volume | PIER Journals

Abstract

We present an empirical mixing model for rectangular cuboid metal inclusions in a host dielectric, suitable for replacing the detailed structure of a layer of on-chip interconnects with a homogeneous dielectric slab. Such an approximation is required to facilitate the accurate and efficient package-level electromagnetic modelling of complicated miniaturised systems, such as System-in-Package. Without such an approach, the direct inclusion of large areas of on-chip interconnect structures often results in intractable computation times. Our model allows us to predict the reflection (transmission) coefficient of impinging plane waves to within 3.5% (0.2%) error for incident angles up to 30^o off-normal, aspect ratios 0.6-3, metal fill factors 0.3-0.6, and host dielectric constants 1-11.7, over the frequency range 1-10 GHz.

1. Stefanski, T. M. and T. D. Drysdale, "Parallel implementation of the ADI-FDTD method," Microwave Opt. Technol. Lett., Vol. 51, No. 5, 1298-1304, 2009.
doi:10.1002/mop.24310

2. Choi , J., M. Swaminathan, B. Beker, and R. Master, "Modeling of realistic on-chip power grid using FDTD method," Proc. IEEE Int. Sym. Electromagnetic Compatibility, Vol. 1, 238-243, 2002.

3. Fontanelly , A., "System-in-Package technology: Opportunities and challenges," Proc. IEEE 9th International Symposium on Quality Electronic Design (ISQED'08), 589-593, 2008.
doi:10.1109/ISQED.2008.4479803

4. Sham , M. L., Y. C. Chen, J. R. Leung, and T. Chung, "Challenges and opportunities in system-in-package business," Proc. IEEE 7th International Conference on Electronics Packaging Technology (ICEPT'06), 1-5, 2006.
doi:10.1109/ICEPT.2006.359838

5. Trigas, C., "Design challenges for system-in-package vs system-on-chip," Proc. IEEE Custom Integrated Circuit Conference (CICC'03), 663-666, 2003.

6. Karkkainen, K., A. Sihvola, and K. Nikoskinen, "Analysis of three-dimensional dielectric mixture with finite difference method," IEEE Trans. Geosci. Remote Sensing, Vol. 39, No. 5, 1013-1018, 2001.
doi:10.1109/36.921419

7. Chylek, P. and V. Srivastava, "Effective dielectric constant of a metal-dielectric composite," Phys. Rev. B, Vol. 30, No. 2, 1008-1009, 1984.
doi:10.1103/PhysRevB.30.1008

8. Sihvola, A., Electromagnetic Mixing Formulas and Applications, IEE Publishing, London, UK, 1999.
doi:10.1049/PBEW047E

9. Lakshminarayann, S., P. J. Wright, and J. Pallinti, "Design rule methodology to improve the manufacturability of the copper CMP process," Proc. IEEE International Interconnect Technology Conference (IITC'02), 99-102, 2002.
doi:10.1109/IITC.2002.1014900

10. Zarkesh-Ha, P., S. Lakshminarayann, K. Doniger, W. Loch, and P. J. Wright, "Impact of interconnect pattern density information on a 90nm technology ASIC design flow," Proc. IEEE 4th International Symposium on Quality Electronic Design (ISQED'03), 405-409, 2003.

11. International Technology Roadmap for Semiconductors, Interconnect and Edition 2007, , http://www.itrs.net/.

12. Rytov, S. M., "Electromagnetic properties of a finely stratified medium," Sov. Phys. JETP, Vol. 2, 466-475, 1956.

13. Maxwell-Garnett, J. C., "Colours in metal glasses and in metallic films," Phil. Trans. R. Soc. London, Vol. 203, 385-420, 1904.

14. Holik, , S. M. and T. D. Drysdale, "Effective medium approximation for electromagnetic compatibility analysis of integrated circuits," Proc. 2nd International Congress on Advanced Electromagnetic Materials in Microwaves and Optics, 413-415, 2008.

15. Holik, S. M. and T. D. Drysdale, "Simplified model of a layer of interconnects under a spiral inductor," Journal of Electromagnetic Analysis and Applications, Vol. 3, No. 6, 187-190, 2011.
doi:10.4236/jemaa.2011.36031

16. Holik , S. M. and T. D. Drysdale, "Simplified model for on-chip interconnects in electromagnetic modelling of system-in-package," Proc. 12th International Conference on Electromagnetics in Advanced Applications, 541-544, 2010.
doi:10.1109/ICEAA.2010.5653910

17. GSolver5.1, Grating Solver Development Company Co., , http://www.gsolver.com/.

18. Pendry, J. B., A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic masostructures," Phys. Rev. Lett., Vol. 76, No. 25, 4773-4776, 1996.
doi:10.1103/PhysRevLett.76.4773

19. Born, M. and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th Ed., Cambridge University Press, Cambridge, UK, 1999.

20. Rouf, H. K., F. Costen, S. G. Garcia, and S. Fujino, "On the solution of 3-D frequency dependent Crank-Nicolson FDTD scheme," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 16, 2163-2175, 2009.
doi:10.1163/156939309790109261

21. Sullivan , D. M., "Frequency-dependent FDTD methods using Z-transform," IEEE Trans. Antennas Propagat., Vol. 40, No. 10, 1223-1230, 1992.
doi:10.1109/8.182455

22. Collin, , S., F. Pardo, R. Teissier, and J. L. Pelouard, "Horizontal and vertical surface resonances in transmission metallic gratings," J. Opt. A: Pure Appl. Opt., Vol. 4, 154-160, 2002.
doi:10.1088/1464-4258/4/5/364

23. Pilozzi, L., A. D'Andrea, and H. Fenniche, "Mirror effect at the Brewster angle in semiconductor rectangular gratings," Phys. Rev. B, Vol. 64, 235319-1-8, 2001.

24. Barbara, A., P. Quemerais, E. Bustarret, T. Lopez-Rios, and T. Fournier, "Electromagnetic resonances of sub-wavelength rectangular metallic gratings," Eur. Phys. J. D, Vol. 23, 143-154, 2003.
doi:10.1140/epjd/e2003-00025-9

Dr. Sonia M. Holik

Prof. John M. Arnold

Dr. Timothy David Drysdale