regions, the asperity contact increases with applied load,

whereas, in "N" regions, new asperity contacts are formed with applied load. The pad-

wafer contact area values obtained from optical measurements are plotted in Fig. 3-3. The










results indicate that the contact area of a given pad asperity increases linearly with

applied load and more importantly the magnitude of contact area obtained from optical

technique is in the same range as obtained from the FTIR technique by Basim (Fig. 3-4).

The discrepancy between this data and Kim's optical microscopy result [124] could be

due to the possibility that some non-contact areas were counted as contact spots due to

poor contrast, as no pad surface modification or coating was mentioned in their study.








1--I
10 micron











(a) (b) (c)

Fig. 3-2. Pad asperity contact spots seen through optical microscope. (a) 0.75 psi. (b) 5
psi. (c) 8.8 psi.



A Various asperity contacts at same pressure
S0.8


S0.6 -i

0.2



0
S0.4 A


0.2 0 .



0 1 2 3 4 5 6 7 8
Applied pressure (psi)
Fig. 3-3. Pad asperity contact area dependence on applied load. Each legend represents a
selected asperity contact.










0.55 :--* ,-- --- ,-- ---,- i "-'--1-- ---, ----,
0.55 .- I I


0.45
0.40 -
0.35 a0.33 ~, pad contact

^ 0.35
o 03" u
-e0.1505 .., .


0.15 *
0.10


0 2 4 6 7 8 10 12

Head Pressuie (psi)

Fig. 3-4. Pad contact area as a function of applied load [125].

The main motivation behind investigating contact area measurements is to get a

realistic value of pad-wafer contact area under CMP conditions. The optical and FTIR

techniques are used in dry conditions, whereas the actual CMP is a wet system.

Combining optical data from this study and FTIR data from Basim [125], it is established

that FTIR with attenuated total reflection (FTIR-ATR) method can be successfully used

to estimate the pad-wafer contact area. The same technique was employed in the present

investigation to measure the contact area in wet condition simulating the CMP

environment.

Fourier transform infrared spectroscopy (FTIR)

To investigate the pad-wafer contact area variation with applied load in various

slurries, FTIR-ATR was used. The contact spots contribute toward the absorbance signal

resulting in quantitative estimation of the pad-wafer contact area depending on signal









intensity. Maximum signal intensity is obtained when the pad surface is in full contact

with the wafer surface. The contact area is obtained by normalizing the measured signal

intensity with the maximum signal intensity [126]. The setup used for contact area

measurements is shown in Fig. 3-5.


Applied load


IR Beam





ATR crystal

Fig. 3-5 Schematic of the FTIR-ATR technique used to measure pad-wafer contact area.

A silicon ATR crystal is used in contrast to the ZnSe crystal employed by Basim

[125] to simulate the silica wafer system. A nitrogen purged Nicolet Magna 760

spectrometer equipped with liquid nitrogen chilled MCTA detector was used to carry out

FTIR analysis for better accuracy. All the spectra were the result of 512 co-added scans at

a resolution of 4 cm 1. The background spectrum for all the experiments was the single-

beam spectrum of the dry silicon crystal. The intensities of the CH2 peaks of the

polyurethane were recorded in the wavenumber range of 3000-2750 cm 1. The

asymmetric and symmetric stretches of CH2 at wavenumbers of 2927 and 2855 cm-1

respectively were analyzed. The contact area is expected not to depend on pad-wafer

relative velocity, hence they are held stationary. The slurries were simulated by using

solutions of varying pH with no other chemicals (passivating agents) or particles added.

This is valid especially in silica CMP as no passivating chemicals are generally added in









slurry formulation. The absence of particles reduces the errors due to scattering. The

water FTIR/ATR signal is subtracted from pad spectrum (both at same pH) to get the

desired signature spectrum (Fig. 3-6). A representative piece of pad sample (IC-1000)

soaked in given solution for one hour was placed on the (Si) ATR crystal and loaded at 4,

7 and 10 psi in the wet state under solution. The solutions studied are nanopure water

adjusted to pH 4, pH 9 and pH10.5 with either 0.5M HNO3 or 0.5M KOH.

Silica CMP is generally performed at slurry pH 10.5, as the silica solubility

increases drastically after pH 10. Thus, there should be minimum silica wafer

modification or "modified layer" formation at pH 4 and pH 9. Whereas, pHl0.5 should

lead to considerable surface dissolution of silica. These conditions are chosen, as all CMP

process variables except pad properties are supposed to be constant in pH range of 4 to 9,

and increased surface modification (dissolution) at pH10.5. The typical absorbance

spectra obtained for a given specimen at different applied loads is shown in Fig. 3-7. The

signal intensities at symmetric and asymmetric stretches are averaged to calculate the

contact area. The results obtained for different pH and dry conditions indicate that contact

area increases linearly with applied pressure for all conditions (Fig. 3-8). The normalized

plot shows the accuracy associated with the measurement technique, which is consistent

for all the conditions used. The linear dependence of pad-wafer contact area on applied

load validates the use of Greenwood-Williamson theory in the CMP model. Pad-wafer

contact area in the wet state was measured to be around 2-3 times the contact area in the

dry state (Fig. 3-9). This implies that the removal rate calculated would be 2-3 times less

if the dry contact area is used in the model. There is no discernible change in pad-wafer

contact area under different pH conditions due to data scatter, possibly due to uncertainty






67

associated with subtraction of water spectrum. Utilizing the value of pad-wafer contact

area obtained and the Greenwood-Williamson assumption, pad asperity modulus is

derived which is used in calculation of pad asperity stress distribution.


SWater: pHl0.5



J V,,


Signature peak


Fig. 3-6. Analysis of the FTIR-ATR spectra.




lopsi
e' 10psi
I I psi
90




2927. 12855
Wavenumber (cm-1)
Fig. 3-7. Absorbance spectra of pad (in pH 4) at different applied pressures.


Pad: pH10.5,7psi





ViL^












2.5


2


1.5


1


0.5


5 7 9


Pressure (psi)
Fig. 3-8. Contact area variation with applied load in dry and wet conditions.


1.2

1


0.8 -

0.6 -

0.4 -

0.2 -

0-


I Pressure = 10 psi


Dry


pH 4.0


pH 9.0


pH 10.5


Fig. 3-9. Contact area in dry and wet systems in various pH conditions.


--Dry
---- pH 4


- -pH 10.5









Atomic force microscopy (AFM)

Contact area increase in the wet state is attributed to changes in the mechanical

properties of the pad. Consequently, surface mechanical properties of pad were

investigated using a colloidal probe atomic force microscope (AFM), where a particle is

attached to AFM tip to measure pad properties. A Digital Instruments Dimension 3100

AFM equipped with a liquid cell adapter was used.

Particle indentation into pad was used to assess pad surface mechanical properties

at pH levels of 4, 9 and 10.5. It was realized that a stiff cantilever is needed to probe the

surface mechanical properties of the pad. Hence a tapping mode cantilever was modified

by cutting the tip area with focused ion beam (FIB) yielding a cantilever with a stiffness

of 75 N/m as compared to 30 N/m before the modification. A 7[tm silica particle was

attached to the tip of cantilever for measuring mechanical properties of the pad.

Nanoindentation measurements were carried out using the modified AFM tip shown in

Fig. 3-10. The pad surface was scanned with the colloid probe to find a relatively flat

surface before indentation data was measured. This is expected to minimize the effect of

surface asperities or roughness on the surface mechanical analysis. Typical indentation

data are shown in Fig. 3-11. Only the approaching curve is used to investigate the pad

surface mechanical properties. The results from AFM are summarized in Fig. 3-12.

The indentation data presented in Fig. 3-12 indicates that the pad surface

mechanical response is markedly different in dry and wet systems. In dry pad case, the

force on AFM probe increases with indentation depth at a constant pace without any

change in stiffness. Whereas, for wet cases at all pH levels employed, a dramatic change

in slope is observed. The indentation data is not reproducible over entire pad surface, as








the pad surface is not perfectly smooth due to asperities. But all the indentation data in

wet state showed the stiffness change in contrast to the dry data. When the indentation

data is aligned such that all curves match the dry pad behavior, it can be seen that the pad

surface is affected by the solution pH which results in different mechanical response

compared to the bulk material (Fig. 3-13). The moduli of pad surface and bulk shown in

Fig. 3-12 were estimated utilizing Hertz theory. The modulus of dry pad is atleast 3-5

times the pad modulus in dry state indicating pad swelling.


(a)

Silica parali


(b)
Fig. 3-10. Colloidal probe AFM tip (a) Modified tapping mode cantilever, dotted line
shows the region of the cantilever removed by FIB. (b) Silica particle attached
to the modified cantilever.









70
--Approaching
50 + Retracting


e 30 Air i Pad
O 0
0
U-
10


-10 f--
-200 0 200 400

Indentation Depth (nm)

Fig. 3-11. Force-distance curve indicating softer "modified layer" on the pad surface.

The surface modification of polyurethane is not entirely unexpected. The

polyurethane polishing pads possess both -COC- and -COOC- functional groups in the

main chain structure which are susceptible to hydrolytic attack [50], especially in alkaline

media [50]. Disruption of hydrogen bonding is reported for pad samples immersed in DI

water for minutes [97]. Schematic of hydrogen bond disruption is shown in Fig. 3-14.

This hydrolytic attack can explain the pad surface mechanical property behavior.

The presence of surface modification on pad surface or pad swelling could impact

the abrasive trapping ability of the pad asperities along with the load transmitted to the

particles during polishing depending on particle size. The change in contact area

observed in wet state indicates that depending on slurry chemistry, the pad-wafer contact

area could be effected, directly influencing the material rate. Hence, when different slurry

chemistries are used in a CMP process, the CMP model needs to incorporate the slurry

effect not only as a modified layer on wafer surface, but also as change in pad-wafer









contact area and abrasive trappability, which has not been accounted for in past CMP

modeling efforts.


100

80


0 50 100


150


Normalized Indetation Depth (nm)

Fig. 3-12. Force-indentation curves from AFM for different conditions. All curves are
offset such that they match in the top portions to clearly show the evidence of
a softer layer on pad in wet systems.


Bulk pad


Softer layer


Bulk pad

(b)


Fig. 3-13. Schematic of pad surface as deduced from AFM data. (a) Dry state. (b) Wet
state.










H H


Hydroged -
Bodg V H


II 1I
0 0


(a) (b)

Fig. 3-14. Schematic of polishing pads (a) Structure showing hydrogen bonding between
neighboring polymer molecules, (b) Water can form hydrogen bonds with
polymer molecule by disrupting hydrogen bonds between the polyurethane
molecules [127].

Pad Asperity Height Distribution

A quantitative understanding of the pad-wafer and pad-particle interface is

fundamental to a comprehensive CMP model. The pad asperities are assumed to remain

constant through the planarization of each wafer. It is known that the asperities involved

in polishing wear out changing in height over time, while the shorter asperities, those that

do not come into contact with the wafer, retain their original height. Thus the pad

roughness or the asperity height distribution changes with polishing, if pad conditioning

is not performed properly. The surface roughness of pad is known to be directly

proportional to the polishing rate [128-130]. Different types of pads have different

asperity height distributions, though they might have similar average surface roughness.

In PERC I, pad asperites were assumed to be spherical and of same size with pad asperity

height averaged out to obtain the pad asperity stress, and pad-wafer contact area. This

implies that the pad asperities are not only assumed to be equal in size and shape, but also

of equal height. This imposes the pad to have contact spots equal in size, experiencing









same contact pressure. Thus, all the particles trapped in these contact spots have same

indentation into the wafer surface leading to equivalent material removal under each

asperity. Thus the previous PERC model was equivalent to having a single asperity

model with no effect of asperity height distribution. Depending on the CMP system and

desired planarization criteria, different pads are used in practice. Therefore, it was

considered necessary to include the asperity height distribution in the revised model

(PERC II). Due to constant asperity height, only an average indentation depth was

derived in the previous model (PERC I) to indicate surface roughness of the polished

wafer. When asperity height distribution is used, asperities at different heights lead to

different indentation depth, resulting in information about distribution of scratches

(indentation depths).This data can be used to estimate the surface roughness as root mean

square roughness (RMS).

To incorporate the asperity distribution, Gaussian distribution of asperities is

assumed, as the reported literature cites Gaussian distribution [116]. The pressure at

contacting asperities were calculated individually to estimate the indentation depth of

trapped particles.

Abrasive Particle Size Distribution

The role of slurry in CMP is two-fold. The chemicals in the slurry are needed to

react with wafer surface resulting in formation of a surface layer which is amenable to

enhanced material removal. The abrasives in the slurry on the other hand, remove this

modified surface layer causing material removal. The effect of chemicals is attributed to

surface layer of different mechanical properties in PERC I model. Whereas, the effect of

abrasives is considered by assuming average size of the particles. The monosized slurry

assumed in the PERC I model is an ideal case, since real CMP slurries are seldom









monosized (Fig. 3-15). Oxide polishing slurries are commonly purchased in concentrated

form and diluted on-site to minimize shipping and labor costs. Some mult-component

tungsten and copper polishing slurries must be combined shortly before use because of

their short postmix lifetime. The slurry stability can change after it is combined with the

oxidizer or due to dilution leading to polydispersity.







0) *





O s .. -/ ... \ ..+- .
0 60 T7 80 90 100

Diameter (nm)

Fig. 3-15. Particle size distribution of silica slurry [118]

Sometimes mixed abrasive slurries are used [32], which invariably exhibit

polydisperse particle size distribution. To account for the particle size distribution effect,

PERC I model was modified to incorporate slurry abrasives with Gaussian size

distribution

PERC II Model Development

Conceptually, the difference between the PERC I and PERC II models can be

illustrated as shown in Figs. 3-16 and 3-17. The PERC I model assumes spherical pad

asperities of equal height all over the pad (Fig. 3-16a). As the slurry is assumed to be





76

monosized, each asperity traps equal number of particles in CMP resulting in equal
removal rate by each asperity and each particle(Fig. 3-16b).




Wafer
Pad aspriilics
. .


\/


Pad asperities
(b)
Fig. 3-16. Schematic of pad, slurry and wafer in PERC I model. (a)Before contact. (b)
During CMP.
Whereas in the PERC II model (Fig. 3-17a), the spherical pad asperities are
assumed to have a height distribution as observed experimentally [116]. As the slurry is
assumed to be polydisperse, each asperity traps different number of particles of different
particle sizes in CMP according to pad asperity height and particle distribution (Fig. 3-
17b). Thus the PERC II model includes realistic contributions of pad and wafer
characteristics compared to the PERC I model. The model formulation is detailed in the
following section.


..........
...............
................
................
................
................
................
.................
..............
. . . .
.............


...........
.........
............
. . . . .
. . . . .
- - - - -
. . . . . .
. . . . .
. . . . . .
. . . . . . .












Wafer


'--hury particles


. . .


\


Pad asperities


Wafer


/. ... ... ... ..
. . . . .


Fig. 3-17. Schematic of pad, slurry and wafer in PERC II model. (a) Before contact.
(b)During CMP

Real contact area (Areal) between pad and wafer due to applied load (L) is given by:


Ar =rNA, (z h)(z)dz



L 4NAoE3/2 z -h)32(z)dz


P(z) = exp
a =~


(3.1)



(3.2)



(3.3)


2
z
2a2


where Nis the number density of the pad asperities (i.e., number of asperities per unit


area), Ao is the total area of the flat wafer surface, and h is the distance between wafer


. . .
. . . .


Wafer


.......... ..
..............
...............
................
.................
..................
...................
...................
...................
....................
................
.................









surface and the pad asperity average plane under the given conditions. E* is the

composite modulus between the two surfaces in contact, defined as

1 1-v2 1v (34)
-- + W (3.4)
E* Ep E

where, E and v are the Young's modulus and the Poisson's ratio, and the subscripts p and

w represent the pad and the wafer, respectively. Equations (3.1) and (3.2) are derived

from Hertz theory as in Greenwood-Williamson model [77, 117], yielding contact area

and load at a given asperity of height 'z' to be:

Areal(Z)=7 P (z-h) (3.5)

L(z)=(4/3)E* 1/ 2(z-h)3/2 (3.6)

where 'h' is calculated from Eq. 3.2, since applied load and pad properties are known.

The underlying assumption for Eq. 3.2 is that the applied normal force on the wafer is

supported entirely by the pad asperities. As was mentioned previously, experimental

measurements indicate that the hydrodynamic pressure is negligible under typical CMP

operational conditions [69].

From equations 3.5 and 3.6, contact pressure and contact area at a given asperity

height can be calculated assuming that the pad asperity distribution is known. The pad

asperity distribution can be determined from routine surface roughness measurement

techniques like optical and force profilometers or atomic force microscopy (AFM).

Contact pressure according to Hertz theory, on an asperity of height z is given by:


P(z) =4E* (z- h)2 (3.7)
3z-f1i
35c/72









Plastic Deformation of Wafer Surface

When an abrasive particle is indented into the wafer surface, elastic and plastic

deformation of wafer and abrasive particle occur. However, in CMP, slurries are

designed such that the chemistry changes the modulus of the wafer surface for enhanced

material removal. In the current model, particles are assumed to be rigid such that they do

not deform during polishing. When the indentation of abrasive particle is beyond the

modified surface layer, the substrate indentation could yield either elastic or plastic

response depending on the substrate, for example in case of silica, the deformation will

still remain plastic whereas for copper, it would be elastic deformation followed by

plastic deformation. Therefore, in material removal calculation, indentation into ductile

wafers is not considered to cause material removal, as it leads to change in shape only,

whereas in the case of brittle material like silica, cracks are developed leading to material

removal.

Slurry Characteristics Particle Size Distribution

The abrasive particles in the slurry are assumed to be spherical in shape with a

given size distribution y(r).As mentioned earlier, particle size distribution Y(r) was

assumed to be Gaussian, given by:-


S(r) ex (r -Ur)2 (3.8)
ao. [2; 2o.2

where [Lr is the mean particle radius and Or the standard deviation.

Material Removal by Single Particle

The overall material removal rate (RR) is assumed to be the multiple of the

removal rate by a single particle and the number of particles trapped between pad

asperities and the wafer:









RR = (1/Ao)J In(r,z) RR,(r,z)drdz (3.9)

where n(r,z) is the number of slurry particles anchored between pad asperity and the

wafer and RR,(r,z) is the volumetric removal rate by a single particle of radius r trapped

by asperity of height z. The overall removal rate, RR is typically described in terms of the

thickness of the wafer surface layer removed per unit time; hence the division by the

nominal wafer area Ao.

Schematic illustration of single particle abrasion is given in Fig. 3-18. The material

removal is viewed as a sliding-indentation process in which the volumetric removal rate

by a single abrasive particle is given by

RR,(r,z)= A,(r,z)V (3.10)

Where A,(r,z) is the cross-sectional area of the particle indented into the wafer

under pressure (hashed area in Fig. 3-18), and Vis the relative velocity between the pad

asperity and the wafer.




I T

Sb Pad

t, Pad t
F. Pad F.




Fig. 3-18 Schematic of single particle abrasion showing the removal of chemically
modified surface layer, (a). co < t; (b). co > t with soft wafer materials.[72]









Assuming that the hard particle maintains its spherical shape,


A, (r,z) = -a(r,z)(r o(r,z))+ r2 arcsin a(r,z) (3.11)
r

where co(r,z) is the indentation depth and a(r,z) is the radius of the circular indentation on

the wafer surface caused by the particle of radius r trapped under asperity of height z.

