An interaction effect in DOE occurs when the effect of one factor on the response depends on the level of another factor. In other words, the factors don't act independently — they work together (or against each other) in ways that can't be predicted from their individual main effects alone.

Example: Etch Process Interaction

• Factor A: RF Power (200W vs. 400W)
• Factor B: Pressure (20 mTorr vs. 50 mTorr)
• Response: Etch Uniformity (%)

• At low pressure: increasing power improves uniformity (3.0% → 2.0%).
• At high pressure: increasing power worsens uniformity (2.5% → 5.0%).
• The effect of power reverses depending on pressure — this is an interaction.

How to Detect Interactions

• Interaction Plot: Plot the response vs. one factor, with separate lines for each level of the other factor. If the lines are parallel, there is no interaction. If the lines cross or diverge, an interaction is present.
• ANOVA: The statistical significance of interaction terms is tested using F-tests in the analysis of variance.
• Interaction Effect Size: $\text{AB Interaction} = \frac{1}{2}[(\text{effect of A at B+}) - (\text{effect of A at B-})]$

Why Interactions Matter

• Misleading Main Effects: If you have a strong A×B interaction, the main effect of A (averaged across B) may be small or zero — even though A has a large impact at specific B levels. Focusing only on main effects would miss this.
• Optimization: The optimal setting for factor A may depend on the level of factor B. You can't optimize A and B independently.
• Process Understanding: Interactions reveal the physics of the process — understanding why two factors interact leads to deeper process knowledge.

Common Semiconductor Interactions

• Power × Pressure in etch: Higher power at low pressure improves anisotropy; at high pressure, it causes more lateral etching.
• Dose × Focus in lithography: The CD response to dose change differs at different focus settings — defining the process window.
• Temperature × Time in diffusion: Diffusion distance depends on both temperature and time nonlinearly.

One-Factor-at-a-Time (OFAT) Misses Interactions

• OFAT varies one factor while holding others constant. It cannot detect interactions — it would find the optimal A at one fixed B, missing that a different A is optimal at a different B.
• This is the primary reason DOE is preferred over OFAT in semiconductor process development.

Interaction effects are often as important as main effects — understanding them is essential for true process optimization rather than finding locally optimal but globally suboptimal conditions.