Accurate Modeling of Spiral Inductors on Silicon From Within Cadence Virtuoso using Planar EM Simulation. Agilent EEsof RFIC Seminar Spring 2004

Transcription

1 Accurate Modeling of Spiral Inductors on Silicon From Within Cadence Virtuoso using Planar EM Simulation Agilent EEsof RFIC Seminar Spring

2 Overview Spiral Inductor Models Availability & Limitations Momentum Technology Overview Key Physical Effects Considered in Momentum RFDE Momentum Solution Process Momentum Application Benchmark Summary Page 2

3 Spiral Inductor Models Availability & Limitations Inductor models can be found in most RFIC Design Kits Spiral inductors are considered critical components in RFIC design Foundry Supplied Design Kit inductor models often suffer from: Limited discrete-parameters set Limited frequency coverage Questionable accuracy outside any design/process variations Static model response to surrounding physical environment Page 3

4 Traditional Characterization Method Measurement-based Modeling Approach Fabricate a large number of discretely varying topologies Positives: Good accuracy over predefined frequency range and discrete parameters samples Negatives: Need to fabricate test wafer(s): Very time consuming and costly Limited discrete-parameter set hindering design options Static lumped-element models unresponsive to component s physical surroundings Need component modeling skills Any updates to existing models can be just as costly as starting a new model Page 4

5 Predictive Modeling & Verification Electromagnetics-based Modeling Approach Perform electromagnetic (EM) simulation Positives: Use Scattering Parameters (S-parameters) data file in frequency-domain circuit simulation Optional: Build lumped element model based on EM data (for time-domain circuit simulation; increased work and possible accuracy impact) Minimal EM modeling insight Good accuracy over predefined frequency range and parameter samples Model s frequency range can be extended with few simple menu selections Model s physical parameters can be extended without any need for wafer run Verify model s performance in its intended physical environment Negative: Requires good characterization of process parameters (e.g. substrate) Page 5

6 Overview Spiral Inductor Models Availability & Limitations Momentum Technology Overview Key Physical Effects Considered in Momentum RFDE Momentum Solution Process Momentum Application Benchmark Summary Page 6

7 RFDE Momentum Electromagnetic Modeling & Verification Physical Structure z Air multilayered medium ε, µ σ h 1 Layer [1] 1 1, 1 planar metallization Port 1 source H(r) E(r) ε, µ σ h 2 Layer [2] 2 2, 2 ε, µ σ h 3 Layer [3] 3 3, 3 Gnd source ω load J s (r) Port 2 load [S] S-parameters Your Virtual Network Analyzer Page 7

8 RFDE Momentum Technology Process Calculate Substrate s Green s Function (system s impulse response ) Mesh strips, vias vias and and slots with rectangles and and triangles (arbitrary surface mesh & mesh refinement) Model surface current in in each mesh cell cell (linear distribution) Build and and solve matrix equation for for the the unknown current coefficients Calculate S-parameters B 1 (r) B 2 (r) B 3 (r) I 1 I 2 I 3 S 1 S 2 I 1 I 2 I 3 L 11 L 12 R 22 L 13 L 22 C 11 C 22 C 12 [Z].[I]=[V] [S] L 23 L 33 Page 8

9 Comparison of Models Spiral Inductors DC Spice Momentum RF Momentum MW Spice model S-parameters RF S-parameters MW quasi-static inductance quasi-static capacitance..... DC conductor loss (σ) DC substrate loss (σ) dielectric loss (tgδ) skin effect loss substrate wave radiation space wave radiation Page 9

10 Momentum Microwave & RF Applications APPLICATIONS Momentum RF Momentum MW High-Speed Digital (SI, BGA) RF Board (FR4, Duroid) RF Package (Plastic) physical size RFIC (Silicon) RF Module (MCM, LTCC) Microwave - hybrid (Alumina) Microwave - MMIC (GaAs) Initial design/ optimization Final design/ optimization Planar Antennas DC frequency 200 GHz Page 10

11 Overview Spiral Inductor Models Availability & Limitations Momentum Technology Overview Key Physical Effects Considered in Momentum RFDE Momentum Solution Process Momentum Application Benchmark Summary Page 11

12 Substrate Coupling & Radiation Resistive loss of metallization Resistivity of Si substrate Capacitive coupling effects to Si substrate Passivation h = 4 µm ε r = 3.6 W = 15 um Copper, t = 4 µm σ= S/m SiO 2 h = 3 µm ε r = 4 Copper, t = 0.66 µm SiO 2 h = 5 µm ε r = 4 Silicon h = 500 µm ε r = 11.9 σ = 7.41 S/m Ground Page 12