Because co(r,z) is very small compared to r, a(r,z)/r is also very small and Equation 3.11

can be linearized about a(r,z)/r as already discussed:


Az (r, a(r, z)(r, z) )+ ( (3.12)
3 r

Furthermore, since a2(r,z)=(2rco(r,z)-co2(r,z)) and co(r,z) is much smaller than r,

Equation 3.12 can be rewritten as


A4 (r, z) 2a3(r,z) (3.13)
3r

Once the indentation depth, co(r,z) (or a(r,z)) is known, the volumetric removal rate

by a single particle can be calculated from Eq. 3.13. It should be noted that co and a are

dependant on particle radius and height of the trapping asperity. Removal rate per particle

is given by:


RR, (r, z) = 2a(rz) V (3.14)
3r

Depending on the relative magnitude of the indentation depth (co(r,z)) as compared

to the surface layer thickness (t), the material removal may be classified into two

different regimes as depicted in Fig. 3-18: (a) o(r,z) < t and (b) o(r,z) > t and can be

calculated using force balance as follows.









Considering that the pad is sufficiently hard as compared to the modified layer, the

value of b in Fig. 3-18 can be close to the particle radius R,

( -1/2
P(z)
a(r,z) = r i when co(r,z) < t (3.15)


and


a(r, z) = r2p(z) + 2(BW Be)rt when co(r,z) > t (3.16)
BI

where, Be is the effective Brinell hardness of the chemically modified surface layer. In

the following section, the number of particles in contact with the wafer surface is

estimated to determine the overall removal rate.

Number of Active Abrasive Particles

When the wafer is pressed against the pad and is in sliding motion relative to the

pad, the slurry particles can be entrapped only in the region where the local distance

between the wafer and the pad asperity is smaller than the particle diameter, 2R. For a

slurry consisting of particles with Gaussian distribution, mean particle size (Rm) is used

to calculate the number of particles that can be trapped on the pad asperity of height z:

N(z) 2Rm -Areai(z) p (3.17)

where Rm is the mean abrasive particle radius and Areai(z) is the real contact area between

the wafer surface and the pad asperity as given by eq. 3.5. p, is the number density of the

particles in the slurry (i.e., number of particles per unit slurry volume), that can be

calculated from the solid loading Ca (wt%) of the slurry particles as

3C, p,
Pn ,= 3a 0p (3.18)
4;r pr3 (r (r)dr









where pa and ps are the densities of the particle and the slurry solution, respectively and

y(r) the slurry particle size distribution. Substitution of Eq. 3.18 into 3.17 gives

3 Rm Caps Area, (z)
N(z) 2=( (3.19)
2 ap, frv ,(r)dr

From eq. (3.19), the number of trapped particles of radius R is given by,


n(R,z)=N(z)*y(R)= 3 Rm C Area (z) (r) (3.20)
2 ;Tr fJr3 V(r)dr

Estimation of the Overall Removal Rate

The overall material removal rate can be determined by following these steps:

h is calculated using eq. 3.2.

Contact pressure P(z) at a given asperity is calculated along with the real

contact area Areai(z) of that asperity with wafer.

Total number of particles N(z), that are trapped are determined, from which

number of particles of given radii, n(r,z) are derived.

From P(z), removal rate by single abrasive of radius r is calculated which is

multiplied with n(r,z) to give removal rate by that particle size. This process

is repeated to account for all the particles of different radii trapped on that

asperity yielding material removal rate by particles trapped on a given

asperity.

It should be noted that there are 4(z)NAo asperities at a given height which

will each contribute the same material removal.









The above step is repeated for all the pad asperities of various heights that

are in contact with wafer (determined by h) to give overall removal rate by

the following equation:



RR = (1/Ao)J In(r,z) RR,(r,z)drdz


-RR= CpN Area(z) ) w(r)(r,z ddz (3.21)
p, r3 y(r) dr h r
r

where, a(r,z) varies as given in eqs.3.15 and 3.16 depending on particle radius and

asperity height.

The indentation depth, co(r,z) is used to calculate the surface roughness RMS of the

polished wafer according to the following equation:


0)2
RMS = (3.22)
n

where coi is the indentation depth.

The overall removal rate predicted by Eq. 3.21 and surface roughness given by

Eq. 3.22 depend on various parameters that represent the geometry of the pad and the

particle (i.e., 3, o and R), material properties (E*, Bw and Be), thickness (t) of the modified

surface layer on wafer, and the relative velocity of the pad (thus the particle) to the wafer

(V). The PERC II model will be validated with respect to critical CMP parameters in the

next chapter.














CHAPTER 4
MODEL ASSESSMENT

The parameters governing the material removal calculation consist of CMP

operating parameters, slurry parameters, pad and wafer parameters, as listed in Table 4-1.

However, some of these parameters, especially the sub-nanometer thick modified layer

hardness and thickness can not be determined experimentally due to equipment

limitations. The remaining parameters are relatively easy to investigate experimentally

for many CMP systems. Hence, modified layer hardness and thickness are used as the

fitting parameters in the model.

Table 4-1. Parameters included in the revised PERC model.
Operating Parameters Pad properties
Pressure Pad modulus
Velocity Asperity height distribution
Asperity radius
Slurry parameters Asperity density
Particle size distribution
Solids loading Wafer properties
Abrasive density Modified layer thickness
Solvent density Modified layer hardness
Wafer hardness



Model Validation

In this section, PERC II model predictions are compared with experimentally

measured values to assess the reliability of the proposed CMP model. The experimental

literature data is also compared with PERC I predictions to assess the advantage of PERC

II over PERC I. Though PERC II is a refined model compared to PERC I, the model is

still a simplified version of real CMP, mainly in estimating the number of trapped









particles and indentation depth considering an abrupt transition between modified layer

and wafer substrate. The removal rate values for both models are normalized by a

constant to have reasonable modified layer thickness values. Surface roughness data is as

produced by the models without any normalizing factor. The size distribution of slurries

given in the respective literature are fit to the closest Gaussian distribution, which is used

in the model.

Silica CMP: Micron Sized Slurries

The polishing results of silica by silica abrasives as reported by Choi et al. [131]

are considered here. Micron sized CMP slurries were formulated by dispersing sol-gel

silica particles of different sizes from Geltech Corporation in deionized water and

adjusting pH values to 10.5. The average diameter of the slurry particles were 0.2, 0.5,

1.0 and 1.5 itm. The size distribution of the slurries is plotted in Fig. 4-1. A 2 |tm thick

silica layer was deposited on p-type silicon wafer by plasma-enhanced chemical vapor

deposition. 1.5 x 1.5 in silica samples were used to mimic the wafers. A Struers RotoPol-

31 tabletop polisher was used with IC 1000/Suba IV stacked pad. The following

conditions were applied: down pressure of 3.5 psi, slurry flow rate of 100 ml/min, and

rotation speed of 150 rpm (110 cm/s). The polishing rates were determined by measuring

oxide film thickness using variable angle spectrometry ellipsometry and surface quality

was assessed by atomic force microscopy (AFM).

The polishing rate was investigated as a function of particle size and solids loading.

The removal rate decreased with increasing particle size (Fig. 4-2). The parameters used

are: wafer Hardness=8 GPa, modified layer Hardness = 450 MPa, modified layer

thickness = 7.2 A and Normalization factor = 100. The PERC II model correlates well









with the experimental values than the PERC I model. The reported literature belongs to

the substrate indentation regime. The model projects that enhanced removal rate can be

obtained by using smaller sized slurries. The surface roughness on the other hand,

increases with particle size on an average for all the slurries considered (Fig. 4-2b). This

is not surprising as the larger size particles have deeper indentation depths increasing

surface roughness. Both the models predict the average trend in surface roughness with

increasing particle size.

25
-- 0.2pm
20 0.5pm
S---- 1.0pm
o 15 1.54n

E -O

0




0 1 2

Particle Size (mn)
Fig. 4-1. Slurries used in oxide polishing [131].

Silica CMP: Nanosilica slurries

The slurry sizes in the earlier study spanned from 0.2 to 1.5 jtm, which is well

above the normal slurry size range (<300 nm). Considering the nanosize slurries of 50-

150nm mean particle sizes, CMP behavior of silica polishing by silica abrasives is

investigated further [116]. Slurries with mean particle diameters of 50, 80, 110 and

140nm were used to polish 100mm diameter, p-type polished silicon wafers that

contained a thickness of 1.3 pm thermally grown oxide. The silica particles were










precipitated from a colloidal solution. The polishing was done at three different levels of

pressure and relative pad-wafer velocities: 18kPa, 0.4m/s; 32kPa, 0.6m/s; and 45kPa,

0.9m/s. The parameters used in the model are: wafer Hardness=8 GPa, modified layer

Hardness = 250 MPa, and modified layer thickness = 9.3 A. The removal rates for the

given set of pressure and velocity with different particle sizes is shown in Fig. 4-3. The

material removal rates with slurry mean sizes of 10 and 20nm were ignored, as the

authors [116] noticed considerable particle staining on the polished surfaces indicating

agglomeration.

The PERC II model corresponds with the experimental results better than the

previous PERC I model. Each set of modeled removal rates for given pressure and

velocity were normalized individually with normalizing factor ranging from 185-200.

The discrepancy in the removal rate at particle size 50nm between experimentally

observed values and modeled values can be attributed to agglomeration, which is

suggested by the authors for that size [116].

250
Experimental
200 1 PERC II Model
---PERCI Model
150

5 100
E
50

0 i i
0 500 1000 1500 2000
Mean Particle Size (nm)

(a)
Fig. 4-2. Silica polishing by slurries in the micron range. (a) Removal rate. (b) Surface
quality

PAGE 1

PARTICLE SCALE MODELING OF MATERIAL REMOVAL AND SURFACE ROUGHNESS IN CHEMICAL MECHANICAL POLISHING By SURESH BABU YERUVA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2005

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Copyright 2005 by Suresh Babu Yeruva

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This document is dedicated to Sri Parama hansa Yogananda, my parents and sister.

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iv ACKNOWLEDGMENTS I would like to express my gratitude a nd appreciation to my advisor, Dr. Brij Moudgil, for his valuable guidance and support throughout this study. His sincere dedication towards his students encouraged me to perform my best and expand my potential. Sincere thanks are also due to Dr Chang-Won Park, for his valuable guidance and support throughout the study. I would also like to acknowledge the other members of my advisory committee, Dr. Rajiv Singh, Dr. Wolfgang Sigmund, Dr. Hassan El-Shall, Dr. Susan Sinnott and Dr. Dinesh Shah, for thei r time, helpful discussions and guidance. I would like to thank Dr. Yakov Rabinovich fo r help with atomic force microscope (AFM) and Fourier transform in frared spectroscopy (FTIR) an alysis, and Gerald Bourne from Major Analytical Instrumentation Center (MAIC) for help with focused ion beam (FIB) and nanoindentation data. Furthermore, I sincerely acknowledge the guidance and support given by Kuide Qin at Praxair Inc. I gratefully acknowledge th e National Science Foundatio ns Particle Engineering Research Center (PERC) for financially suppor ting this research. Special thanks are due to PERC staff members, Gary Schieffele Gill Brubaker, Mike Beasley, and John Henderson who made this work possible. My colleagues, Bahar Basim, Jeremiah Abiade, Su-Ho Jung, Vijay Krishna, Madhavan Esayanur, Scott Brown, Parvesh Sharma, Kyoung-Ho Bu, Pankaj Singh, Debamitra Dutta and Ivan Vakarelski, who ha ve contributed to this research by their valuable discussions and friendship, are also gratefully acknowledged.

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v TABLE OF CONTENTS Page LIST OF TABLES............................................................................................................vii LIST OF FIGURES.........................................................................................................viii ABSTRACT xi CHAPTER 1 INTRODUCTION........................................................................................................1 Multilevel Me tallization...............................................................................................2 Need for Planarization..................................................................................................4 Planarization Techniques..............................................................................................5 Overview of the Chemical M echanical Polishing Process...........................................7 History...................................................................................................................7 Advantages and Disadvantages of Ch emical Mechanical Planarization...............8 General CMP applications.....................................................................................9 Cmp Output Parameters........................................................................................9 Removal rate................................................................................................10 Global planarization.....................................................................................12 Selectivity.....................................................................................................13 Measurement Techniques....................................................................................14 End Point Detection.............................................................................................15 CMP Consumables.....................................................................................................16 CMP Slurry..........................................................................................................18 Rate of surface reaction................................................................................18 Slurry agglomeration....................................................................................19 Chemical Mechanical Polishing Pads.................................................................20 Effect of pad grooves...................................................................................23 Physical and chemical cha nges in pad during polishing..............................23 Effect of temperature change on polishing pad............................................26 Non-uniformity of the polishing pad............................................................27 CMP process in the future..........................................................................................27 Scope of Dissertation..................................................................................................28 2 CMP MODELING: OVERVIEW OF PERC I...........................................................30 Literature Review.......................................................................................................31

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vi Preston Equation..................................................................................................31 Modifications to Preston Equation......................................................................34 Slurry Erosion......................................................................................................36 Pad Considerations in CMP Models....................................................................39 Slurry Considerations in CMP Models................................................................42 PERC I CMP Model...................................................................................................44 Model Development............................................................................................45 Estimation of the Overall Removal Rate.............................................................54 3 PERC II CMP MODEL..............................................................................................59 Assumption Validation...............................................................................................59 Pad-wafer Contact Area......................................................................................59 Optical microscopy......................................................................................61 Fourier transform infrar ed spectroscopy (FTIR)..........................................64 Pad Asperity Height Distribution........................................................................73 Abrasive Particle Size Distribution.....................................................................74 PERC II Model Development.....................................................................................75 Plastic Deformation of Wafer Surface................................................................79 Slurry Characteristics Part icle Size Distribution..............................................79 Material Removal by Single Particle...................................................................79 Number of Active Ab rasive Particles..................................................................82 Estimation of the Overall Removal Rate....................................................................83 4 MODEL ASSESSMENT............................................................................................85 Model Validation........................................................................................................85 Silica CMP: Micron Sized Slurries.....................................................................86 Silica CMP: Nanosilica slurries...........................................................................87 Copper CMP........................................................................................................91 Tungsten CMP.....................................................................................................92 Model Predictions.......................................................................................................94 Removal Rate as a Function of Partic le Size for a Given Solids Loading:.........95 Effect of Modified Layer Thickness....................................................................96 Effect of Modified Layer Hardness.....................................................................99 5 SUMMARY AND SUGGESTIONS FOR FUTURE WORK.................................101 LIST OF REFERENCES .................................................................................................106 BIOGRAPHICAL SKETCH........................................................................................... 118

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vii LIST OF TABLES Table page 1-1. Interconnection delay (RC) in silicon VLSI chip.........................................................3 1-2. Chemical mechanical polishing applications.............................................................10 4-1. Parameters included in the revised PERC model.......................................................85 4-2. Parameter values used for comparing PERC I and II models....................................95 5-1. Process parameter ranges used in sensitivity analysis..............................................103

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viii LIST OF FIGURES Figure page 1-1. Future trends in interconnects ......................................................................................4 1-2. Schematic of a device fabricated using multilevel metallization.................................5 1-3. Different degrees of local and global surface planarity................................................6 1-4. Schematic of chemical mechanical polishing process..................................................7 1-5. Surface layer formation on Cu w ith various slurry chemistries.................................11 1-6. Micro and nanoscale phenomena during CMP ..........................................................13 1-7. Parameters involved in CMP process.........................................................................17 1-8. Chronoamperometry meas urements for tungsten ......................................................19 1-9. Type I CMP pad.........................................................................................................22 1-10. Type II CMP pad......................................................................................................22 1-11 The absorbance spectra of used a nd dry IC 1000 pad along with dried silica slurry.........................................................................................................................25 2-1. Polished wafer surfaces showing nanoscratch surfaces.............................................33 2-2 Pad consideration in PERC I.......................................................................................46 2-3. Schematic of single particle abra sion showing the removal of chemically modified surface layer..............................................................................................51 2-4. Schematic of PERC I predictions for increasing particle size....................................57 2-5. Polishing of silica by nanoslurr y showing optimal particle size................................57 2-6. Polishing of silica at various pressure, velocity and particle sizes showing optimal particle size...............................................................................................................58 3-1. Schematic of the fixture used in measuring pad-wafer (dry) contact area.................62

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ix 3-2. Pad asperity contact spots s een through optical microscope......................................63 3-3. Pad asperity contact area dependence on applied load. Each legend represents a selected asperity contact...........................................................................................63 3-4. Pad contact area as a f unction of applied load............................................................64 3-5 Schematic of the FTIR-ATR technique used to measure padwafer contact area.......65 3-6. Analysis of the FTIR-ATR spectra.............................................................................67 3-7. Absorbance spectra of pad (in pH 4) at different applied pressures...........................67 3-8. Contact area variation with applie d load in dry and wet conditions..........................68 3-9. Contact area in dry and wet sy stems in various pH conditions..................................68 3-10. Colloidal probe AFM tip..........................................................................................70 3-11. Force-distance curve indicating softer modified layer on the pad surface...........71 3-12. Force-indentation curves from AFM for different conditions..................................72 3-13. Schematic of pad surface as deduced from AFM data.............................................72 3-14. Schematic of polishing pads.....................................................................................73 3-15. Particle size distribu tion of silica slurry...................................................................75 3-16. Schematic of pad, slurry and wafer in PERC I model..............................................76 3-17. Schematic of pad, slurry and wafer in PERC II model............................................77 4-1. Slurries used in oxide polishing..................................................................................87 4-2. Silica polishing by slurri es in the micron range.........................................................88 4-3. Silica polishing by colloidal nanosilica......................................................................89 4-4. Silica polishing by nanosized slurries. .....................................................................90 4-5 Copper CMP as a functi on of particle size..................................................................92 4-6. Alumina slurry si ze distributions................................................................................93 4-7. Effect of particle size on tungsten CMP.....................................................................94 4-8. Comparison between PERC I and PERC II mode ls with constant solids loading of different particle sizes..............................................................................................96

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x 4-9. Model comparison with varyin g modified layer thickness........................................98 4-10. CMP performance comparison with varying modified layer hardness..................100 5-1. Sensitivity analysis of silica CMP system................................................................103

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xi Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy PARTICLE SCALE MODELING OF MATERIAL REMOVAL AND SURFACE ROUGHNESS IN CHEMICAL MECHANICAL POLISHING By Suresh Babu Yeruva December 2005 Chair: Brij M. Moudgil Cochair: Chang-Won Park Major Department: Materials Science and Engineering Chemical mechanical polis hing (CMP) is widely adopt ed in producing excellent local and global planarization of microelectronic devices. It has been demonstrated experimentally that the polishing performance is a result of the syne rgistic effect of both the chemicals and the particle s involved in CMP. However, the fundamental mechanisms of material removal and the in teractions of the chemical and mechanical effects are not well understood. A comprehensive model for CM P was developed taking into account both the chemical and mechanical effects for slurries with a given particle size distribution. The model developed (PERC II) is based on a previously developed model (PERC I). The chemical aspect is attributed to the chemical modification of the surface layer due to slurry chemistry, whereas th e mechanical aspect is incorporated by indentation of particles into the modified layer and the substr ate depending on the

PAGE 12

xii operating conditions. In this study, the eff ects of particle size and pad asperity distributions are included in the model. The contact area of pad with wafer was measured in dry and wet conditions in different pH solutions using optical mi croscopy and Fourier transform infrared spectroscopy respectively. Pad surface mechanical properties in dry and wet states were also investigated using atomic force micr oscopy. The contact area results obtained were utilized in modeling to estim ate the pad modulus leading to pad-wafer contact stress distribution. The predictions of the mode l show a reasonable agreement with the experimental data. The model is validated for oxide a nd metal CMP systems. The PERC II model not only predicts the overall removal rate, but also the surface roughness of the polished wafer in selected systems. The developed model can be used to optimize the current CMP systems and provide insights into future CMP endeavors.

