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Modeling and Optimization for VLSI Layout

Modeling and Optimization for VLSI Layout. Professor Lei He lhe@ee.ucla.edu http://eda.ee.ucla.edu/. Programming homework Last lecture: Placement Today: Wrap up placement Interconnect modeling Student presentation: April 29 th , Thermal modeling (by Mehul Shah)

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Modeling and Optimization for VLSI Layout

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  1. Modeling and Optimization for VLSI Layout Professor Lei He lhe@ee.ucla.edu http://eda.ee.ucla.edu/

  2. Programming homework • Last lecture: Placement • Today: • Wrap up placement • Interconnect modeling • Student presentation: • April 29th, Thermal modeling (by Mehul Shah) • May 2nd, Dynamic and leakage power modeling (Phoebe and Qun) • Read: • Three papers on interconnect modeling • Especially [Xu-He’01] (checked on May 2nd)

  3. Chapter 5 Interconnect RLC Modeling • Table and formula based capacitance extraction • Table and formula based inductance extraction • RC or RLC circuit model generation • Numeric based interconnect modeling

  4. Capacitance Extraction • Introduction • Table lookup method • Formula-based method

  5. ++ ++ - - - - What’s Capacitance? +Q -Q • Simplest model: parallel-plate capacitor • It has two parallel plates and homogeneous dielectric between them • The capacitance is •  permittivity of dielectric • A area of plate • d distance between plates • The capacitance is the capacity to store charge • charge at each plate is • one is positive, the other is negative

  6. c12 m2 m1 c23 c13 m3 General Picture • For multiple conductors of any shapes and materials, and in any dielectric, there is a capacitance between any two conductors • Mutual capacitance between m1 and m2 is C12 = q1/v2 • q1 is the charge of m1 • v1 =0 and v3 = 0

  7. c12 m2 • is the self-capacitance for a conductor • e.g., c11 =c12+c13 c11 -c12 -c13 m1 c23 -c21 c22 -c23 C = -c31 -c32 c33 c13 m3 • The charge is given by • e.g., Capacitance Matrix • Capacitance is often written as a symmetric matrix

  8. Application in VLSI Circuits • Conductors: metal wire, via, polysilicon, substrate • Dielectrics: SiO2 ,... • Total cap for a wire • delay, power • Mutual cap between wires • signal integrity

  9. Cx Cx Cx Characteristics of Coupling Capacitance • Coupling capacitance virtually exists only between adjacent wires or crossing wires • Capacitance can be pre-computed for a set of (localized) interconnect structures

  10. 2.5D Capacitance Extraction[Cong-He-Kahng-et al, DAC’97] • Propose and validate five foundations to simplify capacitance extraction • Develop a simple yet accurate 2.5D capacitance extraction

  11. 3.0 1.0 2.5 1.0 Verification of Foundations • Method: 3D analysis by FastCap [Nabors-White, TCAD’91] • Geometrical parameters: 0.18 process [NTRS’94]

  12. dummy metal Key Factor to Enable Foundations • Minimum metal density requirement • Metals occupy > 30% area on anywhere on routing layer • Foundry may introduce dummy metals for metal sparse areas

  13. Foundation IEffect of Ground and Neighbors Both ground, and neighboring wires on the same layer, have significant shielding effects. Thus, both must be considered for accurate modeling.

  14. Shielding Effect of Ground and Neighbors Ci,i Ci,i-2 layer i no GND 458.4 130.1(28.4%) layer i-2 Ci,i lumped capacitance for victim on layer i Ci,i-2 coupling between victim and aggressor on layer i-2

  15. Shielding Effect of Ground and Neighbors Ci,i Ci,i-2 layer i no GND 458.4 130.1(28.4%) + GND 486.6 79.49(16.3%) layer i-2 Ci,i lumped capacitance for victim on layer i Ci,i-2 coupling between victim and aggressor on layer i-2

  16. Shielding Effect of Ground and Neighbors Ci,i Ci,i-2 layer i no GND 458.4 130.1(28.4%) + GND 486.6 79.49(16.3%) + neighbors 1428 24.77(1.8%) layer i-2 Ci,i lumped capacitance for victim on layer i Ci,i-2 coupling between victim and aggressor on layer i-2

  17. Foundation IICoupling between Layers i and i-2 Coupling between wires on layer i and wires on layers i-2 is negligible when the metal density on layer i exceeds a certain threshold.

  18. Coupling between Layers i and i-2 layer i layer i-1 layer i-2 -- 2x 4x 8x 12x Ci,i 486.6 534.5 581.3 622.2 635.9 Ci,i-2 79.49 48.45 21.99 3.47 2.47 Ci,i lumped capacitance for victim on layer i Ci,i-2 coupling between victim and aggressor on layer i-2

  19. Foundation IIICoupling Effect of Layers i+2 and i-2 During capacitance extraction for wires on layer i, layers i+2 and i-2 can be treated as ground planes with negligible error. There is no need to look beyond layers i+2 and i-2.