13 Current Return Path & Frequency Dependency DC 100 MHz 350 MHz 1.4 GHz impedance Current follows the path of least resistance Impedance = R + jωl jωl frequency Page 13

14 Current Distribution & Skin Effects Current distribution in cross section of thick conductor as function of frequency uniform current distribution w edge effect conductor with ground plane single-sided skin effect OR isolated conductor double-sided skin effect t DC t < δ s w < 2δ s Current Density High Low t < δ s w = 2δ s w > 2δ s t = δ s 100 MHz 350 MHz Example: RFIC process copper, w=15µm, t=4µm 2δ s > t > δ s w > 2δ s Skin depth of copper σ=4.5e7 S/m 2 δ = s ωµσ t = 2δ s 1.4 GHz t > 2δ s w > 2δ s frequency 1 MHz 75 µm 10MHz 23.7 µm 100MHz 7.5 µm 1 GHz 2.37 µm Page 14

15 Thick Conductors Effects Influence of the thickness on the external inductance of the trace -Using edge mesh to include edge effect -Using Ohms/square resistance (no skin effect) -Using thick conductor model length = 100 µm t = 2 um t = 4 um t = 8 um thick conductor port 1 port 2 R(ω) L(ω) Passivation h = 4 µm ε r = 3.6 SiO 2 h = 3 µm ε r = 4 SiO 2 h = 5 µm ε r = 4 Silicon h = 500 µm ε r = 11.9 σ = 6.67 S/m W = 15 um Copper, t = 2, 4, 8 µm σ= S/m Copper, t = 0.66 µm Increased thickness: -lower resistance -lower external inductance sheet conductor thick conductor t=2um t=4um t=8um Page 15

16 Thick Conductor Modeling Issues Edge Effect & Skin Effect How does Momentum address Edge Effect and Skin Effect? The edge mesh concept takes the edge effect into account The surface impedance concept takes the skin effect into account How does the inclusion of the edge effect and the skin effect influence the resistance and inductance of a trace? Passivation h = 4 µm ε r = 3.6 SiO 2 h = 3 µm ε r = 4 SiO 2 h = 5 µm ε r = 4 Silicon h = 500 µm ε r = 11.9 σ = 7.41 S/m W = 15 um Copper, t = 4 µm σ= S/m Copper, t = 0.66 µm length port 1 port 2 Note: R(ω) L(ω) R DC = length σ(t w) Page 16

17 Edge effect Influence of the edge effect on the resistance and inductance of the trace using Ohms/square resistance (no skin effect) R(ω) no edge mesh length = 100 µm R DC length = = Ω σ(t w) port 1 port 2 with edge mesh length = 100 µm port 1 port 2 L(ω) no edge edge mesh Edge effect: -higher resistance -lower inductance R(ω) L(ω) Page 17

18 Skin Effects Influence of the skin effect on the resistance and inductance of a trace - using edge mesh to include edge effect - using surface current (sheet) model - using thick conductor expansion port 1 port 2 R(ω) length = 100 µm L(ω)+ L(ω) R DC sheet model 1 sheet model 2 sheet model 3 thick model single-sided skin effect R HF double-sided skin effect no skin effect Passivation h = 4 µm ε r = 3.6 SiO 2 h = 3 µm ε r = 4 SiO 2 h = 5 µm ε r = 4 Silicon h = 500 µm ε r = 11.9 σ = 7.41 S/m W = 15 um Copper, t = 4 µm Copper, t = 0.66 µm Skin Skin effect: effect: -higher -higher HF HF resistance -higher -higher internal internal inductance -lower -lower external external inductance L DC t = δ s L DC t = 2δ s double-sided skin effect no skin effect single-sided skin effect L HF L HF Page 18

19 Skin Effect Discretization Problems How does a 3D volume meshing technology handles thick conductors? L T 0 1 Thick conductor is subdivided into N layers of thickness T/N and conductivity σ H N W Volume current is modeled with piecewise constant current filaments Need at least 3 subdivision per skin depth for convergence!!! Skin depth of copper σ=4.5e7 S/m 2 δ = s ωµσ 1 MHz 75 µm 10MHz 23.7 µm 100MHz 7.5 µm 1 GHz 2.37 µm N = 64 N = 32 N = 16 N = 8 N = 4 N = 2 Page 19

