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Parasitic Extraction

Parasitic Extraction. Luca Daniel University of California, Berkeley Massachusetts Institute of Technology with contributions from: Alessandra Nardi, University of California, Berkeley Joel Phillips, Cadence Berkeley Labs Jacob White, Massachusetts Instit. of Technology. Funct. Spec. RTL.

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Parasitic Extraction

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  1. Parasitic Extraction Luca Daniel University of California, Berkeley Massachusetts Institute of Technology with contributions from: Alessandra Nardi, University of California, Berkeley Joel Phillips, Cadence Berkeley Labs Jacob White, Massachusetts Instit. of Technology

  2. Funct. Spec RTL Behav. Simul. Stat. Wire Model Logic Synth. Gate-level Net. Front-end Gate-Lev. Sim. Floorplanning Back-end Parasitic Extrac. Place & Route Layout Conventional Design Flow

  3. Layout parasitics • Wires are not ideal. Parasitics: • Resistance • Capacitance • Inductance • Why do we care? • Impact on delay • noise • energy consumption • power distribution Picture from “Digital Integrated Circuits”, Rabaey, Chandrakasan, Nikolic

  4. Parasitic Extraction thousands of wires e.g. critical path e.g. gnd/vdd grid Parasitic Extraction • identify some ports • produce equivalent circuit that models response of wires at those ports tens of circuit elements for gate level spice simulation

  5. Electromagnetic Analysis small surface panels with constant charge thin volume filaments with constant current million of elements Model Order Reduction tens of elements Parasitic Extraction (the two steps)

  6. Overview • Setups of Parasitic Extraction Problems • Capacitance Extraction (electrostatic) • RL Extraction (MQS) • Combined RLC Extraction (EMQS) • Electromagnetic Interference Analysis (fullwave) • Electromagnetic solvers • classification (time vs. frequency, differential vs. integral) • integral equation solvers in detail • basis functions • residual minimization (collocation and Galerkin) • linear system solution • fast matrix-vector products • Example: EMQS solution • Conclusions

  7. Consider only electric field (capacitive) coupling Capacitive ExtractionExample: Intel 0.25 micron Process 5 metal layers Ti/Al - Cu/Ti/TiN Polysilicon dielectric. Taken from “Digital Integrated Circuits”, 2nd Edition, Rabaey, Chandrakasan, Nikolic

  8. Capacitive ExtractionWhy? E.g. Analysis of Delay of Critical Path

  9. R4 R2 C2 C4 Ri Ci Capacitance Extraction Why do we need it? 2 • Example: to produce RC tree network for elmore delay analysis • Example: to produce RC tree network for capacitive cross-talk analysis R1 4 1 s R3 C1 3 C3 i

  10. Capacitance ExtractionProblem Formulation • Given a collection of N conductors (of any shape and dimension) Calculate the coupling capacitance matrix C

  11. Capacitance ExtractionSolution Procedure • For i = 1 to N, • apply one volt to conductor i and ground all the others • solve the electrostatic problem and find the resulting vector of charges on all conductors • that is the i-th column of the conductance matrix

  12. Overview • Setups of Parasitic Extraction Problems • Capacitance Extraction (electrostatic) • RL Extraction (MQS) • Combined RLC Extraction (EMQS) • Electromagnetic Interference Analysis (fullwave) • Electromagnetic solvers • classification (time vs. frequency, differential vs. integral) • integral equation solvers in detail • basis functions • residual minimization (collocation and Galerkin) • linear system solution • fast matrix-vector products • Example: EMQS solution • Conclusions

  13. Inductance and Resistance ExtractionExample: IC package Picture Thanks to Coventor wire bonding lead frames IC package

  14. Inductance and Resistance ExtractionWhere do we need to account for inductance? • chip to package and package to board connections are highly inductive • inductance can create Ldi/dt noise on the gnd/vdd network • inductance can limit communication bandwidth • inductive coupling between leads or pins can introduce noise pins or solder balls from package to PCB wire bonding and lead frames or solder balls from IC to package IC package PCB on-package decoupling capacitors on-board decoupling capacitors

  15. Simple Example Inductance and Resistance Extraction Why also resistance? Skin and Proximity effects proximity effect: opposite currents in nearby conductors attract each other skin effect: high frequency currents crowd toward the surface of conductors

  16. Inductance and Resistance ExtractionSkin and Proximity effects (cont.) • Why do we care? • Skin and proximity effects change interconnect resistance and inductance • hence they affect performance (propagation delay) • and noise (magnetic coupling) • When do we care? • frequency is high enough that wire width OR thickness are less than two “skin-depths” • e.g. on PCB at and above 100MHz • e.g. on packages at above 1GHz • e.g. on-chip at and above 10GHz • note. clock at 3GHz has significant harmonics at 10GHz!!

