IMPACT • CMP • 1 04/09/2008

Faculty Presentation: CMPBy David Dornfeld, Mechanical Engineering, UC-Berkeley

2008 IMPACT Workshop

IMPACT • CMP • 2 04/09/2008

Current MilestonesCMP: Modeling and Fundamental Studies

CMP 1. Continue development of comprehensive model of CMPModel building on the abrasive scale, pattern scale capability to integrate additional chemical process elements and coupling elements (including pad/wafer contact elements) to link key influences of chemical and mechanical activity, slurry agglomeration and heating. CMP 2. FEM Analysis of pad-induced effects during planarization- basicFinite element model to predict stress induced by pad on wafer surface including influences of material (geometry and material properties), pad (surface topography and material properties) and process conditions (load, motion) with analysis of pad mechanical behavior, pad/surface interaction and induced stresses in thin films.CMP 3. Assess mechanical properties and behavior of passive films on copper and test patternsNanomechanical techniques used to measure pertinent properties of the films on copper alone, and test patterns to understand the coupling between the electrochemistry, colloid chemistry and mechanical effects. CMP 4. Develop understanding of agglomeration/dispersion effects on CMPBasic understanding of agglomeration/dispersion effects on CMP including rate of agglomeration as a function of chemistry and the wafer surface hardness as a function of chemistryCMP 5. Mechanics of Nanoscale Lapping and PolishingMechanics models for material removal at the nanoscale with validation using microprobe-based experiments and stochastic modeling of nanoscale polishing/lapping.

04/09/2008IMPACT • CMP • 3

CMP - Faculty Team

Mechanical Phenomena

Chemical Phenomena

Interfacial and Colloid

PhenomenaJan B. TalbotChemical EngineeringUCSD

David A. DornfeldMechanical EngineeringUCB

Fiona M. DoyleMaterials Science and EngineeringUCB

Kyriakos KomvopoulosMechanical Engineering

UCB

04/09/2008IMPACT • CMP • 4

CMP - Student Team

Mechanical Phenomena

Chemical Phenomena

Interfacial and Colloid

Phenomena

Robin IhnfeldtChem Eng UCSD

Shantanu TripathiME/MSE UCB

Huaming Xu ME-UCB

Moneer HeluME-UCB (NSF)

Adrien MonvoisonME-UCB

Seungchoun ChoiME UCB

IMPACT • CMP • 5 04/09/2008

Details on the posters!

Research Results

Seungchoun Choi & Shantanu Tripathi: Use of Confocal Microscopy to Characterize Pad Asperity-Wafer Contacts and Abrasive-Wafer Contacts During CMP

Shantanu Tripathi: CMP Modeling as a part of Design for Manufacturing

Adrien Monvoisin: Stress Analysis in Low-K dielectric Materials during the CMP Process

Robin Ihnfeldt: Effects of slurry chemistry on Cu CMP processHuaming Xu: Mechanics of Nanoscale Lapping and Polishing

IMPACT • CMP • 6 04/09/2008

Motivation

Integrated tribo-chemical model of copper CMP considers abrasive and pad properties, process parameters (speed, pressure etc.), and slurry chemistry to predict material removal rates.Information on the abrasive-copper and/or asperity copper interaction force and frequency is needed to complete the integrated tribo-chemical modeling of copper CMP.Confocal reflectance interference contrast microscopy (C-RICM)

has been used to study pad-wafer contacts and shows promise for detection of smaller objects such as agglomerated abrasive particles.Information about the pad-asperity contact area and distribution has important applications in modeling the pattern-dependence of CMP, and in DfM.

Seungchoun Choi

Use of Confocal Microscopy to Characterize Pad Asperity-Wafer Contacts and Abrasive-Wafer Contacts During CMP

IMPACT • CMP • 7 04/09/2008

2008 Main Objective

• Complete comprehensive model of CMP for homogeneous substrate, and start adapting to account for pattern dependence– Complete the model that links mechanical and electrochemical

characteristics using abrasive-wafer and asperity wafer interactions as the physical link.

– Investigate whether the surface potential of the pad influencesmaterial removal rates

– Draw on abrasive scale and pattern scale capabilities to extendmodel to DfM applications.

