FOCAL: A First-Order Carbon Model to Assess Processor Sustainability

Computing emits 2–4% of global greenhouse gases and architects want to help, but carbon data is fundamentally uncertain — supply chains are secret, lifetimes unknown, grids shifting, and efficiency gains rebound into more usage — so FOCAL refuses the data-driven route and builds a first-order model from what architects actually control, using chip area as the embodied-carbon proxy and energy or power as the operational proxy under fixed-work and fixed-time scenarios (the latter formalizing the rebound effect), then declares a design choice STRONGLY sustainable only if it wins under every scenario and weighting — a discipline that re-prices the whole architecture toolbox, blessing multicore, DVFS, and die shrinks, demoting speculation and heterogeneity to conditionally green, and condemning dark silicon, big caches, and turboboost outright.

The argument in one glance

Problem

Architects want to cut carbon, but the numbers are fog

Information technology accounts for 2.1–3.9% of global greenhouse-gas emissions — on par with aviation, and growing. A processor's footprint splits into embodied carbon (manufacturing: fab energy, fluorinated gases, materials) and operational carbon (lifetime electricity). To design greener chips, architects need to compare choices — but manufacturing data hides behind industry secrecy and opaque supply chains, operational footprints depend on lifetimes, usage intensity, and grid mixes nobody knows at design time, and efficiency improvements notoriously rebound into MORE total usage.
What people did

Collect the data: life-cycle assessments and bottom-up models

Life-cycle assessment (LCA) reports tally whole products' footprints; Meta's ACT model assembles fab reports, industry disclosures, and grid data into absolute carbon estimates for architects. Characterization studies (Gupta et al.) established the key empirical split: mobile devices and hyperscale servers are embodied-dominated, always-connected devices operational-dominated.
Why it fell short

The data-driven route hits a wall the data itself builds

ACT's own authors acknowledge a "non-negligible gap" between their estimates and LCA-based numbers, hypothesizing stale emission data for current technologies. LCAs aggregate entire systems into one number — no per-chip carbon figures exist anywhere, making validation of ANY chip-level carbon model essentially impossible. And prior analyses bake in a single usage scenario and a fixed embodied-to-operational ratio, ignoring the rebound effect entirely — so their conclusions silently depend on the least knowable assumptions.
This paper's idea

Embrace the uncertainty: first principles, parameters, and robustness

FOCAL (Lieven Eeckhout, Ghent — a single-author paper) models carbon from what architects control at design time. Embodied proxy: chip die area (chips-per-wafer geometry; industry's binning of defective dies makes perfect-yield a fair approximation). Operational proxy: ENERGY under a fixed-work scenario (lifetime workload fixed) or POWER under fixed-time (a better chip does more work in the same lifetime — the rebound effect, formalized). A weighting parameter α spans embodied-dominated (0.8±0.1) and operational-dominated (0.2±0.1) device classes. The normalized carbon footprint (NCF) compares two designs as a weighted ratio sum — and the taxonomy does the epistemics: a choice is STRONGLY sustainable only if NCF is below one under BOTH scenarios (robust even to rebound), WEAKLY if under one, LESS if neither. Applied across the architecture toolbox this yields 17 findings — multicore, DVFS, pipeline gating, and die shrinks strongly sustainable; heterogeneity, speculation, and software parallelization weakly; dark silicon, large caches, OoO cores, and turboboost not — plus a sober-multicore case study showing 1.41–1.52× performance gains that are strongly sustainable.

Why this problem is worth solving

Sustainability entered architecture conferences as a measurement problem, and this paper argues it must become a decision problem — made under permanent fog. The split that organizes everything is between

EMBODIED carbon is emitted before first boot: fab energy (growing ~11.9% per wafer per year as nodes advance), fluorinated process gases (SF6, NF3, CF4), and upstream materials. OPERATIONAL carbon is the lifetime electricity bill, scaled by the grid’s carbon intensity. Which dominates is device-class-dependent: measured LCAs show mobile devices and hyperscale servers are embodied-dominated, always-on connected devices operational-dominated

— and the fog is thickest exactly where decisions bite. A designer choosing between a bigger cache and a second core cannot know the product’s lifetime, its owners’ usage, the 2030 grid mix, or the fab’s true gas emissions. Worse, the

Jevons’ paradox — efficiency improvements increase total consumption: a faster, more efficient chip gets used more (filling freed idle time with new work) and sells more units (multiplying embodied emissions), potentially INCREASING net emissions from a change intended to cut them. Any carbon analysis that ignores rebound optimizes a fiction

means even perfect data about today would mispredict the consequence of shipping a better chip.

