Finite Element Analysis of the Effects of Package Induced Stress on Micromechanical Resonator Temperature Stability

......................................................................................................................................... iv Introduction ..................................................................................................................................... 1 Finite Element Analysis .................................................................................................................. 5 Static Structural analysis of the package model ......................................................................... 5 Strain on the surface of packaged die at -45 °C .......................................................................... 7 Boundary Conditions and Applied loads ................................................................................ 7 Determining resonator anchor displacement expressions ....................................................... 7 Plastic Encapsulation .............................................................................................................. 9 Die Attach ............................................................................................................................... 9 Wafer Level Bond ................................................................................................................. 10 Low Pressure Chemical Vapor Deposition (LPCVD) of Polysilicon ................................... 11 Total Lateral Deformation at -45 °C ..................................................................................... 11 Strain of packaged die across the operational temperature range ............................................. 12 Temperature dependence of resonant frequency ...................................................................... 14 Temperature Stability Results ....................................................................................................... 20 Conclusion .................................................................................................................................... 21 References ..................................................................................................................................... 25 Appendix A ................................................................................................................................... 27 Appendix B ................................................................................................................................... 28 Appendix C ................................................................................................................................... 29