Mesostructure Evolution: Multiscale Process and Materials Modeling in Microelectronics

Transcription

1 Mesostructure : Multiscale and Materials Modeling in Microelectronics Timothy S. Cale School of Materials, Arizona State University timothy.cale@gmail.com

2 Goals Show results of two multiscale modeling (6 or 7 orders of magnitude in space) efforts Concurrent solutions at all scales Goal is to relate equipment setpoints to responses Summarize our efforts on grain-focused models for polycrystalline films Structures at the mesoscale exist in many areas Our work focuses on allowing you to use your process models to evolve meso-structures

3 Multiscale Model for CVD Focus on transport and chemical reactions SiO 2 CVD from TEOS Keys: Homogenization (M. Gobbert) and EVOLVE (T. Cale) Reactant mixture inlet Wafer surface To pumps Homogeneous Reactions SiE 4 Si(OH)E 3 + C 2 H 4 SiE 4 + H 2 O Si(OH)E 3 + C 2 H 5 OH SiE 4 + Si(OH)E 3 O(SiE 3 ) 2 + C 2 H 5 OH 2Si(OH)E 3 O(SiE 3 ) 2 + H 2 O Susceptor Heterogeneous Reactions SiE 4 + SiG 3 (OH) SiO 2 (D) + SiGE 3 + C 2 H 5 OH SiGE 3 SiG 3 (OH) + C 2 H 4 SiG(OH)E 2 SiG(OH) 2 E + C 2 H 4 SiGE 3 SiG(OH)E 2 + C 2 H 4 SiG(OH) 2 E SiG 3 (OH) + C 2 H 5 OH SiG(OH)E 2 SiGE 3 + C 2 H 5 OH SiG(OH) 2 E SiG 3 E + H 2 O Si(OH)E 3 + SiG 3 (OH) SiO 2 (D) + H 2 O + SiGE 3 To pumps At the equipment, or wafer, scale - solved the continuum transport and reaction model using FIDAP (finite diff.) At the pattern, or die scale, solved the continuum transport and reaction model equations using FIDAP (interfaced with the larger scale through BCs) At the feature (micron then, sub-micron now) scale, solved the free molecular flow and reaction model using EVOLVE (in-house code) Homogenization (here) basically converts rough surfaces to flux-equiv. flat surfaces Gobbert et al., JECS 144, 3945 (1997); Merchant et al., TSF 365, (2000)

4 Multiscale Model for CVD Triethoxysilanol (red high, blue low) Grids: Coupled through BCs ~1 m ~1 m FIDAP ~100 ~100 mm mm FIDAP ~0.1 mm EVOLVE for line-of-sight transport nd complex chemical reactions (no mesh - Growth rate depends on position through triethoxysilanol flux

5 Multiscale Model for CMP Focus on mechanical and fluid modeling local forces needed Keys: Greenwood-Williamson (ME toolbox) and elastohydrodynamics (J. Tichy) Down Force Ball Joint Polish Pad Wafer Carrier Slurry Asperities & Abrasives Wafer (ANSYS) w c Asperity (ANSYS) Carrier Film Abrasive (In house) Wafer w p Contact Interface Platen Unpatterned wafers Kim et al., JECS 150(9), 570 (2003); Seok et al., Wear 254, 307 (2003); Wear 257, 496 (2004);

6 Multiscale Model for CMP Wafer: Tool design, setpoints, pad properties wafer Asperity: Asperity properties, contact area/force (asperity flipped vertically) pad Abrasive: Removal model, Abrasive info, slurry info Fluid flow Pad compression Wafer flexion (ANSYS) Asperity statistics GW homogenization Asperity compression (ANSYS) Slurry drag, aging Slurry Particle Abrasive (slurry) particle statistics Material removal rate model (in-house code)

7 Multiscale Modeling (One of hundreds) Enterprise ($) Fab - VWF Module e.g., pattern transfer AMAT IBM Wafer/ Equipment Pattern/Chip Semi. Int Atomic/Discrete Island/Grain Film/Interconnect Grain Effects are needed for reliability and performance modeling part of a Virtual Wafer Fab IBM Cale, ANSYS PANEL 8/27/08

8 Drivers for a Grain-Focus Models (e.g., thermal and mechanical) that account for grain structure yield different results from those using continuum representations for many systems more common today. Atomistic models are not (yet) suitable for the spatial and time scales needed to answer many engineering questions. Grain-focused models really are needed for some studies... Current/stress induced voiding Grain boundary scattering Resistivity jumps in small lines Conducting AFM measurement G. Schneider et al., J. Vac. Sci. Technol. B 20(6), 3089 (2002). Data are for 230 nm high lines, see Steinhoegl et al. from SISPAD 2003 Bietsch and Michel, APL 80, 3346 (2002).

9 PLENTE*: A Grain-Focused Code Grain boundary-fitted (GBF) meshes are constructed each tet of the mesh belongs to only one grain or material. Each material (grain) is a distinct subdomain and is assigned material dependent properties; e.g., elastic constants, that are used in the FEM. PLENTE exchanges information with other codes (e.g., ANSYS) used for process and materials simulations. PLENTE evolves the grains in time using multiple level sets, according to the simulation results. Bloomfield et al., Phil. Mag. 83(31-34), 3549 (2003) *Parallel Level-set Environment for Nanoscale Topography (

10 3D Grain Boundary Motion Arrays of Cu lines Curvature Induced Motion SiO µm Strain Induced Motion [001] 0.1 µm <hkl> <hkl> Cu <hkl> 0.1 µm SiO µm Si 0.1 µm [100] [010] Directional dependence of Young s Modulus of Cu <100> Front view Bloomfield and Cale, Microelec. Eng. 76, 195 (2004) Bentz et al., JEM 37, (2008) Awo-Affouda et al., in 2007 SISPAD, IEEE, 2007, pp Rear view

11 One Next Step ANSYS, etc. PLENTE (Cale et al.) ~ Get info from atomistic simulations (e.g., ADEPT) during process simulations (e.g., PLENTE interfaced with ANSYS); e.g., to improve how we handle grain boundaries. Interface (code & database) ADEPT (Huang et al.) ~ VASP, etc.

12 Summary Multiscale modeling (6 or 7 orders of magnitude in space) demonstrated for a few processes. Software that evolves mesostructures is needed, and should be useful to engineers; i.e., they can use the process simulators they are already using. We have such a mesostructure -focused code; PLENTE represents and evolves interacting 3D objects using multiple level sets on tet meshes. A continuum approach to modeling materials that are structured at the mesoscale; e.g. Polycrystalline/polygranular films Voids in porous media Cells in biological systems Composite materials Provides refined targets for information from atomistic models; i.e., specific, resolved grain boundaries.