Mean free path in vacuum systems and PVD processes
What mean free path (λ) means, how pressure and gas species affect it, and why it matters for sputtering, evaporation, and chamber design.
By Semiconductor Tools Editorial Team · Last updated: 2026-06-14
The mean free path λ is the average distance a molecule travels between collisions with other gas molecules. It determines whether gas transport in a duct is molecular (wall-dominated) or viscous (intermolecular), and whether sputtered atoms travel ballistically or scatter in the gas phase.
Kinetic-theory estimate
λ = kT / (√2 π d² P)
λ increases as pressure decreases and depends on molecular diameter d (gas-specific). At fixed pressure, lighter/smaller molecules (He, H₂) have longer λ than heavy gases (Xe, SF₆).
Worked example — PVD argon backfill with Mean Free Path Calculator
Magnetron sputter: Ar backfill 3 mTorr, T = 300 K. Source-to-substrate distance 15 cm. Foreline ID 5 cm.
- Calculator: gas Ar, P = 3 mTorr, T = 300 K → λ ≈ 22 mm (2.2 cm).
- λ < throw distance (15 cm): sputtered atoms experience gas-phase scattering—film density and stress may differ from ballistic deposition.
- Knudsen number for foreline: Kn = λ/D ≈ 2.2/5 ≈ 0.44 (transition regime)—molecular conductance formulas are approximate; see molecular vs viscous flow.
- Reduce to 0.5 mTorr in calculator: λ ≈ 130 mm—closer to ballistic transport at 15 cm throw.
Worked example — UHV base pressure
Base pressure 5×10⁻⁸ Torr, Ar, 300 K:
- λ ≈ 1.3 m—molecular flow in any practical piping diameter; conductance formulas from Conductance Calculator apply.