Pattern Dependent Modeling of Polymer Microfluidics Manufacturing Processes Duane Boning and Hayden Taylor Microsystems Technology Laboratories Electrical Engineering and Computer Science Massachusetts Institute of Technology October 24, 2007 2 Spatial Variation in MEMS Processes Wafer Scale Chip/Part Scale Feature Scale 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 3 wafer in cross-section device/die spatial variation wafer/chamber-scale inter- and intra- device ion and radical flux distribution competition for reactants; diffusion aspect ratio- dependent etching (ARDE) wafer- level loading feature-scale Previous Work: Variation in DRIE 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 5 Hot Micro- and Nano-Embossing To choose an optimal process, we need to assign values to Heat Time Load and temperature are constrained by Equipment Stamp and substrate properties t load t hold load temperature Glass transition temperature time stamp polymer 6 6 Hot Micro-Embossing Compared to Nanoimprint Lithography stamp stiff substrate polymer typ. 10 microntyp. 100 nm polymer Sub-micrometer features Chou et al Appl. Phys. Lett. 67(21): 3114 (1995) Micro-embossingNano-imprint 7 PMMA: A Typical Embossing Material Near T g : elasto-plastic ~ 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 8 PMMA in Compression N.M. Ames, Ph.D. thesis, MIT, 2007 9 9 PMMA in Compression, 140 C using model of N.M. Ames, Ph.D. thesis, MIT, 2007 Unload above T G Unload below T G 10 PMMA in Compression using model of N.M. Ames, Ph.D. thesis, MIT, 2007 Compare this ratio, P/Q, to the Deborah number, t material /t load 11 Starting Point: Linear-Elastic Material Model 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 E(T) 12 Response of Material to Unit Pressure at One Location radius, r w General load response: Response to unit pressure in a single element of the mesh: x 1,y 1 x 2,y 2 Unit pressure here F i,j defined here Point load response wr = constant load 13 1-D Verification of Approach for PMMA at 130 C Extracted Youngs modulus ~ 5 MPa 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 14 2-D Characterization Test Pattern stamp cavity protrusion 15 2-D Linear-Elastic Model Succeeds with PMMA at 125 C Lateral position (mm) Topography (micron) 0 15 m Simulation Thick, linear-elastic material model Experimental data 1 mm Si stamp cavity protrusion 16 Linear-Elastic Model Succeeds at 125 C, p ave = 0.5 MPa stamp penetration w p polymer 17 Linear-Elastic Model Succeeds at 125 C, p ave = 1 MPa Features filled, 1MPa 18 Linear-Elastic Model Succeeds Below Yielding at Other Temperatures 19 Extracted PMMA Youngs Moduli from 110 to 140 C 20 Material Flows Under an Average Pressure of 8 MPa at 110 C stamp polymer 21 Scaling Point Load Response Function for Flow 22 Time-Stepped Simulation of Flow stamp polymer stamp polymer stamp polymer stamp polymer t = 0t = tt = 2tt = 3t stamp polymer t = nt 23 2-D Characterization Test Pattern cavity protrusion 24 Scaling Point Load Response Function for Flow 25 Scaling Point Load Response Function for Flow 26 Scaling Point Load Response Function for Flow 27 Yielding at 110 C Simple estimates of strain rate: N.M. Ames, Ph.D. Thesis, MIT, 2007 stamp polymer w penetration to during loading to during hold Local contact pressure at feature corners > 8 MPa 28 Modeling Combined Elastic/Plastic Behavior Compressive stress Compressive strain 0.4 Yield stress Plastic flow De > 1De ~ 1 Consider plastic deformation instantaneous Consider flow to be measurable but not to modify the pressure distribution substantially during hold Deborah number De = t material /t load, hold 29 Modeling Combined Elastic/Plastic Behavior Plastic flow De > 1De ~ 1 fpfp radius Tuned to represent cases from capillary filling to non-slip Poiseuille flow Existing linear-elastic component Material compressed Elastic: E(T) Plastic flow fefe radius Volume conserved 30 Embossing Simulation: Thin Layers Rowland et al., JVST B 23 p.2958 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 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)