GridStack white paperGS-WP-02Rev. 1.0October 2026

Full-chip IR-drop visualization at million-node scale

AbstractA transient power-grid solver that only returns numbers leaves the hardest question unanswered: where on the die is the problem. GridStack reconstructs the full die-level picture directly from the netlist — the metal mesh colored by layer, the rail-aware IR drop and VSS bounce at every node in plane, and the same field lifted into a 3D surface where hotspots stand up off the die. This paper describes the reconstruction method and presents the three views for an 8-layer, 127K-node grid and a 15-layer, 852K-node grid, taken from the full-node back-Euler snapshot at t = 1.0×10⁻⁸ s.

1 / WHY FULL-CHIP VIEWS MATTER

Worst-case droop is a number; fixing it is a map

A single worst-case figure tells a designer that a grid fails, not what to do about it.

Fixing dynamic IR-drop is a spatial problem. Whether the droop is one concentrated hotspot under a switching block or a broad sag across an under-strapped region determines whether the answer is decap, a wider strap, another via array or a floorplan change.

GridStack therefore treats visualization as part of the analysis rather than a downstream report. Every full-node solve can be rendered at die level, so the structure of the grid and the structure of the drop can be read side by side.

2 / RECONSTRUCTION METHOD

Geometry and drop, both from the netlist

No external layout database is required: the geometry comes from the same file the solver reads.

Geometry from the netlist

The IBM benchmark netlists encode physical placement in their node names. GridStack parses the IBM-style coordinates out of the SPICE node names to recover each node's die position and metal layer, then rebuilds the wire segments between them.

The rail-aware drop metric

A power grid carries two distinct rail families, and a single “voltage” plot mixes them incoherently. GridStack separates them and plots the physically meaningful deviation on each:

VDD-like nodes — the drop is VDD − V, how far the supply has sagged below its ideal value.
VSS-like nodes — the bounce is V itself, how far ground has lifted above zero.

Both quantities are volts of margin lost, so they share one scale and one color map, and a single map can be read across the whole die regardless of which rail a node belongs to.

The views are ground truth, not a reduced-model reconstruction. They are taken from the full-node back-Euler solution — every node in the grid, not only the probe nodes — at t = 1.0×10⁻⁸ s, so the rendered field is the transient state the reference solver computed.

Snapshot parameter	Value
Snapshot time	1.0e-8 s
Solver	Direct back-Euler
Coverage	Full-node
Geometry source	SPICE node names

Coordinate recovery relies on the IBM benchmark naming convention. A grid that does not encode placement in its node names needs its geometry supplied separately; format coverage is confirmed during onboarding.

3 / IBMPG2T

8 metal layers, 127K nodes

The mid-size benchmark: 127,565 nodes across 8 metal layers, connected by 208,325 wire segments.

Dense enough to show real spatial structure, small enough that individual straps remain legible.

2D power-grid geometry for ibmpg2t, colored by metal layer — Figure 1a · StructureThe full metal mesh, colored by layer (0–7) across the die.

2D rail-aware IR-drop and VSS-bounce map for ibmpg2t — Figure 1b · 2D dropRail-aware IR drop and VSS bounce at every node, mapped in plane.

3D rail-aware IR-drop and VSS-bounce surface for ibmpg2t — Figure 1c · 3D dropThe same drop as a 3D surface — hotspots stand up off the die.

4 / IBMPG3T

15 metal layers, 852K nodes

The largest of the IBM grids: 852,536 nodes across 15 metal layers, at million-node scale.

The same three views render without downsampling the node set.

2D power-grid geometry for ibmpg3t, colored by metal layer — Figure 2a · StructureA denser, 15-layer mesh — the largest of the IBM grids.

2D rail-aware IR-drop and VSS-bounce map for ibmpg3t — Figure 2b · 2D dropFull-node rail-aware IR drop across the whole million-node die.

3D rail-aware IR-drop and VSS-bounce surface for ibmpg3t — Figure 2c · 3D drop852K nodes lifted into 3D — the worst-case peaks read at a glance.

5 / READING THE MAPS

Three views, three different questions

The views are meant to be read in sequence.

Structure establishes what the grid is — strap pitch, layer stacking and the regions where the mesh thins out. Thin regions are where to look first in the next two views.
2D drop localizes the loss of margin. Because the map is rail-aware, a VDD sag and a VSS bounce in the same region read on one scale and sum to the true margin lost by a cell sitting there.
3D drop separates a sharp, local hotspot from a broad, shallow sag — a distinction that is easy to miss in a flat color map but determines whether the fix is local decap or a structural change to the grid.

Because these views come from the full-node solution, they can be produced for any time point in the transient, not only the snapshot shown here — turning dynamic IR-drop into something that can be watched evolving across the die rather than summarized as a single worst-case number. The transient engine that produces those solutions is described in GS-WP-01.

From evidence to your design

See your own grid, at die level.

Bring a power-grid netlist and the time point you care about. We will discuss geometry recovery, the drop metric and the views that answer your question.

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