1. CMP Modeling as Part of Design for Manufacturing
David Dornfeld
Will C. Hall Professor of Engineering
Laboratory for Manufacturing and Sustainability
Department of Mechanical Engineering
University of California
Berkeley CA

2. Outline Modeling objectives and perspective
CMP process model development
Short review
Towards design for manufacturing (DFM)

3. Levels of Flexibility - Design to Manufacturing
Software driven
Hardware driven

4. (green, sustainability,
Modeling Roadmap for maximum impact
Functional
Model
Feedback
(validation)
Integration
with CAD
Include “islands of
automation” and
existing models)
Include supply
chain with
constraints (e.g.
“quality gates” )
Prototype
based
on model
Extend to “social
impact” constraints
(green, sustainability,
health, safety, etc.)
Minimum cost/CoO
Maximum production
Maximum flexibility
Maximum quality
Minimum environmental
& social impact
Broadest integration *
Through software

5. Is there need for this?
Design
Manf’g
Design
Manf’g

6. What you see depends on where you are standing!+
Design
Manf’g +
Manf’g
Design
Source: Y. Granik, Mentor Graphics

7. What’s your world view?
Process
Process
Process
Design
Design
Design

8. Interfacial and Colloid Phenomena
Components of Chemical Mechanical Planarization
Mechanical Phenomena
Chemical Phenomena
Interfacial and Colloid Phenomena

9. Scale Issues in CMP Material Removal Mechanical particle forces
Scale/size nm µm mm
Material
Removal
Mechanical particle forces
Particle enhanced chemistry
Chemical
Reactions
Active
Abrasives
Pores,
Walls
Grooves
Tool mechanics,
Load, Speed
critical features
dies
Pad
Mechanism
Layout
wafer
From E. Hwang, 2004

10. An overview of CMP research in Berkeley
Cu CMP
Bulk Cu CMP
Barrier polishing
W CMP
Oxide CMP
Poly-Si CMP
Bulk Cu slurry
Barrier slurry
W slurry
Oxide slurry
Poly-Si slurry
Abrasive type,
size and concentration
Dornfeld
Doyle
[oxidizer],
[complexing agent],
[corrosion inhibitor],
pH …
Talbot
Chemical reactions
Mechanical material removal mechanism in abrasive scale
Pad asperity density/shape
Pad mechanical properties
in abrasive scale
Physical models of material removal mechanism in abrasive scale
Pattern
Topography
MIT model
Pad properties in die scale
Models of
WIDNU
Better control of WIWNU
Reducing ‘Fang’
Small dishing & erosion
Ultra low-k integration
Smaller WIDNU
Reducing slurry usage
Uniform pad performance
thru it’s lifetime
Longer pad life time
Reducing scratch defects
Better planarization efficiency
E-CMP
Slurry supply/ flow pattern
in die scale
Pad design
Wafer scale pressure NU
Models of
WIWNU
Wafer scale velocity profile
Fabrication
Fabrication
technique
Wafer bending with zone pressures
Slurry supply/ flow pattern
in wafer scale
Test
model
design goal
Pad development
Pad groove

11. CMP Modeling History in SFR/FLCC*
before
SFR/FLCC
now
DfM/MfD
Preston’s Eqn.
MRR = CPV
Combined eqn.
R=CM/(C+M)
MRR= N  Vol
Luo (SFR)
Tribo-electro-chemical model
Tripathi (FLCC)
Computational efficiency
Flexible in scale
Process links
Choi (FLCC) MRR =
Interfacial/colloidal effects
* According to Dornfeld

