Impingement rate, monolayer time, and Langmuir exposure
How pressure and gas species determine surface flux, monolayer formation times, and Langmuir exposures.
By Semiconductor Tools Editorial Team · Last updated: 2026-06-14
Surface contamination kinetics in vacuum are governed by molecular flux to the surface. The impingement rate Z [molecules/(cm²·s)] quantifies arrival rate; combined with sticking coefficient s, it determines how fast adsorbed films form—critical for UHV chamber conditioning, ALD nucleation discussions, and native-oxide growth estimates.
Key relations
Z ≈ 3.5×10²² · P[Torr] / √(M[g/mol] · T[K])
Monolayer time: tML ≈ NML / (Z · s), with NML ≈ 10¹⁵ molecules/cm². Langmuir exposure: 1 L = 10⁻⁶ Torr·s; exposure for time t at pressure P: L = P[Torr] × t[s] / 10⁻⁶.
Worked example — UHV chamber air exposure (Surface Exposure Calculator)
Chamber vented to dry N₂, then pumped. Residual N₂ at 5×10⁻⁷ Torr, T = 300 K, M = 28, s = 0.3 (partially reactive surface), exposure time after reaching 5×10⁻⁷ Torr: 30 s.
- Enter P = 5e-7 Torr, T = 300 K, M = 28, s = 0.3, NML = 1e15, exposure time = 30 s.
- Tool reports Z ≈ 1.9×10¹⁴ molecules/(cm²·s).
- Monolayer formation time tML ≈ 18 s—surface adsorbs ~1.7 monolayers in 30 s at this pressure.
- Langmuir exposure L ≈ 15 L for 30 s—well beyond single-monolayer coverage.
- Time to 1 L at this P: t1L ≈ 2 s. Even "good" UHV delays matter for moisture-sensitive processes.
Worked example — Compare H₂O vs N₂ at same pressure
At 1×10⁻⁶ Torr, 300 K, compare M = 18 (H₂O) vs M = 28 (N₂), s = 1:
- H₂O: Z is ~1.25× higher than N₂ (√(28/18)), so water monolayer forms faster at equal partial pressure.
- Use the calculator to quantify tML difference—motivation for bake-out and N₂ purge before pumpdown.