Title :
A 3-D minimum-order boundary integral equation technique to extract frequency-dependent inductance and resistance in ULSI
Author :
Fang, Shuzhou ; Wang, Zeyi ; Hong, Xianlong
Author_Institution :
Dept. of Comput. Sci. & Technol., Tsinghua Univ., Beijing, China
Abstract :
The frequency-dependent resistance and inductance can be calculated by solving an eddy current problem. In this paper, a model to describe such a 3D eddy current problem is proposed, called the 3D Omni-A model because both the conducting and nonconducting regions are described in terms of magnetic vector potential A. Therefore, the induced voltages of the conductors may appear as the unknowns directly in the boundary integral equations (BIE). Compared with popular coupled circuit methods, the computational method based on the 3D Omni-A model has two advantages. First, it does not fix the current direction along the axis of conductor, so in this method the perpendicular conductors may have mutual impedance. It could be more accurate in deep submicron (0.1 μm) chips at high speed (10 GHz). Secondly, it only discretizes the surfaces of the conductor, so it can be more efficient
Keywords :
ULSI; boundary integral equations; circuit analysis computing; eddy currents; electric current; electric resistance; inductance; integrated circuit interconnections; integrated circuit modelling; 0.1 micron; 10 GHz; 3D Omni-A model; 3D eddy current problem; 3D minimum-order boundary integral equation technique; ULSI; boundary integral equations; computational method; conducting regions; conductor surface discretization; coupled circuit methods; current direction; frequency-dependent inductance; frequency-dependent resistance; high speed chips; induced conductor voltages; magnetic vector potential; mutual impedance; nonconducting regions; perpendicular conductors; Circuits; Current density; Design automation; Eddy currents; Frequency conversion; Identity-based encryption; Impedance; Inductance; Integral equations; Voltage;
Conference_Titel :
Design Automation Conference, 2002. Proceedings of ASP-DAC 2002. 7th Asia and South Pacific and the 15th International Conference on VLSI Design. Proceedings.
Conference_Location :
Bangalore
Print_ISBN :
0-7695-1441-3
DOI :
10.1109/ASPDAC.2002.994939
