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Published equation contexts

Ypackage≈∏i=1nyiY_{\text{package}} \approx \prod_{i=1}^{n} y_i

Why this formula appears here

The arithmetic behind that claim is a plain probability composition, and it is worth writing down because it is the one piece of real math in advanced packaging that most design reviews skip past. If each of n chiplets bonded into one package has an independent per-die yield yiy_i , the assembly’s final yield is approximately Ypackage≈∏i=1nyiY_{\text{package}} \approx \prod_{i=1}^{n} y_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. 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…

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YpackageY_{\text{package}}

Symbol Y_package

YpY_package is part of the quantity the equation computes from the expression on the right.

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ii

Symbol i

i appears in the bound of this product. The bound states where the repeated operation starts, ends, or which values it includes.

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nn

Symbol n

n appears in the bound of this product. The bound states where the repeated operation starts, ends, or which values it includes.

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i=1i=1

Starting index or lower bound: i=1

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

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nn

Ending index or upper bound: n

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

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How to interpret it

Its accuracy depends on the assumptions and range of use described in the article. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

Ypackage≈∏i=1nyiY_{\text{package}} \approx \prod_{i=1}^{n} y_i

Equation 3 · Semiconductors

Chiplets and Advanced Packaging in Practice: An Advanced Technical Guide

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

The arithmetic behind that claim is a plain probability composition, and it is worth writing down because it is the one piece of real math in advanced packaging that most design reviews skip past. If each of n chiplets bonded into one package has an independent per-die yield yiy_i , the assembly’s final yield is approximately Ypackage≈∏i=1nyiY_{\text{package}} \approx \prod_{i=1}^{n} y_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. 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…

Meanings in this article

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