interaction effect
**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 (%)
| Run | Power (A) | Pressure (B) | Uniformity |
|-----|-----------|-------------|------------|
| 1 | 200W (−) | 20 mT (−) | 3.0% |
| 2 | 400W (+) | 20 mT (−) | 2.0% |
| 3 | 200W (−) | 50 mT (+) | 2.5% |
| 4 | 400W (+) | 50 mT (+) | 5.0% |
- 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.