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1 CHAPTER 1 INTRODUCTION The past three decades have witnessed rapid growth of the electronics industry and its impact on human lifestyle. Ultra-largescale integrated (ULS I) circuits, with 108 or more devices on a chip, can now be fabricat ed on semiconductor wafers, reducing cost and increasing the performance of electroni c products. The number of components on a memory chip has approximately doubled ever y two years over the past two decades, following the famous Moores law [1]. Th e advancement in fabrication technology shrinks the minimum dimension of the device -feature by about 13% per year. This trend is expected to continue in the future even as 65 and 45 nm processes are set for production in 2005 [2] and near future. The relentless competitor and customer driven demand for increased circuit density, functionality and versat ility has led to revolutionary advances in the front end of the chip manufacturing line where the circuit elements ar e fabricated, and the back end where these elements are appropriately wi red within the integrat ed circuit (IC) [3]. Chip interconnections, or interconnects, serve as local and gl obal wiring, connecting circuit elements and distributing power [4]. To incorporate and accommodate the improvements such as decreased feature size, increased device speed and more intricate designs, research in the back end of line (BEOL) processes has become equally important as the development of the front end of line (FEOL) processes to reduce gate oxide thickness and channel length.

PAGE 14

2 While recent path breaking innovations [5-7] in the field of lithography and patterning have brought progressive de vice scaling, the development of a planar BEOL approach, which incorporates the use of chemical mechanical polishing (CMP) to planarize inter-level dielectrics and meta l stud levels, represents a significant advancement in BEOL processes. Innovation in BEOL technology is required in each technology generation, since only part of the de nsity increase could be achieved with improvements in lithography. Multilevel Metallization In earlier stages, the complementary metal oxide semiconductor (CMOS) device structure had multiple isolated devices conne cted by a single level of interconnect wiring. Scaling down of the devices was very effectiv e in achieving the goals of increased device density, functional complexity and performa nce. However, device scaling became less profitable, and speed and complexity we re dependant on the characteristics of interconnects that wired them [8]. With the single level metallization scheme, the total area occupied by the wiring on the chip signifi cantly increased with the increase in the active density on the chip. The interconnect delay is usually measured as RC time delay, which is the total time taken by the voltage at one end of the me tal line to reach 63% of the total value of the step input applied at the other end. Th is reduction is due to resistance of the interconnect wiring metal (R) and the interlay er dielectric capacitance (C) [9]. The resistance of the line is given by R = l/wd (1.1) where is the resistivity of the wiring material l, w, and d are the length, width, and thickness of the wiring material respectivel y. The capacitance of the line is given by

PAGE 15

3 C = wl/t (1.2) where is the relative permittivity and t is the thickness of the insulator. The total RC delay can be given by RC = l/wd wl/t = l2/td (1.3) Thus, it can be seen from Eq. (1.3) that RC delay is independent of the line width and further scaling of line width translates into reduction of IC line thickness which in turn increases the RC delay. Othe r factors such as parasitic capacitances and cross-talk become dominant for sub 0.5 m integrated circuits. One approach to decrease the RC delay is by incorporating metals of low resist ivity, and interlayer dielectrics of lower dielectric constant. Table 1-1 gives the simple RC time constants calculated for a few metals of given Rs (sheet resistance) and 1 mm length on 1 m thick SiO2 [9] The other approach implemented widely in the industr y is forming multileve l metallization schemes where different levels of metal interconnections are isolated by dielectrics and are connected by vertical vias. Table 1-1. Interconnection delay (RC) in silicon VLSI chip. Metal Bulk resistivity ( cm) Polycrystalline film resistivity ( cm) Film thickness () Rs ( /square) Delayi (ps/mm) Polysilicon ~1000 5000 20 690 CoSi2 10 15 2500 0.6 21 MoSi2 ~35 ~100 2500 4 138 TaSi2 45 55 2500 2.2 76 TiSi2 13 15 2500 0.6 21 WSi2 ~25 70 2500 2.8 97 W 5.65 8-10 2500 0.32-0.4 11-14 Mo 5.2 8-10 2500 0.32-0.4 11-14 Al 2.65 2.7 2500 0.11 4 Cu 1.67 2.0 2500 0.08 3 iDelay=RC=34.5 Rs (ps/mm) for 1 mm length conductor on 1 m thick SiO2 [10].

PAGE 16

4 The increase in the levels of the metallization lines implies that packing density need not keep pace with the device density and the minimum metal line feature does not have to scale at the same pace as the gate width. The foremost reason behind the implementation of multilevel metallization sc hemes is the reduction in the length of the metal lines, thereby reducing the RC delay sizably ( Eq. 1.3 ), and allowing direct routing of the active devices. In places where metal wiring length cannot be reduced, routing can be done at the upper levels without reducing the metal line width, thus reducing the RC delay due to the higher surface area. Starting wi th two levels of me tallization, the levels of metallization have increased up to 8 by 2001 [11]. The future trends in the levels of metallization can be seen in Fig. 1-1 [12]. Fig. 1-1. Future trends in interconnects [12] Need for Planarization Deposition of multiple layers leads to conformation of deposited layer on the substrate features or already deposited pattern. When multilevel metallization is carried out without any planarization step, non-planarized surface topography (Fig. 1-2a) results

PAGE 17

5 in several processing difficulties. The irregul ar surface causes a hindrance in conformal coating of the photoresist and efficient pattern transfer with contact lithography. The anomalies in the surface cause the variation of the thickness in fine line widths (sub 0.5 m) depending on photoresist thickness. Fig. 1-2 shows a comparison between planarized and non-planarized surface topography. Effectivel y planarized surfaces have a number of benefits such as (a) higher photolithography an d dry etch yields, (b) elimination of step coverage concerns, (c) minimi zation of prior level defects, (d) elimination of contact interruption, undesired contact s and electro-migration eff ects, (e) reduction of high contact resistance and inhomogeneous metallization layer thickness, and (f) limitation in the stacking height of metalliz ation layers. Thus the demand for developing devices with enhanced performance nece ssitates planarization. Fig. 1-2. Schematic of a device fabricated using multilevel meta llization. (a) Nonplanarized structure. (b) Pl anarized structure [8, 13] Planarization Techniques Techniques such a spin on deposition (S OD), reflow of boron phosphorous silicate glass (BPSG), spin etch plan arization (SEP), reactive ion etching and etch back (RIE EB), SOD + EB and chemical mechanical polishing (or chemical mechanical planarization) (CMP) are the most prominent of several competing technologies available

PAGE 18

6 to achieve local and global planarization (Fi g. 1-3). The plasma enhanced chemical vapor deposited oxides have limited capability of gap filling and are restricted in their gap filling ability below patterns having 0.3m feature size. High-density plasma deposited oxides have acceptable gap filling capabiliti es; however, they produce variation in surface topography at local as well as global level. Even though spin-on deposited (SOD) doped and undoped oxides and polymeric materi als have acceptable ability for gap filling, CMP is the only technique whic h produces excellent local and global planarization of microe lectronic materials. Fig. 1-3. Different degrees of local and global surface planarity [14].

PAGE 19

7 Overview of the Chemical Mechanical Polishing Process Current semiconductor fabrication tec hnology for logic and memory devices requires CMP to achieve the required multilevel interconnection densities. Indeed, each silicon wafer can be exposed to 15 or more CMP steps before final device assembly. A schematic diagram of the CMP process is shown in Fig. 1-4 In CMP, the wafer is pressed face down against a rotating polishing pad, while a chemical and physically abrasive slurry fed between pa d and wafer planarizes the wafe r. The material removal in simplest terms takes place by synergistic mechanism between chemical reaction on the wafer surface due to the slurry, and physical re moval of the reacted material by the slurry abrasives. The various mechanisms between pa d, slurry and wafer are tailored to enhance material removal, planariza tion, surface finish and higher selectivity compared to the underneath layer. Fig. 1-4. Schematic of chemical mechanical polishing process. History The modern day application of the CMP pr ocess in the semiconductor industry was for polishing the raw silicon wafers to ach ieve a global flatness. One of the most widespread applications of CMP outside th e semiconductor industry is in optical lens

PAGE 20

8 polishing. In fact, the first semiconductor CM P machine was an innovation of the lens polishing industry. The first wafers polished us ing CMP were commercially available in the early 1960s [15]. There was wide spread industrial implementation of the different variants of the CMP by companies such as NEC, National Semiconductor, Hitachi, etc. [10]. This led to the introduction of the firs t commercial polisher designed specifically for CMP by Cybeg, Japan in 1988. Later, Interna tional Sematech identified CMP as a technology critical for the future of IC ma nufacturing and launched a project to develop competitive and advanced CMP tools in th e US [16]. Once the technology and required equipment were available, CMP was used beyond polishing of inter-level dielectric layers to polishing of tungsten, which was deposited in via openings between metal layers. Copper was not used for interconnects until th e availability of CMP even though it has lower resistivity than aluminum [17], as it could not easily be etched by reactive ion etching. This enabling polishing technology has sp read to several othe r applications, the significant one being in shallow trench isolation (STI) [18]. Advantages and Disadvantages of Ch emical Mechanical Planarization The advantages of CMP are (a) it achieves global planarization, (b ) a wide range of materials can be planarized, sometimes in th e same polishing step, (c) it reduces severe topography to allow fabrication with tighter design rules, (d) it provides an alternate means of patterning metal, eliminating the need to plasma etch, (e) it improves metal step coverage due to reduction in topography a nd (f) it does not use hazardous gasses common in dry etch processes. Conversely, the disadvantages of the CM P process are (a) poo r control over the process with narrow latitude in process vari ables, (b) new types of defects introduced by the CMP process itself (scratch es, particle residue, etc.), (c) difficult end-point detection

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9 for desired thickness and (d) expensive to operate because of costly equipment and consumables. General CMP applications The process of CMP was initially develope d and implemented for planarization of SiO2 which is used as an interlayer dielec tric in a multilevel metallization scheme. Tungsten is used as an interconnect plug to the source, drain, and gates of transistors in Si microprocessor chips. Initially Ti and Ti N barrier layers are deposited, followed by chemical vapor deposition of W to fill the contact vias. Proceeding from achieving local and global planarization of SiO2, removal of excessive tung sten from the horizontal surfaces on the wafer pattern proved to be an asset for subsequent Al metallization. Hence CMP was developed with a two-fold a pproach of (a) planar izing oxide and (b) removing the via fill metal from the horizontal surfaces. Along with its successful implementation for the achievement of th e above-mentioned objectives, CMP is now extended to (a) polishing of different metals like Al, Cu, Pt, Au, Ti, Ta, etc., (b) polishing of different insulators like SiO2, Si3N4, various low-k dielectrics, doped and undoped oxides of silicon, (c) polysilicon, (d) ceramic s like SiC, TiN, TaN, etc., (e) multichip modules, (f) packaging; (g) optoelectronic components, (h) flat panel displays, (i) microelectromechanical systems (MEMS), and (j) magnetic recording heads and CD read write drives [19]. The major applic ations of CMP are summarized in Table 1-2 Cmp Output Parameters The critical output parameters of CM P are described below. Depending on the application, different output parameters are optimized.

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10 Table 1-2. Chemical mechanic al polishing applications. Materials Application Metal Al Cu Ta Ti TiN, TiNxCy W Dielectric Cu-alloys Al-alloys Polysilicon SiO2 BPSG PSG Polymers Si3N4 or SiOxNy Other Aerogels ITO High k dielectrics High Tc superconductors Optoelectronic materials Plastics, ceramics Silicon on Insulator (SOI) Interconnection Interconnection Diffusion barrier/adhesion promoter Diffusion barrier/adhesion promoter Diffusion barrier/adhesion promoter Interconnection e-emitter Interconnection Interconnection Gate/interconnect ILD ILD ILD ILD Passivation layer, hard mask ILD Flat panel Packaging Interconnection/packaging Optoelectronics Packaging Advanced device/circuits Ref. [19] Removal rate The polishing steps involving CMP of STI and metal mainly emphasize removing an overburden of one material and stop on another material leaving a planar surface. A high material removal rate is one of the ke y outputs desired from such CMP processes. The removal rate of the material being polishe d is strongly influenced by slurry chemistry and pressure distribution, i.e., chemical ac tion of the slurry chemicals on the material, interplay of the different complexing agents, oxidizers and corrosi on inhibitors and the mechanical abrasion of the particles on the wafer. Chemicals such as oxidizers and corrosion inhibitors vastly affect the reaction rate of the slurry with similar particle nature, size and distributions.

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11 Fig. 1-5. Surface layer formation on Cu with various slurry chemistries. [20] Fig. 1-5 shows the variation of the reaction rate of the different slurry components on Cu when the reaction kinetics were studi ed using electrochemical chronoamperometry [20]. It can be seen from the figure that the surface rate kinetics reach approximately 60 /s when Cu is immersed in distilled wate r. The reaction rate in creases to around 120 /s when 5% H2O2 is added. However upon addition of 10 mM BTA, the reaction rate decreased considerably. Therefore, the chemi cal contribution is very important in the CMP process. The other important factor is the down pressure used. However, for effective CMP of materials, the enhancem ent of removal rate by increasing the down force should not be at the cost of surface quali ty (for example, increase in wafer to wafer and within wafer non-uniformity, delamination, dishing, erosion, etc.) [21, 22] of the wafer. For this reason, the process throughput is compromised to polish the wafers at lower applied load, thereby achieving globa l planarization and be tter surface quality.

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12 Global planarization In contrast to glass or si licon wafer polishing, the objective of the CMP process in interlayer dielectric (ILD) polishing is to planarize the topogra phy created by previous semiconductor processing steps. The pad and slurry play key roles in achieving global planarization, concurrently maintaining the removal rate and producing a defect free wafer surface. If mechanical removal predominates, hi gh frictional forces are produced which result in surface defectivity. Also variation in local polishing pressure leads to variable removal rates within the wafer, which seri ously compromises globa l planarization [20], whereas, if chemical removal dominates, etch ing and corrosion [23] can occur. The key to a good polishing process is dependent on synergy between chemical etching and mechanical planarization. For this purpose, a passivation layer is created on the wafer surface by reaction with slurry a nd removal of this passivation (or modified) layer occurs due to mechanical abrasi on of slurry particles ( Fig. 1-6) For example, in Cu polishing, the formation of the passivation layer is achieved by oxidizers such as hydrogen peroxide, potassium ferricynate, ferric chlo ride, and ferric iodate. Corrosion damage to the surface is prevented by adding corrosion inhi bitors such as benzotriazole (BTA). In tungsten polishing, a rapid formation of surf ace passivation layer is due to the use of peroxygen compounds and stabilizing agents [24] The purpose of the passivation layer in the case of silica polishing is to soften the surface, which is inherently hard resulting in minimal material removal. For this purpose, maintenance of alkaline pH is sufficient in most cases [25, 26]. During Ta polishing, formation of stable Ta2O5 helps in uniform removal of material from the surface [27] To achieve optimal CMP performance, the time to form the passivation layer of desired thickness should be minimized.

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13 Fig. 1-6. Micro and nanoscale phenomena during CMP [20] Selectivity The difference in the removal rate of one material versus another in a given system represents the measure of the slurry selec tivity for these two materials. The higher the slurry selectivity, the more e ffective the end point detection is for the given CMP process. This is due to a marked change between the tribological properties of the material being polished, and the underlayer. The difference in tribological properties can be monitored in-situ using techniques such as motor curren t, force or acoustic emission for better end point detection. Selectivity is a very impor tant criterion in designing any slurry for multilevel metallization. For STI, the slurry must affect the oxide that is being planarized, and not the underlying nitride laye r. For polishing Cu, the slurry needs to react selectively on Cu and spare the barrier la yer Ta and underlying layers of silica or low-k dielectric material. Typically slurry se lectivity of 10 has been repo rted for Cu polishing [20].

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14 The selectivity could be cons iderably improved up to 1000 by introducing a particle free slurry [28, 29]. The reduction in mechanical component due to lack of abrasive implies that the majority of material removal occurs due to the solution ch emistry which can be made highly selective. Addition of specialized chem icals that can act as catalysts in the chemical interaction between slurry and the polished ma terial thereby increasing the rate of the chemical reaction considerably is a co mmon approach for improving the slurry selectivity. Tetramethyl ammoni um hydrate can be added to Cu slurries to considerably decrease the silica polishing rate [30]. An increase in the polishing rate of TaN with addition of phosphoric acid in alumina and colloi dal silica slurry is also observed. Mixed abrasive slurries (MAS) contai ning alumina/silica and alumin a/ceria particles have been developed to improve the sele ctivity of the CMP slurry. Th e details of the experiments with these novel mixed abrasive slurries have been published by Jindal et al. [31, 32]. Though highly selective slurries might help in avoiding defects such as erosion of sub layers, planar defects such as dishing s till exist causing waferto-wafer nonuniformity (WTWNU) due to the differential polishing pressures in the process. Measurement Techniques The outputs of the CMP process are quantif ied by a host of metrics. Material removal rate (e.g., nm/min) is commonly measur ed in terms of thic kness loss per time or weight loss per time. In terms of global planar ization at the wafer scale, film thickness is measured at points across the wafer surf ace and used to calculate within-wafer-nonuniformity (WIWNU). Most commonly, a 49-point measurement grid is used to determine the WIWNU, which is the variation of those measurements with respect to the average thickness. Similarly, a within-die nonuniformity (WIDNU) calculates a similar

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15 variation but just across the area of one die. At the feature-scale of the process, metrics such as step height reduction are used to indicate efficiency of the CMP process. Selectivity of the slurry is more often char acterized by estimating the erosion or polishing of the underneath layer. End Point Detection Theoretically, the end of a polishing step can be realized by setting a time limit to the process. However, this is only a rough estimate because varia tions of polishing pad surface property, fluctuations in slurry chemis try, particle size dist ribution, feeding rate, pad conditioning issues, and other potential variables can cause ove ror under-polishing. Therefore, in-line monitoring or automatic e nd-point detection of CM P is needed. Initial oxide CMP relied on process times and control of removal rate stability to achieve target thicknesses. As the CMP environment is hostile for in-situ metrology, the earlier endpoint techniques relied on indirect methods. One of the commercialized indirect methods monitors the motor current cha nge [33] while driving the carr ier or platen rotation. This technique measures changes in friction forces between the pad and the wafer surface. It is mostly successful for tungsten CMP than for copper or STI CMP processes, because the frictional forces between the polishing pad and exposed films do not differ significantly in the case of copper or STI scenarios. The method sufficiently sensitive for STI, dielectric and metal CMP processes is the vibration monitoring me thod [34]. Vibrations during the CMP process are det ected using an acceleromete r on the carrier behind the wafer. This method is used to detect delami nation of low-k dielectric films in copper dual damascene process [35]. Optical reflectometry is the preferred method for endpoint detection. But, the method is highly intrusive, requiring extens ive polisher modifications. Various other

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16 endpoint techniques have been developed in recent years, many of which are currently adapted to the high volume production stage [35]. CMP Consumables The CMP market in the year 2003 was $1.7B with slurry (24%) and pad (15%) amounting to 40%. The CMP equipment was estimated to comprise 55% with the remaining 6% accounting for conditioner and othe r consumables. The market is expected to grow to $3.3B in the year 2008. The rapi d growth of CMP and its application for polishing various materials, necessitated deve lopment of a variety of slurries, pads, complex process recipes, more complex slur ry mixing and distribution systems. Polishing of different materials and customized n eeds of the various semiconductor industries resulted in more complex CMP equipment with different process dynamics such as linear, orbital and fixed head machines [ 35]. The process of CMP has gone through a lot of evolution from first being used just for s ilicon dioxide planariza tion to the present day planarization applications in pre-metal dielectric (PMD), ILD, STI, metal and gate oxide, etc. While the CMP process seems fundament ally easy to understand, there are a staggering number of process variables (F ig. 1-7) that complicate the underlying interaction between the pad, slurry and wa fer, preventing full comprehension of the process. The most widely accepted mechanis m for the material removal is that the chemicals in the slurry react with the surface of the wafer (e.g., oxide, copper, etc.) and create a modified layer that can be removed easily. The mechanical action of the abrasives trapped in pad asperities then physically abrade and remove the modified material [24, 36, 37].