The paper’s stance is that this uncertainty is not a data collection backlog but a permanent condition — secrecy, markets, and human behavior are not going to be measured away — and that the correct response is a model whose conclusions are robust across the unknowns rather than dependent on them. That epistemically humble design has teeth: run the same analysis under both usage scenarios and both weightings, and the architecture toolbox sorts itself into choices that are green under every assumption, green only if rebound never comes, and never green at all. Several of the field’s proudest mechanisms land in the last two bins.

What people did before, and where it broke

LCA reports. Rigorous whole-product accounting — but one aggregate number per system, useless for attributing carbon to a cache versus a core, and unavailable for chips individually. The paper openly calls on manufacturers to publish per-processor carbon characterizations.
ACT (bottom-up, data-driven). The architect-facing state of the art, assembling fab and industry data into absolute footprints. Invaluable where data exists — and honest about the “non-negligible gap” versus LCAs where it does not. FOCAL positions itself as ACT’s complement: ACT for detailed late-stage estimates, FOCAL for early-stage direction-finding that the data fog cannot deflect.
GreenChip, CarbonExplorer (the latter covered elsewhere on this site). Tools for upgrade-timing and datacenter design space — valuable, but single-scenario: prior work implicitly assumes fixed-work and a fixed embodied-to-operational ratio, exactly the assumptions rebound and device diversity violate.
The habitual metrics. Architects already optimize area, energy, and power — but separately, and never trading embodied against operational. Sustainability is precisely that trade, and no existing metric expressed it.

How FOCAL works

Two proxies, two scenarios, one weight, three verdicts

Embodied proxy: die area new

The fab's unit of production is the wafer; per-chip embodied carbon is inversely proportional to chips-per-wafer, a pure geometry function of die area (with an empirical edge-loss term). Yield complicates this — bigger dies fail more — but industry sells defective dies as lower bins, approaching the perfect-yield curve, so area alone is a fair first-order proxy. Area is also exactly what architects control.
↓ →
Operational proxy: energy OR power, by scenario new

FIXED-WORK (the device does a set amount of work over its life — strong-scaling HPC, a video decoder at fixed frame rate): footprint ∝ ENERGY = power × time. FIXED-TIME (a better device is used for the same lifetime and does MORE work — weak scaling, always-on services, datacenters refilling freed capacity): time is constant, so footprint ∝ POWER. Fixed-time is the rebound effect made computable.
↓ →
The E2O weight α new

Total footprint = α·(embodied ratio) + (1−α)·(operational ratio). Since the true ratio is unknowable at design time, FOCAL sweeps device-class scenarios from the LCA literature: embodied-dominated α = 0.8±0.1 (mobile, hyperscale servers) and operational-dominated α = 0.2±0.1 (always-connected devices), reporting error bars over the ranges.
↓ →
NCF: the comparison metric new

NCF(X,Y) = α·(A_X/A_Y) + (1−α)·(E_X/E_Y or P_X/P_Y). Below one: X is greener than Y under that scenario and weighting. Ratios, not absolutes — sidestepping every quantity the fog hides, because unknown constants cancel.
↓ →
The taxonomy: strong / weak / less sustainable new

STRONGLY sustainable: NCF < 1 under BOTH fixed-work and fixed-time — greener under all circumstances, rebound included. WEAKLY: under one scenario only — green if and only if usage does not grow. LESS: under neither. The taxonomy converts scenario disagreement from a nuisance into the signal: robustness across the unknowns IS the conclusion.
↓ →
Applied: 17 findings and a case study new

Using Hill-Marty/Amdahl-style analytical models, CACTI, McPAT, and published measurements, FOCAL prices the toolbox: multicore, DVFS, pipeline gating, die shrinks, low-complexity cores — strong; heterogeneity, branch prediction, runahead, software parallelization — weak; dark silicon, large caches, OoO-vs-InO, turboboost — less. A closing case study designs a next-node multicore soberly: 4–6 cores strongly sustainable at 1.41–1.52× performance; 7–8 cores weakly or not.

A charming methodological footnote: the entire analysis runs on analytical models — Amdahl/Hill-Marty extensions, CACTI, published numbers — which, the author notes, minimizes the environmental footprint of the research itself compared to simulation campaigns.

The idea

Model what you control; parameterize what you cannot know. FOCAL’s proxies are chosen by an architect’s reachability: die area, energy, and power are design-time levers, while fab gas inventories and 2030 grid mixes are not. Everything unreachable collapses into one parameter (α) swept over ranges, and everything absolute cancels in ratios. The payoff is epistemic: when a conclusion holds across both scenarios and the whole α range — multicore is greener, turboboost is not — it holds despite the fog; when a conclusion flips between scenarios, the flip itself is the finding (this choice is a bet on usage not growing). This is the same refusal to fake certainty that this site’s OS-isolation page showed with its partial safety ordering — rank only what is defensibly rankable, and make incomparability explicit.