Seungchoun Choi

IMPACT • CMP • 8 04/09/2008

The Problem

• Lack of understanding of abrasive-pad interaction on pad asperities:

- Inability to predict and control material removal rate and defects

- Limits application to Design for Manufacturing (DfM) and Manufacturing for Design (MfD)

Removal Rate (RR)

Slurry chemistry(pH, conc. of oxidizer, inhibitor & complexing agent)

Pad propertieslayers’ hardness, surface potential, structureAbrasiveType, size & conc. Polishing conditions(pressure P, velocity V)

Material being polished

Planarization, Uniformity, Defects

Incoming topography

Integrated tribo-chemical model

1. Passivation Kinetics2. Mechanical Properties

of Passive Film3. Abrasive-copper Interaction

Frequency & Force

• Lack of understanding of abrasive-pad interaction on pad asperities:

- Inability to predict and control material removal rate and defects

- Limits application to Design for Manufacturing (DfM) and Manufacturing for Design (MfD)

Removal Rate (RR)

Slurry chemistry(pH, conc. of oxidizer, inhibitor & complexing agent)

Pad propertieslayers’ hardness, surface potential, structureAbrasiveType, size & conc. Polishing conditions(pressure P, velocity V)

Material being polished

Planarization, Uniformity, Defects

Incoming topography

Planarization, Uniformity, Defects

Incoming topography

Integrated tribo-chemical model

1. Passivation Kinetics2. Mechanical Properties

of Passive Film3. Abrasive-copper Interaction

Frequency & Force

Seungchoun Choi

IMPACT • CMP • 9 04/09/2008

Mechanical Interaction: Frequency & Force*

Can be found if we can measure/calculate:- Number, size & distribution of wafer-asperity contact- Number & distribution of abrasives per asperity-wafer contact.

∫ +=τ

τρ 00 )( dttti

nFMRR Cu

Time (µs)

Stre

ss (M

Pa)

Time (ms)St

ress

(MPa

)

wafer

Muldowney, MRS Symp. Proc. Vol. 816pad asperity

abrasive particles

We can lump multiple abrasive contacts within an asperity.

MCu : Atomic mass of copperρ : density of coppern : # e- transferredF : Faraday’s constanti : oxidation rate

Interval between two abrasive-copper

contacts (τ)

* Tripathi et al, 2006 Proceedings of VLSI Multilevel Interconnection Conf.

t0 : time immediately after an abrasive-copper interactiont : time since an abrasive-copper interaction, before the next interaction

IMPACT • CMP • 10 04/09/2008

Wafer-Asperity Contact*

Pad asperity-wafer contacts were studied by using C-RICM

C-RICM image of asperity cluster contact on VP3000TM pad

C-RICM image sequence of VP3000TM pad at increasing applied pressure

C-RICM image of asperity cluster contact on VP3000TM pad

C-RICM image sequence of VP3000TM pad at increasing applied pressure* C. L. Elmufdi and G. P. Muldowney,

MRS Symp. Vol. 914, 2006

Seungchoun Choi

IMPACT • CMP • 11 04/09/2008

Schematic depiction of reflecting interfaces in pad asperity-wafer contact area

C-RICM utilizes the interference of light at material boundaries to identify contact points between surfaces

Cover slip

pad asperity

abrasive particles slurry

Rcoverslip-abrasive

Rpad-abrasive

Rslurry-abrasive

Rcoverslip-pad

Rslurry-pad

Rslurry-coverslip

IMPACT • CMP • 12 04/09/2008

Anticipated Experimental Procedure

• Slurry Abrasives- 40 wt% α-alumina slurry- 150nm average aggregate diameter - 20nm primary particle diameter• Copper CMP slurry - Filtered DI water with 1 mM KNO3, 0.1 M glycine and 0.1 wt % H2O2 + small amount of α-alumina particles• pH of slurry will be adjusted using KOH or HNO3• Copper nano-particles- 0.12 mM to simulate removal of copper surface during CMP- <100 nm in diameter

Confocal Microscopy (reflection mode)

- Four samples will be prepared for slurry pH of 4, 9 and 10 without Cu particles and pH 7.5 with Cu particles- SMART pads developed under earlier award will be useful for calibrating the images, and providing brightness information for each interface.