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17 In terms of the CMP input parameters the process variab les are generally categorized into chemical and mechanical parameters. The chemical nature of the CMP process typically relates to the constituent makeup of the slurry and how those chemicals react with the wafer surface to create a passivated or modified layer, keeping the particles well suspended in the slurry. The chemicals in the slurry are highly dependent upon the type of CMP being used. For example, in oxi de polishing, an alkali ne solution is used along with various buffering and oxidizing agents, whereas for metal CMP as in Cu CMP, acidic slurry can be used. The mechan ical aspects of CMP largely depend on the polishing pad, wafer pattern, and process condi tions like pressure and relative pad-wafer velocity. Fig. 1-7. Parameters involved in CMP process.

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18 Polishing in its simplest sense is controll ed chemo-mechanical material removal to produce a globally flat, defect free surface. The main components of CMP are the CMP slurry and the pad. The complexity of thes e CMP components and their interactions are discussed further in the following sections. CMP Slurry CMP slurry consists of two major co mponents: abrasives and chemicals. Depending on the material of the wafer, the chemistry of the slurry, and the synergy between them, each kind of slurry behaves diffe rently [38]. CMP is influenced to a great extent by numerous slurry parameters such as pH, solution chemistry, particle charge type, concentration and particle size dist ribution of abrasives, complexing agents, oxidizers, buffering agents, surfactants, corros ion inhibitors, etc.[19, 39]. An ideal CMP slurry should be well suspended with good slur ry stability, and be able to achieve high removal rate, excellent global planarizati on, prevent corrosion (in case of metal, especially Cu), and result in good surface fi nish, low defectivity and high selectivity. Rate of surface reaction The reaction between the wafer and slurry chemicals to form a modified layer of desired thickness should be fast enough to avoid material removal by mechanical indentation of the bare wafer. The time scal e in which the passivation layer is formed should be less than the average time of successive particle indentations into the wafer for abrasion to achieve optimal CMP performance. Fig. 1-8 shows the electrochemical chronoamperometry (potentiostatic) analysis of Tungsten by first keeping the samples at cathodic potential to avoid surf ace oxidation and then anodi zing them. The generation of current, which corresponds to surface reac tion rate, is monitored on a millisecond scale

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19 as shown. It can be seen form the figure that Tungsten surface quickly passivates which is conducive for mechanical removal of the material. Fig. 1-8. Chronoamperometry measurements for tungsten [20] For selectivity purposes, the reaction of slurry chemical s with the underneath layer should be significantly low compared to the su rface layer. In terms of operational hazard, the chemicals used in the slurry should not make it hostile for the operators performing CMP and the post-CMP chemicals should be treated to avoid environmental damage. Slurry agglomeration The ideal slurry will have abrasives behavi ng as discrete single particles during the CMP process. However, particles in a real CM P slurry apart from being discrete can also exist in the form of agglomerates [38, 40] An agglomerate is a collection of particles that come together into packed clumps due to phys ical or chemical inte ractions and act as a single entity. Although CMP slurries are compos ed of very fine particles up to 200 nm (0.2 m), large particles of 1 m and greater are often obs erved during the process. Such particles can be due to agglomerati on or contamination from foreign material. These are not desirable for CMP as they can cause micro scratches and pits due to deep

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20 indentation or non-uniformity due to varyi ng polishing pressure. Even minimal and undetectable concentration of larger sized particles are shown to produce surface defects in CMP [41]. The agglomeration of slurry can be prevented by proper slurry design, which includes appropriate use of chemicals, and/or surfactants and the suitable order of their addition to design the slur ry [42]. Other than adding chem icals, the particle surfaces can also be altered to make the suspen sion stable during the CMP process [42, 43]. In order to prevent the particle aggl omeration during the distribution stage, dispense filters are used which filter out the agglomerated particles before slurry delivery. Care is taken so that the filtration of th e agglomerated particles does not change the particle distribution and slurry composition. Th e drop in slurry pressure and flow due to filtration is minimized by using a series of filters instead of a single filter. Chemical Mechanical Polishing Pads The pad traps the slurry particles on its asperities, and executes the polishing action by transmitting the normal and shear forces fo r polishing, thereby playing a very crucial role in process optimization [19]. The pol ymeric polishing pad must have sufficient mechanical integrity and chemical resistance to be effective for numerous polishing runs through its life. The pad must be able to with stand the aggressive sl urry chemistries used in CMP without degrading, delaminating, warpi ng or blistering. Slurry chemistries range from highly alkaline near pH 11 used for po lishing of inter-layer dielectric to highly acidic near pH 2 used for metal polishing. Slur ries also contain oxidi zing agents such as hydrogen peroxide and potassium iodate. The pa d material should be resistant to such environments. As the polishing slurries ar e aqueous based, pad s hould be hydrophilic to allow circulation of slurry to whole wafer during polishing.

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21 The polishing pad is made up of a matrix of cast polyurethane foam with filler material to tailor the hardne ss of the polyurethane impregna ted felts for the specific CMP process. Polyurethanes have a unique prope rty of combining high strength to resist tearing during polishing a nd, an acceptable level of hardness and good abrasion resistance to prevent excessive pad w ear during polishing. The CMP pads can be categorized into four types differentiated by th eir microstructure [44] They are: Polymer impregnated felts (type 1), Poromerics (t ype 2), Filled polymer sheets (type 3), and Unfilled textured polymer sheets (type 4). Pa ds of type 1 and 2 are shown in Figs. 1-9 and 1-10. The figures indicate the variety of pad surface textures or asperities involved in CMP. The polyurethane polymer consists of two major components/blocks of alternating hard organic isocyanates and soft polyols. Each of these segments has different properties, the characteristic properties of a given pad de pend on the relative ratios of these hard and soft segments. Isocyanates, th e more rigid blocks, influence the hardness, modulus, tear strength and stab ility, specifically at elevated temperatures. Polyols on the other hand tend to affect the elasticit y, toughness, abrasion re sistance and the low temperature stability of polymer. For uniform polishing, the pad needs to be in contact with the whole wafer surface with the same contact pressure and relative ve locity between pad and wafer in all contact regions. But wafers are not fl at and typically have some degree of curvature due to stresses induced during manu facture process or differing coefficients of thermal expansion of the various deposited oxide a nd metal layers on the substrate. This necessitates the polishing pad to be flexib le enough to conform to the wafer-scale flatness. This is achieved by laminating a sti ff polishing pad to a fl exible underlying base

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22 pad, which is typically a more compressible material. This improves polishing uniformity across the wafer without unduly compromising th e stiffness of the top polishing pad. A stacked pad consisting of an IC 1000 top la yer on a Suba IV sub-pad (Rodel Inc., Newark, DE) is currently the pad system of choice to obtain both good global wafer uniformity and high removal rate for various CMP systems. (a) (b) Fig. 1-9. Type I CMP pad. (a) Surf ace. (b) Cross-section [44]. (a) (b) Fig. 1-10. Type II CMP pad. (a) Surface. (b) Cross-section [44].

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23 Effect of pad grooves Polishing pads have macrostructure, which can be either perf orations through the pad thickness or surface groove designs. The motivation behind designing pad grooves is to prevent hydroplani ng of the wafer, ensure uniform distribution of slurry over the wafer, and to remove the polishing debris from the pad surface through these chemicals [44]. The groove designs can be circular with either concentric or spiral grooves, crosshatched patterns arranged as an X-Y grid across the pad surface, other regular design such as hexagons, triangles and tire-tread t ype patterns, or irregul ar designs such as fractal patterns, or their combinations. The effect of pad textur e on tribological and kinetic properties of polishing pad has been studied by Philipossian and Olsen [45]. Real time monitoring of coefficien t of friction (COF) was done to estimate the normal shear forces originating during a particular CMP processes fo r a given pad. Frictional and removal rate data were taken on Rodel IC 1000 flat, perforated, XYand K-grooved pads. The Somerfeld number, COF, a new parameter called tribological mechanism indicator (TMI) and materials removal rate were some of the parameters monitored during the experiments. Philipossian and Ol sen [45] reported that flat and XY-grooved pads begin in boundary lubrication and migrat e to partial lubrica tion as Sommerfeld numbers increase. Thus different pad surface te xtures showed different material removal mechanisms. However, the variation of the mechanical properties need to be studied further on a microscale to gage its impact on the CMP process and material removal mechanism. Physical and chemical chan ges in pad during polishing Since polishing is a wet process, the mechan ical properties of the pad must not vary considerably when the pad is wet during CM P. However, the hydrophilic pad material

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24 looses modulus and hardness and gains ductility because water acts as a plasticizer. These changes are reversible [44] and pad properties revert to the dr y values, when the pad is in dry state, indicating that the chemical at tack is minimal [46]. The surface of the polyurethane pad has been studi ed and reported in literature [47] The quantitative analysis of the physical and chemical cha nges that occur in th e polishing pad during polishing was performed by Lu et al. [48]. In thei r research, Lu et al. studied the effect of polishing cycles on the pore size and shape of the commercially available IC 1000/Suba IV polishing pad. It was reported that the por e size and shape distri bution were modified by polishing cycles. Polishing induced a perman ent distortion in the radial direction due to the oscillatory motion of the wafer, while no change was seen in pad pore size in the transverse direction (direction of pad motion). The change wa s attributed to pore closure by surface reflow of the polymer during polishing or conditioning and not due to debris filling. The surface profiles gene rated using white light interferomery showed that the overall micro roughness of the pad decreases with polishing and there is a smoothening effect over a period of time due to polishing cycles. Along with physical changes, the pad undergoes surface chemical modification and degradation due to polishing slurry chemicals. No pad degradation of the bulk ma terial of the polishing pad was observed. The change in spectrum (Fig. 1-11) and shifting of the peaks of the used pad as compared to the new one has been attributed to the realignment of the molecules of the damaged pad surface layer. The porous structure of the polishing pad encourages water seepage. The presence of water in the polymer pore significantly affects the mechanical properties of the polishing pad. Li et al. [47] studied the effect of pad soaking time on the mechanical

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25 properties of the polishing pad using dynami c mechanical analysis (DMA). The dynamic shear modulus decreased to two thirds of its original value when th e pad is soaked for 5 h. Further, the rate of decrease in dynami c shear modulus decreases at around 14 h but does not reach a steady state. No significan t change in the rem oval rate was observed when pads with different soaking time are used in oxide polishing. This shows that removal rate is more of a surface characteristic of the pad and is not affected by the bulk material. Fig. 1-11 The absorbance spectra of used and dry IC 1000 pad along with dried silica slurry. [48] Modification of the pad-wafer contact m echanics can directly impact the CMP process performance. The modified surface can even change the mechanism of material removal during a polishing process [49]. During polishing, the pad surf ace layer degrades decreasing the pad surface roughness. The pad surface which is flattened or glazed needs to be rejuvenated to bring the polishi ng performance back to the original value. The roughening of the pad by a diamond condition er is known to resu lt in pad revival. Along with wafer polishing, the conditioner made of diamond grit considerably alters the surface of the polishing pad. The process of conditioning essentially removes some amount of top pad surface and is performed eith er in-situ (during the polishing run) or ex-

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26 situ in between two polishing runs. The pad damage due to insufficient conditioning is termed as glazing. Experiments were performed on the CMP pad by Lawing [49] at different conditioning levels of aggressiveness (expressed as low, medium and high). The change in polishing rate corre lated better with the predicte d surface contact area rather than the average surface roughness. Effect of temperature change on polishing pad The polishing pad might be subjected to el evated temperatures during the course of the CMP process [19]. The heating is due to the frictional forces generated by solidsolid contact between pad and wafer during polishin g. There is some alle viation of heating when the polishing is done in hydrodynamic c ontact mode [48]. However, there is an overall increase in the pad temperature ir respective of the mech anism of polishing. The effects of pad heating are compounded if the chemical reaction between slurry and pad is exothermic [38]. The mechanical, physical and chemical properties of the polyurethane material can be permanently or temporar ily altered if the pad is heated beyond a particular temperature [50]. DMA, th ermomechanical analysis (TMA) and thermogravimeteric analysis have been used for material characterization of the polishing pad [47, 48]. The applicability for DMA for polishing pads has been elaborately studied by Lu et al. [48]. Based on the results of previous experiments performed by Li et al., [47], DMA was performed to evaluate the structurepr operty relationship of polyurethane pads. The glass transition temperature is the temper ature at which the macromolecules of the polyurethane break away from entanglem ents and undergo micro-Brownian motion. Investigation of glass transition temperature of the polyurethane pa d is important as it

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27 corresponds to a sharp decrease in the hardness and modulus of the pad which in turn affects the removal rate a nd global planarization. Non-uniformity of the polishing pad The pad might be directly responsible for several process defects like WTWNU where there is non-homogeneity of polishing wh en one wafer is compared to another or WIWNU where there is non-homogeneity of pol ishing at different areas of the same wafer. The scanning ultrasound transmissi on (UST) is a nondes tructive technique developed that works on the principle of ultrasound permeability through absorbing visco-elastic medium [51, 52]. The difference in the ultrasound absorption in the areas of varying density and viscoelasticity is used to determine the non-uniformity within a single pad there by giving an in-depth idea of the physical characteristics of the given pad. In order to improve the yield of the CMP process and, to get a highly planar, defect free uniform wafer surface with reduced overall manufacturing costs involved, there is a need to extensively study the fundamental properties of the CMP pads on the whole. CMP process in the future The semiconductor industry has effectiv ely adapted its CMP technology for the 300 mm wafer [53]. Beyond the adoption of coppe r interconnects, several technologies are necessary to continue the sh rinkage of device dimensions and the increase of packing density in ULSI manufacturing. The use of ultr a low-k materials as in terlayer dielectrics has been at the forefront for decreasing the C part of the RC delay. However, polishing of ultra low-k dielectr ics which are mechanically weak (soft) is a daunting task. The single and dual damascene structures comp rising of ultra low-k porous or polymeric materials are more prone to buckling and cr ushing failures due to significantly lower hardness and Youngs modulus as compared to silicon dioxide. Acco rding to the ITRS

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28 roadmap [12] materials with dielectric constant 2.2 will be integrated in the IC by year 2007. Also, there needs to be a marked improvement in slurry selectivity for accurate end point detection when the constituent layers of the damascene structure namely, metal, hard mask, cap layer, barrier layer and di electric are polished. Furthermore, it is necessary to explore the niche of the CMP process in STI and other applications such as backside polishing and the fabrication of micro-electro-mechanical systems (MEMS). Here, the CMP process must be integrated ho rizontally and vertical ly to achieve high throughput and performance. In MEMS app lications, horizontal integration ensures reliability and good performance of a specifi c CMP process run. The development of new polishing pads and pad architectures, novel slurries, new metrology techniques, etc. comes within the scope of horizontal CMP integration. Vertical integration ensures success of every successive CMP operation. This includes the integration of the upstream processes such as Cu/barrier deposition, et ching and downstream processes such as ILD deposition and lithography. This opens a wide scope of research for further optimization and development in Cu CMP process. Due to intricate interactions of the processes involved in any CMP process, modeling e fforts are needed to get a systematic understanding of the process and pr edictability of the CMP outputs. Scope of Dissertation The importance of polishing and the vari ous available planarization techniques with emphasis on CMP have been discussed in Chapter 1. A general overview of the parameters involved in CMP are discussed w ith prominent interactions between them. Chapter 2 gives an overview of the CMP m odeling efforts and the framework of the PERC I CMP model. The models challenges are described, which necessitated the

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29 development of the PERC II model. The assump tions of the PERC I model are refined as necessary in chapter 3. Model development is also delineated with critical differences between PERC I and II models. Chapter 4 va lidates the PERC II model comparing to experimental literature data and comments on the predictive capability of the model. Chapter 5 summarizes the findings of the st udy along with the suggestions for future work.

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30 CHAPTER 2 CMP MODELING: OVERVIEW OF PERC I Like most semiconductor manufacturi ng processes, simultaneous tuning of process variables is a formidable task due to many varying parameters. Unfortunately, much of the commercial CMP process deve lopment cycle is based on nearly blind design-of-experiment (DOE) testing. While these empirical tests help to optimize parameters in a very small range, the overall approach does not necessarily facilitate a deeper understanding of the process. Thus, CMP research has focused on developing process models in order to gain further insi ght on the process mechanics for better control over the CMP outputs. The ultimate goal is to model at three scales of CMP, namely, the particle, die and wafer scales. The models at the particle scale are needed to understand the mechanisms involved in interactions between slurry pa rticles, chemicals, polishing pad and wafer during blanket wafer polishing. The models at the feature or die scale are needed to address the topography evolution of integrated circuit (IC) chips as a function of pattern density, line width, pitc h width and polishing time. The wa fer-scale models also need to address the issues related to the material removal non-uniformity over the entire wafer surface. To satisfy the manufacturability requi rements in the sub-micron IC fabrication, the margin of the profile non-uniformity is us ually limited in the range of several hundred nanometers. The material removal non-uniformity across the wafer is rooted in the nonuniform distributions of pressure and veloci ty over the wafer surface, which in a large

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31 degree, are determined by the configurations of CMP equipment. A mo del at this scale, therefore, needs to consider the e quipment configurati ons appropriately. Literature Review In the last decade, various kinds of m odels have been proposed by researchers, concentrating on different aspects of CMP cove ring the particle, die and wafer scales. But the effectiveness of die and wafer scale mode ls depends strongly on the robustness of the particle scale models, as the die and wa fer-scale models are developed based on the particle scale models. Therefore, in order to understand and predic t the performance of CMP in wafer scale, the current study aims to understand the behavior of CMP at particle scale. As the current work focuses mainly on particle scale modeling, only related models will be reviewed here. Preston Equation The Preston equation [54] as an empirica l relation for optical glass polishing was substantiated by Cook [24] who co nsidered that the interacti on between abrasive particles and wafer surface leads to removal of atomic clusters due to bond breakage. Preston provided a simple model of material remova l in glass polishing tools which is often adopted for CMP processes also. But, experime ntal results have shown that slurry and pad properties also significantly influence the process along with down pressure and platen speed [55, 56]. In or der to explain the non-Prest onian behavior, many modeling efforts have been carried out in the past decade and is still a topic of considerable interest. The three most important elements in the CMP material removal process are the wafer being polished, slurry and polishi ng pad. Researchers adopted two main approaches in modeling the CMP proce ss. One approach is based on fluid hydrodynamics, where material removal is cons idered to be caused mainly by slurry

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32 erosion. Slurry film thickness, hydrodynamic pressure and removal rate are generally calculated by solving Reynolds or Navier-S tokes equation [57-62]. The other approach uses the theory of contact mechanics, which assumes that the material removal occurs by particle indentation into the wafer su rface. Pad surface roughness and hardness are generally used to calculate th e particle indentation into the wafer thereby calculating the removal rate [27, 63-67]. Finite element modeli ng (FEM) has also been used to determine the pad asperity mechanical properties recently [68, 69]. It is generally agreed that the typica l CMP process conditions lead to major material removal by particle abrasion rather than by slurry erosi on [70]. Experimental observations of polished surfaces have revealed that material removal in CMP occurs as a consequence of a combination of chemical reac tion of the slurry chemicals with the wafer surface and ploughing (repeated sliding, rolling, or indentation) of the abrasive particles against the wafer surface that is already m odified. The chemical reaction results in formation of a thin layer on surface whic h is of different modulus than the substrate/wafer, aiding in material removal [71]. When particles are introduced between w earing surfaces, the wear is due to the particles embedded in one of the sliding surf aces. This process is referred to as threebody abrasion. In the CMP process, the particle s acting as single point cutting tools, dig into the wafer and plow a series of groove s in it. Therefore, the CMP process is essentially a three-body abrasive wear. The an alysis of the texture of polished surfaces also supports this observation. Fig. 2-1 illust rates typical post CMP surfaces as examined via an optical surface profiler. The surface texture consists of a number of randomly