Rebound is not a footnote — it is half the model. The fixed-time scenario is the paper’s sharpest construction: rather than treating Jevons’ paradox as an unmodelable sociological caveat, it becomes a first-class usage scenario in which better performance converts to more work, making POWER (not energy) the operational proxy. The taxonomy then gives rebound its proper weight: “strongly sustainable” means green even if the rebound comes, and “weakly” flags every mechanism whose greenness is hostage to usage staying flat. Software parallelization is the emblematic case — it cuts the footprint 23% under fixed work and raises it 53% under fixed time — a two-edged sword no single-scenario analysis could see.

Re-price the toolbox, and some sacred cows get gored. The findings read as a sustainability audit of thirty years of architecture: dark silicon — tens of accelerators, mostly powered off — is a pure embodied-carbon liability (~2.5× footprint at embodied-dominated weights) that its own defining constraint prevents from amortizing; large caches fail the same test; the OoO-versus-InO gap is a carbon trade, with complexity-effective middle points (the Forward Slice Core: −32–53% footprint for −6.3% performance versus OoO) emerging as the sweet spot. And the die-shrink analysis lands the historical punch: shrinks are strongly sustainable even as per-wafer manufacturing carbon grows 25% per node — chips would have gotten greener for decades had architects shrunk them, but Moore’s transistors were spent on more cores, more cache, more accelerators instead. Jevons’ paradox, operating inside the chip.

FOCAL in action, from formula to verdict

Pricing an accelerator, then a whole roadmap

NCF < 1 = greener than baseline. α = embodied-to-operational weight (0.8 embodied-dominated, 0.2 operational-dominated). Numbers from the paper's analyses.

Step 1 of 6

A design question arrives

Should this SoC add an H.264 accelerator? Published data: +6.5% chip area, similar performance to the out-of-order core, 500× less energy when active. The old habit weighs performance per watt and says obviously yes. FOCAL asks two more questions: which footprint dominates this device class, and how often will the accelerator actually run?

area feeds the embodied ratio; energy/power feed the operational ratio
the usage fraction becomes an explicit axis, not an assumption

Why it works

Per-chip embodied carbon is geometry (chips per wafer) plus manufacturing constants that cancel in ratios → die area is a proxy the fog cannot corrupt, and it is precisely the lever architects hold.
Fixed-work and fixed-time bracket the true usage future (energy vs power as the operational proxy) → the rebound effect stops being an unmodelable caveat and becomes one of two computable scenarios.
Ratios plus a swept weight α replace absolute footprints → every industry secret and grid unknown either cancels or lands in a parameter range → conclusions are claims about robustness, not about hidden constants.
Requiring NCF < 1 under BOTH scenarios defines strong sustainability → the taxonomy separates mechanisms green under all futures from those hostage to flat usage → the toolbox sorts into actionable bins rather than one fragile ranking.
Analytical models (Amdahl/Hill-Marty, CACTI, published measurements) suffice for first-order questions → the whole audit runs without simulation campaigns, is reproducible by inspection, and — fittingly — carries a minimal footprint itself.

What it costs

First-order means first-order. Area ignores packaging, assembly, and test; energy/power proxies ignore idle-time structure, aging, and workload mix. FOCAL is explicitly NOT for fine-grained trade-offs where real data exists — that is ACT’s job.
Validation is impossible, by the problem’s own nature. No per-chip carbon data exists to test against; the model’s defense is principled construction and robustness sweeps, not empirical error bars — an honest but real limitation.
The α scenarios inherit LCA assumptions. The embodied/operational device-class split comes from a small set of published characterizations; if those shift (grid decarbonization, longer lifetimes), the weightings shift.
Markets are out of scope. FOCAL prices a design against a design; it cannot price increased deployment (the other arm of Jevons), business models, or policy — the paper says so plainly and points to legislation as the missing force.
Sober designs must sell. The case study’s strongly sustainable options concede peak performance; a benchmark-driven market pushes toward exactly the 7–8-core options FOCAL flags — the model informs, but incentives decide.

The evaluation

Not benchmarks but an audit: 17 findings across nine archetypal mechanism families, each computed under four scenario/weighting cells with error-bar sweeps, grounded in classic analytical models and published measurements, plus a technology-node case study joining the embodied (+25.2%/node wafer energy) and operational sides.