IMPACT • CMP • 13 04/09/2008

Challenges with Confocal Microscopy

Resolution:- Determined by rlateral = 0.4 λ / NA where λ is the wavelength of light and NA is the numerical aperture of the objective- In practice, the best horizontal resolution is about 200 nm - Particles smaller than 200 nm cannot be resolved if they are closer than 200 nm each other.Airy Disk:- Due to Fraunhofer diffraction of light passing through a circular aperture- Distinguishing the Airy pattern from real contact points may need substantial image processing technique.

Use fluorescent quantum dots, or abrasives to which a fluorescent marker is selectively adsorbed as tracers to assist the optical imaging, if needed

IMPACT • CMP • 14 04/09/2008

Future Goals

Confocal imaging for various slurry chemistriesComplete integrated tribo-chemical model of copper CMPUsing the results of this research, determine whether material

removal is due to abrasive particles being forced against the wafer by asperities, to convective transport of abrasive particles suspended in the slurry to the wafer surface where they interact, or to a combination of these mechanisms.

Seungchoun Choi

IMPACT • CMP • 15 04/09/2008

Motivation

Boning et al. MIT

CMP causes non uniform removal on patterned device wafers: defects like dishing & erosion.

CMP challenges (from ITRS)Reliably predicting and controlling post-CMP topography

– dishing & erosion < 10% interconnect height

Integration of ultra low-K dielectric materials

– predicting stresses and damage

Designing new planarization processes for new materials and new requirements.

CMP Modeling as a part of Design for Manufacturing

Shantanu Tripathi

IMPACT • CMP • 16 04/09/2008

2008 Main Objective

Continue development of comprehensive model of CMP:Continue development of model building on the abrasive scale, pattern scale capability to integrate additional chemical process elements and include coupling elements for linking key influences of chemical and mechanical activity and slurry agglomeration and heating. Consider pad/wafer contact elements.CMP model validation and design for manufacturing validation:Validate model capability with full scale model verification bysimulation and test (with industrial partners). Development of strategies for model-based process optimization. Consider use of model for DfM relative to process variation.

Shantanu Tripathi

IMPACT • CMP • 17 04/09/2008

Challenges

Present methods treat CMP process as a black box; are blind to process & consumable parametersNeed detailed process understanding

– For modeling pattern evolution accurately– Present methods do not predict small feature CMP well

– For process design (not based on just trail and error)Multiscale analysis needed to capture different phenomena:

– At sufficient resolution & speed CMP process less rigid than other processes: possibility of optimizing consumable & process parameters based on chip design

– MfD & DfMSource of pattern dependence is twofold:

– Asperity contact area (not addressed yet)– Pad hard layer flexion due to soft layer compression (addressed by previous

models)

Shantanu Tripathi

IMPACT • CMP • 18 04/09/2008

Present Modeling ApproachPresent Approach adopted by CAD companies

• Helps in dummy fill-- Partial product design improvement but no process

optimization• Optimization should be across process & product:

- Need to be able to tune all the available control knobs

CMPTest-Pattern

Wafer

ModelCalibration

ProductDesign Layout

CMPEvolution

Model

Full-Chip Prediction

Measurements & Parameter Extraction

Simulation

Model Inputs

DesignOptimization

Extensive tests/ measurements required

Specific to particular processing conditions

Present methods:Treat CMP process as a black box

– Lack of process understandingUse trial & error for process design, no process optimization

Model drawbacks:Do not predict small features correctlyCaptures only 1 source of pattern dependencyCoarse (resolution ~10µm)

Shantanu Tripathi

IMPACT • CMP • 19 04/09/2008

Proposed Pattern Evolution Framework

),(),(

yxKyxMRR

ρ=

R

Time stepevolution Asperity contact area (µm)

Empirically fit, based onpad flexion (scale=mm)

Space Discretization: Data Structure

STI oxide evolution* 0.112μm/0.1681μm

before 40sec CMP

*Choi, Tripathi, Dornfeld & Hansen, “Chip Scale Prediction of Nitride Erosion in High Selectivity STI CMP,”Invited Paper, Proceedings of 11th CMP-MIC, 2006

• Consumables• Polishing Conditions

Material Removal Model

∫ +=τ

τρ 00 )( dttti

nFMRR Cu

Small feature prediction problems

IMPACT • CMP • 20 04/09/2008

Summary of Current Progress

Pad/Wafer (~m)

