1. Nelson Applied Research, Inc. 2142 – N. 88 th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com Study of Heat Flux in a Thin Silicon MEMS Wafer with Coolant and Air Filled Regions A Finite Element Model (FEA) using flexPDE Craig E. Nelson - Consultant Engineer

2. Nelson Applied Research, Inc. 2142 – N. 88 th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com Goal for the Numerical Study A steady state finite element model is to be developed that aids understanding of heat flux within a silicon MEMS wafer. Heat is produced in a rectangular, constant intensity (power per unit area), source region. The heat then diffuses into the surrounding silicon regions and is carried away by cooling fluid flowing in rectangular passageways. Quadrant symmetry will be used to reduce the solution domain complexity.

3. Nelson Applied Research, Inc. 2142 – N. 88 th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com Model Geometry

4. Nelson Applied Research, Inc. 2142 – N. 88 th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com Model Geometry Air Boundary Symmetry Boundary Heat Source Region Air Filled Region Coolant Filled Region

5. Nelson Applied Research, Inc. 2142 – N. 88 th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com Numerical Solution Grid

6. Nelson Applied Research, Inc. 2142 – N. 88 th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com Solution Plots

7. Nelson Applied Research, Inc. 2142 – N. 88 th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com Temperature Field - Contour Plot Notice “Refraction” at boundary

8. Nelson Applied Research, Inc. 2142 – N. 88 th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com Temperature Field - Contour Plot Notice “Refraction” at boundary

9. Nelson Applied Research, Inc. 2142 – N. 88 th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com Temperature Field - Surface Plot

10. Nelson Applied Research, Inc. 2142 – N. 88 th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com Heat Flux Field - Vector Plot Region of Maximum Heat Flux

11. Nelson Applied Research, Inc. 2142 – N. 88 th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com Heat Flux Field - Vector Plot - Normalized Region of Maximum Heat Flux

12. Nelson Applied Research, Inc. 2142 – N. 88 th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com Heat Flux on Source Region Perimeter

13. Nelson Applied Research, Inc. 2142 – N. 88 th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com Summary A steady state finite element model has been developed that aids understanding of heat flux and temperature within a silicon MEMS wafer. Heat is produced in a rectangular, constant intensity (power per unit area), source region. The heat then diffuses into the surrounding silicon regions and is carried away by cooling fluid flowing in rectangular passageways. Because the thermal conductivity is different in different regions, the resultant temperature field is complex and interesting. Quadrant symmetry was used to reduce the solution domain complexity.