Physical Design Challenges in the Chip Power Distribution Network - PowerPoint PPT Presentation

Physical Design Challenges in the Chip Power Distribution Network Farid N. Najm Professor & Chair ECE Dept, University of Toronto f.najm@utoronto.ca

Outline ■ Introduction ● Power grid topology ● Physical design challenges ■ Power grid verification ● EDA: simulation, vectorless verification ● Engineering solution: over-design, and over-kill ■ Constraints-based verification ● Voltage variations ● Electromigration ■ Constraints generation ■ Conclusion F. N. Najm Challenges in Power Grid 2

Power Grid Topology V dd ■ ~ a Billion nodes ■ ~ 2,000 C4 pads Pads RLC RLC RLC Pkg, PCB ● 1,000 V dd , 1,000 V ss RC Layer ■ All levels of metal stack RC Layer RC Layer ■ Hundreds of millions of Circuit current instances of logic cells sources F. N. Najm Challenges in Power Grid 3

Power Grid Topology ■ Package, motherboard, and VRM model; inductance! F. N. Najm Challenges in Power Grid 4

Power-Managed Chip Grid V dd V dd Pads Pads RLC RLC RLC RLC RLC RLC ■ Gated Pkg, PCB Pkg, PCB Global (un-gated) Grid supplies M7 (RC Layer) M6 (RC Layer) M5 (RC Layer) M4 M4 (RC Layer) M4 M4 (RC Layer) ■ Voltage Local (gated) Grid islands M3 M3 (RC Layer) M3 M3 (RC Layer) M2 M2 (RC Layer) M2 M2 (RC Layer) ■ Active M1 M1 (RC Layer) M1 M1 (RC Layer) devices! Gate Gate Circuit current Circuit current FET FET sources sources F. N. Najm Challenges in Power Grid 5

Mesh Layer Structure ■ In every layer, the grid is mostly a regular mesh. Metal 4 Gnd 3 Vdd l a t Gnd e M Vdd Gnd Vdd ■ Note: ● Many variations on this central theme ● Top layer C4 pads typically on a ~200 µ m grid ● Local non-uniformities make room for signal routing F. N. Najm Challenges in Power Grid 6

Physical Design ■ With hundreds of millions of instances on die and clocks running at GHz rates, the total power is high ● High performance SOCs might consume over 150 Watts ● Very hard to keep supply regulated under such conditions ■ Physical design of the grid can have big impact: ● Voltage variations in bottom layers impact circuit timing ● Voltage overshoot (inductive kick) impact I/O signal noise ● Electromigration damage can be catastrophic throughout ■ N ightmare: ensure circuit is safe from all this while distributing over 150 Amps to >400 million instances F. N. Najm Challenges in Power Grid 7

Power Grid Verification F. N. Najm Challenges in Power Grid 8

Power Grid Verification ■ Verification is needed to check the grid design: ● Early high-level grid verification and planning ● Incremental verification during redesign cycles ● Detailed grid verification at sign-off time ■ Key problem: ● The circuit currents are unknown or highly uncertain! ■ Need reliable verification in the face of uncertainty. F. N. Najm Challenges in Power Grid 9

Existing Commercial Solutions ■ Simulation ● Decouple grid from underlying circuit ● Simulate the grid for given current source stimulus ● Expensive and incomplete; inconclusive ■ Existing solutions for vectorless verification ● Voltage variations: timing windows, random scenarios ● Electromigration: Black’s model, current density check ● Questionable results ■ Engineering solution: over-design, but also over-kill ■ Problem: running out of metal area for signal routing! F. N. Najm Challenges in Power Grid 10

Constraints-Based Verification F. N. Najm Challenges in Power Grid 11

Constraints-Based Verification ■ Given: ● Power Grid (DC, RC, or RLC netlist) ● Tolerance for grid node voltage fluctuations ( V th ) ● Tolerance for grid branch current densities (EM) ● Peak budgets (current constraints) for block currents ■ Find: ● Worst-case voltage variations for every grid node ● Worst-case current variations in every grid branch ■ Features: ● Based on user-provided current constraints (budgets) ● Search/optimization (LP) approach for verification ● Allows vectorless early high-level power grid verification F. N. Najm Challenges in Power Grid 12

Current Constraints - Example ■ Local Constraints Global Constraint 1 1 2 3 + - V dd I 3 I 2 4 5 6 I 5 ■ Global Constraints 8 7 9 I 7 I 9 Global Constraint 2 F. N. Najm Challenges in Power Grid 13

