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Zone 00 · Clean Room

The Wafer's Journey

Follow Lot #0190 through a $1.6M process optimization decision. The etch team wants to test five recipe parameters. The full factorial costs $1.6M. A fractional factorial costs $400K. Master Design of Experiments through the one methodology that separates a data scientist from a data analyst in a fab.

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Today's Subject
Design of Experiments
Fractional factorial DoE for semiconductor process optimization

The OFAT Trap

The etch team has been optimizing their recipe for six weeks. Their method: change RF power while holding everything else constant, find the best setting, then change pressure while holding RF power at its new value, then change gas flow. One Factor At a Time. It is intuitive. It is systematic. It is wrong. OFAT misses interaction effects: the combination where high RF power and low pressure together produce a result neither factor achieves alone. In semiconductor etch, interaction effects are not noise. They are frequently the dominant signal. Lot #0190 is the first lot in a properly designed experiment.

01
Define the Factor Space
List every process parameter believed to affect the yield response. For Lot #0190: RF Power (1000-1400W), Pressure (30-50 mTorr), Gas Flow (150-250 sccm), Temperature (170-200C), Electrode Gap (25-35mm). Five factors, two levels each.
02
Choose the Resolution
A full 2^5 factorial requires 32 runs. A Resolution IV half-fraction (2^5-1) requires 16 runs and aliases no main effect with another main effect or two-factor interaction. A Resolution III quarter-fraction (2^5-2) requires 8 runs but aliases some two-factor interactions with each other.
03
Randomize Run Order
Assign the 16 experimental wafers to runs in random order. This is not optional. Systematic run order confounds time-related process drift with the treatment effects you are trying to measure. A chamber that drifts over the day will corrupt the experiment if all high-RF-power runs happen to be scheduled in the morning.
04
Estimate Effects and Interactions
Fit a linear model with main effects and interaction terms. The contrast method gives each effect estimate as a weighted sum of responses. Resolution IV ensures main effects are estimable without bias from two-factor interactions. The interaction terms tell you what OFAT would have missed.

The fractional factorial is not an approximation of the full factorial. It is a deliberate information-theoretic choice: you trade knowledge of certain high-order interactions (which are rarely significant in physical processes) for a 50-75% reduction in experimental cost.

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