Die (~cm)

Asperity (~µm)

Feature (45nm-10µm)

Abrasive contact (10nm)

Integrated chemo-mechanical modeling of material removal

Pattern Evolution Model for HDPCVD STI

Data structure for capturing multiscale behavior: tree based

multi-resolution meshes

Pattern density

Chip Layout

Evolution

IMPACT • CMP • 21 04/09/2008

Multiscale Optimization Example

Slurry

Address WIDNU (Within die non-uniformity) at different levels depending on available flexibility

Within die non-uniformityNitride Thinning in STI

Change pad hardness (tree level 1)

Inflexibility: scratch defects, pad supplier

Dummy fill (chip, array level)

Inflexibility: design restrictions

Change incoming topography (feature level)

Inflexibility: deposition process limitation

Change chemical reactions, abrasive concentration (abrasive level)Inflexibility: removal rate requirements

Storage Space Speed

MIT/Cadence Approach ~10MB (@20 µm resolution) ~60s (@20µm resolution)

New Approach * ~0.01MB(@20µm)100MB(@200nm)

~0.6s (@20µm resolution)

Computational Performance Prediction: New approach based on adaptive meshes

*Based on: Udeshi T, Parker E; J. COMPUTING & INFORMATION SCIENCE, MAR 2004

IMPACT • CMP • 22 04/09/2008

Future Goals

Continued development of CMP process modelsProgress of data structure implementationVerification of the proposed DfM approach

Shantanu Tripathi

IMPACT • CMP • 23 04/09/2008

2008 Main Objective

Introduction of Low-k dielectric materials (LKD, k<3.5) and Copper to reduce RC interconnects delay: LKD have poor mechanical properties hence delamination and cracks may occur during the CMP process: need to understand these phenomena

Create a model on ABAQUS using the Finite Elements Method (FEM model)Set up the Boundary Conditions and the Loads to reproduce the CMP conditions. The model has various parameters such as the Young Modulus of the Low-K dielectric material used, the thickness of the copper layer removed, the pressure applied on the wafer, …

Analyze the stresses induced by the CMP processFrom the FEM results, analysis of the Von Mises stresses which can lead to the propagation of cracks in the sub layers polished.Understand the creation and propagation of cracks in low-k interfaces

Adrien Monvoisin

Stress Analysis in Low-K dielectric Materials during the CMP Process

IMPACT • CMP • 24 04/09/2008

Abaqus Model

Boundary Conditions:– No displacement / rotation at the bottom– Periodic Boundary conditions on the sides

Loads:– Downward constant pressure: 2 psi– Horizontal Frictional Force: 0.7 psi

Materials:– Copper– Tantalum – Low-K 5-20Gpa

Adrien Monvoisin

IMPACT • CMP • 25 04/09/2008

Abaqus Results

E=5 GpaE=20 Gpa

E=5 Gpa E=20 Gpa

• Cu thickness = 250nm • Cu thickness = 50nm

• Highest stresses located at the edge. Cracks may first appear at these locations.

• Higher stresses for low-K with a lower E (poor mechanical Properties)

• Stresses are higher with Cu layer is thicker (when CMP starts)

Low-k material

5 GPa

20 GPa

Stre-sses

190 kPa

67 kPa

Stre-sses

177 kPa

62 kPa

Adrien Monvoisin

IMPACT • CMP • 26 04/09/2008

Tradeoff solution

Low-k, E=20Gpa

Low-k, E=5Gpa

Tradeoff solution with 2 layers of low-k stacked: one with a higher E to resist to the stress and one with a lower E underneath, less affected by the stresses induced by CMP to reduce the RC interconnect delay because of its porosity.

Adrien Monvoisin

IMPACT • CMP • 27 04/09/2008

Fatigue Phenomenon

Stress on the 2nd layer more important than those on the 1st layer: need to consider the “fatigue phenomenon”

Masako KoderaDependence of CMP-induced delamination on number of low-k dielectric films stacked

Patrick Leduc

The delamination increases with number of layers because of the effect of the stack residual stress and elasticity.

