Goal: Virtual Prototyping via Predictive Process, Property, Performance Modeling

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Task VI Predictive Modeling and
MetrologyPredictive Modeling and Simulation
PI Timothy Cale Associated faculty Antoinette
Maniatty, Mark Shephard Post Docs Ottmar Klaas,
David Richards (Avant!), Vinay Prasad Students
Max Bloomfield, Jing Lu, Suchira Sen

• Goal Virtual Prototyping via Predictive Process,
  Property, Performance Modeling
• Microstructure Formation and Evolution
• Amorphous, polycrystalline, single crystal?
• Texture, grain size, composition, defects
• Multiscale Modeling and Simulation
• Reactor scale to feature scale done for selected
  processes (CVD, ECD)
• Adding grain and atomic scales to complete the
  spatial scales

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Predictive Processing, Property, Performance
Models

• Replace correlations and empirical guidelines
  with predictive models
• Material models
• Process models
• P4 modeling and simulation is a long term vision
• Structure as a function of processing
• Effects of structure on properties and
  performance
• Initial focus is on nanoscale polycrystalline
  films
• Help synthesize the disparate/fragmented global
  efforts to predict interconnect relevant
  microstructure evolution

Unit Ops
West et al, 2001
Sen et al.
Nucleation, Growth
Metrology Support
Roughness
Geer et al.
J.-Q. Lu et al.
Jing Lu et al.
Bloomfield et al.
Prasad et al.
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Current IFC Projects

• Microstructure formation and evolution
• Create 3D microstructure simulation tools and
  couple them to property and performance models in
  order to evaluate materials and processes.
• Multiscale modeling
• Create models that relate process setpoints to
  microstructure evolution and performance
  predictions.
• Process support
• Create models that support 1 and 2 above, and
  activities in other tasks
• Atomic layer deposition Barriers, seeds
  (UAlbany - Eisenbraun)
• (This is a good example of transient feature
  scale simulation.)
• Roughness evolution - Waveguide fabrication (RPI
  Persans)
• Stress Evaluating 3D protocols (RPI Gutmann)

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Continuum Modeling vs. Grain Structure
Cale, Borucki, Merchant
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Polycrystalline Film Modeling - State of the Art

• Grains are artificially generated.
• Created in 2D to match size distributions (top
  view)
• Extruded to make 3D grains
• Grains assigned properties, like orientation,
  using distributions
• Very idealized grain boundaries
• This Grain Continuum approach has been very
  useful to understand performance.
• We have developed 3D FE grain continuum models
• Grain size and orientation, anisotropy, film
  thickness, hardening due to dislocation pile-ups,
  thermal recovery, electromigration and stress
  driven diffusion.

z
y
sxx
x
Columnar grain structure model (blue) with mesh
(yellow) (Borucki, Klaas).
Inhomogeneous thermal stresses in copper film.
Notice stress gradients between grains of
differing orientations.
Data for passivated copper from Vinci, Zielinski,
and Bravman, Thin Solid Films (1995).
lt111gt fiber texture applied to film.
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The Missing Link Grain-Continuum Modeling
Finite-element mesh conforms to grain
Grainboundaries, surfaces
Material properties assigned to grains and grain
boundaries REPRESENTATION?
Discrete/continuum inter-conversion, as needed.
Store statistical information about each grain
regenerate details as needed. Mathematical and
software opportunities.
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Modeling with Grain-Continuum Representations

• Objectives
• Create 3D microstructure simulation tools and
  couple to property and performance models to
  evaluate materials and processes.

• Approach
• Atomic scale KLMC models provide data on
  formation and growth of islands (nuclei).
• Discrete islands/grains are encapsulated in a
  finite element mesh and perhaps coarsened.
• Multilayer microstructure is represented.
• Grain-continuum representation can be included in
  multiscale processing models to predict island
  coalescence and grain evolution from reactor
  set-points.

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Texture Competition and Grain Formation

• Atomic scale KLMC models provide data on
  formation and growth of islands (nuclei).
• Discrete (atomistic) to continuum (FE) conversion
  at reasonable island sizes (encapsulation)
• Grain-continuum - 3D surface and microstructure
  evolution using a finite element based level set
  approach.
• Grain-continuum representation can be included in
  multiscale processing models to predict island
  coalescence and grain evolution from reactor
  set-points.

