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Equation 6 · How Chiplets and Advanced Packaging Actually Work

What does this equation mean?

narea(p)  ∝  1p2,n_{\text{area}}(p) \;\propto\; \frac{1}{p^{2}},

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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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narean_{\text{area}}

Symbol n_area

nan_area 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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pp

Symbol p

the pitch.

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p2p^{2}

Symbol p^2

the square of p; the pitch.

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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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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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superscript

superscript

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

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11

Numerator: 1

The complete quantity above the fraction bar.

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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

Density itself is worth being precise about, because pitch and area density do not scale the same way. If interconnects sit on a roughly square grid of pitch p , the number that fit per unit area scales as narea(p)  ∝  1p2n_{\text{area}}(p) \;\propto\; \frac{1}{p^{2}}. not as 1/p . imec’s demonstrated step from 400-nanometre to 200-nanometre hybrid-bond pitch [ 4 , 3 ] is therefore not a doubling of achievable interconnect density but close to a quadrupling of it — the reason pitch numbers that look like modest, incremental reductions on a roadmap chart translate into much larger jumps in how many independent signals a bonded pair of dies can actually exchange per square millimetre.

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