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.