$$\rho(p) \;\approx\; \frac{1}{p^{2}}$$

Equation 2 · AI Hardware & Semiconductors

Chiplets and Advanced Packaging in 2035: Scenarios, Signals, and Falsifiable Predictions

This equation gives an approximation: it relates the quantities while allowing an approximation.

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 $\rho(p) \;\approx\; \frac{1}{p^{2}}$. 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…

Meanings in this article

• $p$: the pitch.
• $p^{2}$: the square of p; the pitch.

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