20 Momentum Modeling of Thick Metal Field Equivalence Theorem: decomposition into external and internal problem Thick conductor External Problem Internal Problem σ w t h = J s (r) Surface current t + σ t w Surface impedance E( r) = σ J( r) metal trace port 1 port 2 E s ( r) = Zs Js jωl( ω) ( r) Z s (t, σ, ω) R( ω) + jω L( ω) Takes skin effect into account! R(ω) L(ω)+ L(ω) L(ω)=external inductance L(ω)=internal inductance Patent Pending! Page 20

21 Thick Conductor Modeling E E s,1 s,2 External Problem ( r) = Z s ( r) = Z J s,2 (r) J s,1 (r) Surface current s ( ( t 2 t 2, σ, ω) J, σ, ω) J t s,1 s,2 ( r) ( r) + Internal Problem σ t w Surface impedance Z s (t, σ, ω) 2-layers surface current [3] σ, t/2 [2] [1] σ, t/2 h3 h2=t h1 3 substrate layers 2 strip layers + 1 via layer Volume of thick conductor is divided into two equal sheet conductor layers, one at the top surface and one at the bottom surface, with same conductivity and half of the thickness Additional via layer (perfect conducting) to short out differential mode Actual distribution of top and bottom layer currents not enforced, but follows from solution of EM equations, yielding improved model for resistance and inductance Accuracy decreasing (horizontal currents on via layers missing) when w/t decreases (w/t < 2) (this will be addressed in a future release) Page 21

22 Overview Spiral Inductor Models Availability & Limitations Momentum Technology Overview Key Physical Effects Considered in Momentum RFDE Momentum Solution Process Momentum Application Benchmark Summary Page 22

23 RFDE Momentum Solution Process Steps Define Substrate stack & layer mapping Make Momentum cell from design Map Momentum ports to Cadence pins Define simulation options: frequency plan, mesh settings Perform simulation and review results Transpose new model to schematic for more accurate circuit simulation Page 23

24 RFDE Momentum Solution Process Step 1 Define Substrate stack & layer mapping S = 5 umw = 15 um Copper, t =1.75 µm SiO 2 h = 3 µm ε r = 4 Copper, t = 0.66 µm SiO 2 h = 5 µm ε r = 4 Silicon h = 500 µm ε r = 11.9 σ = 6.67 S/m Page 24

25 RFDE Momentum Solution Process Step 1 Define Substrate stack & layer mapping Page 25

26 RFDE Momentum Solution Process Step 1 Define Substrate stack & layer mapping Page 26

27 RFDE Momentum Solution Process Step 2 Make Momentum Cell Page 27

28 RFDE Momentum Solution Process Step 3 Assign Ports to Cadence Pins Momentum Ports Cadence Pins Page 28

29 RFDE Momentum Design Flow Step 3 Assign Ports to Cadence Pins Physical ports ports electrically short distance electrically short distance Unphysical ports ports electrically long distance +ref -ref port Page 29

30 RFDE Momentum Solution Process Step 4 Define Simulation Options Frequency plan Mesh settings Metallization properties Page 30

31 RFDE Momentum Solution Process Step 5 Perform EM Simulation & Review Results Page 31

32 RFDE Momentum Solution Process Step 5 Perform EM Simulation & Review Results Page 32

33 RFDE Momentum Solution Process Step 5 Perform EM Simulation & Review Results Page 33

34 RFDE Momentum Solution Process Step 6 Make Schematic View for New Model Page 34

35 RFDE Momentum Solution Process Step 6 Transpose New EM Model to Schematic Schematic Actions: 1. Insert Momentum components in Composer 2. Set/Alter simulation control: identical to case where no Momentum components are used 3. Run circuit simulation 4. View/Analyze results Momentum Component Momentum from from Composer Can Can be be used used with with Agilent Agilent circuit circuit simulator and and Cadence Spectre Spectre (v5.0.33) (v5.0.33) Page 35

36 Overview Spiral Inductor Models Availability & Limitations Momentum Technology Overview Key Physical Effects Considered in Momentum RFDE Momentum Solution Process Momentum Application Benchmark Summary Page 36

37 Momentum Application Benchmark Momentum validated against results for standard parts This leads to a substantial improvement in phase noise of a 4GHz test oscillator Dr. M P Wilson Source: Modeling of of integrated VCO resonators using Momentum Dr. Dr. M P Wilson, Tality UK. UK. Page 37

38 Momentum Application Benchmark 2.5 Turn Octagonal Spiral Inductor Three Three test test inductors were were compared with with measured results. results. All All three three inductor examples show show good good agreement with with measured results, results, showing that that we we could could produce produce reliable reliable Momentum models models for for the the particular process process used. used. Dr. Dr. M P Wilson. Wilson. Page 38

