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Equation 2 · Part 4 · Chiplets and Advanced Packaging in 2035: Scenarios, Signals, and Falsifiable Predictions

fraction

ρ(p)  ≈  1p2.\rho(p) \;\approx\; \frac{1}{p^{2}}.
fraction

What this part means

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

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

The passage around this formula

Analysis. The physical reason pitch matters this much is a simple scaling relationship worth making explicit. For interconnects arranged on a roughly square grid at pitch p , the number of connections available per unit of bonding area scales as ρ(p)  ≈  1p2\rho(p) \;\approx\; \frac{1}{p^{2}}. Halving the pitch is therefore not a doubling of available interconnect density; it is close to a quadrupling. That is the assumption doing the work every time a packaging roadmap reports a pitch number: the 2024-to-2026 move from 400 to 200 nanometres in imec and EV Group’s demonstrated wafer-to-wafer results is not a twofold gain in what a fixed bonding area can carry, it is closer to a fourfold one [ 5 , 4 ] . The comparison…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.