1. 2013 DAC Designer/User Track Presentation Inductor Design for Global Resonant Clock Distribution in a 28-nm CMOS Processor Visvesh Sathe 3, Padelis Papadopoulos 2, Alvin Loke 3, Tarek Khan 1, Anand Raman 2, Gerry Vandevalk 3, Nikolas Provatas 2, Vincent Ross 1 1 Advanced Micro Devices, Inc. 2 Helic, Inc. 3 Formerly at Advanced Micro Devices, Inc.

2. AMD/Helic, Inductor Design for Resonant-clocked Processor Outline Resonant Clock Distribution Inductor Design and Analysis Challenges Helic VeloceRaptor/X Inductor Extraction using VeloceRaptor/X Silicon Correlation Conclusion Slide 1

3. AMD/Helic, Inductor Design for Resonant-clocked Processor Processor Global Clock Distribution Slide 2 Significant global clock loading  7-ps clock skew target across > 20-mm 2 core area  Constrained clock latency from grid to timing elements clocking 24% standard cells 19% gaters 16% macros 18% flops 18% bus 5% Typical core-power breakdown consumption AMD “Piledriver”

4. AMD/Helic, Inductor Design for Resonant-clocked Processor Basic Resonant Clocking Operation Rely on efficient resonance between L tank and C clk near ω 0 Efficient operation around ω 0 Driving clock at much lower frequencies  Reduced efficiency, warped clock waveform Slide 3

5. AMD/Helic, Inductor Design for Resonant-clocked Processor AMD Resonant Clocking 90 inductors distributed over custom power grid, signal wires, and core circuitry Slide 4

6. AMD/Helic, Inductor Design for Resonant-clocked Processor Inductor Design Clock macro, bump pitch constrain inductor size Metal sharing with existing power → cut-aways Centered power straps, HCK tree for  mutual inductance Slide 5

7. AMD/Helic, Inductor Design for Resonant-clocked Processor Inductor and Grid Problem Summary 87 x 65 μm spiral over 113 x 126 μm custom grid 12 metal layers (2 thick)  Width: 0.13 to 5.7 μm  Thickness: 0.1 to 1.2 μm >5μm/μm 2 interconnect length to be extracted! Slide 6

8. AMD/Helic, Inductor Design for Resonant-clocked Processor Inductor Design Methodology Goal: Achieve desired L with maximum Q on a highly customized inductor Available design variables  Winding width, outer spacing, inner spacing (NESW)  Winding height, winding width Multiple extractions within reasonable time is vital Extraction customization per-metal is crucial  Top metal layers dominate magnetic interaction, lower level metals have minimal interaction  Per-metal extraction/merging mode selection (R/C/RC/RLC/RLCk) Process-aware, temperature-sensitive extraction Slide 7

9. AMD/Helic, Inductor Design for Resonant-clocked Processor What is VeloceRaptor/X ? Rapid, high-capacity multi-GHz EM extraction Maxwell equations-based RLCk model per metal segment Inductance calculations based on magnetic vector potential  Skin and proximity effects, substrate losses, capacitive and magnetic coupling Silicon-proven accuracy Use model:  In situ selection of nets and pin definition  Netlist and symbol creation for the marked nets  Model annotation and simulation Slide 8

10. AMD/Helic, Inductor Design for Resonant-clocked Processor VeloceRaptor/X Offers… High capacity and speed Multithreading support S-parameters and RLCk netlist output  Temperature-aware model  Mixed-mode R/C/RC/RLC/RLCk per any net layer  Layout-dependent effects captured Direct GDS extraction Batch-mode support Numerical network reduction Slide 9

11. AMD/Helic, Inductor Design for Resonant-clocked Processor Inductor-over-Grid Model Validation Slide 10 Mixed-mode extraction per net layer:  M11- M x : RLCk  M x-1 - M3: RC RLCk extraction below M07 has negligible impact Increasing interconnect density, runtime, memory requirement No improvement in model accuracy when adding more RLCk layers Metals Density (µm/µm 2 ) Extraction Time (sec) RAM (MB) Netlist Size (KB) M11-M10: RLCk3.12E-01 517880 87 M11-M9: RLCk5.78E-01 5281020 95 M11-M8: RLCk1.34E+00 34023650 96 M11-M7: RLCk2.27E+00 68956624 97 M11-M6: RLCk2.93E+00 1003312564 99 M11-M5: RLCk3.85E+00 1405521564 102 Best tradeoff between model accuracy and runtime/memory requirements

12. AMD/Helic, Inductor Design for Resonant-clocked Processor Turnaround Time vs. Metal Density Slide 11

13. AMD/Helic, Inductor Design for Resonant-clocked Processor Test Chip Silicon Validation Very good agreement between measured and extracted L and Q Slide 12

14. AMD/Helic, Inductor Design for Resonant-clocked Processor Conclusions Resonant clocking feature reduces global clock power distribution Use of multiple distributed on-chip inductors poses a significant challenge to inductor extraction – Metal-rich extraction environment – Significant mutual inductance with underlying and adjacent circuits and power grids Exploiting design structure and VeloceRaptor/X capabilities enabled efficient inductor optimization Batch mode and per-metal per-net extraction for extraction of a model with sufficient detail to accurately model silicon behavior. Slide 13