MEMS Heat Transfer Arnoldi-based Macromodels and the Study of Minimum Required Orders

Yao-Joe Yang; Che-Chia Yu; K.-Y.  Shen

doi:10.6180/jase.2005.8.3.01

MEMS Heat Transfer Arnoldi-based Macromodels and the Study of Minimum Required Orders

Mechanical Engineering

Yao-Joe Yang ¹, Che-Chia Yu¹ and K.-Y. Shen¹

¹Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 106, R.O.C.

Received: February 17, 2005
Accepted: April 25, 2005
Publication Date: September 1, 2005

Download Citation: ||https://doi.org/10.6180/jase.2005.8.3.01

ABSTRACT

In this work, a model order reduction (MOR) technique for heat-transfer system-level modeling is presented. A heat transfer solver using the finite difference method (FDM), which is appropriate for MEMS thermal analysis, is implemented. The numerical models generated by the FDM solver then were successfully reduced into low-order compact models by an Arnoldi-based model-order-reduction technique. The compact macromodels can be easily inserted into system-level or circuit simulators. We have demonstrated that the macromodel results for a thermal actuator are in good agreement with the experimental results. We also use the same technique on periodic surface heat flux problems to observe the relationship between frequency and minimum required order of the reduced model under specific error tolerance.

Keywords: MEMS, Model Order Reduction, Heat Transfer, Arnoldi Algorithm, Macromodel

REFERENCES

[1] Senturia, S. D., Microsystem Design, Kluwer Academic Publishers (2001).
[2] Wang, F. and White, J., “Automatic Model Order Reduction of a Microdevice Using the Arnoldi Approach,” International Mechanical Engineering Congress and Exposition, Anaheim, CA, U.S.A., pp. 527530 (1998).
[3] Odabasioglu, A., Celik, M. and Pileggi, L. T., “PRIMA: Passive Reduced-Order Interconnect Macromodeling Algorithm” IEEE Transaction on ComputerAided Design of Integrated Circuits and Systems, Vol. 17(8), pp. 645654 (1998).
[4] Yang, Y.-J., Kamon, M., Rabinovich, V. L., Ghaddar, C., Deshpande, M., Greiner, K. and Gilbert, J. R., “Modeling Gas Damping and Spring Phenomena In MEMS With Frequency Dependent Macro-Models,” in Proc. IEEE Microelectromech. Syst., Interlaken, Switzerland, pp. 365368 (2001).
[5] Yang, Y.-J. and Yu, C.-C., “Extraction of Heat-transfer Macromodels for MEMS Devices,” Journal of Micromechanics and Microengineering, Vol. 14, pp. 587596 (2004).
[6] Rudyni, E. B. and Korvink, J. G., “Review: Automatic Model Reduction for Transient Simulation of MEMSbased Devices,” Sensors Update, Vol. 11, pp. 333 (2002).
[7] Bechtold, T., Rudnyi, E. B. and Korvink, J. G., “Automatic Generation of Compact Electro-thermal Models for Semiconductor Devices,” IEICE Transactions on Electronics, Vol. E86C, N3, pp. 459465 (2003).
[8] Mills, A. F., Heat Transfer, Richard D. IRWIN, Inc., (1992).
[9] Iserles, A., A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press (1996).
[10] MUMPS Design Handbook, Cronos, Inc. (1999).
[11] Huang, Q. A. and Lee, N. K. S., “Analysis and Design of Polysilicon Thermal Flexure Actuator,” Journal of Micromechanics and Microengineering, Vol. 9, pp. 6470 (1999).
[12] Butler, J. T., Bright, V. M. and Cowan, W. D., “Average Power Control and Positioning of Polysilicon Thermal Actuators,” Sensors and Actuators, Vol. 72(1), pp. 88 97 (1999).