ima workshop on multiscale models for surface evolution and reacting flows june 5-9, 2000 taking on...

IMA Workshop on Multiscale Models for Surface Evolution and Reacting Flows June 5-9, 2000

Taking on the Multiscale ChallengeEven Small-Scale Victories are Good

Len Borucki

Digital DNA LabMotorola, Inc.Phoenix, AZ


Why do multiscale modeling? - Perspective from semiconductor manufacturing.

Typically, tool “knobs”control tool physics on the~0.1-1 meter scale

0.2 m

However, the goal is to controlan outcome at the micron scale orbelow over a wide area of the wafer.

0.1 m

Deposited Filmwafer

Tools are expensive, so optimizing their use is important.

T Merchant


Several spatial scales may be involved.

Equipment or Wafer ScaleDie (Chip) Scale

Feature Scale

~1 cm

Differences in feature packing densities within a die or across a wafer may affect local feature scale uniformitydue to depletion of reactants or other effects related to feature density.


Starting at the atomic level, the goal of modeling may be to predict structureand properties at much larger length and time scales. There are huge gaps.

~10-10 m and ~10-12 secFilm precursors.Gas phase and surfacechemistry.

A. Korkin, N. Tanpipat

Film nucleation, growth, grainstructure and transport properties.

~10-9 - ~10-5 m and ~102 sec

VoidNucleation

C-L Liu

D. Richards

MetalLifetime

~10-4 - ~10-3 m and ~104 - ~108 sec

Electronic properties

Film thickness ~10-9-~10-8 m


Challenge: Film Nucleation, Growth

Source: J. Zhang, J. Adams, Arizona State UniversitySee http://ceaspub.eas.asu.edu/cms/

Facet growth during physical vapordeposition with surface diffusion. KLMC.

Activation energies for diffusion along andbetween facets. Embedded atom method.

Grain Nucleation (FCC nuclei with {100}, {111} or {110} facets, randomly rotated and cut)

Grain growthfor an isotropicor unidirectionalsource. Stringalgorithm, not alevel set method.

Isotropic Source


Challenge: Calculation of properties of polycrystalline structures.


Calculating transport properties of large polycrystalline structures - an example.

tf = e−βv

D(v)dv

0

1

where β = l /l c

D

Aj

x

Di =Dg +m?(δ /W) ? Dgb?sin(ϑ j / 2) ?cos(Aj)( )j=1

Ngbi

Tilt AngleW=Line Width

δ = Grain Boundary Width

This very simplemodel produces afairly convincingstatistical failuretime distribution.

IMA Workshop on Multiscale Models for Surface Evolution and Reacting Flows June 5-9, 2000IMA Workshop on Multiscale Models for Surface Evolution and Reacting Flows June 5-9, 2000

Joule Heating in a Snake


A Different Reacting Flow Multiscale Problem: Chemical-Mechanical Polishing

Figure 1: Idealized model of a single wafer CMP tool. The polishing platen,wafer carrier, and conditioning tool rotate at independent rates while the carrierand conditioner oscillate radially over the pad surface. A thin, elastic carrier film(not shown) is sometimes used between the wafer and wafer carrier. A soft pad(Suba pad) may also be inserted between the polishing pad and the platen.

ωP

Table (Platen)

Pad

Slurry

Wafer

Wafer Carrier

ωw

Force Fw

d (t)w

rw

d (t)c

Conditioner

rc

Force Fcωc

A chemically reactive slurrycontaining ~0.1 m particles is sprayed on a rotatingpolyurethane pad in front ofa rotating wafer. The slurryattacks the surface layer on thewafer, allowing the particlesto more easily abrade andsmooth the layer.


The polyurethane pad containsnumerous voids averaging ~30microns in diameter.

Voids exposed at the surface fill with slurry. The slurrylayer is very thin in highly compressed areas betweenthe voids. Slurry particles probably contact the waferin these compressed regions.

Chemical-Mechanical Polishing


Somehow, this surface structure plays arole in the details of the development ofsuction fluid pressure under the wafer.

The suction pressure may in turn affect theuniformity of the removal rate on the waferscale.

Shan, Georgia Tech

Chemical-Mechanical Polishing

Question: How to describe the pad surface and utilize the information in a model with alonger length scale; eg. the Reynolds equation?


Summary

Multiscale models either Start at equipment scale and connect with the feature scale. Start at the atomic level and progress toward longer length and time scales.

Very significant gaps exist, for example, Modeling of nucleation and growth of polycrystalline films, particularly in 3D and with topography. Prediction of properties of polycrystalline materials. Better mathematical and numerical methods.

ima workshop on multiscale models for surface evolution and reacting flows june 5-9, 2000 taking on...

Documents