This paper describes the alternating-direction implicit finite-difference time-domain (ADI-FDTD) method for physical modeling of high-frequency semiconductor devices. The model contains the semiconductor equations in conjunction with the Maxwell's equations which describe the complete behavior of high-frequency active devices. Using ADI approach leads to a significant reduction of the full-wave simulation time. We can reach over 99% reduction in the simulation time by using this technique while still have a good degree of accuracy compared to the conventional approaches. As the first step in the performance investigation, we use the electrons flow equations in the absence of holes and recombination as semiconductor equations in this paper.
2. Afrooz, K., A. Abdipour, A. Tavakoli, and M. Movahhedi, "Time domain analysis of active transmission line using FDTD technique (application to microwave/MM-wave transistors)," Progress In Electromagnetics Research, Vol. 77, 309-328, 2007.
3. Alsunaidi, M. A., S. M. S. Imtiaz, and S. M. El-Ghazaly, "Electromagnetic wave effects on microwave transistors using a full-wave time-domain model," IEEE Trans. Microw. Theory Tech., Vol. 44, No. 6, 799-808, Jun. 1996.
4. Feng, Y. K. and A. Hintz, "Simulation of sub-micrometer GaAs MESFET's using a full dynamic transport model," IEEE Trans. Electron Devices, Vol. 35, 1419-1431, Sep. 1988.
5. Li, Z.-M., "Two-dimensional numerical simulation of semiconductor lasers," Progress In Electromagnetics Research, Vol. 11, 301-344, 1995.
6. Liu, Q. H., C. Cheng, and H. Z. Massoud, "The spectral grid method: A novel fast SchrÄodinger-equation solver for semiconductor nanodevice simulation," IEEE Trans. Computeraided Design Integ. Circuit Sys., Vol. 23, No. 8, Aug. 2004.
7. Cheng, C., J.-H. Lee, K. H. Lim, H. Z. Massoud, and Q. H. Liu, "3D quantum transport solver based on the perfectly matched layer and spectral element methods for the simulation of semiconductor nanodevices," Journal of Comput. Physics, Vol. 227, No. 1, 455-471, Nov. 2007.
8. Namiki, T., "3-D ADI-FDTD method --- Unconditionally stable time-domain algorithm for solving full vector Maxwell's equations," IEEE Trans. Microw. Theory Tech., Vol. 48, No. 10, 1743-1748, Oct. 2000.
9. Zheng, F., Z. Chen, and J. Zhang, "Toward the development of a three-dimensional unconditionally stable finite-difference time-domain method ," IEEE Trans. Microw. Theory Tech., Vol. 48, No. 9, 1550-1558, Sep. 2000.
10. Kong, K. B., S. O. Park, and J. S. Kim, "Stability and numerical dispersion of 3-D Simplified sampling biorthogonal adi method," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 1, 1-12, 2010.
11. 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.
12. Movahhedi, M. and A. Abdipour, "Efficient numerical methods for simulation of high-frequency active devices," IEEE Trans. Microw. Theory Tech., Vol. 54, No. 6, 2636-2645, Jun. 2006.
13. Cangellaris, A. C. and R. Lee, "On the accuracy of numerical wave simulations based on finite methods," Journal of Electromagnetic Waves and Applications, Vol. 6, No. 12, 1635-1653, 1992.
14. Castillo, S. and S. Omick, "Suppression of dispersion in FDTD solutions of Maxwell's equations," Journal of Electromagnetic Waves and Applications, Vol. 8, No. 9-10, 1193-1221, 1994.
15. Garcia, S. G., F. Costen, M. F. Pantojal, A. Brown, and A. R. Bretones, "Open issues in unconditionally stable schemes," Progress In Electromagnetics Research Symposium Abstracts, Vol. 841, Beijing, 2009.
16. Kung, F. and H. T. Chuah, "Stability of classical finite-difference time-domain (FDTD) formulation with nonlinear elements --- A new perspective," Journal of Electromagnetic Waves and Applications, Vol. 17, No. 9, 1313-1314, 2003.
17. Liang, F. and G. Wang, "Fourth-order locally one-dimensional FDTD method," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 14-15, 2035-2043, 2008.
18. Zhou, X. and H. Tan, "Monte Carlo formulation of field-dependent mobility for AIxGa1-xAs," Solid-Sate Electronics, Vol. 38, 567-569, 1994.
19. Morton, K. W. and D. F. Mayers, Numerical Solution of Partial Differential Equations, 2nd Ed., University Press, New York, Cambridge, 2005.
20. Bau III, D. and L. N. Trefethen, "Numerical linear algebra," Philadelphia: Society for Industrial and Applied Mathematics, 1997.
21. Tomizawa, K., Numerical Simulation of Submicron Semiconductor Devices, Artech House, Norwood, MA, 1993.
22. Sun, G. and C. Trueman, "A simple method to determine the time-step size to achieve a desired dispersion accuracy in ADI-FDTD," Microw. Optic. Tech. Lett., Vol. 40, No. 6, Mar. 2004.
23. Hussein, Y. A. and S. M. El-Ghazaly, "Extending multiresolution timedomain (MRTD) technique to the simulation of high-frequency active devices," IEEE Trans. Microw. Theory Tech., Vol. 51, No. 7, 1842-1851, Jul. 2003.