Adrien Monvoisin

IMPACT • CMP • 28 04/09/2008

Future Goals

Determine what is the theoretical fracture energy for the low-k dielectric that I used and evaluate the driving force caused by CMP.

Confirm these results with SEM experimental tests.

Expand this model to any low-k and investigate the crack propagation (crack path)

Analyze the influence of the damascene process: Coefficient of Thermal Expansion influences the resistance of low-k dielectric materials regarding fractures .

Investigate the influence of the “fatigue” phenomenon.

Adrien Monvoisin

IMPACT • CMP • 29 04/09/2008

2008 Main Objectives

– Colloidal behavior measured by zeta potential and agglomerate size distribution - effects of chemical additives and presence of copper

– Studied effects of slurry chemistry on copper surface hardness and etch rate

– Used agglomerate size distribution, nanohardness and etch rates in model of CMP

Effects of slurry chemistry on Cu CMP process

Robin Ihnfeldt

IMPACT • CMP • 30 04/09/2008

Measuring Nanohardness and Etch Rates

Hardness Measurements - TriboScope Nanomechanical Testing system, Hysitron Inc.–1000 nm Cu sputter deposited on 30 nm Ta on 1 cm2 silicon wafer pieces –10 min exposure in 100 ml of solution (without abrasives), removed, dried with air and measured–Maximum applied load varied from 50-3000 μNEtch Rates - wafer pieces weighed before and after immersion in solution

IMPACT • CMP • 31 04/09/2008

Nanohardness Before Chemical Exposure

Hardness technique Material ValueNanohardness (GPa) Cu1 2.5 ± 0.3

Ta2 3.3 ± 1.5Si3 12 ± 2Cu2O* 17 ± 5

*as measured in this study

0

2

4

6

8

10

0 50 100 150 200 250

Indentation Depth (nm)

Hw

(GPa

)

Average Hw=2.6 GPaNanohardness versus indentation depth

• Nanohardness near surface (<20nm) is >Cu metal indicating copper oxide

• At >30nm, hardness of Cu metal

1D. Beegan, S. Chowdhury, and M. T. Laugier, Surface and Coatings Technology, 210, 5804 (2007).2A. Jindal and S.V. Babu, J. Electrochemical Soc., 151 (10), G709-G716 (2004).3M. Ueda, C. M. Lepienski, E.C. Rangel, N. C. Cruz, and F. G. Dias, Surface and Coatings Technology, 156, 190 (2002).4A. Szymanski and J. M. Szymanski, Hardness Estimation of Minerals Rocks and Ceramic Materials, Elsevier Science Publishers B. V., New York, NY (1989).

Hardness technique Material ValueMoh's hardness4 Cu(OH)2 2.0-2.5

Cu metal 3CuO 3.5Cu2O 4Ta 6.5Si 6.5

IMPACT • CMP • 32 04/09/2008

Effect of pH on Hardness

• Near surface (<40nm) hardness increases as the pH increases

• Consistent with potential-pH equilibrium diagrams which indicate that copper oxides are more stable at higher pH*

• Nanohardness is that of Cu metal for >70nm

0

1

2

3

4

5

6

7

8

0 20 40 60 80 100 120 140

Indentation Depth (nm)

Hw

(GPa

)

pH 2.9

pH 8.3

pH 11.7

*M. Pourbaix, Atlas of Electrochemical Equilibria in Aqueous Solutions, National Association of Corrosion Engineers, Houston, Texas (1974).

Robin Ihnfeldt

IMPACT • CMP • 33 04/09/2008

Effect of Additives on HardnessNanohardness versus indentation depth after exposure to aqueous solutions with 0.1M glycine and 2wt% H2O2 at various pH Possible Surface Reactions:

passivation 2Cu + H2O -> Cu2O + 2H+ + 2e Cu2O + H2O -> 2CuO + 2H+ + 2e

complex formation Cu2O+4HL ->2CuL2(s)+H2O + 2H+ + 2e CuO + 2HL -> CuL2 (s) + H2O

dissolution CuL2 (s) -> CuL2 (l)

decomposition H2O2 + e- > OH* + OH-

• At pH 8.3 the film is very soft (possibly porous) and etch rate is large (56 nm/min)• H2O2 decomposition occurs faster at higher pH.*• At pH 10.0, large etch rate, 33 nm/min, indicating possibly a thick passivation layer

forms which inhibits Cu-glycine complex formation. * G. Xu, H. Liang, J. Zhao, and Y. Li, J. Electrochemical Soc., 151, (10) G688 (2004).

