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