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Equation 4 · Part 1 · Chiplets and Advanced Packaging in Practice: An Advanced Technical Guide

Symbol y_i

yiy_i
yiy_i

What this part means

the independent per-die yield.

Its job in the formula

yiy_i is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Where the article explains it

If each of n chiplets bonded into one package has an independent per-die yield yiy_i , the assembly’s final yield is approximately YpackageY_{\text{package}} ≈\approx ∏i=1n\prod_{i=1}^{n} yiy_i which is a first-order model — it assumes bonding introduces no additional defects and that die yields are independent, both of which are simplifications addressed separately below.

The passage around this formula

which is a first-order model — it assumes bonding introduces no additional defects and that die yields are independent, both of which are simplifications addressed separately below. Even under this optimistic assumption, four chiplets each yielding 95% compose to roughly 81% assembly yield, and a twenty-die stack at the same per-die yield falls to roughly 35% — the industry’s own framing of why an unscreened stack becomes uneconomical fast as die count rises [ 4 ] . The entire purpose of KGD testing is to push each yiy_i as close to 1 as pre-bond screening allows, since the model shows the product is unforgiving of even small per-die shortfalls once several dies are chained together.

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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