# Kinetic Theory Example

 Pressure density mean free path mean velocity flux to surface "growth rate" (Torr) (molecules/cm3) (microns) (cm/sec) (molecules/cm2 sec) (microns/minute) 0.1 3.2E15 500 47,000 3.8x1019 10 10 3.2x1017 5 47,000 3.8x1021 1000 760 2.5x1019 0.07 (70 nm) 47,000 2.9x1023 77,000

T = 300 °K [room temperature, at least if you like things toasty]

Nitrogen (N2 molecule), M = 28 gm/mole a = 3.7 Å

[the "growth rate" is the approximate amount of solid material that would be formed if each nitrogen molecule were incorporated into a solid on the surface -- shown here to demonstrate the very high growth rates that would be possible if every molecule was incorporated at high partial pressures of a precursor material]

## Things to note:

• At 47,000 cm/second: a molecule will cross a 1-meter chamber in 2 msec -- about 1,000 miles/hour!
• The impingement-limited growth rate greatly exceeds actual growth rate. This means either the actual deposition precursor is rare (partial pressure at surface << total pressure) OR the probability of incorporation into the surface is small

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