39 Momentum Application Benchmark It It can can be be seen that the the Balun circuit improves phase noise by by means of of an an increase in in the the effective Q of of the the resonator. This clearly shows the the benefit of of the the custom modeling facility given by by Momentum. Dr. M P Wilson Page 39

40 Overview Spiral Inductor Models Availability & Limitations Momentum Technology Overview Key Physical Effects Considered in Momentum RFDE Momentum Solution Process Momentum Application Benchmark Summary Page 40

41 Summary Spiral inductors are critical RFIC design components Foundries supplied models may limit design options Electromagnetic-based modeling approach has many advantages Method-of-Moments EM technique is best suited for modeling spirals Momentum industry track record RFDE Momentum solution process is a simple few steps process RFDE Momentum is fully integrated with Cadence Virtuoso RFDE Momentum added accuracy greatly enhances first-pass design success Page 41

42 Appendix Momentum Substrate Stack Definition Modeling Metal Losses Page 42

43 Momentum Substrate Definition Momentum uses a text file for the description of the substrate definition, which includes: Layers stack definition Dielectric layers physical properties Metal layers physical properties Page 43

44 1. Layers Stack Definition Page 44

45 2. Dielectric Layers Physical Properties Page 45

46 3. Metal Layers Physical Properties Page 46

47 Momentum Substrate Definition Example Page 47

48 Modeling Metal Losses Default Model: Sheet Conductor Model external problem J s (r) Surface current E s ( r) = Zs Js t ( r) + internal problem Z s σ w Surface impedance (t, σ, ω) Surface impedance based on 1-dimensional field approximation (only variation in z- direction), valid for good conductors (σ > ωε) with a high width/thickness ratio (typically w/t > 5) Models a uniform current distribution over entire cross section at low frequencies, yielding the correct DC resistance value Models a concentrated current distribution over skin depth δ s at high frequencies, over estimates HF resistance (depending on closeness of return current in ground plane) Models the external inductance for zero thickness with higher internal inductance (skin effect), hence over estimates inductance t Page 48

49 Modeling Metal Losses Surface Currents Sheet Conductors thick conductor 1-layer surface current t σ J(r) u n J s (r) strip (σ, t) E s ( r) = Zs Js jωl( ω) ( r) Volume of thick conductor is modeled as an infinitely thin conductor layer Surface current flows in one sheet conductor layer External inductance L(ω) is independent of conductor thickness (t) Page 49

50 Modeling Metal Losses Surface Currents Thick Conductors thick conductor 2-layers surface current t σ J(r) t u n J s,1 (r) J s,2 (r) strip (σ, t/2) via (perfect conducting) strip (σ, t/2) Volume of thick conductor is divided into two equal conductor layers, one at the top surface and one at the bottom surface, with same conductivity and half of the conductor thickness Additional via layer (perfect conducting) included to short out differential mode Actual distribution of top and bottom layer currents not enforced, but follows from solution of EM equations External inductance L(ω) is dependent on conductor thickness As conductor thickness (t) increases: mutual inductance decreases external inductance decreases; also, high frequency resistance decreases Page 50

51 Modeling Metal Losses 1-dimensional surface impedance model thick conductor E s ( r) = Zs Js ( r) t σ J(r) Z (t, σ, ω) Z coth( jk t) s = with Z jk c c c jωµ = σ + jωε = jωµ ( σ + jωε) c Distribution of the current inside the conductor is based on 1-dimensional field approximation (only variation in z-direction), valid for good conductors (σ > ωε) with a high width/thickness ratio (typically w/t > 5) Yields analytic model for the surface impedance Z s (t,σ,ω) Resistance R(ω) and interior inductance L(ω) are dependent on: conductor thickness, conductivity, and frequency (skin effect) Page 51

52 Modeling Metal Losses 1-dimensional surface impedance model Zs (t, σ, ω) = with Z jk c c = = Z c coth( jk jωµ σ + jωε jωµ ( σ + jωε) c t) low frequencies (LF): 1 µ t Z s (t, σ, ω) + jω σt 3 high frequencies (HF): 1 Zs (t, σ, ω) σδ s ( 1+ j) R DC + jω L DC R HF + jω L HF skin depth δ s 2 = ωµσ drawn on single layer (σ, t) σ t SINGLE-SIDED SKIN EFFECT σ δ s LF current runs in entire cross section of the metallization HF current runs in SINGLE skin depth surface layer (proximity of ground) Typical Application: microstrip circuit Page 52