Nucleation data (Yang, Cale)
QD nuclei (Oktyabrsky)
Multiple lattice KLMC simulations (Huang, Gilmer)
Continuum islands
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Holy Grail Predictive Process, Property,
Performance Models
Optimize Design/Setpoints to achieve specified
performance
Atomistic (Å)
ECD Reactor (dm)
Property and Performance Models
Die (mm)
Grain (0.1 - 1 mm)
Feature (0.1 - 1mm)
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Multiscale Modeling
(b)
(a)

• Objectives
• Develop techniques to move information between
  different scales and different physics.
• Apply these techniques to models of currently
  relevant processes.

• Approach
• Use finite element meshes with extreme local
  refinement to directly bridge length scales.
• Use homogenization and rates from tables, then
  combine to produce boundary conditions for
  different scales.
• Partition computation across multiple
  processors/machines to speed results.

(a) ELD mechanism schematic and reaction step
Tseng et al. JECS, 148(5) 2001. (b) 3D FEM
simulation of deposition onto Cu nuclei (c)
Partition of reactor across processors (d)
Intermediate pattern-scale loading of Cu ion
across patterned regions.
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Geometric model and mesh
Encapsulation Convert discrete islands into
continuous islands
Interface velocities
Evolve interfaces
Extract 3D interfaces
KLMC Nucleate and grow discrete or atomistic
islands
Reconciliation
Reinitialization
Redistancing
Discrete
Process
Grain-continuum
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Atomic Layer Deposition

• Objectives
• Support current ALD efforts.
• Predict limits of operating trajectories for
  atomic layer deposition (ALD) while maintaining
  conformal deposition.
• Track transient behavior, including sub-monolayer
  coverage, during deposition.

• Approach
• Solve the (linear) Boltzmann transport equation
  for true transient approach.
• Use predicted number density and heterogeneous
  kinetics, e.g., Langmuir adsorption model, to
  obtain quantitative deposition rates and required
  operating conditions (pulse times) for conformal
  deposition.

Conformal deposition in an L-shaped bend in an
interconnect trench of aspect ratio 2.25.
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Atomic Layer Deposition

• Deposition occurs during reaction step due to
  reaction of gaseous reactant with adsorbed
  reactant.
• Model predicted growth rates as functions of
  reactant pulse times show fair agreement with
  experimental data (van der Straten et al., U.
  Albany, 2001) for the choice of rate constants.

Growth rate dependence on reactant pulse times
for TaNx ALD using TBTDET and NH3 as precursors.
Experimental data is from van der Straten et al.,
U. Albany (2001).
Film thickness and growth rate vs. time for ALD
in a 1 mm deep by 0.25 mm wide trench.
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Electrochemical Deposition - Bumping
(a)
Expanding corner decreases coverage.

• Objectives
• Provide tools to assist the development of models
  of unit operation.
• Validate and improve process and models by
  comparing to detailed measurements.

Contracting corner increases coverage.

• Approach
• Continue to develop transient feature scale
  simulators.
• Use interface tracking developments to extend
  current feature scale simulators, attach to
  larger and smaller scales in transient manner.
• Evaluate models of processes from the literature
  and in turn, use these models to test out new
  transient tools.

(b)
(c)
(a) Explanation of bumping via accelerator
coverages. (b) Effect of aspect ratio on bump
formation. Model adapted from Josell et al.,
JECS (2001). (c) SEM of accelerator deposited Cu
showing bumps. West et al., JECS, (2001).
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Modeling Surface Roughness Evolution
a

• Objective
• Develop models that allow optimization of
  roughness-sensitive structures e.g., optical
  waveguides and vertical cavity lasers.

• Approach
• Develop models with non-linear chemical
  mechanisms that predict the development of
  roughness that occurs in etch and deposition
  processes.
• Use Boltzmann solver developed by Gobbert et al.
  to do fully 3D evolution of nanoscale features
  using a 3D level set moving algorithm.
• Leverage experimental and metrology expertise of
  New York team to develop models.
• Use simulators to predict roughening as function
  of processing conditions.

b
AFM images of 100 mm2 region of plasma etched
Si(100). (a) 30 min., (b) 60 min. (Image from
Y.-P. Zhao et al.)
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Roughness Modeling

• Understand roughening fundamentals using 3D/2D
  simulations.
• to understand origins of roughening, to
  control/minimize roughening
• to evaluate transport and reaction models
• Trends of RIE simulations (center) agree with
  polymer etch experiments done at RPI (by Persans,
  et al. at left)
• Smoother surfaces (decreased interface
  thicknesses) at higher pressures (radical/ion
  ratio up). RMS roughness becomes constant at
  long times for high pressures, but increases
  linearly with material removed at low pressures.
• Small correlation length increase with etch
  depth.
• ALD type depositions can smooth surfaces

radical dominance
Persans, et al.
ion dominance
Atomic layer deposition
Reactive ion Etching
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Modeling Support for Holographic Imaging

• Objectives
• Provide models and tools to assist the
  development of advanced 3D metrology tools.
• Validate and improve process and materials models
  by comparing to detailed measurements.

