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Equation 3 · Part 7 · Chiplets and Advanced Packaging in Practice: An Advanced Technical Guide

subscript

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

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

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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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.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the surrounding passage

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