Impingement Rate · Monolayer Time · Langmuir

Estimate how fast molecules hit and cover a surface at a given pressure, temperature, and gas species. Useful for analysing surface contamination, exposure budgets, and UHV requirements.

Calculator

Estimate impingement rate (molecular flux), monolayer formation time, and Langmuir exposure for a given pressure, temperature, and gas species.

Example: 1e-6 Torr for typical UHV background pressure.

Example: N₂ ≈ 28, Ar ≈ 40, H₂ ≈ 2.

s ≈ 1 for very reactive/clean surfaces, much lower for saturated or inert surfaces.

A typical value is ~1e15 molecules/cm².

Used to compute Langmuir exposure L = P[Torr]·t / 1e-6.

Impingement rate Z

3.833e+14 molecules/cm²·s

Effective flux (Z·s)

3.833e+14 molecules/cm²·s

Monolayer rate

0.383300 ML/s

Monolayer time (1 ML/s)

2.6089 s

≈ 0.043482 min

Langmuirs for t = 1 s

1.0000 L

≈ 1.0000 monolayers (assuming s)

Time for 1 Langmuir at this pressure

1.0000 s

1 Langmuir (1 L) = 1e-6 Torr·s and roughly corresponds to one monolayer of exposure for s ≈ 1. Real systems often have lower sticking coefficients and surface saturation effects, so use these results as order-of-magnitude guidance.

Technical Explanation

Impingement Rate (Molecular Flux)

The impingement rate Z is the number of gas molecules striking a unit area of surface per unit time. For an ideal gas, a widely used approximation (with P in Torr, T in K, M in g/mol) is:

Z ≈ 3.5 × 10²² · P[Torr] / √(M · T)   molecules/(cm²·s)

This shows that flux is proportional to pressure and inversely proportional to the square root of temperature and molecular mass. Heavier gases (larger M) deliver fewer molecules to the surface at the same pressure.

Monolayer Time

A "monolayer" is often taken as ~10¹⁵ molecules/cm² on a surface. For a sticking coefficient s (0–1), the effective flux that actually adsorbs is Z·s, so the monolayer formation time is roughly:

t_ML ≈ N_ML / (Z · s)

At 10⁻⁶ Torr with s ≈ 1, t_ML is on the order of 1 second, which is why even brief exposures at "good" vacuum can still lead to rapid surface contamination.

Langmuir Exposure

The Langmuir is a convenient unit for exposure defined as:

1 L = 10⁻⁶ Torr·s

For many surface-science contexts, an exposure of ~1 L at s ≈ 1 is taken to correspond to roughly one monolayer. The tool computes Langmuirs for a given pressure and exposure time, and converts this to an approximate number of monolayers using the chosen sticking coefficient.

Practical Interpretation

These estimates help answer questions like "How fast does my surface get dirty at 10⁻⁶ Torr?" or "How long can a wafer be exposed before a monolayer of contamination forms?" Real systems may deviate due to surface chemistry, roughness, multi-layer adsorption, and temperature, so treat the results as order-of-magnitude guides rather than exact predictions.