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33 oriented nano-grooves (Fig. 21). The width and depth of the grooves are determined by the penetration depth of the abrasive particles into the wafer surface. (a) (b) Fig. 2-1. Polished wafer surfaces showing nanoscr atch surfaces. (a) Si lica wafer [72]. (b) Si wafer [73]. The material removal process in CMP can be considered as sliding of the indented slurry particles over a chemically influen ced thin layer over the wafer surface. The

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34 knowledge of critical factors that effect the CMP proce ss and the interactions among them is critical to select the respective parameters and de sign an enhanced CMP process, predicting material removal rate, and surface quality (roughness, defects, etc.). The most popular material removal equation is the Pr estons Equation [54], which was initially introduced for glass polishing, MRR= KePV, (2 1) where MRR is the material removal rate, Ke an all-purpose coefficient, P the down pressure and V the relative velocity over the wafer-pad inteface. It demonstrates a linear dependency of material removal rate on the pr essure and velocity. Not all experimental MRR data in CMP, especially in metal CM P, support the linear dependency between material removal and the product of pressure and velocity. Modifications to Preston Equation In order to explain the non-Prestonian behavior of the CMP process, revised Prestons equations were proposed by several researchers. For example, considering that the material removal rate does not extrapolat e to zero, Maury et al. [74] introduced a fitting parameter MRR0 into Prestons equation MRR= KePV + MRR0 (2.2) Later, the nonlinear equation MRR= KeP V, (2.3) where and are two fitting parameters, was proposed by Wrschka et al. [75] to get a better fit for the experimental data. The major problem with Prestons equati on and its revisions are that they are empirical modeling efforts. Therefore, they do not shed any light on gaining insight into

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35 the process especially regard ing other process variables. By extending Browns model [76] of the metal polishing to the silic on polishing, Cook [24] developed a physical model to address this limitati on. The interactions between th e abrasive particles and the wafer surface is proposed as a Hertzian elastic penetration [77] of a spherical particle under uniform pressure P into the wafer surface, sliding along the surface with a velocity V and removing material volume proportional to the penetration. The MRR formulation was proposed was MRR= PV/(2E) (2.4) where E is the Youngs modulus of the wafer material. This model can be taken as a theoretical equivalent to the Prestons equation since it suppo rts the linear dependency of MRR on pressure and velocity. The relati onship between the wafer surface roughness Ra the down pressure P, and abrasive size can also be obtained based on this model Ra=3/4 b (P/2k1E)2/3 (2 5) where k1 is the particle concentration, which is unity for a filled close hexagonal packing [24] and b the diameter of th e slurry particles. A similar model was developed by Liu et al [78] based on the statistical method and He rtzian elastic penetra tion. Besides the wafer material properties including wafer hardness Hw and wafer Youngs modulus Ew this model included pad hardness Hp and abrasive Youngs modulus Es resulting in V P E E E E H H H C MRRw s w s p w w e (2.6) where Ce is a coefficient to account for the effects of slurry chemicals and other consumable parameters. This model, similar to Cooks model, suggests that the material removal is proportional to the appl ied pressure and relative speed

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36 The advantages of Cooks and Lius mode ls over Prestons equation are that they provide more insights into the roles of the consumable parameters. The contributions of the slurry abrasives and pad, fo r example, have been attributed to their size and hardness. An additional benefit is that not only material removal rate, but also surface quality issues such as roughness (Eq. 2.5) can be addressed using these models. Slurry Erosion In Cooks and Lius models, the mechanic al removal by abrasive particles was assumed to be the dominant mechanism. However, some researchers instead assumed the material removal to be by slurry erosion approach, i.e., due to mechanical-enhanced erosion. Runnels et al. [79-81] developed an erosion-based model for CMP. They assumed that a fluid film exists between th e wafer and pad interface, which affects the erosion/material removal rates at each si ngle point through the fluid stress tensors. Motivated by observations at feature scal e, modification to Prestons equation was proposed, with relative velocity V, replaced by the tangential stress on the wafer surface; MRR=Cetn (2.7) where Ce is an all purpose coefficient, t is the shear stress due to the slurry flow and n the normal stress. The model uses a steady state incompressi ble Navier-Stokes equation to model the slurry flow at the wafer-polishing pad interface. The wafer surface is assumed to be smooth and spherical with a large radius of curvature. The fluid layer thickness and the angle of attack between the pad and the wa fer are obtained through an iterative procedure satisfying force and momentum balance. Runnels model has been integrated into several particle-scale models by researchers in cluding Tseng and Wang [82] and Zhang and

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37 Busnaina [83]. Tseng and Wang attributed the normal stress at the pa rticle-wafer contact to the elastic indentation of th e particle into the wafer surf ace, which is similar to that proposed by Cook and calculated the normal stress over the wafer-particle interface as 2 c nr F (2.8) where F is the force acting on the spherical part icles, which is proporti onal to the pressure P. The radius of particle-wafer contact, rc is given by E E F d rc 2 2 31 1 8 3 (2.9) where d is the diameter of particles, and the Poissons ratios of wafer surface and the particle and E and E the elastic modulii of the wafer and particles, respectively. The shear stress due to the slurry flow can be approximated as 0VPA Ce t (2.10) where is the dynamic viscosity of the slurry and A0 the area of wafer surface respectively. Substitution of equations (2 8) and (2 10) into (2 7) yields MRR=KeP5/6V1/2 (2 11) where Ke is the parameter to account for ma terial properties, slurry abrasive concentration and chemical processes. This model demonstrated a nonlinear relationship between the material removal and the product of pressure and velocity. Tsengs model attempted to connect the elastic indentation to the erosion rate, whereas Cooks and Lius models connect it to the mechanical ab rasion. While the down pressure dependency (P5/6) is quite close to linear depe ndency, the velocity dependency (V) however, is quite nonlinear. This is because the contribution of velocity has been attributed to the slurry

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38 flow instead of abrasive sliding. Due to pad porosity and surface asperities, such a slurry film is bound to be interrupted by solid-s olid contact. Thus hydrodynamic lubrication may be responsible for distributing the slurr y, while the material removal occurs mainly through solid-solid contact. Cooks, Lius and Tseng and Wangs models attributed the penetration of the abrasive particles to Hertzian elastic contact. Zhang and Busnaina [83] estimated the contact pressure between the particle and the contact surface in their model and found that it is larger than the yi eld stress of the polished materi als. Therefore, they proposed that plastic deformation is a more likely deformation mechanism in polishing. The contact pressure over the particle-wafer interfaces is sugge sted to be equal to the hardness Hw of the wafer materials. Replacing the nor mal stress (Eq 2 8) in Tseng and Wangs model with the hardness Hw yields the following material removal rate formulation MRR= Ke(PV)1/2 (2 .12) where Ke is the parameter to account for ma terials properties, slurry abrasive concentration and chemical processes. Both Tseng and Wang; and Zhang and Busnamas models suggest a nonlinear pressure times velo city dependency of material removal rate. Moreover, it is noted that besides the external force applied on the particles from the pad, Zhang and Busnaina also proposed that an a dhesion force, either va n der Waals force or electrostatic force depending on the separa tion distance between the particle and the wafer, contributes to the indent ation. This has been integrated into another particle-scale model by Zhang et al. [84]. In a series of articles by Ahmadi and Xia [85], and Mazaheri and Ahmadi [86, 87], a thermodynamic work parameter Wa of adhesion was added to account for its effects on the indentation of ab rasive particles. Mazaheri and Ahmadi [86]

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39 introduced a double layer (dl) force into the indentation force, whose magnitude is a function of the zeta pote ntial of the abrasives and the wa fer. Beside the abrasive wear, Ahmadi and Xia [85] also considered the a dhesion wear of the wafer in their model. Moreover, while most of the models treated the abrasives as having a spherical shape, Mazaheri and Ahmadi represented them as spheres with a number of hemispherical bumps around their surface. The penetrations of slurry abrasives are modeled using the penetrations of the bumps. The above models imply that the abrasives are embedded in the pad and indent into the wafer surface. It should be noted that some modeling efforts also assume that the abrasive particles float in the slurry and impact the wafer surface from time to time causing material removal [88]. Pad Considerations in CMP Models The pad is assumed to be smooth in the earl ier particle-wafer interaction models. It has been observed that the pad topography and pad material play an important role in material removal processes. For example, the material removal rate has been reported to increase with the pad surface roughness [55] Without conditioning of the polishing pad surface, the material removal rate decreases exponentially with polishing time [89]. In consideration of this, Yu et al. [63] developed a pad-based model. They approximated the peaks on the pad surface by hemisphe rical asperities with consta nt radius and the asperity heights to follow Gaussian distribution. Base d on the model, the real contact area is smaller than the nominal (apparent) contact area and linearly proportional to the down pressure. Steigerwald et al. [19] proposed that the material re moval rate is proportional to the number of abrasive partic les over the contact area. Combining this argument with

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40 Yus model yields a linear dependency of the material removal rate on the down pressure, which agrees with Prestons equation. Zhao and Shi [90] also proposed a model based on the wafer-asperity contact. Unlike Yus model [63], this model does not consider the Gaussian distribution of the asperity heights. The contact area between an asperity and the wafer is given by Aa P2/3 based on Hertz elastic contact theory. By comb ining Steigerwalds argument, the material removal rate formulation can be obtained as MRR= K(V)P(2/3) (2.13) where K(V) is a function of the relative ve locity V and other CM P parameters. It is further considered by Zhao and Shi [90] that when the particles are rolling against the wafer surface, their contribution to material re moval will be negligible. They argued that whether the particle is rolling or not is determined by the surface friction between the particles and the wafer, and only when the dow n pressure P is larger than a threshold down pressure Pth, the pure rol1ing can be avoided. Th e material removal rate is given as: MRR = K(V)(P2/3 Pth 2/3) for P Pth (2.14a) and MRR = 0 for P< Pth (2.14b) The fundamental difference between the a bove pad-based models and the particlebased models by Cook and others is that pad-based models a ttribute the material removal rate to the number of abrasive particle s captured by the polishi ng pad while the later attributes the material removal rate to the interaction between a si ngle abrasive and the wafer.

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41 A particle-pad interaction is critical to th e particle scale models considering that the function of the pad is to trap the abrasive par ticles and transmit load to the particle-wafer interface. Cooks model [24]suggested a clos e-packing of spherical abrasives onto the pad. It is assumed that the wafer and pad ar e separated completely by the abrasives and no direct pad-wafer contact exists. The for ce applied on a single abrasive under these assumptions is given by 1 2Pr 3 2 k F (2 15) where P is the polishing pressure, r the abrasive size and k1 the particle fill fraction on the pad. This particle-pad interaction model has been integrated into the material removal model of Cook. It is also used by Ahmadi and Xia [85] to evaluate the force on a particle in their case of a hard-pad and a larger con centration of abrasive particles. Later, Zhao and Shi [90] proposed that when the pad is soft enough, the abrasive particles will be embedded deeply into the pad and the force from the wafer is supported by the pad and abrasives together. This idea has been applied by Luo and Dornfeld [27, 91, 92] and Fu et al. [93] in their model. Luo and Dornfelds m odel [27, 91, 92] suggested that this force is proportional to the contact pressure multiplied by the abrasive size by assuming that the abrasives are closely packed to each othe r and these closely packed abrasives are enclosed by the pads so that the effective co ntact area between wafer and pad is equal to that without abrasives. More over, the size of the abrasive s that may be captured by the pad is assumed to be a function of abrasive size distribution and pad properties. Their model, however, neglects the lower sizes of the particle size distribution in material removal calculation. Fu et al. [93] later assu med that the abrasives are dispersed evenly over the pad surface and used a beam model to evaluate the wafer-pad direct contact

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42 between two single abrasives. The force s upported by a single abrasi ve can be obtained from the beam model and is a function of ab rasive size, down pressure and pad material properties [93]. Besides the force, the sec ond purpose of an abrasive-pad interaction model is to evaluate the number of abrasive s involved in the material removal process. Fu et al. [93] considered the number of trapped particles as an independent parameter in their model. This may be misleading considering that vari ous parameters, for example, the abrasive weight concentration and abrasive size, have an influence on the number [27, 72, 91, 92]. Luo and Dornleld considered more complex scenarios and suggested that only a portion of abrasives are involved in the material removal process, which is not reasonable. Slurry Considerations in CMP Models The contribution of slurry chemicals to the material removal is either neglected in earlier models or represented by an all-pu rpose coefficient. Cook [24] suggested a complete but complicated scenario of the chemical effects. Besides the mechanical removal, it is proposed that the surface re moval during polishing include the following five chemical processes (i) the slurry chemi cal diffusion into the wafer surface, (ii) the subsequent wafer material dissolution under th e load imposed by the abrasive particles, (iii) the adsorption of the dissolution product on to the surface of the polishing grain, (iv) the re-deposition of the polishing materials back onto the wafer surface, and (v) the corrosion rate between particle impacts. Thes e steps are not considered in most of the early models as they are complex to model quantitatively. The major contribution of slurry chemi cals on the material removal process has been attributed to the formation of a surf ace layer. This idea is well demonstrated by Kaufman et al. in their Tungsten CMP model [37].

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43 Kaufman et al. proposed that this passivat ion layer is removed by slurry abrasives and the fresh tungsten surface is exposed, whic h is subsequently passivated and removed. This mechanism of continued passivation and removal can be used to explain the copper, aluminum and other metal CMP systems as well. A similar mechanism is supposed to work in silicon, silica and low-k CMP system s. Paul [94] and Zhao et al. [95] have proposed detailed surface kinetics models to connect the slurry chem ical concentrations and fresh metal surface sites available to the formation rate of the surface layer. Their models can explain the material removal rate as a function of chemical and abrasive weight concentration. Borst et al. [62] have proposed a five-step model for CMP of SiLK dielectrics (i) mass transport of reactant from the slurry to the slurry /wafer interface, (ii) adsorption of reactant to available surface site (iii) reaction between adsorbed reactant and specific wafer surface to form an alte red wafer surface layers, (iv). mechanical removal of the altered wafer surface layer, a nd (v) mass transport of removed material to the bulk slurry. In their work, the mass trans portation, slurry chemical concentration and reaction rate to the formation of the surface layer were inco rporated. This detailed model was suggested to be able to be extended to the CMP of other materials. The idea of continuous surface modification and removal has been applied in the model developed by Qin and co-workers [96]. A similar approach has also been used in Luo and Dornfelds model [91]. They exte nded Kaufmans model by proposing that the surface layer is a bi-layer structure, though in reality there might be a gradual transition between the layers. They did not cover the details on how the formation rate of the surface layer is affected by the slurry chemi cals. But Luos model assumes that all the

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44 asperities contact the wafer and that the part icles fill the asperity-wafer contact spots, which is not necessarily true. The slurry chemicals affect not only the wafer but also the slurry abrasives and polishing pad. Their contribution to material removal is therefore not only reflected through surface kinetics, but also through alte ration of the abrasive and pad properties such as the abrasive shape, abrasive si ze and pad Youngs modulus. There are not many modeling efforts on these two interactions ye t. A recent model by Castillo-Mejia et al. [97] tried to explain the effect of water-pad interaction in CMP. The water is proposed to plasticize the polishing pad and reduce its elas tic modulus. A formulation on the ratio of the Youngs modulus of wet pad to the dry pad is suggested. This Youngs modulus is then used in a wafer-pad contact mode l to evaluate the material removal. Many of these models were also extended to patterned wafers along with other modeling concepts including combination of the solid-solid contact and slurry erosion approaches [98-109]. Polishing mechanisms we re also based on surface reaction kinetics [95, 110, 111] and modeled using mo lecular dynamics simulations [112-115]. PERC I CMP Model Most of the earlier models have concentr ated on one or two interactions of the CMP process parameters. They are useful fo r identifying the input parameters. However, they may not be sufficient for understanding the whole material removal process. The effects of the same input parameters may be contrary to each other when acting in different conditions. A comprehensive model of CMP integrating the main interactions together is therefore needed. For this purpos e, a model was develope d by Qin et al.[72], taking into consideration most critical CMP parameters. This section discusses the

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45 assumptions on which the model is built, its effectiveness in predicting the CMP process variables and the model limitations. Model Development The chemicals in a slurry alter the propertie s of the wafer surface that is in contact with them. Since the chemical influence is restricted to a thin region near the wafer surface, a thin surface layer w hose mechanical properties are different from those of the bulk wafer is assumed. This surface layer can be formed by chemical reactions at the surface or by the diffusion of slurry ionic speci es into the wafer. The surface layer is then removed by mechanical action of the slurry part icles and/or by dissolution into the slurry through a convective diffusion process. Alt hough there may be a few exceptional cases [Luo98], material removal by the di ssolution is small compared to that by the mechanical action of the slurry particles, and it is not c onsidered in this model. Fig. 2-2 describes schematically the physical situation that is considered in the present analysis. The pad asperities that are in contact with the wa fer surface act as the anchoring sites for the slurry particles. The anchor ed particles then gouge the ch emically altered wafer surface or the bulk wafer depending on th e indentation depth re sulting in material removal. In the following section, various parameters cons idered in the present analysis and the underlying assumptions are described followed by the details of the model development. Topology of a pad surface has been charac terized and described statistically by various researchers [63, 116] Their measurem ents indicated that pad asperity heights were in the order of tens of microns and appeared to have a normal (or Gaussian) distribution. In Fig. 2-2, the topology of the pad surface is shown schematically along with a statistical description characterizi ng the pad asperities. In this figure, is the

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46 mean radius of curvature of the tip of the pad asperities, is the distribu tion function for the height of the asperities, and the standard deviation of the pad asperity heights, respectively. P V Wafer Pad Asperity Mean Height z (z) h Asperity Height, z (a) (b) Fig. 2-2 Pad consideration in PERC I. (a) Sche matic of the pad surface that is in contact with the chemically modified laye r formed on the wafer surface; (b) Distribution of the pad aspe rity heights (When the height of an asperity is greater than the average gap h between th e pad and the wafer, that asperity is in contact with the wafer surface.) [72]

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47 Since the characteristic length scale fo r the roughness of the pad surface (e.g., ) is much larger than the feature sizes on the wa fer, it was assumed that the wafer surface is smooth and flat compared to the pad surface. This assumption makes it possible to use the Greenwood-Williamson model [117] th at describes the contact area, Areal, between a flat surface and a randomly rough surface under a normal force (or load), L : dz z h z NA Ah o real (2.16) dz z h z E NA Lh o 2 3 2 1 *3 4 (2.17) where N is the number density of the pad asperities (i.e., number of asperities per unit area), Ao is the total area of the flat wafer su rface, and h is the average gap between the smooth wafer and the rough pad under the give n conditions. Then, the down-pressure, P, applied to the wafer with an area Ao is L/Ao whereas the actual mean contact pressure, Pr, is L/Areal if the normal force applied to the wafer is entirely supported by the pad asperities in contact with the wafer. That is L = PAo = PrAreal (2.18) E* is the composite modulus between the two surfaces in contact, that is defined as w w p pE E E2 2 *1 1 1 (2.19) where E and are the Youngs modulus and the Po issons ratio, and the subscripts p and w represent the pad and the wafer, respectively. Equations 2.16, 2.17 and 2.18 provide an explicit relationship between the contact area ( Ar) and the down pressure ( P ) that is needed in modeling the CMP process. From Eqs. 2.16 and 2.17,

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48 dz z h z dz z h z E L Ah h real 2 / 3 2 / 14 3 (2.20) Following Yu et al.[63] the normal distribution function may be used for the distribution of the asperity height, When 2 22 z exp 2 1 zis substituted into Equation 2.20, the integral cannot be obtaine d in an explicit form. Instead, a numerical integration should be preformed. Johnson showed that the ratio of the two integrals in Eq. 2.20 is nearly a constant for a broad range of h / [77]. Thus, 2 / 1 1 2 / 1 1E PA C E L C Ao real (2.21) where C is a constant whose value is between 0.3 and 0.4 when h / is in the range of 0.5 and 3.0. Recalling that is the standard devi ation of the asperity height distribution, h / =3.0 represents a situation where only 0.13% of the pad as perities are in contact with the wafer whereas about 30.85% is in contact when h / =0.5. Practical situation in a typical CMP process is well within this range of h / value. From Eqs. 2.18 and 2.21, 2 / 1E C Pr (2.22) It should be noted that the contact area ( Ar) increases linearly with the downpressure whereas the contact pressure ( Pr) remains constant due to the linear increase of Ar with P The underlying assumption for Eq. 2.18 is that the applied normal force on the wafer is supported entirely by the pad asperities. As is mentioned previously, experimental measurement on the friction co efficient indicates that the hydrodynamic