Three instruments for carbon-aware architecture

Property	LCA reports & industry disclosures	ACT (bottom-up, data-driven)
What it produces
Relationship to data uncertainty	Source of truth, but sparse and aggregate
Rebound effect	Invisible
Sample verdicts	—
Intended stage	Post-hoc accounting	Late-stage estimation with real numbers

Modeling substrate: Hill-Marty/Amdahl extensions (Woo-Lee power terms, γ=0.2 leakage), CACTI/McPAT for caches and cores, published measurements for accelerators (H.264: +6.5% area, 500× energy), branch predictors (TAGE-SC-L: 4.4% of chip area), runahead (PRE: −6.8% energy, +29.8% power); Imec node-scaling data (+25.2% wafer energy, +19.5% gases per node); de Vries chips-per-wafer geometry with Murphy yield.Underlined values explain themselves when clicked.

Where this stops working

What to keep in mind

FOCAL trades precision for robustness by design: its proxies are first-order (area omits packaging and test; manufacturing dominance of the embodied footprint is itself an empirical claim), its verdicts are relative rather than absolute, and validation against ground truth is impossible because per-chip carbon data does not exist — the paper’s call for manufacturer disclosure is load-bearing. The findings inherit their inputs: published measurements for specific mechanisms, LCA-derived α scenarios, and analytical performance models with their own idealizations. And the model prices designs, not markets — increased deployment, the other arm of Jevons’ paradox, sits outside it, as do the business incentives that currently favor exactly the design points FOCAL flags as unsustainable.

Background

The architect-facing entry in the sustainability arc

This site’s sustainability cluster — datacenter design with renewables, carbon-aware virtualization, and repurposed devices, covered elsewhere on this site — mostly operates above the chip; FOCAL brings the carbon question down to the microarchitect’s desk and, in doing so, re-prices mechanisms other pages here celebrate: runahead execution (weakly sustainable), big caches (not), dark silicon accelerators (not). Methodologically it rhymes twice. The strong/weak taxonomy is dominance reasoning across scenario axes — the same refusal to collapse incommensurables into one score as the OS-isolation page’s safety poset. And the embrace of parameterized uncertainty over false precision echoes the recurring lesson that models should be exactly as detailed as their data deserves. The deepest thread, though, is Jevons’ paradox as computing’s recurring villain: the fixed-time scenario formalizes at the chip level what the datacenter pages meet as demand growth — efficiency is never automatically green; only efficiency that survives the rebound is.

If you remember only three things

1. Carbon-aware processor design is decision-making under permanent fog — manufacturing data is secret, lifetimes and grid mixes unknowable, and Jevons' paradox means efficiency gains can raise total emissions — so bottom-up data-driven models (ACT) admit non-negligible gaps, and single-scenario analyses quietly stake their conclusions on the least knowable assumptions; FOCAL responds with first principles: die area as the embodied proxy, energy (fixed-work) or power (fixed-time — rebound formalized) as the operational proxy, and a swept embodied-to-operational weight, all in ratios where unknown constants cancel.
2. The taxonomy converts uncertainty into verdicts: STRONGLY sustainable choices cut the normalized carbon footprint under both scenarios (robust even to rebound) — multicore, DVFS, pipeline gating, die shrinks, complexity-effective cores (FSC: −32–53% footprint for −6.3% performance vs OoO); WEAKLY sustainable ones win only if usage stays flat — heterogeneity, branch prediction, runahead, and even software parallelization (−23% fixed-work, +53% fixed-time); LESS sustainable ones lose everywhere — dark silicon (~2.5×, structurally unable to amortize its silicon), large caches, turboboost.
3. The historical finding stings and the pathway encourages: die shrinks are strongly sustainable even with per-wafer manufacturing carbon growing 25% per node, so chips would have gotten steadily greener had architects shrunk them — instead Moore's transistors bought more cores, caches, and accelerators (Jevons inside the chip); the case study shows the sober alternative — 4–6 cores in the next node deliver 1.41–1.52× performance with a strictly lower footprint, while the market-default 7–8-core designs are weakly sustainable at best.

Check yourself

Check your understanding

1. A single H.264 accelerator (+6.5% area, 500× less energy) can be strongly sustainable, yet dark silicon — a chip two-thirds covered in such accelerators — is condemned as not sustainable. Predict the structural reason.
2. Why does FOCAL insist on evaluating every design under BOTH fixed-work and fixed-time scenarios — and what does it mean when a mechanism's verdict flips between them, as software parallelization's does (−23% vs +53%)?
3. FOCAL deliberately uses cruder inputs than ACT — area instead of fab data, swept parameters instead of measured ratios. Why is LESS data the right choice for its intended job?
4. The die-shrink analysis finds shrinks strongly sustainable even though manufacturing a wafer emits 25% more carbon each node. What historical conclusion follows — and what does the closing case study offer in its place?

Sources

ACM DL: FOCAL: A First-Order Carbon Model to Assess Processor Sustainability — ASPLOS 2024 (open access)