Resistance extraction All these methods calculate dc resistance a Suitable for analysis of local interconnects, or analysis under lower frequency a High frequency: R of simple geometry estimated with skin depth; R of complex geometry extracted along with L ■ Reference a W. Kao, C-Y LO, M. Basel and R. Singh, "Parasitic extraction Current state of the art and future trends proceedings of eee, vol 89,pp.729-739,2001 a Xiren Wang, Deyan Liu, Wenjian Yu and Zeyi Wang, "Improved boundary element method for fast 3-D interconnect resistance extraction, "IEICE Trans. on Electronics, Vol. E88-C, No. 2, pp 232- 240.Feb.2005 16
16 ◼ All these methods calculate DC resistance Suitable for analysis of local interconnects, or analysis under lower frequency High frequency: R of simple geometry estimated with skin depth; R of complex geometry extracted along with L ◼ Reference W. Kao, C-Y. Lo, M. Basel and R. Singh, “Parasitic extraction: Current state of the art and future trends, ” Proceedings of IEEE, vol. 89, pp. 729-739, 2001. Xiren Wang, Deyan Liu, Wenjian Yu and Zeyi Wang, "Improved boundary element method for fast 3-D interconnect resistance extraction," IEICE Trans. on Electronics, Vol. E88-C, No.2, pp.232- 240, Feb. 2005. Resistance extraction
Capacitance Eⅹ traction
17 Capacitance Extraction
Outline Introduction to parasitic extraction Resistance extraction a Capacitance extraction a Fundamentals and survey a Volume discretization method a Boundary element method 口 Future issues Inductance and rlc extraction 18
18 Outline ◼ Introduction to parasitic extraction ◼ Resistance extraction ◼ Capacitance extraction Fundamentals and survey Volume discretization method Boundary element method Future issues ◼ Inductance and RLC extraction
Capacitance extraction ■Prob| em formulation D A parallel-plate capacitor tage:V=的-n Q andQ are induced on both plates Q is proportional to v The ratio is defined as c: C=Q/V If the dimension of the plate is large compared with spacing d, C-.s =8.85×1012C2/N.m2 47×9×10 a other familiar capacitors interdigital capacitor coaxial capacitor 19
19 ◼ Problem formulation A parallel-plate capacitor ◼ Voltage: ◼ Q and –Q are induced on both plates; Q is proportional to V ◼ The ratio is defined as C: C=Q/V ◼ If the dimension of the plate is large compared with spacing d, Other familiar capacitors Capacitance extraction V = − 1 2 coaxial capacitor interdigital capacitor
Capacitance extraction ■Prob| em formulation a Capacitance exists anywhere a Single conductor can have capacitance a Conductor sphere C=4丌EnR D N-conductor system, capacitance matrix is defined [q[g=∑U master conductor. 1V t1) Coupling capacitance ii Total capacitance Electric potential grounded substrate 20
20 ◼ Problem formulation Capacitance exists anywhere ! Single conductor can have capacitance ◼ Conductor sphere N-conductor system, capacitance matrix is defined: Capacitance extraction Coupling capacitance Total capacitance Electric potential Q C U =