EARLY VS. MATURE YIELD

No process starts out fully tuned

yield climbs as the process matures

A brand-new process, just moved from development to production, almost always yields lower than the same process will a year later. Every engineering fix, every tool tweak, every root cause chased down from a wafer map nudges the number up, a little at a time.

The 'learning curve' is yield engineering, made visible as a graph.

A SIMPLE YIELD MODEL

Defect density times die area

Y = e^{-D₀ * A}

A simple model treats killer defects as landing randomly, at density D₀ per unit area, across a die of area A. The chance a die catches zero killer defects, and so passes, works out to roughly e^{-D₀ times A}. It's a simplification, but it captures the core trade: bigger die and dirtier processes both hurt yield.

Double the die area, and this model roughly squares the odds against you.

A WORKED EXAMPLE

Turning the model into a number

D₀ = 0.2/cm², A = 1 cm² gives about 82%

With a defect density of 0.2 defects per square centimeter and a die area of 1 square centimeter, the model gives roughly e^-0.2, about 82% yield. Shrink the die to half that area and yield rises to roughly 90%; double it and yield falls to about 67%.

The same process, on a different die size, can look like a completely different yield.

THE LEARNING CURVE

How yield actually improves

Find the pattern A wafer map or control chart points at a suspect step

Chase the root cause Engineers isolate exactly what's driving that pattern

Fix it, then confirm A process change is made, then watched to see if D₀ actually drops

Repeat, for years Each fix buys a little more yield, long after a product first ships

A mature process isn't a finished one: it's one that's been through this loop many times.

UNIT 36 STUDY COMPLETE

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Ready for the Fab Challenge?

You've covered turning defect density into a yield number, and how yield improves over time.