arde (aspect ratio dependent etch)

ARDE (Aspect Ratio Dependent Etching) describes how etch rate systematically decreases as feature aspect ratio increases. **Root cause**: Transport limitations - both reactant delivery and product removal become harder in deeper, narrower features. **Knudsen transport**: In molecular flow regime (mean free path > feature width), species undergo random reflections off sidewalls. Probability of reaching bottom decreases exponentially with AR. **Ion angular distribution**: Ions with off-normal angles are shadowed by feature walls, reducing ion flux to bottom of high-AR features. **Consequences**: Dense features etch slower than isolated features. Small features etch slower than large features on same wafer. **Magnitude**: Etch rate can drop 30-50% or more at AR > 10:1 compared to open areas. **Compensation**: Overetch required to clear high-AR features, which stresses selectivity. **Mitigation strategies**: Lower pressure (more directional ions), higher bias (faster ions), pulsed plasma, cyclic etch-dep processes. **Impact on design**: Features of different AR need different etch times, causing integration challenges. **3D NAND**: Extreme example where ARDE limits practical channel hole depth. **Process optimization**: Characterize etch rate vs AR curve and adjust target to compensate.