12. Interactions between Input Variables
Four Interactions: Wafer-Pad Interaction; Pad-Abrasive Interaction;
Wafer-Slurry Chemical Interaction; Wafer-Abrasive Interaction
Velocity V
Vol
Chemically Influenced Wafer Surface
Wafer
Abrasive particles on Contact area with number N
Abrasive particles in Fluid (All inactive)
This is our 2-D Micro-view of wafer-pad interface. There are several critical interaction interfaces in the model. First, let us look at the interaction between the wafer and pad. The pad is a rough surface with micro-scale asperities. The wafer and pad will contact over these asperities only. This indicates that the contact area is much smaller than the area of the wafer. Contact pressure on the asperities is much larger than the down pressure. The slurry with slurries are distributed over the wafer-pad interface. The second and third interactions is the interactions between the slurry and wafer and those between the slurry and wafer. Two elements exist in the slurry, one chemical and the other the abrasives, which is the cutting tools. The slurry chemicals will react with the wafer surface and a chemical affected layer will be formed over the wafer surface. Part of slurry abrasives will float in the slurry. Other part of slurry abrasives will sit on the wafer-pad contact area. We use a term active abrasive to describe the abrasives in the contact area. This chemical affected layer will be removed continuously by the abrasives sitting on the wafer-pad contact area. This is a bigger view of the wafer-abrasive-pad contact. Once we know the abrasive number in the contact area, which is based on the slurry-pad contact, and the volume removed by a single abrasive, which is based on wafer-pad contact, then we can evaluate the material removal in this part of interface. These should be based on the clarification of the three interactions between the three elements. In the following, we will discuss step by step how these interactions are modeled.
Polishing pad
Pad asperity
Active abrasives on Contact area
Source: J. Luo and D. Dornfeld, IEEE Trans: Semiconductor Manufacturing, 2001

13. Pad Materials/Shape Effects
Stage 1
Stage 2
Stage 3
Dishing and erosion
Linear Viscoelastic Pad
Dishing d 3
Erosion e 2 1 Df
S1=Df1
S=S0
H=Hcu0+Hox0
H= Hstage1
Hcu0
Hox0
Pad/wafer contact modes in damascene polishing

14. Effect of Pattern Density - Planarization Length (PL)
ILD
Metal lines
Planarization Length
High-density region
Low-density region
Global step

15. Modeling of pattern density effects in CMP
Effective pattern density
a=320um
a=640um
a=1280um
< Effective density map >
< Test pattern >
< Post CMP film thickness prediction at die-scale >
Planarization length
(window size) effect
on “Up area”

16. Feature level interaction between pad asperities and pattern topography
Z(x,y)
Z_pad
Reference height (z=0)
F_tent > F_die ?
F_tent < F_die ?
++Z_pad
--Z_pad No
Yes
Z_pad dz
Z(x,y) z
Z_pad

17. Characterization of Pad Surface
Asperity Height (µm)
Probability Density (µm-1) a
active asperities b
(source : A.Scott Lawing, NCCAVS, CMPUG 5/5/2004)

18. Model for the simulation
fitting parameter accounting for chemical reactions, abrasive size distribution etc.
abrasive particle size
asperity radius
pad/film properties
polishing speed
pad asperity height distribution
New model
pattern density effect
Mean distance between asperities
hardness of material polished

19. HDP-CVD Deposition Model
Modeling Overview
Chip Layout
Pattern density
Line space
Line width
CMP Input Thickness
HDP-CVD Deposition Model
CMP model
Evolution
Nitride thinning

20. Adding the electro-chemical effects
Develop a transient tribo-electro-chemical model for material removal during copper CMP
Experimentally investigate different components of the model
Using above model develop a framework for pattern dependency effects.
Slurry chemistry
(pH, conc. of oxidizer, inhibitor & complexing agent)
CMP
Model
1. Passivation Kinetics
2. Mechanical Properties
of Passive Film
3. Abrasive-copper Interaction
Frequency & Force
Pad properties
layers’ hardness, structure
Removal Rate (RR)
Abrasive
Type, size & conc.
Planarization, Uniformity, Defects
Incoming topography
Polishing conditions
(pressure P, velocity V)
Polished material

21. Application: Polishing induced stress
Pressure concentrated locally (about 300 psi)
 Risk of cracking in the sub layers

22. FEM Analysis: Model COPPER Layer E = 129.8 GPa ; α = 0.34
TANTALUM Layer
E = GPa ; α = 0.34
LOW-K Layer
E = 5 – 20 GPa ; α = 0.25
BOUNDARY CONDITIONS:
- Fixed at the bottom
- Periodic Boundary Conditions (symmetry)
LOADS:
- Downward Constant Pressure – 2psi
- Horizontal Shear (friction) stress – 0.7psi

