Fa st Inductance and Re sistance Extraction of 32D VLSI Interconnects Ba sed on the Method of K Element

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1 ACTA ELECTRONICA SINICA Vol. 33 No. 8 Aug K,,, (, ) : GHz,, K ( ),,,,, FastHenry : ; ; K ; ; : TN47 : A : (2005) Fa st Inductance and Re sistance Extraction of 32D VLSI Interconnects Ba sed on the Method of K Element WEI Hong2chuan, YU Wen2jian, YANG Liu,WANG Ze2yi ( Department of Computer Science and Technology, Tsinghua University, Beijing , China) Abstract : In the integrated circuits with frequency above several GHz,parasitic inductive effect has greatly influenced the cir2 cuit performance,therefore requiring efficient algorithm for extraction of frequency2dependent inductance and resistance. Based on good localization property of the K element (inverse of the partial inductance method),a fast algorithm for interconnect inductance and re2 sistance extraction is proposed in this paper. With an efficient window selection technique,filament partitioning,and two improvements on calculating filament inductance and inverting the global admittance matrix,complex structures of multilayered interconnects can be handled very well. While preserving good accuracy,the presented method exhibits about 100x speed2up over the FastHenry for some actual examples. Key words : 32D VLSI interconnect ;extraction of inductance and resistance ; K element ;high frequency ;the window technique 1, GHz., low2k,, [1,2 ].,,Ruehli PEEC(partial element equivalent circuit) [3 ],, PEEC,,.,, [4 ].,,, [5 ] Halo [6 ] Shell [7 ] (shell),., [8 ].,Devgan 2000 K [9,10 ]. K,, [10 ]., [11 ] K, 2002,, [8 ] K RKC, : ; : : 863 (No. 2004AA1Z1050) ; (No )

2 ,, [8 ] K,,,,,, MIT FastHenry [12 ] 2 K 211 K L, K L [9 ] : K = L - 1 (1) L loop = 0 0 C0-1 [9 ]., K, K, K, [8 11 ]. K : ( a) i, ( ) W i ; ( b) W i L i, i W i K, i K ( c) ( a), ( b), K K K,, RKC [10 ]. RLC, K [11 ].,, ( ( a) ) 212,. (filament),, PEEC, Y, Z. Z,, [12 ]. MIT FastHenry, [12 ]. Z = R + j L,, K = L - 1 Y = Z - 1., K, : ( a) i, ( ) W i ; ( b) W i, Z f ; ( c) i 1V, 0V, V f ; ( d) Z f I f = V f, I f ; ( e) I f, I c, I c i W i Y ( ) ; ( f) I c Y Y all, i Y ; ( g) ( a) ( f ), Y all ; ( h) Y all, Z all = Y - 1 all. Z all,, Y K,, ( a), ( b) ( h) 3,,,, ;,. [8 ],,,,.,,, (, ).,, 1 1 Y, XOY, a b c d. XOY, [8 ], x, x, X

3 8 : K 1367 ( ),. : ( a) XOY, YOZ ZOX,, i xy i XOY ( b) XOY X Y, YOZ ZOX, 6 ( c) XOY X, i, : ( i) j = i + 1, j xy i xy ; ( ii) j xy i xy, j xy i xy, j = j + 1, ; ( iii) j xy k xy, k xy i xy, k i j i, j = k, ; ( iv) j xy ( i xy, x ), j xy i xy min{ } + 1. j xy, ; ( v) ( i) ( iv), i xy, i xy s xy i xy i xy s xy, ( d) 5 ( c) i j,. 1 XOY, a,, ( ) ; b, ( iv) 1; c, d c ( ), c, d, d 1; c, d, b d, c ,, Zf,, [10 ] : L ij = l i l j dv 4 a i a j Vi Vj r i - r j j dv i (2), V i V j i j, a i a j, l i l j, r i r j i j, A B, A B (2), A B C D, A B C D, ( 2). A B C D,, FastHenry, 9, 6, 3.,, 9,, 9,, (2),,,.,,,, 3, D1 D2 D3 D4 C, 2 2 (2), C D1, D2 D3 D4 ( 3 ).,,,,.,,.,, 6,

4 , 3, 4 ( ). (2).,, Z f 412 Y all, Z all., ( ),, Z all, : X, Y, ( ). 5, I X, II Y, III,, Y ( 3 ), 5, I II Y,,, I II,, III. 5 FRLE(Fast Resistance and Inductance Extractor),, FastHenry, Sun Ultra V880 ( 750 MHz) 1 VLSI, 5 P/ G, 2 m, P/ G 10, 0. 4 m, 2 m, 60 m,,, 0. 8 m, P/ G 2 m. 6, X, Y, 4 m ( 6 ). 10GHz, 4 4, 6, x = , 4 FRLE, 4 FastHenry, 2 ( ),, 1 1 Y (s) FastHenry FRLE( ) FRLE( ) ( FastHenry ) < 3 % 3 % 6 % 6 % 9 % 9 % 12 %12 % 15 % > 15 % % % 9. 3 % % % % % % Y (s) FastHenry FRLE( ) FRLE( ) ( FastHenry ) < 3 % 3 % 6 % 6 % 9 % 9 % 12 % 12 % 15 % > 15 % ( ) % % % % % 0 ( ) % % % % 0 0 ( ) % % % % % 0 ( ) % % % % 0 0 1, FRLE FastHenry 100, Y,, Y,, 2 2,FRLE (, ). 2, 260, X 150, Y 30, GHz, 4 (4, 3, x = FRLE , FRLE FastHen2 ry 78, 4. 4, FRLE, 2,

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