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Equation 1 · Advanced Semiconductor Fabrication in 2035: Scenarios, Signals, and Falsifiable Predictions

What does this equation mean?

D∝1CPP×HcellD \propto \frac{1}{\mathrm{CPP} \times H_{\mathrm{cell}}}

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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DD

Symbol D

D is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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HcellH_{\mathrm{cell}}

Symbol H_cell

HcH_cell occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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fraction

fraction

Divide the expression above the line by the one below it.

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∝

∝

Proportional to; the scale factor is not shown.

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multiplication

multiplication

Multiply the quantities on either side.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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11

Numerator: 1

The complete quantity above the fraction bar.

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CPP×Hcell\mathrm{CPP} \times H_{\mathrm{cell}}

Denominator: CPP × H_cell

The complete quantity below the fraction bar; it must be nonzero for this division.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction.

What the article says around this equation

Analysis. The more granular figures behind that roadmap show what CFET is actually buying, and expose the assumption underneath the 2033 date. Reporting on the same 2026 forum gives contacted poly pitch (CPP) and standard-cell height across successive nodes: A14 in 2028 at roughly 45-nanometre CPP and 115-nanometre cell height, with High-NA EUV introduced at that stage; A10 around 2030 holding CPP near 42 nanometres, a point past which “further scaling of CPP is expected to face fundamental limitations”; A7 — CFET’s likely starting point, with adoption itself described as uncertain — at that same 42-nanometre CPP; and A5, arriving around 2035–2036, still at 42-nanometre CPP but with cell…
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Analysis. The more granular figures behind that roadmap show what CFET is actually buying, and expose the assumption underneath the 2033 date. Reporting on the same 2026 forum gives contacted poly pitch (CPP) and standard-cell height across successive nodes: A14 in 2028 at roughly 45-nanometre CPP and 115-nanometre cell height, with High-NA EUV introduced at that stage; A10 around 2030 holding CPP near 42 nanometres, a point past which “further scaling of CPP is expected to face fundamental limitations”; A7 — CFET’s likely starting point, with adoption itself described as uncertain — at that same 42-nanometre CPP; and A5, arriving around 2035–2036, still at 42-nanometre CPP but with cell height down to roughly 64 nanometres [ 6 ] . Layout density is, to a first approximation, inversely proportional to the area of one contacted cell, which scales with pitch times cell height: D∝1CPP×HcellD \propto \frac{1}{\mathrm{CPP} \times H_{\mathrm{cell}}}. Treat this as a simplified proportionality, not a physical law — real layout density also depends on track count, via pitch and design-rule detail this expression ignores. Applied to imec’s own published figures, it makes the assumption behind the CFET scenario explicit. Between A14 (2028) and A5 (2035–2036), CPP shrinks by only about 7 percent (45 to 42 nanometres) while cell height shrinks by roughly 44 percent (115 to 64 nanometres), together implying close to a 93 percent density gain over that span [ 6 ] — almost all of it arithmetically attributable to cell-height and architecture change, not to lithographic pitch. CFET’s economic case rests on exactly that arithmetic: it buys cell-height reduction, which is why the roadmap can hold CPP essentially flat across A10, A7 and A5 while still projecting a rising density curve. Note also what the roadmap does not resolve: A5, the first full node after CFET’s stated A7 introduction, sits inside this article’s 2035 horizon, and CFET adoption at A7 is explicitly flagged as uncertain. No leading logic manufacturer besides imec’s own roadmap appears to have published its own calendar year for CFET production; 2033 is imec’s institutional projection for its member ecosystem, not a manufacturer’s shipping commitment.

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