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Equation 5 · Part 7 · From Origins to Frontier: A History of Chiplets and Advanced Packaging

subscript

Ypkg=Yassy∏i=1NYi.Y_{\text{pkg}} = Y_{\text{assy}} \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 reputation is straightforward and still governs every multi-die package built today. A packaged part’s yield is not the yield of its worst component; it is the product of every component’s yield together with the yield of the assembly step that joins them. Write the package yield YpkgY_{\text{pkg}} as a function of the assembly yield YassyY_{\text{assy}} and the yield YiY_i of each of N individual die placed into the package: Ypkg=Yassy∏i=1NYiY_{\text{pkg}} = Y_{\text{assy}} \prod_{i=1}^{N} Y_i . Multiplication is unforgiving at scale. Every die added to a package is another factor less than one, so a package holding several die each individually manufactured at a very respectable yield can still fail at an uncomfortable rate…

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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.