23. FEM Analysis in CMP Von Mises stresses Step1 Step2 Step3 Step3
Low-k: E = 5GPa
Low-k: E = 20GPa

24. Modeling Challenges
Present methods treat CMP process as a black box; are blind to process & consumable parameters
Need 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 & DfM
Source of pattern dependence is twofold:
Asperity contact area (not addressed yet)
Pad hard layer flexion due to soft layer compression (addressed by previous models)

25. Present Approach (Praesegus/Cadence, Synopsys)
Extensive test/measurements required
Model:
captures only 1 source of pattern dependency
coarse (resolution ~10µm)
Helps in dummy fill
- Design improvement but no process optimization
Optimization should be across process & design:
- Need to be able to tune all the available control knobs
Specific to particular processing conditions
Source: Praesegus Inc.

26. Pattern Related Defects
Low pattern density
High pattern density
erosion & dishing
residue film
Initial topography
Non-uniform removal
Local planarization
End point
Over polishing
Present Approach
MRR(x,y) = material removal rate at (x,y)
K = Blanket MRR
ρ(x,y) = effective pattern density at (x,y) R
Time step
evolution
ρ(x,y) calculated as a convolution of a weighted function (elliptic) over evaluation window.
Evaluation window size (R) determined empirically.
Nominal Pattern density = Area(high features) / (Total Area)

27. Need a “GoogleEarth” view of modeling
We are here

28. CMP phenomena at different scales
Head
Platen
Pad
down-
force
slurry supply
rotation of wafer head
Wafer 4-12”
Copper
Feature
pad asperity
abrasive particles
100nm-10µm
~1µm
1-10µm
Pad asperity
Abrasive
Pad/Wafer
Die
Feature/Asperity
Abrasive Contact

29. Pattern Evolution Framework
Consumables
Polishing Conditions
Material Removal Model
STI oxide evolution*
0.112μm/0.1681μm
before
40sec CMP
Small feature prediction problems R
Time step
evolution
Space Discretization:
Data Structure
Asperity contact area (µm)
Empirically fit, based on
pad flexion (scale=mm)
*Choi, Tripathi, Dornfeld & Hansen, “Chip Scale Prediction of Nitride Erosion
in High Selectivity STI CMP,” Invited Paper, Proceedings of 11th CMP-MIC, 2006

30. Effects to Capture Multiscale Behavior Far-field Effects
Material removal operates on different scales and contributes to the net material removed in the CMP process
Material removal at any location is affected by its position in different scales
Different models need to be used to capture behavior at different scales
Far-field Effects
Most IC manufacturing processes are only dependant on local features
CMP performance depends on both local as well as far-field features

31. CMP Model Tree
Tree based data structure will encapsulate both wafer features and pattern evolution at various scales

32. Data Structure Efficient surface representation is required
Mesh-based representations allow for fast processing, and have been widely used
Need to capture repeating features
Use tiles/modular units
For “similar” features, use property inheritance from modular features
Multiscale analysis
Use multiresolution meshes – allow for querying in mm/um/nm scales
Also support querying of far-field features along with local features nm m cm mm μm
Multiresolution meshes will allow for querying in different scales - resolution will be determined by feature scales; tiling will be used for repeating features.

33. Data Structure Model precision vs. Level of Detail
analysis time
Level of Detail
Tradeoffs between LOD, analysis time, and accuracy
Resolve into
smaller features
larger features
Data Structure
Model precision vs. Level of Detail
Identify tradeoffs between speed of analysis and the accuracy of the models used
Data Structure design motivated by physical considerations
Tree levels ≡ phenomenon scale
object properties ≡ physical phenomena.
Inheritance:
Inherit properties from parents at higher levels of tree and from generic object at that level
accuracy
Example of property inheritance from parent features and base features applied in CMP process model
Asperity
(feature)
CMP Process Model on Asperity Scale
Pad
(parent)
Properties inherited from pad
Specific asperity properties
Generic Asperity
Properties inherited from generic feature

34. Multiscale Optimization Example
Address WIDNU at different levels depending on available flexibility:
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)
Within die non-uniformity
Nitride Thinning in STI

35. Thank you for your attention!