Mean Free Path Calculator

Calculate mean free path (λ) from pressure and gas type. Supports Ar, N2, H2, He, Kr, Xe. Use to compare with target–substrate distance and estimate scattering in vacuum processes.

Calculator

Mean Free Path

52.7757 mm

Gas: Argon (d = 3.64 Å) at 300 K

Technical Explanation

What is Mean Free Path?

Mean free path (λ) is the average distance a molecule travels between collisions. In vacuum and thin-film processes, it indicates whether the process is in the molecular flow regime (λ > chamber dimensions) or viscous flow regime (λ << chamber dimensions). Comparing λ with target–substrate distance helps predict scattering and film uniformity in sputtering, evaporation, and PVD.

Formula

For an ideal gas with hard-sphere collisions:

λ = kT / (√2 π d² P)

where k = Boltzmann constant (1.38×10⁻²³ J/K), T = temperature (K), d = collision diameter (m), P = pressure (Pa). Supports Ar, N2, H2, He, Kr, Xe.

Semiconductor Applications

In PVD and sputtering, λ > target–substrate distance implies less scattering and better step coverage. In high vacuum (e.g. mTorr), heavier gases (Ar, Kr, Xe) have shorter λ than lighter ones (He, H2), affecting process design and gas selection.

References & Disclaimer

Collision diameters from NIST and Handbook of Chemistry and Physics. For critical applications, verify values independently.

Engineering Guide

Why this calculation matters

Mean free path λ determines molecular vs viscous flow, gas-phase scattering in PVD, and whether conductance formulas apply. λ compared to pipe diameter gives Knudsen number.

In semiconductor equipment work: PVD argon backfill selection, Knudsen regime checks before conductance calc, explaining throw distance vs pressure tradeoffs.

Input parameters

Pressure
Pa, Torr, mTorr, mbar, or bar.
Gas species
Ar, N₂, H₂, He, Kr, Xe with literature collision diameter.
Temperature
Default 300 K; affects λ linearly.

Output interpretation

λ (mm)
Mean free path from λ = kT/(√2 π d² P).

If λ < throw distance in sputter, expect gas-phase scattering. If Kn = λ/D < 0.01, molecular conductance formulas may not apply.

Assumptions

  • Hard-sphere collision model; diameters from NIST/CRC.
  • Single gas species; no mixture correction.
  • Uniform T and P in volume.

Limitations

  • Collision diameters are approximate; λ uncertainty ~10–20% typical.
  • Near transition regime, neither molecular nor viscous limit is exact.

Worked example

Magnetron sputter — Ar at 3 mTorr, 300 K

  1. λ ≈ 22 mm vs 150 mm throw → significant scattering possible.
  2. Foreline D = 5 cm → Kn ≈ 0.44 (transition) at same pressure.
  3. Reduce to 0.5 mTorr → λ ≈ 130 mm, closer to ballistic transport.