Equation 14 · Part 5 · When the Substrate Became the Product

Symbol Y_i

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

Y_i

What this part means

the dies with individual probabilities.

Its job in the formula

$Y_i$ is an input to the expression that computes the quantity on the left.

Full expressionSymbol Y_iArticle meaning

Where the article explains it

If a package contains dies with individual probabilities $Y_i$ of being good, and the assembly itself succeeds with probability $Y_{\mathrm{assy}}$ , then $Y_{\mathrm{pkg}} = Y_{\mathrm{assy}} \prod_{i=1}^{N} Y_i$ .

The passage around this formula

A multi-die package inherits a property that a single die does not have: its yield is a product, not a term. If a package contains dies with individual probabilities $Y_i$ of being good, and the assembly itself succeeds with probability $Y_{\mathrm{assy}}$ , then $Y_{\mathrm{pkg}} = Y_{\mathrm{assy}} \prod_{i=1}^{N} Y_i$ . Multiplication is brutal at scale. Eight components at 99 percent each land near 92 percent together before assembly loss is counted; the same eight at 95 percent land near 66 percent.…

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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 →

See this notation across published equations →

Sources cited in the article section

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