Voltage Drop: The RC Case ■ Define as the vector of worst-case voltage drops, at all nodes, over all transient currents in space ■ Define: shorthand notation for element-wise max:  max i ∈ F [ v 1 ( i )]  max i ∈ F [ v 2 ( i )]     emax i ∈ F [ v ( i )] =   .  .  .     max i ∈ F [ v n ( i )] ■ Use upper-bound: F. N. Najm Challenges in Power Grid 14

Performance F. N. Najm Challenges in Power Grid 15

Voltage Drop/Rise: The RLC Case F. N. Najm Challenges in Power Grid 16

Electromigration: The Mesh Model Traditional EM ■ model is “series” But power grid has ● much redundancy Vector-based mesh ■ model approach 3-4X lifetime! ● Can be 30-40X ● Vectorless Mesh ■ model approach F. N. Najm Challenges in Power Grid 17 Chatterjee 2013, Fawaz 2013

Progress Towards Failure F. N. Najm Challenges in Power Grid 18

Progress towards failure Series ¡ F. N. Najm Challenges in Power Grid 19

Progress towards failure Series ¡ F. N. Najm Challenges in Power Grid 20

Progress towards failure Series ¡ F. N. Najm Challenges in Power Grid 21

Progress towards failure Series ¡ F. N. Najm Challenges in Power Grid 22

Failure when v(t) > v th Series ¡ Mesh ¡ F. N. Najm Challenges in Power Grid 23

Results: MTF Comparisons ■ MTF estimation for the largest grid, with 1M nodes required 97 Monte Carlo iterations and 13.5 hrs. F. N. Najm Challenges in Power Grid 24

But … there is a Problem ■ Ongoing development: ● Electromigration verification ◆ Physical models to further reduce pessimism ● Fast hierarchical/modular verification ◆ Boundary conditions to ensure sub-grid safety ■ But there is a fundamental issue with usability of the constraints-based approach: The constraints are hard to specify F. N. Najm Challenges in Power Grid 25

Constraints Generation F. N. Najm Challenges in Power Grid 26

Alternative Approach ■ Constraints Generation (the “inverse” problem): ● Generate circuit current constraints which, if satisfied by the underlying circuitry, would guarantee grid safety ■ Applications: ● Encapsulate much useful information about the grid, captured in useful quality metrics (peak power, other) ● Provides power budgets to drive design process, allowing rebudgeting, or early hints for grid redesign or new floorplan ● During low level physical design, allow local checks for block compliance with grid safety constraints w/o grid simulation ● Local checks in safety “islands” may be enough F. N. Najm Challenges in Power Grid 27

Voltage Islands (RC case) ■ Typically, we find the constraints decoupled into “islands” ■ Checking of the local regions, independently ■ Parallel flow for verification F. N. Najm Challenges in Power Grid 28

Container ■ Definition: F. N. Najm Challenges in Power Grid 29

Safe Container ■ Rewriting the upper-bound on the exact worst-case voltage drop: where and ■ We want to generate such that , from which and the grid is safe! ■ Definition: A container is said to be safe if: F. N. Najm Challenges in Power Grid 30

All Safe Containers ■ Let and define the two sets: V th ■ Lemma: is safe for any , and: ● All possible safe containers may be found as either specific instances of , or as subsets of such instances. F. N. Najm Challenges in Power Grid 31

Maximal Container ■ It’s enough to look at the set of all safe containers: ■ Define a safe container to be maximal if it’s not a subset of any other safe container. ■ We are interested in maximal containers! F. N. Najm Challenges in Power Grid 32

All Maximal Containers ■ Theorem: Maximal V th Irreducible Safe F. N. Najm Challenges in Power Grid 33

Desirable Maximal Containers ■ The space of maximal safe containers represents a quality assessment for a power grid ● What levels of current will this grid safely distribute? ■ Example: suppose the chip is expected to draw a peak power of 150W at 1V supply ● A grid may be deemed unacceptable if no safe container for it can be found that allows a peak total supply current of 150A ■ Design objectives must drive the choice of container! F. N. Najm Challenges in Power Grid 34

Container Generation Algorithms ■ Peak Power Problem (P1): ● Generate a container that allows the largest possible peak power dissipation (instantaneous, total) ■ Uniform Current Problem (P2): ● Generate a container that does not severely limit the allowed supply current anywhere on the die F. N. Najm Challenges in Power Grid 35

Algorithms ■ P1: peak power ■ P2: uniform budgets ● One LP ● One LP ■ We can prove that both resulting are maximal! F. N. Najm Challenges in Power Grid 36