Spatial Variation in MEMS Processes

1. Pattern Dependent Modeling of Polymer Microfluidics Manufacturing ProcessesDuane Boning and Hayden TaylorMicrosystems Technology LaboratoriesElectrical Engineering and Computer ScienceMassachusetts Institute of TechnologyOctober 24, 2007

2. Spatial Variation in MEMS Processes • Many MEMS processes face uniformity challenges due to: • Equipment limitations • Layout or pattern dependencies • Variations often highly systematic and thus can be modeled • Models can help improve process to minimize variation • Models can help improve design to compensate for variation Wafer Scale Chip/Part Scale Feature Scale

3. Previous Work: Variation in DRIE wafer in cross-section device/‘die’ spatial variation feature-scale wafer/chamber-scale inter- and intra-device aspect ratio-dependent etching (ARDE) ion and radical flux distribution wafer-level ‘loading’ competition for reactants; diffusion F X

4. Current Focus: Hot Embossing • Goal: • Formation of surface structures in polymer or other materials • Microfluidics & other applications • Key Issue: • Embossing requires flow of displaced material: pattern dependencies Hot Embossing

5. Hot Micro- and Nano-Embossing stamp Glass transition temperature temperature load polymer time tload thold • To choose an optimal process, we need to assign values to • Heat • Time • Load and temperature are constrained by • Equipment • Stamp and substrate properties 5

6. Hot Micro-Embossing Compared toNanoimprint Lithography stamp stamp polymer stiff substrate polymer typ. 10 micron typ. 100 nm Sub-micrometer featuresChou et al Appl. Phys. Lett.67(21): 3114 (1995) Micro-embossing Nano-imprint 6

7. PMMA: A Typical Embossing Material • Near Tg: elasto-plastic • ~125-170 C: rubbery • Higher temperatures: viscous fluid Stress-strain curves for PMMA at various temperatures, strain rate 0.001/s (solid line is data; dashed line is model)Ames et al.Proc. ICOMM 2006

8. PMMA in Compression N.M. Ames, Ph.D. thesis, MIT, 2007 8

9. PMMA in Compression, 140 °C Unload below TG Unload above TG using model of N.M. Ames, Ph.D. thesis, MIT, 2007 9

10. PMMA in Compression Compare this ratio, P/Q, to the Deborah number, tmaterial/tload using model of N.M. Ames, Ph.D. thesis, MIT, 2007 10

11. Starting Point: Linear-Elastic Material Model E(T) • Embossing done at high temperature, with low elastic modulus • Deformation ‘frozen’ in place by cooling before unloading • Wish to compute deformation of a layer when embossed with an arbitrarily patterned stamp • Take discretized representations of stamp and substrate 11

12. Response of Material to Unit Pressure at One Location load radius, r General load response: Point load response wr = constant w Response to unit pressure in a single element of the mesh: Fi,j defined here x2,y2 x1,y1 Unit pressure here 12

13. 1-D Verification of Approach for PMMA at 130 °C • Iteratively find distribution of pressure consistent with stamp remaining rigid while polymer deforms • Fit elastic modulus that is consistent with observed deformations Extracted Young’s modulus ~ 5 MPa at 130 °C 13

14. 2-D Characterization Test Pattern stamp cavity protrusion 14

15. 2-D Linear-Elastic Model Succeeds with PMMA at 125 °C 1 2 3 4 Topography (micron) 6 5 8 7 Lateral position (mm) Lateral position (mm) Si stamp cavity protrusion 1 mm 15 μm Simulation 0 Thick, linear-elastic material model 1 2 3 4 5 6 7 8 Experimental data 15

16. Linear-Elastic Model Succeeds at 125 °C, pave = 0.5 MPa stamp penetration polymer w p 16

17. Linear-Elastic Model Succeeds at 125 °C, pave = 1 MPa Features filled, 1MPa 17

18. Linear-Elastic Model Succeeds Below Yielding at Other Temperatures 18

19. Extracted PMMA Young’s Moduli from 110 to 140 °C 19

20. Material Flows Under an Average Pressure of 8 MPa at 110 °C stamp polymer 20

21. Scaling Point Load Response Function for Flow 21

22. Time-Stepped Simulation of Flow stamp stamp stamp stamp polymer polymer polymer polymer stamp polymer t = 0 t = Δt t = 2Δt t = 3Δt t = nΔt 22

23. 2-D Characterization Test Pattern cavity protrusion 23

24. Scaling Point Load Response Function for Flow 24

25. Scaling Point Load Response Function for Flow 25

26. Scaling Point Load Response Function for Flow 26

27. Yielding at 110 °C stamp penetration polymer w Simple estimates of strain rate: 10-3 to 10-1 during loading 10-4 to 10-3 during hold N.M. Ames, Ph.D. Thesis, MIT, 2007 Local contact pressure at feature corners > 8 MPa 27

28. Modeling Combined Elastic/Plastic Behavior Compressive stress Yield stress Compressive strain 0.4 Plastic flow Deborah number De = tmaterial/tload, hold De << 1 De ~ 1 De >> 1 Consider plastic deformation instantaneous Consider flow to be measurable but not to modify the pressure distribution substantially during hold 28

29. Modeling Combined Elastic/Plastic Behavior Plastic flow Elastic: E(T) De << 1 De ~ 1 De >> 1 Plastic flow Existing linear-elastic component Tuned to represent cases from capillary filling to non-slip Poiseuille flow fe fp Material compressed Volume conserved radius radius 29

30. Embossing Simulation: Thin Layers Rowland et al., JVSTB 23 p.2958 30

31. Status and Future Directions – Polymer Hot Embossing Model • The merits of a linear-elastic embossing polymer model have been probed • This simulation approach completes an 800x800-element simulation in: ~ 45 s (without filling) ~ 4 min (with some filling) • Our computational approach can be extended to capture yielding and plastic flow • Is a single pressure distribution solution sufficient to model visco-elasto-plastic behaviour? • Abstract further: mesh elements containing many features 31

32. Conclusions • Spatial variation a concern in MEMS fabrication processes • Semi-empirical modeling approach developed: • Physical model basis • Process characterization for tool/layout dependencies • Applications: • Current focus: Polymer hot embossing • Deep reactive ion etch (DRIE) • Chemical-mechanical polishing (CMP)

33. Acknowledgements • Singapore-MIT Alliance (SMA) • Ciprian Iliescu and Bangtao Chen (Institute of Bioengineering and Nanotechnology, Singapore • Nici Ames, Matthew Dirckx, David Hardt, and Lallit Anand (MIT); Yee Cheong Lam (NTU)