Mean free path (vacuum) calculator
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KEY POINTS
The mean free path λ = kT/(√2·πd²p) is inversely proportional to pressure: for nitrogen it is about 70 nm at atmospheric pressure, about 7 mm at 1 Pa and about 70 m at 10⁻⁴ Pa. Pipe conductance and step coverage differ between viscous flow, where λ is shorter than the vessel, and molecular flow, where it is longer. Sputtering and dry etching run at low pressure so atoms and ions travel straight without scattering.
Inputs
The monolayer formation time is a minimum estimate that assumes every incoming molecule sticks to 10¹⁵ cm⁻² surface sites. Real sticking probabilities are below 1 and depend on the main residual gas (water in high vacuum).
Pressure and mean free path (at the entered temperature)
Mean free path at typical process pressures
| Example pressure | Pa | λ (Argon (Ar)) | Kn (L = 50 mm) |
|---|---|---|---|
| Atmospheric pressure | 1.01×10⁵ | 69 nm | 1.38×10⁻⁶ |
| LPCVD (about 0.3 Torr) | 40 | 175 µm | 3.50×10⁻³ |
| Dry etching (about 10 mTorr) | 1.33 | 5.26 mm | 0.105 |
| Sputtering (about 0.5 Pa) | 0.5 | 14 mm | 0.28 |
| High vacuum (10⁻⁴ Pa) | 1.00×10⁻⁴ | 69.9 m | 1,400 |
| Ultra-high vacuum (10⁻⁷ Pa) | 1.00×10⁻⁷ | 69.9 km | 1.40×10⁶ |
How mean free path shapes equipment design
The mean free path is the average distance a gas molecule travels before colliding with another, and it is inversely proportional to pressure. For nitrogen it is about 70 nm at atmospheric pressure, about 7 mm at 1 Pa and about 70 m at 10⁻⁴ Pa, a change of more than six orders of magnitude. When the mean free path is shorter than the vessel dimensions, collisions between molecules dominate (viscous flow); when it is longer, molecules fly from wall to wall (molecular flow), and the formulas for pipe conductance change accordingly.
In sputtering, the number of collisions an atom undergoes between the target and the substrate affects film quality and step coverage. Lowering the pressure so that the mean free path exceeds the target-to-substrate distance lets atoms travel in straight lines and arrive with their energy intact (long-throw sputtering). Dry etching uses low pressure for a similar reason: less ion scattering means more vertical incidence and more anisotropic etching.
FAQ
What is the Knudsen number?
The mean free path divided by a characteristic length such as pipe diameter. Below about 0.01 the flow is viscous, above about 0.5 it is molecular, and in between it is transitional.
How fast does a surface get contaminated in vacuum?
At 10⁻⁴ Pa, a monolayer can form in seconds if every molecule sticks. In ultra-high vacuum around 10⁻⁷ Pa, it takes on the order of an hour or more.
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Last updated: October 23, 2026