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






Return to Tutorial Table of Contents
Book version of the CVD Tutorial