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49 pressure is negligible under typical CMP operational conditions. Furthermore, commercial pads often have grooves or perf orations to prevent hydroplaning (i.e., to prevent a large pressure development due to a lubrication flow) a nd to ensure uniform slurry distribution. Thus, the assumption that the hydrodynamic pressure is negligible is justifiable. Small Plastic Deformation of the Thin Layer on the Wafer Surface Considering the fact that the deformation of the surface layer by the slurry particles under the contact pressure is ve ry small in the order of seve ral nanometers, the mode of deformation can be assumed to be plastic de formation. In the case of oxide CMP, it is known that the silica surface is softened when it is in contact with an aqueous solution. A surface layer (or so-called gel layer) is form ed due to the diffusion of water molecules into the silica surface alteri ng the surface properties. The situation may be different in the case of metal CMP. Since an oxidizer is added in most metal CMP processes, metal oxide is formed on the wafer surface creating a structure mismatch at the interface betw een the oxide layer and the bulk wafer underneath. Thus, delamination or microcrack ing of the oxide layer may occur at the interface during the metal CMP process. However, as evidenced in previous sections, it is likely that plastic deformati on is still the dominant mode of deformation because the indentation depth by the slurry particles is small (e.g., less than several nanometers). Furthermore, the oxide layer may be soft due to hydration in an aqueous environment. Thus, the assumption that the chemically alte red thin surface layer on the wafer exhibits plastic deformation is plausible. This assump tion enables us to apply the abrasive wear theory in deriving the expre ssion for the material removal rate. When the indentation depth is beyond the surface layer, the deformation of the unaltered wafer material may be

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50 either plastic or elastic depending on the hard ness of the wafer material and the slurry particles. Material Removal by a Single Particle In the present analysis, it is assumed that the slurry particles are monosized and of radius R. The overall material removal rate is assumed to be the multiple of the removal rate by a single particle and the number of particles in contact with the wafer: (RR) = n (RR)v/Ao (2.23) where n is the number of slurry particles anc hored in the region of the pad that is in contact with the wafer, and (RR)v is the volumetric removal rate by a single particle. The overall removal rate, (RR), is typically desc ribed in terms of the thickness removed per unit time; hence the division by the nominal wafer area Ao. Schematic illustration of single particle abra sion is given in Fig. 2-3. The material removal is viewed as a sliding-indentation process in which the volumetric removal rate by a particle is given as (RR)v = AiV (2.24) where Ai is the cross-sectional area of the part icle immersed in th e wafer under pressure (hashed area in Fig. 2-3a), and V is the relative velocity of the pad to the wafer. Assuming that the hard particle maintains its spherical shape, R a R R a Aiarcsin2 (2.25) where is the indentation depth and a the radius of the circular indentation on the wafer surface by the particle of radius R. Because is very small compared to R, a/R is also very small and Equation 2.25 can be linearized about a/R to give

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51 R O a Ai1 3 4 (2.26) Thus the volumetric removal rate is V a RRv 3 4 ) ( (2.27) (a) (b) F a F a Padt Wafer t R b Pad Wafer a Fig. 2-3. Schematic of single particle ab rasion showing the removal of chemically modified surface layer. (a). t. (b). > t with soft wafer materials. Because a2=(2R 2) and is much smaller than R, Equation 2.27 can be rewritten as R V a RRv3 2 ) (3 (2.28) Once the indentation depth (or a) is known, the volumetric removal rate by a single particle can be readily calculated from Eq. 2.28. Depending on the relative magnitude of the indentation depth ( ) to the surface layer thickness (t), the material removal may be classified into two different regimes as depicted in Fig. 2-3; (a) t and (b) > t.

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52 Indentation depth smaller than th e surface layer thickness (i.e., t) When the chemically modified surface la yer is thick enough, the indentation depth will be no greater than the surface layer thickness and only plastic deformation within the surface layer occurs. In this case, (or a ) can be obtained from the force balance imposed on the particle by the pad and the wafe r that depends on the indentation depth of the particle into the wafer su rface. The force imposed on a particle by the pad is given as r aP b F2 (2.29) where b is the radius of the circular indentation into the pad as described in Fig. 2-3a, and Pr is the contact pressure given by Eq. 2.22. The force on the particle by the deforming wafer can be given as e aB a F2 (2.30) where Be is the effective Brinell hardness of the chemically modified surface layer. The term effective is used because its value is influenced by the thickness of the chemically modified surface layer and the material prope rty of the underlying substrate. The pad is supposed to hold the particles in place th ereby transmitting the normal force to the particles that cause indentat ion of the wafer surface. The pad should be soft enough to provide stable anchoring of the particles on its surface. However, if it is too soft, the particles will be embedded too deeply into the pad diminishing the material removal capability of the particles. Thus, the pad shoul d be sufficiently hard to make the value of b in Fig. 2-3 to be close to the particle radius R. Then, from equations 2.29 and 2.30 with b=R,

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53 2 / 1 e rB P R a (2.31) This equation along with equations 2.22 a nd 2.28 gives the following expression for the volumetric removal rate by a single particle of radius R. V B E R C RRe v 2 3 4 3 2 2 33 2 ) ( (2.32) Indentation depth greater than the surface layer thickness (i.e., > t) When the bulk wafer material beyond the surface layer is relatively soft (e.g., copper) compared to the hardness of the particle s, it is possible for the particle to cause deformation into the wafer beyond the surface layer (Fig. 2-3b). As it was described in the previous section, the deformation is expe cted to be plastic for both the surface layer and the bulk wafer, and the force causi ng the deformation may be given as w e aB tR a tRB F) 2 ( 22 (2.33) where Bw and Be are the Brinell hardness of the bulk wafer material and the chemically modified surface layer, respectively. Because this force is equivalent to the one imposed on the particle by the down-pressure, Eq 2.33 is equated with Eq. 2.29 with b=R to give 2 / 1 2) ( 2 w e w rB Rt B B P R a (2.34) Then, Eq. 2.28 for the volumetric removal ra te by a single particle is reduced to R V Rt B B R B E C RRw e w v 2 3 2 2 11 2 3 2 ) ( (2.35)

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54 While equation 2.35 describes a situation where the deformation reaches into the bulk wafer beyond the surface layer, deformatio n of the bulk wafer may not occur if the bulk wafer material is very hard. This lim iting case corresponds to the situation of infinitely large Bw in equation 2.35 that is reduced to V t R RRv 2 / 3 2 / 13 2 4 ) ( (2.36) Equations 2.32, 2.35 and 2.36 indicate that the volumetric removal rate by a single slurry particle depends on the geometry of the pad and the particle (i.e., and R), the material properties (E*, Bw and Be), the thickness of the surface layer (t), and the relative velocity of the pad (thus the particle) to the wafer (V). It may be interesting to note that (RR)v is independent of the down pressure, P. It is due to the fact that the contact pressure, Pr, is independent of P. As equation 2.21 indicates, the contact area of the pad with the wafer (Ar) increases linearly with P. Consequently, the mean contact pressure, Pr, which is PAo/Ar, is independent of P. In the following section, the number of particles in contact with the wafer surface is estimat ed to determine the overall removal rate. Estimation of the Overall Removal Rate When the wafer is pressed against the pad and is in sliding motion relative to the pad, the particles can be entrapped onl y in the region where the local distance between the wafer and the pad asperity is smaller than the particle diameter, 2R. Thus, the number of particles that can be trappe d on the pad asperities is n = 2RAreal n (2.37)

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55 Here Ar is the real contact area between the wafer surface and the pad asperities as it was described in previous section. n is the number density of the particles in the slurry (i.e., number of particles per unit slurry volum e), that can be calculated from the solid loading Ca (wt%) of the slurry particles as a s a nR C 34 3 (2.38) where a and s are the densities of the particle a nd the slurry solution, respectively. Substitute of Eqs. 2.38 into 2.37 gives r a s aA R C n 22 3 (2.39) By combining Eqs. 2.39 and 2.18, the number of particles anchored on the pad asperities becomes 2 / 1 22 3 E PA R C C no a s a (2.40) Now that (RR)v and n are given in terms of various pr ocessing variables and material properties, the overall material removal rate in a CMP process can be estimated from Eqs. 2.32, 5.27 and 2.40 for the two different cases described above: Removal Rate: Indentation depth smaller than su rface layer thickness (i.e., t), PV B E C C RRe a s a 2 / 3 2 / 1 4 1) ( (2.41) Removal Rate: Indentati on depth larger than surface layer thickness (i.e., > t),

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56 PV R t B B B E C E C C RR/ w e w * a s a 2 3 2 1 2 11 2 1 1 (2.42) As Eq. 2.23 indicates, th e overall removal rate, (RR), is the thickness removal rate which is the volumetric removal rate divided by the nominal wafer area Ao. We may recall that C is a constant whose value is about 0.35 when h/ is between 0.5 and 3.0 [Joh85]. The overall removal rate given above is reminiscen t of Prestons equation in that the material removal rate is proportiona l to the down-pressure, P, and the relative velocity, V. It should be noted that the Prestons coefficient Kp, whose value relies on empiricism, is now given as a function of various proce ssing variables and material properties. The model predicts the removal rate as a f unction of pressure and velocity product (PV) very well [72]. The removal rate is usually only considered as a function of PV in many modeling efforts, ignoring other processing parameters. But the PERC I model considers the particle size effect, which is crucial for any CMP system. Equation 2.41 indicates that th e overall removal rate is inde pendent of the particle size R whereas Eq. 2.42 indicates a decrease in (RR) with increasing particle size. When the indentation-depth is smaller than the surface layer thickness (i.e., t), the volumetric removal rate by a single particle (RR)v is proportional to R2 (Eq. 2.32). The number of particles in contact, on the other hand, is inversely proportional to R2 as the Eq. 2.40 indicates. Consequently, the par ticle size effect is negated. Thus the model predicts as shown in Fig. 2-4 that the removal rate is either independent of particle size in the modified layer removal regime or decreases with particle size in the substrate indentation re gime. But, the reported literature has shown

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57 that removal rate also increases with particle size in a given range, and that there is an optimal particle size at which enhanced polis hing can take place as shown in Figs. 2-5 and 2-6. To overcome these limitations, a (PERC II) model is developed by analyzing the crucial assumptions in PERC I, and refining them when necessary. The following chapter deals with assumption validation and PERC II model development. Particle Size Removal Rate Wafer removal Modified layer removal Particle Size Removal Rate Wafer removal Modified layer removal Fig. 2-4. Schematic of PERC I predic tions for increasing particle size. 0 50 100 150 200 01020304050607080 Mean Particle Size (nm)Removal Rate (nm/min) Fig. 2-5. Polishing of silica by nanoslurry showing optimal particle size [118].

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58 0 100 200 300 400 500 600 256095130 Mean Particle Size (nm)Removal Rate (nm/min) 18 kPa, 0.4 m/s 32 kPa, 0.6 m/s 45 kPa, 0.9 m/s Fig. 2-6. Polishing of silica at various pr essure, velocity and pa rticle sizes showing optimal particle size [116].

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59 CHAPTER 3 PERC II CMP MODEL The previous chapter highlighted the basic concepts involved in PERC I model [96] development, along with various challenges faced by it. In this chapter, some of the critical model assumptions are verified a nd refined as necessary. The changes are incorporated into the basic framework of the PERC I model to develop the PERC II CMP model. Assumption Validation The critical components in the CMP proce ss are the wafer, pad and slurry. As the wafer is fixed in a given CMP process, th e contributions from pad and slurry are investigated to include their most crucial char acteristics into the model. The main role of the pad in CMP is to trap the abrasive partic les for material removal and transmit the load applied onto the trapped partic les. In particle scale modeli ng, the function of the pad in global planarization need not be considered. Pad-wafer Contact Area The pad-wafer contact area strongly influen ces the number of part icles that can be trapped under each pad asperity. The greater the contact area between pad and wafer, the higher the number of particles th at can be trapped resulting in enhanced material removal. The changes in pad properties during polishing are important to model the CMP process. Often dry properties of the pad are investigated [119], rather than the more appropriate wet properties. The pad charac terization investigations are also limited to the bulk [48,

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60 68, 120] of the material rather than the su rface. These bulk properties in dry state are usually employed in conventional CMP modelin g efforts [68]. Since, polishing involves the interfacial behavior of pa d, abrasive, and wafer, pad surface properties should be used rather than the bulk properties. Surface pr operties of the pad rapidly change due to immersion in slurry [121, 122], quickly reaching equilibrium values [46]. There is one fundamental question that n eeds to be answered. What is the real contact area between pad and wafer? A nd is the Greenwood-Williamson model [117], which states that contact area is linearly pr oportional to the applied load applicable in CMP systems? A basic assumption of the PERC I model is that removal rate is linearly dependant on the pad-wafer contact area. Abrasive particles trapped between pad asperities and wafer are considered to be re sponsible for material removal. As applied load on the wafer increases, the pressure at the pad asperity-wafer interface is supposed to remain constant due to elasticity of the pad, while the pad-wafer contact area increases. This behavior is predicted by the Green wood-Williamson model, which assumes that the pad asperity tips contact the wafer under Hertz elastic theory conditions. Although a number of CMP models have employed this concept [63, 109], no systematic attempts are reported that provide validity of this assumption. Similarly, some researchers have assumed the contact area to be proportional to the power of two-thirds [90] of pressure without any experimental basi s. In the past, pad-wafer c ontact area has been generally derived mathematically [27, 123]based on sta tistical surface roughness rather than actual experimental measurements. The pad-wafer c ontact area reported in literature including theoretical calculations varies from 0.0005% to 20% [27, 49, 63, 109, 124, 125]. Considering the importance of reliable valu e of the pad-wafer contact area and its

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61 dependence on applied load in CMP modeli ng, a systematic attempt was made to measure it under CMP conditions. Kim et al. [ 124] have measured the pad-wafer contact area using optical microscopy and have reported a value of 5%. On the other hand, Basim [125] has reported the value to be 0.3% in dry state based on FTIR measurements. To investigate the pad-wafer contact area, a relia ble technique is needed. To establish the reliability of optical microscopy and/or FT IR techniques, contact area measurements were performed on pad using optical microscopy. Optical microscopy The average pad asperity radius is around 30 m for a typical CMP pad and the RMS roughness around 5m. Therefore, an optical micros cope can be used to study the contact spots, the majority of which can be expected to be over a micron in size. To simulate the wafer, a microscope coverslip was used. To minimize the bending of the coverslip under applied load, a fixture was fabr icated as shown in Fig. 3-1 which enabled easy access to the microscope objective lens for translation in in-plane direction. The fixture consists of a base plate with a window hole of 10mm x 5mm to allow optical observation of the contact spots with mini mum bending of the coverslip under applied load. Optical measurements were performed in dry environment using Leika microscope equipped with frame grabber. One inch s quare coupons were punched out from IC1000 pad, which was used for polishing. The pad was ex-situ conditioned using a grid-abrade diamond pad conditioner. Minimal contrast be tween contact and non-contact regions was obtained, when the pad specimens were analyz ed under the given load. This was not even sufficient for qualitative anal ysis. Measurable distinction between contact and non-

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62 contact spots was achieved with coating of the pad surface with a 5-10 nm thick goldpalladium layer using the Denton sputter coater. The thin coated layer is not expected to affect the pad-wafer contact area results, as the attempt here is to measure the contact area under dry conditions. Fig. 3-1. Schematic of the fixture used in measuring pad-wafer (dry) contact area. Measurements were performed in two mode s. Mode I consisted of measuring the contact area of selected aspe rities as a function of applied load and mode II consisted of measuring various contact spots under appl ied load by translating the microscope objective to cover the entire sp ecimen in view. The optical micrographs were analyzed using Spot and Image-Pro softwares to calculate the percent contact area. The micrographs obtained in mode I are s hown in Fig. 3-2. The regions P and N indicate the pad asperities that are of interest in all three figures, though only Fig.32a is labeled for clarity. In P regions, the asperity contact increases with applied load, whereas, in N regions, new asperity contac ts are formed with applied load. The padwafer contact area values obtained from optical measurements are plotted in Fig. 3-3. The

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63 results indicate that the contact area of a given pad asperity increases linearly with applied load and more importantly the magnit ude of contact area obtained from optical technique is in the same range as obtained from the FTIR technique by Basim (Fig. 3-4). The discrepancy between this data and Kim s optical microscopy result [124] could be due to the possibility that some non-contact areas were counted as contact spots due to poor contrast, as no pad surface modification or coating was mentioned in their study. N P N P (a) (b) (c) Fig. 3-2. Pad asperity contact spots seen through optical mi croscope. (a) 0.75 psi. (b) 5 psi. (c) 8.8 psi. 0 0.2 0.4 0.6 0.8 1012345678 Applied pressure (psi)Pad asperity contact area (%) Fig. 3-3. Pad asperity contact area dependen ce on applied load. Each legend represents a selected asperity contact. Various as p erit y contacts at same p ressure

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64 Fig. 3-4. Pad contact area as a function of applied load [125]. The main motivation behind investigating contact area measurements is to get a realistic value of pad-wafer contact area unde r CMP conditions. The optical and FTIR techniques are used in dry conditions, whereas the actual CMP is a wet system. Combining optical data from this study and FT IR data from Basim [ 125], it is established that FTIR with attenuated total reflection (FTIR-ATR) method can be successfully used to estimate the pad-wafer contact area. The same technique was employed in the present investigation to measure the contact area in wet condition simulating the CMP environment. Fourier transform infrared spectroscopy (FTIR) To investigate the pad-wafer contact area variation with applied load in various slurries, FTIR-ATR was used. The contact spot s contribute toward the absorbance signal resulting in quantitative estimation of th e pad-wafer contact area depending on signal

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65 intensity. Maximum signal intensity is obtai ned when the pad surf ace is in full contact with the wafer surface. The contact area is obtained by normalizing the measured signal intensity with the maximum signal intensit y [126]. The setup used for contact area measurements is shown in Fig. 3-5. IR Beam Pad Applied load ATR crystal IR Beam Pad Applied load ATR crystal Fig. 3-5 Schematic of the FTIR-ATR technique used to measure pad-wafer contact area. A silicon ATR crystal is used in contrast to the ZnSe crystal employed by Basim [125] to simulate the silica wafer sy stem. A nitrogen purged Nicolet Magna 760 spectrometer equipped with liqui d nitrogen chilled MCTA dete ctor was used to carry out FTIR analysis for better accura cy. All the spectra were the result of 512 co-added scans at a resolution of 4 cm 1. The background spectrum for all the experiments was the singlebeam spectrum of the dry silicon crystal. The intensities of the CH2 peaks of the polyurethane were recorded in the wavenumber range of 3000 cm 1. The asymmetric and symmetric stretches of CH2 at wavenumbers of 2927 and 2855 cm-1 respectively were analyzed. The contact area is expected not to depend on pad-wafer relative velocity, hence they are held stationary. The slurries were simulated by using solutions of varying pH with no other chemi cals (passivating agents) or particles added. This is valid especially in silica CMP as no passivating chemicals are generally added in

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66 slurry formulation. The absence of particle s reduces the errors due to scattering. The water FTIR/ATR signal is subtracted from pad spectrum (both at same pH) to get the desired signature spectrum (Fig 3-6). A representative piec e of pad sample (IC-1000) soaked in given solution for one hour was plac ed on the (Si) ATR crystal and loaded at 4, 7 and 10 psi in the wet state under solution. The solutions studied are nanopure water adjusted to pH 4, pH 9 and pH10.5 with either 0.5M HNO3 or 0.5M KOH. Silica CMP is generally performed at slur ry pH 10.5, as the silica solubility increases drastically after pH 10. Thus there should be minimum silica wafer modification or modified layer formation at pH 4 and pH 9. Whereas, pH10.5 should lead to considerable surface dissolution of s ilica. These conditions are chosen, as all CMP process variables except pad properties are suppose d to be constant in pH range of 4 to 9, and increased surface modification (dissolu tion) at pH10.5. The typical absorbance spectra obtained for a given specimen at different applied loads is shown in Fig. 3-7. The signal intensities at symmetric and asymmetric stretches are averaged to calculate the contact area. The results obtaine d for different pH and dry cond itions indicate that contact area increases linearly with applied pressure for all conditions (Fig. 3-8). The normalized plot shows the accuracy associated with the measurement technique, which is consistent for all the conditions used. The linear depende nce of pad-wafer cont act area on applied load validates the use of Greenwood-Williamson theory in the CMP model. Pad-wafer contact area in the wet state was measured to be around 2-3 times th e contact area in the dry state (Fig. 3-9). This implies that the re moval rate calculated w ould be 2-3 times less if the dry contact area is used in the model. There is no discernible change in pad-wafer contact area under different pH conditions due to data scatter, possibly due to uncertainity

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67 associated with subtraction of water spectru m. Utilizing the value of pad-wafer contact area obtained and the Greenwood-Williamson assumption, pad asperity modulus is derived which is used in calculation of pad asperity stress distribution. Fig. 3-6. Analysis of the FTIR-ATR spectra. Fig. 3-7. Absorbance spectra of pad (in pH 4) at different applied pressures.