  17. Inductance and Resistance ExtractionProblem Formulation • Given a collection of interconnected N wires of any shape and dimension • Identify the M input ports Picture by M. Chou • Calculate the MxM resistance and the inductance matrices for the ports, • that is the real and immaginary part of the impedance matrix

  18. Inductance and Resistance ExtractionSolution Procedure • Typically instead of calculating impendance we calculate the admittance matrix. • For each pair of input terminals, • apply a unit voltage source and solve magneto quasit-static problem(MQS) to calculate all terminal currents • that is one column of the admittance matrix [R+jwL]-1

  19. Overview • Setups of Parasitic Extraction Problems • Capacitance Extraction (electrostatic) • RL Extraction (MQS) • Combined RLC Extraction (EMQS) • Electromagnetic Interference Analysis (fullwave) • Electromagnetic solvers • classification (time vs. frequency, differential vs. integral) • integral equation solvers in detail • basis functions • residual minimization (collocation and Galerkin) • linear system solution • fast matrix-vector products • Example: EMQS solution • Conclusions

  20. Combined RLC ExtractionExample: current distributions on powergrid input terminals

  21. Combined RLC Extraction Example: analysis of resonances on powergrid * 3 proximity templates per cross-section - 20 non-uniform thin filaments per cross-section

  22. Combined RLC ExtractionExtraction Example: analysis of substrate coupling

  23. Combined RLC ExtractionExample: resonance of RF microinductors • At frequency of operation the current flows in the spiral and creates magnetic energy storage (it works as an inductor: GOOD) • But for higher frequencies the impedance of the parasitic capacitors is lower and current prefers to “jump” from wire to wire as displacement currents (it works as a capacitor: BAD) Picture thanks to Univ. of Pisa

  24. Combined RLC ExtractionProblem Formulation • Given a collection of interconnected N wires of any shape and dimension • Identify the M input ports Picture by M. Chou • Calculate the MxM IMPEDANCE matrix for the ports, • that is the real and immaginary part of the impedance matrix

  25. Combined RLC ExtractionSolution Procedure • Same as RL extraction. • Typically calculate admittance matrix • For each pair of input terminals, • apply a unit voltage source and solve electro-magneto quasit-static problem (EMQS) to calculate all terminal currents • that is one column of the admittance matrix [R+jwL]-1

  26. Overview • Setups of Parasitic Extraction Problems • Capacitance Extraction (electrostatic) • RL Extraction (MQS) • Combined RLC Extraction (EMQS) • Electromagnetic Interference Analysis (fullwave) • Electromagnetic solvers • classification (time vs. frequency, differential vs. integral) • integral equation solvers in detail • basis functions • residual minimization (collocation and Galerkin) • linear system solution • fast matrix-vector products • Example: EMQS solution • Conclusions

  27. IC PCB IC PCB The Electromagnetic Interference (EMI)Problem description • Electronic circuits produce and are subject to Electromagnetic Interference (EMI). • in particular when wavelengths ~ wire lengths • EMI is a problem because it can severely and randomly affect analog and digital circuit functionality!!!

  28. EMI analysisEMI at board, package and IC level • Traces on PCB can pick up EMI and transmit it to IC’s • IC’s can produce high frequency conducted emissions that can radiate from PCB’s • IC’s themselves can directly produce radiated emissions • high-frequency current loops Vdd-decap-gnd on package or inside IC’s. • high-frequency current loops inside IC (near future) • IC radiation amplified by heat sinks! IC IC PCB IC PCB

  29. EMI a problem for ICs design? • So far: dimensions too small and wavelengths too large • Trend: larger chip dies and higher frequencies • Today’s PCB: • clocks ~ 300MHz • harmonics ~ 3GHz • wavelengths ~ 10cm • dimensions ~ 10cm this gives resonances on PCB today, hence it might on IC tomorrow! • Future’s IC: • clocks ~ 3GHz • harmonics ~ 30GHz • wavelengths ~ 1cm • dimensions ~ 1cm

  30. EMI analysisSolution Procedure • Typically, EMI analysis is a two-step process: 1) determine accurate current distributions on conductors • 2) calculate radiated fields from the current distributions E

  31. Need for full-board analysis • Interconnect impedances depend on complicated return paths. • Unbalanced currents generate most of the interference. • Hence need FULL-BOARD analysis