(Geer et al.)
Optical hologram of etched features

• Approach
• Provide model-generated surface profiles for
  prediction of holographic signatures to compare
  with holographic data. This will help automate
  identification of defects.
• Predict 3D maps of elastic properties to generate
  images from ultrasonic tool.
• Compare simulations to measured 3D profiles for
  model development of high-aspect ratio etching,
  or early stages of deposition.

(Geer et al.)
Ultrasonic holography (Geer et al.)
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Predicting Stresses and Instabilities

• Objective
• Develop modeling tools that predict stresses in
  multilayer stacks, with film thicknesses lt 100
  nm e.g., for 3-D interconnect systems.

• Approach
• Start by using existing tools to evaluate
  stresses in proposed multilayer structures.
• Consider strain and surface energies as well as
  potential diffusion mechanisms that could lead to
  surface instabilities/roughening.
• Combine dislocation theory with grain-continuum
  film model to predict stress and strain behavior
  in thin films (lt 100 nm thick).
• Couple with adhesion and grain evolution models
  to predict overall mechanical behavior in 3-D
  multilayer interconnect systems.

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Stress Analysis of Through-Wafer Via

• ANSYS was used to evaluate the stresses caused by
  thermal expansion mismatch between copper and
  silicon (assuming ECD Cu, then downstream heating
  to 400 C).
• Conservative assumptions lead us to predict no
  silicon failure due to copper expansion.
• Reasonable assumptions result in stress along
  weakest plane 111 of 220 MPa, compared to
  failure stress of 1 GPa.
• Barrier materials have little effect on stress.

K.-S. Chen et al., J. of the Amer. Ceramic Soc.,
83 (6), June 2000.
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Plans
(a)

• Begin a molecular/materials modeling effort
  needed for
• Nanotube growth/doping/bending
• Reaction pathways
• Collaboration with Dieter Wolf at ANL being
  defined. He will contribute in microstructure
  evolution.

(b)
Functionalized carbon nanotubes. (a) silicated
nanotube, (b) oxygen-doped defect in carbon
nanotube.
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Virtual Prototyping via Predictive Process,
Property, Performance Modeling

• Tools
• Atomistic/energetic/pathway models
• Microstructure models
• Multiscale process, materials and performance
  models

• Predict performance from
• Materials properties
• Process conditions
• Operating environment

• Performance
• Thin film performance
• Failure analysis / lifetime
• Assess process flows
• Identify trouble spots

• Properties
• Spatial variation - processes
• Thin-film-specific effects
• Thermo-mechanical stress
• Diffusion through multilayers
• Adhesion

• Structure
• Texture (grain orientation)
• Grain sizes
• Interface morphology (e.g., roughness) and
  composition
• Defect distributions (interface and bulk)

5-8 yrs
1-3 yrs
3-7 yrs
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Summary

• Multiscale microstructure modeling for predictive
  simulation tool development.
• Both discrete and continuum models will be needed
  for property and performance predictions.
• Structural and property predictions to be coupled
  with performance models.
• Materials and process models can be used to
  assess process flows and materials sets.
• Integrate microstructure tools with equipment
  models.
• See posters 1) an overview of our effort, 2)
  multiscale microstructure modeling

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Driver Relationships
All Drivers Support evaluation and selection of
materials, structures, and processes (unit
operations). Deploy modeling to help gain
process understanding. Driver I Single-Chip
Network Element Predict microstructure,
properties, and performance of multi-layer
designs at or near atomic dimensions. Driver II
Collaborative Node (System-on-a-Chip) Predict
microstructure, properties, and performance of
heterogeneous interfaces (opto/CMOS and
RF/CMOS). Driver III Interconnect
Nanotechnology Predict microstructure,
properties, and determine performance of proposed
novel materials, processes, structures etc. for
rapid evaluation and selection.