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68 0.5 1 1.5 2 2.5 3 357911 Pressure (psi)Normalized Contact Area Dry pH 4 pH 9 pH 10.5 Fig. 3-8. Contact area vari ation with applied load in dry and wet conditions. Fig. 3-9. Contact area in dry and we t systems in various pH conditions.

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69 Atomic force microscopy (AFM) Contact area increase in the wet state is attributed to changes in the mechanical properties of the pad. Consequently, surf ace mechanical properties of pad were investigated using a colloidal probe atomic fo rce microscope (AFM), where a particle is attached to AFM tip to measure pad prope rties. A Digital Instruments Dimension 3100 AFM equipped with a liquid cell adapter was used. Particle indentation into pad was used to assess pad surface mechanical properties at pH levels of 4, 9 and 10.5. It was realized that a stiff can tilever is needed to probe the surface mechanical properties of the pad. Hence a tapping mode cantilever was modified by cutting the tip area with focused ion beam (FIB) yielding a cantile ver with a stiffness of 75 N/m as compared to 30 N/m before the modification. A 7m silica particle was attached to the tip of cantil ever for measuring mechanical properties of the pad. Nanoindentation measurements were carried out using the modified AFM tip shown in Fig. 3-10. The pad surface was scanned with the colloid probe to find a relatively flat surface before indentation data was measured. Th is is expected to minimize the effect of surface asperities or roughness on the surface mechanical analysis. Typical indentation data are shown in Fig. 3-11. Only the appro aching curve is used to investigate the pad surface mechanical properties. The results from AFM are summarized in Fig. 3-12. The indentation data presented in Fig. 3-12 indicates that the pad surface mechanical response is markedly different in dry and wet systems. In dry pad case, the force on AFM probe increases with indentat ion depth at a constant pace without any change in stiffness. Whereas, for wet cases at all pH levels employed, a dramatic change in slope is observed. The indentation data is not reproducible over en tire pad surface, as

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70 the pad surface is not perfectly smooth due to asperities. But all the indentation data in wet state showed the stiffness change in contrast to the dry data. When the indentation data is aligned such that all curves match th e dry pad behavior, it can be seen that the pad surface is affected by the solution pH which results in different mechanical response compared to the bulk material (Fig. 3-13). The moduli of pad surf ace and bulk shown in Fig. 3-12 were estimated utilizing Hertz theo ry. The modulus of dry pad is atleast 3-5 times the pad modulus in dry state indicating pad swelling. Attached Particle Attached Particle (a) Silica particle 7 m Silica particle 7 m (b) Fig. 3-10. Colloidal probe AFM tip (a) Mo dified tapping mode cantilever, dotted line shows the region of the cantilever remove d by FIB. (b) Silica particle attached to the modified cantilever.

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71 Fig. 3-11. Force-distance curve indicating softer modified layer on the pad surface. The surface modification of polyuretha ne is not entirely unexpected. The polyurethane polishing pads possess both -C OCand -COOCfuncti onal groups in the main chain structure which are susceptible to hydrolytic attack [50], especially in alkaline media [50]. Disruption of hydrogen bonding is re ported for pad samples immersed in DI water for 5minutes [97]. Schematic of hydr ogen bond disruption is shown in Fig. 3-14. This hydrolytic attack can explain the pa d surface mechanical property behavior. The presence of surface modification on pa d surface or pad swelling could impact the abrasive trapping ability of the pad aspe rities along with the load transmitted to the particles during polishing depending on part icle size. The change in contact area observed in wet state indicates that depending on slurry chem istry, the pad-wafer contact area could be effected, directly influencing the material rate. Hence, when different slurry chemistries are used in a CMP process, the CMP model needs to incorporate the slurry effect not only as a modified layer on wafe r surface, but also as change in pad-wafer

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72 contact area and abrasive tr appability, which has not been accounted for in past CMP modeling efforts. Fig. 3-12. Force-indentation curves from AFM for different conditions. All curves are offset such that they match in the top portions to clearly show the evidence of a softer layer on pad in wet systems. (a) (b) Fig. 3-13. Schematic of pad surface as dedu ced from AFM data. (a) Dry state. (b) Wet state.

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73 (a) (b) Fig. 3-14. Schematic of polishing pads (a ) Structure showing hydrogen bonding between neighboring polymer molecules, (b) Water can form hydrogen bonds with polymer molecule by disrupting hydr ogen bonds between the polyurethane molecules [127]. Pad Asperity Height Distribution A quantitative understanding of the padwafer and pad-particle interface is fundamental to a comprehensive CMP model. The pad asperities are assumed to remain constant through the planarization of each wafer. It is known that the asperities involved in polishing wear out changing in height over time, wh ile the shorter asperities, those that do not come into contact with the wafer, re tain their original height. Thus the pad roughness or the asperity height distribution changes with polishing, if pad conditioning is not performed properly. The surface r oughness of pad is known to be directly proportional to the polishing rate [128-130]. Di fferent types of pads have different asperity height distributions, though they might have similar average surface roughness. In PERC I, pad asperites were assumed to be s pherical and of same si ze with pad asperity height averaged out to obtain the pad asperi ty stress, and pad-wafer contact area. This implies that the pad asperities are not only assu med to be equal in size and shape, but also of equal height. This imposes the pad to have contact spots equal in size, experiencing

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74 same contact pressure. Thus, all the particle s trapped in these cont act spots have same indentation into the wafer surface leading to equivalent material removal under each asperity. Thus the previous PERC model was equivalent to having a single asperity model with no effect of aspe rity height distribution. De pending on the CMP system and desired planarization criteria, different pads are used in practice. Therefore, it was considered necessary to include the asperity height distribution in the revised model (PERC II). Due to constant asperity height only an average indentation depth was derived in the previous model (PERC I) to indicate surface roughness of the polished wafer. When asperity height di stribution is used, asperities at different heights lead to different indentation depth, resulting in information about distribution of scratches (indentation depths).This data can be used to estimate the surface roughness as root mean square roughness (RMS). To incorporate the asperity distribution, Gaussian distribution of asperities is assumed, as the reported literature cites Ga ussian distribution [ 116]. The pressure at contacting asperities were calcu lated individually to estima te the indentation depth of trapped particles. Abrasive Particle Size Distribution The role of slurry in CMP is two-fold. Th e chemicals in the slurry are needed to react with wafer surface resul ting in formation of a surface layer which is amenable to enhanced material removal. The abrasives in the slurry on the other hand, remove this modified surface layer causing material removal. The effect of chemicals is attributed to surface layer of different mechanical propertie s in PERC I model. Whereas, the effect of abrasives is considered by assuming average si ze of the particles. The monosized slurry assumed in the PERC I model is an ideal cas e, since real CMP slurries are seldom

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75 monosized (Fig. 3-15). Oxide po lishing slurries are commonly purchased in concentrated form and diluted on-site to minimize shi pping and labor costs. Some mult-component tungsten and copper polishing slurries must be combined shortly before use because of their short postmix lifetime. The slurry stabil ity can change after it is combined with the oxidizer or due to dilution leading to polydispersity. Fig. 3-15. Particle size distri bution of silica slurry [118] Sometimes mixed abrasive slurries are used [32], which invariably exhibit polydisperse particle size distribution. To acco unt for the particle size distribution effect, PERC I model was modified to incorporat e slurry abrasives with Gaussian size distribution PERC II Model Development Conceptually, the difference between the PERC I and PERC II models can be illustrated as shown in Figs. 3-16 and 3-17. The PERC I model assumes spherical pad asperities of equal height all over the pad (Fig. 3-16a). As the slurry is assumed to be

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76 monosized, each asperity traps equal number of particles in CMP resulting in equal removal rate by each asperity and each particle(Fig. 3-16b). (a) (b) Fig. 3-16. Schematic of pad, slurry and wa fer in PERC I model. (a)Before contact. (b) During CMP. Whereas in the PERC II model (Fig. 3-17a ), the spherical pad asperities are assumed to have a height distribution as obser ved experimentally [116]. As the slurry is assumed to be polydisperse, each asperity trap s different number of particles of different particle sizes in CMP according to pad asper ity height and particle distribution (Fig. 317b). Thus the PERC II model includes rea listic contributions of pad and wafer characteristics compared to the PERC I model. The model formulation is detailed in the following section.

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77 (a) (b) Fig. 3-17. Schematic of pad, slurry and wafer in PERC II model. (a) Before contact. (b)During CMP Real contact area (Areal) between pad and wafer due to applied load (L) is given by: dz z h z NA Ah o real (3.1) dz z h z E NA Lh o 2 3 2 1 *3 4 (3.2) 2 22 z exp 2 1 z (3.3) where N is the number density of the pad asperities (i.e., number of asperities per unit area), Ao is the total area of th e flat wafer surface, and h is the distance between wafer

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78 surface and the pad asperity averag e plane under the given conditions. E* is the composite modulus between the two surfaces in contact, defined as w w p pE E E2 2 *1 1 1 (3.4) where, E and are the Youngs modulus and the Po issons ratio, and the subscripts p and w represent the pad and the wafer, respectiv ely. Equations (3.1) and (3.2) are derived from Hertz theory as in Greenwood-Williams on model [77, 117], yielding contact area and load at a given asperity of height z to be: Areal(z)= (z-h) (3.5) L(z)=(4/3)E*1/2(z-h)3/2 (3.6) where h is calculated from Eq. 3.2, since applied load and pad properties are known. The underlying assumption for Eq. 3.2 is that the applied normal force on the wafer is supported entirely by the pad asperities. As was mentioned previously, experimental measurements indicate that the hydrodynamic pressure is negligible under typical CMP operational conditions [69]. From equations 3.5 and 3.6, contact pressu re and contact area at a given asperity height can be calculated assuming that the pa d asperity distributi on is known. The pad asperity distribution can be determined from routin e surface roughness measurement techniques like optical and force profilomet ers or atomic force microscopy (AFM). Contact pressure according to Hertz theory, on an asperity of height z is given by: 2 1 2 1 *3 ) ( 4 ) (h z E z P (3.7)

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79 Plastic Deformation of Wafer Surface When an abrasive particle is indented into the wafer surface, elastic and plastic deformation of wafer and abrasive particle occur. However, in CMP, slurries are designed such that the chemistry changes th e modulus of the wafer surface for enhanced material removal. In the current model, partic les are assumed to be rigid such that they do not deform during polishing. When the indent ation of abrasive particle is beyond the modified surface layer, the substrate indenta tion could yield either elastic or plastic response depending on the substrate, for exampl e in case of silica, the deformation will still remain plastic whereas for copper, it would be elastic deformation followed by plastic deformation. Therefore, in material removal calculation, indentation into ductile wafers is not considered to cause material re moval, as it leads to change in shape only, whereas in the case of brittle material like si lica, cracks are developed leading to material removal. Slurry Characteristics Particle Size Distribution The abrasive particles in the slurry are assumed to be spherical in shape with a given size distribution (r).As mentioned earlier, particle size distribution (r) was assumed to be Gaussian, given by:2 22 exp 2 1 ) (r r rr r (3.8) where r is the mean particle radius and r the standard deviation. Material Removal by Single Particle The overall material removal rate (RR) is assumed to be the multiple of the removal rate by a single part icle and the number of par ticles trapped between pad asperities and the wafer:

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80 RR = (1/A0) n(r,z) RRv(r,z)drdz (3.9) where n(r,z) is the number of slurry particles an chored between pad asperity and the wafer and RRv(r,z) is the volumetric removal rate by a single particle of radius r trapped by asperity of height z. The overall removal rate, RR is typically described in terms of the thickness of the wafer surface layer removed per unit time; hence the division by the nominal wafer area Ao. Schematic illustration of single particle abra sion is given in Fig. 3-18. The material removal is viewed as a sliding-indentation process in which the volumetric removal rate by a single abrasive particle is given by RRv(r,z) = Ai(r,z)V (3.10) Where Ai(r,z) is the cross-sectional area of the particle indented into the wafer under pressure (hashed area in Fig. 3-18), and V is the relative velocity between the pad asperity and the wafer. Fig. 3-18 Schematic of single particle ab rasion showing the removal of chemically modified surface layer, (a). t ; (b). > t with soft wafer materials.[72]

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81 Assuming that the hard particle maintains its spherical shape, r z r a r z r r z r a z r Ai) ( arcsin ) ( ) ( ) (2 (3.11) where r,z is the indentation depth and a(r,z) is the radius of the circular indentation on the wafer surface caused by the particle of radius r trapped under asperity of height z. Because r,z is very small compared to r, a (r,z)/r is also very small and Equation 3.11 can be linearized about a(r,z) /r as already discussed: r z r O z r z r a z r Ai) ( 1 ) ( ) ( 3 4 ) ( (3.12) Furthermore, since a2(r,z)=(2r (r,z) 2(r,z)) and r,z) is much smaller than r, Equation 3.12 can be rewritten as r z r a Ai3 ) ( 2 z) (r,3 (3.13) Once the indentation depth, r,z) (or a (r,z)) is known, the vol umetric removal rate by a single particle can be calculated fr om Eq. 3.13. It should be noted that and a are dependant on particle radius a nd height of the trapping asper ity. Removal rate per particle is given by: r z r a z r RRv3 ) ( 2 ) (3 V (3.14) Depending on the relative magnitude of the indentation depth ( (r,z)) as compared to the surface layer thickness (t), the material removal may be classified into two different regimes as depi cted in Fig. 3-18: (a) (r,z) t and (b) (r,z) > t and can be calculated using force balance as follows.

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82 Considering that the pad is sufficiently hard as compared to the modified layer, the value of b in Fig. 3-18 can be clos e to the particle radius R, 2 / 1) ( ) ( eB z P r z r a when (r,z) t (3.15) and 2 / 1 2) ( 2 ) ( ) ( w e wB rt B B z P r z r a when (r,z) > t (3.16) where, Be is the effective Brinell hardness of the chemically modified surface layer. In the following section, the number of part icles in contact with the wafer surface is estimated to determine the overall removal rate. Number of Active Abrasive Particles When the wafer is pressed against the pad and is in sliding motion relative to the pad, the slurry particles can be entrapped only in the region where the local distance between the wafer and the pad asperity is smaller than the particle diameter, 2 R For a slurry consisting of particles with Gaussi an distribution, mean particle size (Rm) is used to calculate the number of particles that can be trapped on the pad aspe rity of height z: N(z) = 2RmAreal(z) n (3.17) where Rm is the mean abrasive particle radius and Areal(z) is the real contact area between the wafer surface and the pad asperity as given by eq. 3.5. n is the number density of the particles in the slurry (i.e., number of pa rticles per unit slurry volume), that can be calculated from the solid loading Ca (wt%) of the slurry particles as dr r r Ca s a n) ( 4 33 (3.18)

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83 where a and s are the densities of the particle a nd the slurry soluti on, respectively and (r) the slurry particle size distribution. Substitution of Eq. 3.18 into 3.17 gives dr r r z A C R z Na real s a m) ( ) ( 2 3 ) (3 (3.19) From eq. (3.19), the number of trapped particles of radius R is given by, n(R,z)=N(z)* (R)= dr r r r z A C Ra real s a m) ( ) ( ) ( 2 33 (3.20) Estimation of the Overall Removal Rate The overall material removal rate can be determined by following these steps: h is calculated using eq. 3.2. Contact pressure P(z) at a given asperity is calcul ated along with the real contact area Areal(z) of that asperity with wafer. Total number of particles N(z), that are trapped are determined, from which number of particles of given radii, n(r,z) are derived. From P(z), removal rate by single abrasive of radius r is calculated which is multiplied with n(r,z) to give removal ra te by that particle size. This process is repeated to account for all the particles of diffe rent radii trapped on that asperity yielding material removal rate by particles trapped on a given asperity. It should be noted that there are (z)NA0 asperities at a given height which will each contribute the same material removal.

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84 The above step is repeated for all the pad asperities of va rious heights that are in contact with wafer (determined by h) to give overall removal rate by the following equation: RR = (1/A0) n(r,z) RRv(r,z)drdz RR= hr real r a s a mdz dr r z r a r z z A dr r r N C VR ) ( ) ( ) ( ) ( ) (3 3 (3.21) where, a(r,z) varies as given in eqs.3. 15 and 3.16 depending on particle radius and asperity height. The indentation depth, (r,z) is used to calculate the surface roughness RMS of the polished wafer according to the following equation: n RMSn i i1 2 (3.22) where i is the indentation depth. The overall removal rate predicted by Eq. 3.21 and surface roughness given by Eq. 3.22 depend on various parameters that represent the geometry of the pad and the particle (i.e., and R ), material properties ( E*, Bw and Be), thickness ( t ) of the modified surface layer on wafer, and the relative velocity of the pad (thus the particle) to the wafer ( V ). The PERC II model will be validated with re spect to critical CMP parameters in the next chapter.

