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Equation 6 · Part 7 · How Chiplets and Advanced Packaging Actually Work

superscript

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

What this part means

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.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

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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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

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