Equation 14 · Part 6 · When the Substrate Became the Product

=

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

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

Full expression=Article meaning

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. And the loss is not proportional to the failing part — scrapping a package destroys every good die in it plus the assembly work. This is precisely why known-good-die testing dominates the discussion: the whole point is to move the $Y_i$ …

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

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