Modeling of 3-D Interconnect Line Using ADI-FDTD Method

ADI-FDTD 방법을 이용한 3차원 인터커넥트 모델링

  • Choe, Ik-Jun (Dept.of Electronics Electric Engineering, Inha University) ;
  • Kim, Yeon-Tae (Dept.of Electronics Electric Engineering, Inha University) ;
  • Won, Tae-Yeong (Dept.of Electronics Electric Engineering, Inha University)
  • 최익준 (인하대학교 전자전기공학부) ;
  • 김연태 (인하대학교 전자전기공학부) ;
  • 원태영 (인하대학교 전자전기공학부)
  • Published : 2002.08.01

Abstract

In this paper, we developed a numerical analysis model by using ADI-FDTD method to analyze three-dimensional interconnect structure. We discretized maxwell's curl equation by using ADI-FDTD. We introduced PML(Perfectly Matched Layer) absorbing boundary condition to solve the effect of the reflected wave at the interface. Evaluating the numerical model of PML and ADI-FDTD, we simulated the electric field distribution in time domain. We compare standard FDTD with ADI-FDTD, and analysis the result.

본 논문에서는 3차원 인터커넥트(3-D interconnect) 구조를 해석하기 위하여 ADI-유한차분시간영역(ADI-FDTD, Alternating Direction Implicit Finite Difference Time Domain)방법으로 맥스웰 회전방정식(Maxwell's curl equation)을 계산하는 수치 해석 모델을 개발하였다. 3차원 인터커렉트 모델내의 전자기파 문제를 해석하기 위하여 맥스웰 회전 방정식을 ADI-유한차분시간영역방법으로 이산화 하였으며, ADI-유한차분시간영역의 경계에서 발생하는 반사파를 해결하기 위하여 흡수 경계 조건인 완전 정합 층 방법(PML, Perfectly Matched Layer)을 도입하였다. 개발한 ADI-유한차분시간영역방법 및 완전 정합 층의 수치 모델을 검증하기 위하여 3차원 마이크로스트립 전송선(microstrip transmission line) 구조를 3차원 그리드(grid) 구조로 모델링한 후, 시간영역에서 전계 분포를 컴퓨터로 모의 실험하였다. 그리고 본 논문에서 제안한 ADI-유한차분시간영역방법과 종래의 스탠다드 유한차분시간영역방법의 수치적 성능을 정량적으로 비교, 분석하였다.

Keywords

References

  1. Paul C. Cherry and Magdy F. 'FDTD Analysis of High Frequency Electronic Interconnection Effects,' IEEE Trans. Microwave Theory Tech, Vol. 43, pp. 2445-2451, Oct. 1995 https://doi.org/10.1109/22.466178
  2. A.Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2 ed. Artech House, Boston, MA, 1995
  3. T. Namiki, 'A new FDTD algorithm based on alternating-direction implicit method,' IEEE Trans. on Microwave Theory and Techniques, Vol. 47, pp. 2003-2007, Oct. 1999 https://doi.org/10.1109/22.795075
  4. T. Namiki, '3-D ADI-FDTD method-Unconditionally stable time-do-main algorithm for solving full vector Maxwell's equations,' IEEE Trans. Microwave Theory Tech, Vol. 48, pp. 1743-1748, Oct. 2000 https://doi.org/10.1109/22.873904
  5. Charlie C.-P. Chen, 'Generalized FDTD-ADI: An Unconditionally Stable Full-Wave Maxwell's Equations Solver for VLSI Interconnect Modeling,' Computer Aided Design, 2000. ICCAD-2000. IEEE/ACM International Conference on 2000, pp. 156-163, Nov. 2000 https://doi.org/10.1109/ICCAD.2000.896466
  6. YuXuePing, 'Used FDTD method with PML and Mur ABC to Calculate Effective Dielectric Constant,' Asia-Pacific Conference on Environmental Electromagnetics, pp. 262-265, May. 2000 https://doi.org/10.1109/CEEM.2000.853945
  7. J.-P.Berenger, 'Perfectly Matched Layer for the FDTD Solution of Wave- Structure Interaction Problems,' IEEE Trans. on Antennas and Propagation, Vol. 44, No. 1, pp. 110-117, 1996 https://doi.org/10.1109/8.477535
  8. G. Liu and S. D. Gedney, 'Perfectly matched layer media for an unconditionally stable three-dimensional ADI-FDTD method,' IEEE Microwave Guided Wave Letters, Vol. 10, No. 7, pp. 261-263, 2000 https://doi.org/10.1109/75.856982