$$n_{\text{area}}(p) \;\propto\; \frac{1}{p^{2}}$$

Equation 6 · AI Hardware & Semiconductors

How Chiplets and Advanced Packaging Actually Work

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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 $n_{\text{area}}(p) \;\propto\; \frac{1}{p^{2}}$. 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.

Meanings in this article

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

Equation guide → · Article →