  32. Need for full-wave analysis • Circuit dementions are not negligible compared to wavelength coupling NOT instantaneus, speed of light creates retardation Need to solve FULLWAVE equations (same as for RLC extraction plus wave term)

  33. Overview • Setups of Parasitic Extraction Problems • Capacitance Extraction (electrostatic) • RL Extraction (MQS) • Combined RLC Extraction (EMQS) • Electromagnetic Interference Analysis (fullwave) • Electromagnetic field solvers • classification (time vs. frequency, differential vs. integral) • integral equation solvers in detail • basis functions • residual minimization (collocation and Galerkin) • linear system solution • fast matrix-vector products • Example: EMQS solution • Conclusions

  34. Example: the most intuitive FDTD in one dimension using Forward Euler (easier to explain) Maxwell differential equations: In one dimension: Using forward Euler:

  35. Example: 1D-FDTD with Forward Euler (cont.) Iteration formulas: t n+1 n x m m+1

  36. Time-domain vs. frequency domain methods Time-domain methodsFrequency-domain methods can handle non-linearitiesproblems with non-linearities run a long simulation excitingsolve for specific frequency all significant modes and thenpoints of interest take an FFT can produce insightfulcan exploit new techniques animationsfor model order reduction

  37. Differential vs. Integral methods Differential methodsIntegral Methods discretize entire domain discretize only “active” regions create huge but sparse create small but dense linear systems linear systems good for inhomogeneousproblems with materialsinhomogeneous materials problems with opengood for open boundary boundary conditionsconditions

  38. Electromagnetic Solvers Classification Differential Integral Methods Methods Time-domain FDTD PEEC Methods Finite DifferencePartial Element Time DomainEquivalent Circuits Frequency-domain FEM MoM, PEEC Methods Finite Element Method of Moments Method

  39. Overview • Setups of Parasitic Extraction Problems • Capacitance Extraction (electrostatic) • RL Extraction (MQS) • Combined RLC Extraction (EMQS) • Electromagnetic Interference Analysis (fullwave) • Electromagnetic solvers • classification (time vs. frequency, differential vs. integral) • integral equation solvers in detail • basis functions • residual minimization (collocation and Galerkin) • linear system solution • fast matrix-vector products • Example: EMQS solution • Conclusions

  40. Maxwell Differential Equations • Maxwell Differential Equations can be written in terms of • the electric scalar potential • and the magnetic vector potential

  41. resistive effect magnetic coupling charge-voltage relation current and charge conservation Maxwell equations in integral formMixed potential Integral Equation (MPIE)

  42. resistive effect magnetic coupling charge-voltage relation current and charge conservation Full-wave (for EMI) vs. quasi-static EMQS (for RLC extraction) QUASI-STATIC QUASI-STATIC

  43. resistive effect magnetic coupling EMQS (for RLC extraction)vs. MQS (for RL extraction) MQS MAGNETO QUASI-STATIC charge-voltage relation current and charge conservation

  44. current and charge conservation EMQS (for RLC extraction)vs. electro-static (for capacitance extraction) ELECTRO-STATIC resistive effect magnetic coupling charge-voltage relation ELECTRO-STATIC

  45. Overview • Setups of Parasitic Extraction Problems • Capacitance Extraction (electrostatic) • RL Extraction (MQS) • Combined RLC Extraction (EMQS) • Electromagnetic Interference Analysis (fullwave) • Electromagnetic solvers • classification (time vs. frequency, differential vs. integral) • integral equation solvers in detail • basis functions • residual minimization (collocation and Galerkin) • linear system solution • fast matrix-vector products • Example: EMQS solution • Conclusions

  46. Basis Functions • Basis for vector space • Basis functions for functional vector space • Examples • exponentials • cos sin • pieacewise constant • pieacewise linear

  47. Piecewise Constant Basis Functions. E.g. Capacitance Extraction Electrostatic problem Integral Equation: Discretize Surface into Panels Panel j

  48. Overview • Setups of Parasitic Extraction Problems • Capacitance Extraction (electrostatic) • RL Extraction (MQS) • Combined RLC Extraction (EMQS) • Electromagnetic Interference Analysis (fullwave) • Electromagnetic solvers • classification (time vs. frequency, differential vs. integral) • integral equation solvers in detail • basis functions • residual minimization (collocation and Galerkin) • linear system solution • fast matrix-vector products • Example: EMQS solution • Conclusions

  49. Residual Definition and Minimization

  50. Residual Minimization using Test Functions Note: Weighted Residual = Galerkin when using piecewise constant basis functions

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