Ion deflection due to sheath field curvature

Plasma sheath electric fields, hence ion motions, deviate near patterned substrate features. This results in a basic directionality limit to ion-assisted processes. Ion deviation is here derived analytically for dc sheaths, and expressed as an ‘‘ion isotropy ratio,’’ the fraction of ions bombarding a trench sidewall instead of its bottom. This ratio is equal to (trench depth/ion acceleration distance) multiplied by a factor of about 0.5. Thus, ion deviation is especially significant for discharges with small sheath heights and yields a fundamental tradeoff between ion directionality, ion energy, and permissible ion current.