02468

101214161820

0 100 200 300 400 500

Indentation Depth (nm)

Hw

(GPa

)

0.1M Glycine, 2.0wt% H2O2 pH 8.3

0.1M Glycine, 2.0wt% H2O2 pH 10.0

Robin Ihnfeldt

IMPACT • CMP • 34 04/09/2008

Conclusions

Surface hardness is very sensitive to the chemistry of the solution!

– Small changes in chemistry (pH, additive concentration, etc.) can cause large changes in the hardness (0.1 – 20 GPa)

Future WorkStudy effects of exposure time of solution on hardness (film formation due to fast reaction or slow reaction) Surface hardness measurements performed in this study may not berepresentative of surface hardness that occurs during a CMP process

– Different measurement technique? Study effects of temperature

Robin Ihnfeldt

IMPACT • CMP • 35 04/09/2008

Motivation

Increasing demands for extremely high-density recording have led to very tight tolerance requirements for the head-disk interface. This has necessitated ultra-smooth (rms < 0.2 nm) recording head surfaces.

Optimization of the lapping/polishing process to achieve extremely high-density recording – with direct implications to other technologies relying on surface smoothness and flatness.

Development of stochastic mechanics models for material removal rate at the nanoscale.

Mechanics of Nanoscale Lapping and Polishing

Huaming Xu

IMPACT • CMP • 36 04/09/2008

2008 Main Objective

Analyze the mechanisms of the plate charging process and developmechanics models.

Analyze the mechanisms of the lapping process and develop analytical models for material removal rate and resulting surface roughness.

Bridge the gap of knowledge in nanoscale lapping mechanics, in particular as it pertains to ultra-smooth surfaces of magnetic recording head media.

Analyze material removal processes in terms of important lappingparameters and material properties.

Huaming Xu

IMPACT • CMP • 37 04/09/2008

The Problem

Low diamond particles density of charged lapping plate.Mechanism of single diamond particle embedment processProbabilistic analysis of embedded diamond particles on the lapping plate

Insufficient longevity and efficiency of lapping plates.Parametric study of the longevity of the lapping plate Study on material removal mechanism during lapping process

Demand for sub-nanometer surface roughness for magnetic recording heads

Probabilistic analysis of lapping process

Huaming Xu

IMPACT • CMP • 38 04/09/2008

Charging Process Models

Mean gap distance

Fluid Properties(Viscosity)

Load

Geometry

Kinematics(Tool , Plate rpm )

Topography properties

Particle distribution

Charge Density

Friction Coefficient

Material PropertiesParticle Debonding

ExperimentsExperiments of

Charging ProcessHydrodynamic

Model Probabilistic

Model

DebondingModel

Output

Huaming Xu

IMPACT • CMP • 39 04/09/2008

Hydrodynamic ModelPurpose: Estimate the mean gap between the two surfaces during the charging process.

Assumptions:(1) The charge ring is tilting(α, β).(2) Self-balance for Moments.

Numerical Methods:(1) Finite Difference Method(2) Newton-Raphson Method

Tin Plate

Charge Ring L

F

yM

xM

Basic Equations:(1) Modified Reynolds equation

(2) Local gap distance

(3) Boundary conditions

(4) Force and moment equilibrium equations

( ) ( )

3 3( 1) 1 ( 1)( ) ( )6 6

r

h hrU U

rh g h gr

r r r

φ

θ θφ

β θ β θμ φ μ φ

∂ ∂+ =

∂ ∂

∂ ∂ − ∂ ∂ −+

∂ ∂ ∂ ∂

( , , )h f h α β=

min 0 max 0( ) ; ( )p r r p p r r p= = = =

max

min

max

min

max

min

2

0

22

0

22

0

( , , ) ( ) 0

( , , ) sin 0

( , , ) cos 0

r

atmr

r

xr

r

yr

F h p p rd dr L

M h pr d dr

M h pr d dr

π

π

π

α β θ

α β θ θ

α β θ θ

⎧= − − =⎪

⎪⎪⎪ = =⎨⎪⎪⎪ = =⎪⎩

∫ ∫

∫ ∫

∫ ∫

Huaming Xu

IMPACT • CMP • 40 04/09/2008

Hydrodynamic Model(cont’d)

Geometry (along radial direction):

Conclusions: The mean gap distance decreases with increasing load (pressure).

