Equation 5 · Part 3 · From Origins to Frontier: A History of Chiplets and Advanced Packaging

Symbol i

Y_{\text{pkg}} = Y_{\text{assy}} \prod_{i=1}^{N} Y_i .

i

What this part means

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

Its job in the formula

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

Full expressionSymbol iArticle meaning

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 $Y_{\text{pkg}}$ as a function of the assembly yield $Y_{\text{assy}}$ and the yield $Y_i$ of each of N individual die placed into the package: $Y_{\text{pkg}} = Y_{\text{assy}} \prod_{i=1}^{N} Y_i$ . 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 variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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