  20. Coupling Effect of Layers i+2 and i-2 layer i+2 i+1 i i-1 i-2 418.9 Ci,i Ci,i+1 52.35 Ci,i-1 52.26 Ci,i lumped capacitance for victim on layer i Ci,i+1 coupling between victim and central crossover on layer i+1 Ci,i-1 coupling between victim and central crossunder on layer i-1

  21. Coupling Effect of Layers i+2 and i-2 layer i+2 i+1 i i-1 i-2 418.9 418.9 Ci,i Ci,i+1 52.35 52.59 Ci,i-1 52.26 52.53 Ci,i lumped capacitance for victim on layer i Ci,i+1 coupling between victim and central crossover on layer i+1 Ci,i-1 coupling between victim and central crossunder on layer i-1

  22. Foundation IVCoupling Effect of Neighbors Coupling analysis to wires on the same layer need only consider nearest neighbors independently, with the widths of same-layer neighbor wires having negligible effect on the coupling.

  23. Cl Cr Effect of Non-immediate Neighbors victim layer i Ci,i 1436 C l 616.6 Cr 616.5 Ci,i: lumped capacitance for victim.

  24. Cl Cr Cl Cr Effect of Non-immediate Neighbors victim victim layer i Ci,i 1436 1436(0%) C l 616.6 639.8(+3%) Cr 616.5 639.5(+3%) Ci,i: lumped capacitance for victim.

  25. victim layer i w w Effect of Neighbor Widths W 1 2 3 4 Ci,i 764.5 765.2 764.9 764.4 Ci,i varies less that 0.3% for different neighbor widths.

  26. S1 S1 2 Independence of Neighbors S2 S2 S1 S2 victim (S1,S2) (1,2) (1,3) (1,4) (1,) lhs 639.2 600.0 582.5 559.7 rhs 638.0 597.1 578.9 553.1 Ci,i differs less than 1.0%.

  27. Foundation VInteraction between Layers i-1 and i+1 The joint interaction of layers i-1 and i+1 on layer i is negligible; therefore, corrections for orthogonal crossovers and crossunders can be performed independently.

  28. couplings between victim and crossunders No crossover 36.01 37.20 36.99 37.58 Independence of Crossovers and Crossunders layer i+2 i+1 i i-1

  29. couplings between victim and crossunders No crossover 36.01 37.20 36.99 37.58 Full of crossovers Independence of Crossovers and Crossunders layer i+2 i+1 i i-1

  30. couplings between victim and crossunders No crossover 36.01 37.20 36.99 37.58 Full of crossovers 35.66 36.87 36.70 37.35 Independence of Crossovers and Crossunders layer i+2 i+1 i i-1

  31. Table-Based 2.5D Capacitance Extraction • Table (Cap coefficients) generation • One-time use of 3-D method • Capacitance computation • table lookup with linear interpolation and extrapolation

  32. layer i Table Generation for Lateral, Area and Fringe Capacitances w s s • Functions of (w,s) • Pre-computed for per-side per unit-length

  33. s sc layer i wc sc w Table Generation for Crossing Capacitances • Function of (w,s,wc,sc)

  34. Ci,i Per-corner Cover(w,s,wc,sc) = 4 Table Generation for Crossing Capacitances s s sc wc wc sc sc w w

  35. victim Compute the lumped cap for victim Illustration of Capacitance Computation

  36. Find Nearest Neighbors on Same Layer victim

  37. S1 L1 w Per-side lateral capacitance = CL(w,s1) * L1 Per-side area capacitance = CA(w,s1) * L1 Per-side fringe capacitance = CF(w,s1) * L1 • Add in Per-Side Area, Fringe and Lateral Capacitances victim

  38. Add in Per-Side Area, Fringe and Lateral Capacitances victim

  39. Find All Crossovers and Crossunders victim

  40. w One-corner crossover correction = Cover(w,S1,wc,sc) • Add in Crossing Capacitances Corner-by-Corner victim S1 wc sc

  41. w One-corner crossover correction = Cover(w,S1,wc,) • Add in Crossing Capacitances Corner-by-Corner victim S1 wc

  42. w One-corner crossover correction = Cover(w,,wc,) • Add in Crossing Capacitances Corner-by-Corner victim S1 wc

  43. w One-corner crossover correction = Cover(w,,wc,sc) • Add in Crossing Capacitances Corner-by-Corner victim wc sc

  44. Sum of capacitance components in above steps is the lumped capacitance of the victim. Summary of Capacitance Computation • Find nearest neighbors on the same layer • Add in per-side lateral, area and fringe capacitances w.r.t. each neighbor • Find all crossovers and crossunders • Add in crossing capacitances corner-by-corner w.r.t. each crossover and crossunder

  45. Experimental Results 2 1/2-D 3-D Error net1 6.53552pF 6.5713pF -0.54% net2 3152.42pF 3261.17pF -3.33% Good match in terms of lumped capacitance!

  46. Formula based on horizontal and vertical parameters • [Sakurai-Tamaru,ED’83][Wu-Wong-et al, ISCAS’96] • single line • parallel lines • …...

  47. Single Line [Sakurai-Tamaru,ED’83] w • Unit-length cap • Error less than 6% when t Ff Ff h Fp

  48. Single Line of Length L[Sakurai-Tamaru,ED’83] w • Line of length L t h

  49. Parallel Lines on Same Layer [Sakurai-Tamaru,ED’83] s w w • Unit-length cap t h • Error less than 10% when

  50. Parallel Lines on Same Layer [Wu-Wong-et al, ISCAS96] s s w w w • Unit-length cap t h • Recall [Sakurai-Tamaru,ED’83]

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