Parameters:

Tin Plate

Fluid

m inr m axr

0p

Charge ring velocity 20 rpm Maximum radius 67.5 mmPlate velocity 30 rpm Minimum radius 30 mmViscosity 3.2 cp Distance between centers 130 mm

Results:

Huaming Xu

IMPACT • CMP • 41 04/09/2008

slurry

L'z

"zhv

z

Probabilistic Charging Model

Charging Process

Assumption:Diamond particles with sizes larger than the local gap can be embedded into the tin layer.

Particle density function n ( particles/unit area):

Slurry

'

2

1 ( ) '( ') "( '') '' 'kd h z

k kk

n f d f z f z dz dz ddd

− −

−∞

= ∫ ∫ ∫

'( '), "( ") :f z f z PDFs of height distribution of top and bottom surfaces( ) :kf d PDF of diamond particle size distribution:h Mean gap distance between two surfaces

Huaming Xu

IMPACT • CMP • 42 04/09/2008

Probabilistic Charging Model(cont’d)Input parameters:

Results:

Conclusions:(1) Particle density decreases with mean gap distance.(2) For mean gap distance larger than mean particle size, the charge density increases with surface roughness; otherwise, the charge density decreases with surface roughness.

21 215 ; 15 ; 100 ; 15 ; 1d dnm nm nm nm A mσ σ μ σ μ= = = = =

1:Variable top surface σ 2:Variable bottom surface σ

IMPACT • CMP • 43 04/09/2008

Debonding ModelReason: When a diamond particle is not sufficiently embedded into the tin layer, it could be removed upon application of a lateral force.

Debonding Condition:Input: Effective particle radius, friction coefficient, material properties.

δin tL

F L

FM

in tM

L

in tL

F

piτ

Rβ

γ

θr

intFM M>

Equations:

Conclusion:

/ 2 3 2int 0 0

3 2 2

2 2int

4 sin cos 4

sin (2 )

(2 ) 4

i i

F m m

F m i

M R d d R

M FR p R p R R

M M p R R R

π θτ β γ β γ τ δ

μ π θ μ π δ δ

μ π δ δ τ δ

= =

= = = −

> ⇒ − >

∫ ∫

4 42 2 ,i crit i i

m m m

fR p R p p

τ δ τ τδ μμπ μπ

⎛ ⎞< − ⇒ = − = ⎜ ⎟

⎝ ⎠

Huaming Xu

IMPACT • CMP • 44 04/09/2008

Probabilistic Model-Debonded ParticlesProbability after particle debonding

Particle density function n:

Parameters:

2

'

2

1 ( ) ( )

1 ( ) '( ') "( '') '' 'k

k k kk

d h z

k kk

n P z d f d ddd

f d f z f z dz dz ddd

α

α

− −

−∞

= <

=

∫

∫ ∫ ∫

'

( ) ( ) '( ') "( '') '' 'kd h z

crit k kP z d P z d f z f z dz dzα

δ α− −

−∞

+ < = < = ∫ ∫2 ( 1)i

mpτα α

μπ= ≤

Result:

1 215 ; 15 ;

100 ; 15 ;

/ 1/ 6( )d d

i m

nm nm

nm nm

p fully plastic deformation

σ σ

μ σ

τ

= =

= =

≈

IMPACT • CMP • 45 04/09/2008

Future Goals

Experimental verification of hydrodynamic and probabilistic models of the particle charging process.Analysis of the material removal mechanism and estimation of final surface roughness after lapping.Slip-line plasticity analysis and FEM modeling of single diamond particle plowing through a ceramic surface.Estimation of the gap between the recording head surface and thelapping plate during lapping.Lapping mechanics studied by nanoscratching experiments with diamond tips of different size/shape and contact loads.Friction coefficient measurements and lubricant effect on material removal rate and metal transfer/smearing.Lubricated lapping experiments under various loads and speeds using glycol and other hydrocarbon-based lubricants.

Huaming Xu