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85 CHAPTER 4 MODEL ASSESSMENT The parameters governing the material removal calculation consist of CMP operating parameters, slurry parameters, pad and wafer parameters, as listed in Table 4-1. However, some of these parameters, especia lly the sub-nanometer thick modified layer hardness and thickness can not be determin ed experimentally due to equipment limitations. The remaining parameters are rela tively easy to investigate experimentally for many CMP systems. Hence, modified la yer hardness and thickne ss are used as the fitting parameters in the model. Table 4-1. Parameters incl uded in the revised PERC model. Model Validation In this section, PERC II model predictions are compared with experimentally measured values to assess the reliability of the proposed CMP model. The experimental literature data is also compared with PERC I predictions to assess the advantage of PERC II over PERC I. Though PERC II is a refined model compared to PERC I, the model is still a simplified version of real CMP, mainly in estimating the number of trapped Operating Parameters Pressure Velocity Slurry parameters Particle size distribution Solids loading Abrasive density Solvent density Pad properties Pad modulus Asperity height distribution Asperity radius Asperity density Wafer properties Modified layer thickness Modified layer hardness Wafer hardness

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86 particles and indentation dept h considering an abrupt tran sition between modified layer and wafer substrate. The removal rate values for both models are normalized by a constant to have reasonable modified layer thickness values. Surface roughness data is as produced by the models without any normalizi ng factor. The size distribution of slurries given in the respective literature are fit to the closest Gaussian distribution, which is used in the model. Silica CMP: Micron Sized Slurries The polishing results of silica by silica abra sives as reported by Choi et al. [131] are considered here. Micron sized CMP slurri es were formulated by dispersing sol-gel silica particles of different sizes from Ge ltech Corporation in deionized water and adjusting pH values to 10.5. The average diamet er of the slurry particles were 0.2, 0.5, 1.0 and 1.5 m. The size distribution of the slurries is plotted in Fig. 4-1. A 2 m thick silica layer was deposited on p-type silic on wafer by plasma-enhanced chemical vapor deposition. 1.5 x 1.5 in silica samples were used to mimic the wafers. A Struers RotoPol31 tabletop polisher was used with IC 1000/Suba IV stacked pad. The following conditions were applied: down pressure of 3. 5 psi, slurry flow rate of 100 ml/min, and rotation speed of 150 rpm (110 cm/s). The pol ishing rates were determined by measuring oxide film thickness using variable angle sp ectrometry ellipsometry and surface quality was assessed by atomic force microscopy (AFM). The polishing rate was investigated as a function of particle size and solids loading. The removal rate decreased with increasing pa rticle size (Fig. 4-2). The parameters used are: wafer Hardness=8 GPa, modified la yer Hardness = 450 MPa, modified layer thickness = 7.2 and Normalization factor = 100. The PERC II model correlates well

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87 with the experimental values than the PERC I model. The reported literature belongs to the substrate indentation regime. The model pr ojects that enhanced removal rate can be obtained by using smaller sized slurries The surface roughness on the other hand, increases with particle size on an average for all the slurries consid ered (Fig. 4-2b). This is not surprising as the larger size particles have deeper indentati on depths increasing surface roughness. Both the models predict the average trend in surface roughness with increasing particle size. Fig. 4-1. Slurries used in oxide polishing [131]. Silica CMP: Nanosilica slurries The slurry sizes in the earlie r study spanned from 0.2 to 1.5 m, which is well above the normal slurry size range (<300 nm). Considering the nanosize slurries of 50150nm mean particle sizes, CMP behavior of silica polis hing by silica abrasives is investigated further [116]. Slurries with mean particle diameters of 50, 80, 110 and 140nm were used to polish 100mm diameter, p-type polished silicon wafers that contained a thickness of 1.3 m thermally grown oxide. The silica particles were

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88 precipitated from a collo idal solution. The polishing was done at three different levels of pressure and relative pad-wafer velocities : 18kPa, 0.4m/s; 32kPa 0.6m/s; and 45kPa, 0.9m/s. The parameters used in the model are: wafer Hardness=8 GPa, modified layer Hardness = 250 MPa, and modified layer thic kness = 9.3 The removal rates for the given set of pressure and velocity with differe nt particle sizes is s hown in Fig. 4-3. The material removal rates with slurry mean sizes of 10 and 20nm were ignored, as the authors [116] noticed considerable particle staining on the polishe d surfaces indicating agglomeration. The PERC II model corresponds with the experimental results better than the previous PERC I model. Each set of mode led removal rates for given pressure and velocity were normalized individually w ith normalizing factor ranging from 185-200. The discrepancy in the removal rate at particle size 50nm between experimentally observed values and modeled values can be attributed to agglomeration, which is suggested by the authors for that size [116]. (a) Fig. 4-2. Silica polishing by sl urries in the micron range. (a) Removal rate. (b) Surface quality

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89 (b) Fig. 4-2. Continued. Fig. 4-3. Silica polishing by colloidal nanosilica. The surface roughness of wafers polished wa s reported to be 6 on an average. The PERC II model predicts the surface roughness to be from 5.8 6.2 which is in good agreement with the experimental result s. The PERC I model predicts an average indentation depth of 5.5 to 6 wh ich is also in good correlation.

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90 As the model correlated well with th e micron and submicron sized slurries, nanosized slurries in the low-end regime ( 10-100nm) are considered further. Colloidal particles of size 12, 25,45, 75nm were used to polish thermal oxide (silica) wafers with potassium iodate (KIO3) in the slurry [118]. The remova l rate was reported to increase with particle size, r each an optimum and then decrease wi th particle size (Fig. 4-4). The parameters used are: wafer Hardness=8 GPa, modified layer Hardness = 200 MPa, modified layer thickness = 5.1 and No rmalizing factor=330. The PERC I model predicts the removal rate to remain consta nt with particle size, whereas the PERC II model predicts the optimal particle size at which enhanced material removal can take place. The surface roughness predicted is higher than the reported values. (a) Fig. 4-4. Silica polishing by nanosized slur ries. (a) Removal rate. (b) Surface quality.

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91 (b) Fig. 4-4. Continued. Copper CMP As the model is found to correlate well w ith the brittle wafer polishing, metal CMP process is now considered to review the comprehensive nature of the model. Copper wafers were polished with particles of size 100, 200 and 300 nm [132]. The chemicals used were 5 wt% H2O2 and 1 wt% glycine with pH adjusted to pH 4. The parameters used are: wafer Hardne ss=1.75 GPa, modified layer Hardness = 300 MPa, modified layer thickness = 15 a nd Normalizing factor=7. The PERC I model predicts removal rate independe nt of particle size, while th e PERC II correlates well with the observed values (Fig. 4-5). The opposing trend of surface roughness between experimental and observed values is surpri sing. The discrepancy in surface quality predictions could indicate pr esence of few bigger sized part icles or agglomeration which can result in high surf ace roughness than predicted [125] The presence of larger size particles or slurry agglomeration, is however not mentioned by the authors.

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92 Tungsten CMP Bielman et al., [133] have conducted CMP of tungsten with alumina slurries of size distributions shown in Fig. 4-6. The slurry contained K3Fe(CN)6 as the chemical additive with pH adjusted to pH 3. The rem oval rate at 15wt% solids loading is shown in Fig. 4-7. The parameters used are: wafer Hardness=6.5 GPa, modified layer Hardness = 1.5 GPa, modified layer thickness = 9 a nd normalization factor = 23. The PERC II model correlates well with the experimental removal rate values compared to the PERC I model (Fig. 4-7a). The surface roughness valu es predicted by PERC I and II are both higher compared to the observed values, but the surface roughness trend with particle size matches very well. 0 100 200 300 400 500 50100150200250300350400 Mean Particle size (nm)Removal Rate (nm/min) Experimental PERC II Model PERC I Model (a) Fig. 4-5 Copper CMP as a function of particle size. (a) Removal rate, (b) Surface quality.

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93 (b) Fig. 4-5 Continued. Fig. 4-6. Alumina slurry size distributions [133].

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94 0 200 400 600 800 1000 05001000150020002500 Mean Particle Size (nm)Removal Rate (nm/mi Experimental PERC II Model PERC I Model (a) 0 5 10 15 20 25 05001000150020002500 Mean Particle Size (nm)Surface Quality (Angstroms) Experimental PERC II Model PERC I Model (b) Fig. 4-7. Effect of particle size on tungst en CMP. (a) Removal rate, (b) Surface quality. Model Predictions The better match of PERC II model predictions than the PERC I model indicates that the refinements made to the PERC I model assumptions are indeed significant and add to the predictive capability of the model. In the following sections, predictive capability of PERC II model is explored, comparing with the PERC I model. The

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95 enhanced performance of the proposed m odel (PERC II) is compared with PERC I predictions considering the case of a brittle wafer as in Silica CMP. The parameters used for comparison are listed in Table 4-2. Table 4-2. Parameter values used for comparing PERC I and II models. Pad modulus 60 MPa Pad asperity density 2 x 108/m2 Mean pad asperity radius 50 m Pad asperity height distribution 6.7 m Pressure 6.5 psi Velocity 1 m/s Particle size 200 nm Particle size distribution r 16 nm Abrasive density 2.2 gm/cc Solids loading 10 wt% Wafer hardness 8 GPa Layer hardness 600 MPa Layer thickness 10 Removal Rate as a Function of Partic le Size for a Given Solids Loading: The comparison of the two models with varyin g particle size is shown in Fig. 4-8. As discussed earlier (in chapter 3), materi al removal rate as per PERC I model is independent of particle size. The PERC II model, however, predicts an increase in removal rate with particle size during modified layer re moval, and as the particle indentation proceeds into wafer substrate, the removal rate decr eases smoothly with particle size, as also observed experimentally. Decrease in re moval rate with particle size in wafer indentation is caused by the substr ate being harder compared to the modified layer. The PERC II model differs with the PERC I model mainly in estimation of the modified layer removal and transition regi mes and not considerably in the substrate removal regime. The smooth transition from mo dified layer removal regime to substrate removal regime is attributed by inclusion of pad asperity distribution into the model. Whereas, the removal rate increase with par ticle size in the modified layer removal

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96 regime is due to the inclusion of slurry pa rticle size distribution and strongly depends on it. Fig. 4-8. Comparison between PERC I and PERC II models with constant solids loading of different particle sizes. (a) Removal rate. (b) Surface roughness. The other feature of the PERC II model is the estimation of surface quality as root mean square surface roughness and maximum scratch depth. The PERC I model on the other hand, gave an estimation of surface roughness through average indentation depth. 0 100 200 300 400 500 0100200300400500 Mean Particle Size (nm)Removal Rate (nm/min ) PERC II Model PERC I Model (a) 0 2 4 6 8 10 12 0100200300400500 Mean Particle Size (nm)Surface Roughness RMS (Angstroms) PERC II Model PERC I Model ( b )

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97 The PERC II model, however gives the scra tch (indentation) depth under each contacting pad-asperity due to each trapped particle size. This information is used in calculation of the surface roughness (RMS) as de scribed in the previous chapter. The PERC I model yielded an average scratch depth whose de pendence on particle size suddenly changed when the particle was large enough to indent pa st the modified layer into the substrate. PERC II also reveals that particle indentation into the substrate takes place at a smaller mean particle size as compared to that predicted by PERC I model. This is expected, as some of the larger partic les in the slurry indent into the substrate, while most others indent into the modified layer alone keeping the average particle size lower. Indentation in to the wafer substrate below the modified layer is not a desirable feature, as it negates the purpose of CMP. But, as long as the substrate removal is minimal with low indentation depths, it can be tolerated. Effect of Modified Layer Thickness The chemical reaction between slurry chemicals and wafer surface leads to the modified layer, whose thickness and mechani cal properties are strongly dependent on the type of chemicals present in the slurry. The thickness of the modified layer in an optimized CMP process should be such that the particle indents completely into the modified layer and not into th e substrate below. However, in a slurry with particles of various sizes, not all particle sizes can indent/remove the entire modified layer. From Figs. 4-9 a and b, the transition from modifi ed layer to substrate indentation regime occurs around 8 which corresponds to 200nm pa rticle size. Therefore, as the modified layer thickness decreases below 8 keeping a ll the other parameters constant, the slurry particles indent into the substrate and the removal rate decreases. Whereas, when the modified layer thickness increases beyond 8 the indentation becomes more and more

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98 limited to modified layer alone. Thus, after a critical thickness, the removal rate remains constant, even if the modified layer thickness increases. This indicates that the chemical aggressiveness of the slurry should not focu s on forming a thicker layer, but on forming modified layer faster of desired thickness. 0 100 200 300 400 500 05101520 Modified Layer Thickness (Angstroms)Removal Rate (nm/min ) PERC II Model PERC I Model (a) 0 1 2 3 4 5 6 7 05101520 Modified Layer Thickness (Angstroms)Surface Roughness RMS (Angstroms) PERC II Model PERC I Model (b) Fig. 4-9. Model comparison with varying modi fied layer thickness. (a) Removal rate, (b) Surface quality.

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99 Effect of Modified Layer Hardness As the modified layer hardness increases, less and less indentation of the particles take place, resulting in lower material removal rates (Fig.s 4-10 a and b). Thus, if there is no surface modification due to slurry chemicals in silica, minimal removal rate will be observed. As 200nm particle was in the transi tion region, with incr easing modified layer hardness, most of the particles indent onl y the modified layer. The transition from modified layer to substrate indentation is depicted more clea rly by the PERC II model than by the abrupt transition predicted by the PERC I model. Combining the model predictions and valid ation of metallic and dielectric CMP systems, the PERC II model can be used as a CMP parameter selection guide for emerging CMP systems and to optimize the current CMP processes. The fitting parameters, modified layer hardness and thicknes s are in the range of expected values for the respective CMP systems. The thickness of the modified layer determines the optimal particle size predicted, whereas the modifi ed layer hardness in comparison to wafer hardness determines the sharp decrease in re moval rate after transition from modified layer to substrate removal. The increase in re moval rate with particle size in the modified layer removal regime is influenced solely by the abrasive particle size distribution. The normalizing factor is found to be sp ecific to the CMP system and strongly dependent on the toolset used. The normalizing values of 185-200 for three sets of pressure and velocities used in silica CMP by nanosilica slurries [116], indicate that the normalizing value is influenced strongly by th e toolset used. This is expected, as the ability of pad to trap the pa rticles is strongly dependent on the toolset configuration. The normalizing factor is also e xpected to depend on type of wafer being polished and the slurry used. For example, if pa rticles are attracted to wafer due to electrostatic attraction,

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100 the number of trapped particles will be mu ch less compared to the system, where particles are repelled by the wafer surface charge. The next chapter summarizes the findings in this study and future work is s uggested based on the insights obtained through the study. 0 250 500 750 1000 00.250.50.751 Modified Layer Hardness (GPa)Removal Rate (nm/min ) PERC II Model PERC I Model (a) 0 2 4 6 8 10 12 00.250.50.751 Modified Layer Hardness (GPa)Surface Roughness RMS (Angstroms) PERC II Model PERC I Model (b) Fig. 4-10. CMP performance comparison with varying modified layer hardness. (a) Removal rate, (b) Surface quality.

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101 CHAPTER 5 SUMMARY AND SUGGESTIONS FOR FUTURE WORK The device shrinkage in microelectro nics industry nece ssitates chemical mechanical polishing and continues to de mand stringent performance of CMP. The material removal mechanism needs to be unders tood with the relative contributions from particle-wafer, pad-wafer, a nd pad-particle interfaces and the reaction of slurry with wafer and pad materials. In this study, a mode l is developed to predict process parameters for designing an optimal CMP process. Most of the CMP modeling efforts concentr ated mainly on explaining the Prestons equation. Therefore, most of them were focu sed on product of pressure and velocity (PV) as the operating parameter and not on other important parameters like slurry and pad variables. The PERC II model is devel oped based on PERC I model [72]. The assumptions in PERC I model were refined to include particle size distribution of slurry and pad asperity height dist ribution. Though recently a model developed by Luo [27] incorporated particle size di stribution, part of the distri bution was neglected and hence doesnt incorporate the proce ss variables appropriately. The pad-wafer contact area dependence on applied load is generally assumed in many CMP models with no basis of a systematic study. The material removal rate is directly proportional to the pad-wafer cont act area. Therefore, the magnitude of pad contact area is significant in modeling the process. The earlier studi es focused on contact area in dry state and the results reported were not consistent. The contact area was investigated in dry and wet states in the current study. Contact area in dry state was

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102 studied using optical microscopy. The change in contact area due to presence of aqueous environment and different pH conditions is i nvestigated using Fourie r transform infrared spectroscopy. The contact area was found to be 2-3 times the contact area in dry state. The pad surface mechanical properties were al so investigated at different pH conditions using Atomic force microscopy. The slurry was found to react with pad surface layer (~50nm thick), modifying its mechanical prope rties. Both the padwafer contact area and contact stresses are strongly dependent on pad asperity height distri bution. To incorporate the effects of contact area and contact stresse s, Gaussian asperity height distribution of asperities is incorporated into the PERC II model. The slurry used in commercial CMP is se ldom monosized. The size distribution of the particles can strongly aff ect the process. Hence, the slurry abrasive sizes were assumed to be Gaussian in distribution were incorporated into the PERC II model. The developed model correlates well with expe rimental data for oxide and metal CMP systems. The model can be used as a sele ction tool for choosin g the proper parameter values optimizing the CMP process. For optimizat ion of the process, a sensitivity analysis can be performed to narrow down the parame ters that are of utmost importance. An example is shown here of silica CMP system with the parameter ranges shown in table 51. SOBOL analysis was performed with 4608 data sets (using SimLab software) assuming particle size distributi on to be Gaussian with stan dard deviation equal to the one-fourth the mean particle size. The result s revealing the first order and interaction effects of parameters on removal rate are s hown in Fig. 5-1. The sensitivity analysis indicates that the particle size has the signifi cant effect on removal ra te compared to all the other parameters. The particle size dete rmines if the material removal will be in

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103 modified layer regime or will extend to s ubstrate indentation regime. Depending on the indentation regime, the hardness of the ma terial being removed strongly effects the material removal. Table 5-1. Process parameter ranges used in sensitivity analysis. Factor Limits Pressure 2-8 psi Mean Particle Size 10-500 nm Asperity Radius 20-100 m Asperity Height S.D 1-20 m Asperity Density 0.0220 x 109/m2 Pad Modulus 20-200 MPa Modified Layer Hardness 200-500 MPa Modified Layer Thickness 5-10 Fig. 5-1. Sensitivity analysis of silica CMP system. The reported findings in this study pr ovide insight into the fundamental understanding of the polishing mechanism and can give guidelines for optimizing any given CMP system.

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104 Suggestions for Future Work The insight provided by the current study in to the CMP process in general can be used to conduct further studies to bett er understand the process from various perspectives. The study focuses on slurry with ri gid abrasive particles. With the advent of low-k dielectric polishing, so fter abrasives are being us ed. Inclusion of non-rigid abrasives into the model will facilitate better exploitation of the process potential and faster adaptation of emerging CMP systems to the industry requirements. Recently, many commercial slurries are de signed with surfactants or particle surface modification for slurry stability. Add ition of these extra factors can significantly effect the CMP process. For example, it is shown by Basim [125] that polishing performance is degraded with addition of certain surfactant cocentration to the slurry. These steric effects or electro static effects due to ionic sp ecies in the slurry should be included in the model for comprehensiv e understanding of the effects involved. Similarly, effects of pH and ionic speci es on CMP processes [134-137] can also be included. The current model assumes that there are no stresses involved in the wafer, which could affect the CMP process. But, it has b een shown by McGarth et al. [138] that if the stresses induced in the wafer due to mate rial deposition and ot her processes are not relieved, the CMP process could be affected Inclusion of such a stressed wafer could help in understanding the e ffect of deposition process on CMP process performance. One of the experimental challenges faced in this study was the measurement of the modified layer properties. Nanoindentation and AFM were used to investigate the modified layer on the silica and copper surfaces. But, the instruments were not sensitive

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105 enough to detect the modified layer propertie s quantitatively. It is suggested that a diamond tipped AFM cantilever with a narrow ne edle type tip be used to sense the modified layer properties, wit hout any interference from the substrate. This data can be used to incorporate gradual transition between modified layer and substrate compared to the abrupt transition employed now. The current model assumes formation of a modified layer on the wafer surface which is critical in material removal pro cess. Based on the AFM data of pad surface, even a modified layer on the pad can be a ssumed to assess the trapping capability of abrasives and load transmittal of pad onto the wafer through the abrasives. Developing a model including such a layer on pad will re sult in better predictive capability when different slurry chemicals are used that effect pad properties. The model developed shows predictive capability in the particle scale. Therefore, it can be extended to die and wafer scales to predict the topogr aphy evolution during polishing. Such a model extension would also involve including the se lectivity aspect of the CMP slurry, dishing and erosion.

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118 BIOGRAPHICAL SKETCH Suresh Babu Yeruva was born on Feb 18th, 1978, in Machilipatnam, Andhra Pradesh, India. He finished his undergradua te education at the Indian Institute of Technology, Madras (IITM), India. He pursued his Master of Science at Washington State University in the Department of Mate rials Science and Engineering. In 2001, he started his Ph.D. program with Professor Br ij Moudgil at the University of Florida.