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Daniel M. Dobkin
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Kinetic Theory Example
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T = 300 °K [room temperature]
Nitrogen (N2 molecule), M = 28 gm/mole a = 3.7
Å
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Pressure
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density
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mean free path
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mean velocity
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flux to surface
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"growth rate"
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(Torr)
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(molecules/cm3)
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(microns)
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(cm/sec)
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(molecules/cm2 sec)
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(microns/minute)
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0.1
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3.2E15
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500
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47,000
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3.8E19
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10
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10
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3.2E17
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5
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47,000
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3.8E21
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1000
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|
760
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2.5E19
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0.07 (70 nm)
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47,000
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2.9E23
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77,000
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[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:
- 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 rates:
- 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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