You want to deposit a few layers of atoms on a substrate To

You want to deposit a few layers of atoms on a substrate. To do this you place the clean, polished substrate in a vacuum chamber at ultra-high vacuum (UHV). and above it put a hot puck of the metal you want to deposit onto the substrate. The metal evaporates off and hits your (colder) substrate, where they stick. Atoms are equally likely to hit anywhere on your substrate. You want 6 atomic layers. Assuming the chance of an atom (of size ~ 1 ) hitting any given spot on your substrate (which is big. say 1cm^2) is equal and (obviously) very low, what distribution should describe the probability of having an atom at a given spot on the substrate? Your run your deposition until the mean film thickness is 6 atomic layers. What is the fraction of surface that has no metal at all? What fraction is 3 atoms thick? What fraction is 6 atoms thick?

Solution

i. The area of the metal atom is very less than that plate area. Probability of atom hitting the substrate is veryvery less than one . Hence we can poisson distribution

W(n)=(6ⁿ/n!)e^-6

ii)

1) No metal atom hitting the substrate, n =0

W(0)=(6⁰/1!) e^-6=0.00247=0.0025=0.003

2) for 3 atom layer thickness W(3)=(6³/3!) e^-6=0.089

3) for 6 atom layer thickness W(6)=(6⁶/6!) e^-6=0.161