Taking on the Multiscale Challenge Even Small-Scale Victories are Good Len Borucki Digital DNA Lab

1. Taking on the Multiscale Challenge Even Small-Scale Victories are Good Len Borucki Digital DNA Lab Motorola, Inc. Phoenix, AZ

2. Why do multiscale modeling? - Perspective from semiconductor manufacturing. 0.2 m 0.1 mm wafer Deposited Film TMerchant Typically, tool “knobs” control tool physics on the ~0.1-1 meter scale However, the goal is to control an outcome at the micron scale or below over a wide area of the wafer. Tools are expensive, so optimizing their use is important.

3. Several spatial scales may be involved. ~1 cm Equipment or Wafer Scale Die (Chip) Scale Feature Scale Differences in feature packing densities within a die or across a wafer may affect local feature scale uniformity due to depletion of reactants or other effects related to feature density.

4. Tushar three scale slide

5. Tushar results slide

7. Starting at the atomic level, the goal of modeling may be to predict structure and properties at much larger length and time scales. There are huge gaps. Electronic properties Void Nucleation Film thickness ~10-9-~10-8 m D. Richards A. Korkin, N. Tanpipat ~10-10 m and ~10-12 sec Film precursors. Gas phase and surface chemistry. Metal Lifetime C-L Liu Film nucleation, growth, grain structure and transport properties. ~10-9 - ~10-5 m and ~102 sec ~10-4 - ~10-3 m and ~104 - ~108 sec

8. Facet growth during physical vapor deposition with surface diffusion. KLMC. Activation energies for diffusion along and between facets. Embedded atom method. Challenge: Film Nucleation, Growth Grain Nucleation (FCC nuclei with {100}, {111} or {110} facets, randomly rotated and cut) Isotropic Source Grain growth for an isotropic or unidirectional source. String algorithm, not a level set method. Source: J. Zhang, J. Adams, Arizona State University See http://ceaspub.eas.asu.edu/cms/

9. Challenge: Calculation of properties of polycrystalline structures.

10. = Grain Boundary Width Tilt Angle W=Line Width j A D x Calculating transport properties of large polycrystalline structures - an example. This very simple model produces a fairly convincing statistical failure time distribution.

11. Mesh with embedded network.

12. Numerical method for FE mesh with embedded network.

13. Joule Heating in a Snake IMA Workshop on Multiscale Models for Surface Evolution and Reacting Flows June 5-9, 2000

14. A Different Reacting Flow Multiscale Problem: Chemical-Mechanical Polishing A chemically reactive slurry containing ~0.1 mm particles is sprayed on a rotating polyurethane pad in front of a rotating wafer. The slurry attacks the surface layer on the wafer, allowing the particles to more easily abrade and smooth the layer.

15. Chemical-Mechanical Polishing The polyurethane pad contains numerous voids averaging ~30 microns in diameter. Voids exposed at the surface fill with slurry. The slurry layer is very thin in highly compressed areas between the voids. Slurry particles probably contact the wafer in these compressed regions.

16. Chemical-Mechanical Polishing Shan, Georgia Tech Somehow, this surface structure plays a role in the details of the development of suction fluid pressure under the wafer. The suction pressure may in turn affect the uniformity of the removal rate on the wafer scale. Question: How to describe the pad surface and utilize the information in a model with a longer length scale; eg. the Reynolds equation?

17. 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.