Sticking coefficient - Alchetron, The Free Social Encyclopedia

Sticking coefficient is the term used in surface physics to describe the ratio of the number of adsorbate atoms (or molecules) that adsorb, or "stick", to a surface to the total number of atoms that impinge upon that surface during the same period of time. Sometimes the symbol S_c is used to denote this coefficient, and its value is between 1 (all impinging atoms stick) and 0 (no atoms stick). The coefficient is a function of surface temperature, surface coverage (θ) and structural details as well as the kinetic energy of the impinging particles.

Derivation

When arriving at a site of a surface, an adatom has three options. There is a probability that it will adsorb to the surface ( P a ), a probability that it will migrate to another site on the surface ( P m ), and a probability that it will desorb from the surface and return to the bulk gas ( P d ). For an empty site (θ=0) the sum of these three options is unity.

P a + P m + P d = 1

For a site already occupied by an adatom (θ>0), there is no probability of adsorbing, and so the probabilities sum as:

P d ′ + P m ′ = 1

For the first site visited, the P of migrating overall is the P of migrating if the site is filled plus the P of migrating if the site is empty. The same is true for the P of desorption. The P of adsorption, however, does not exist for an already filled site.

P m 1 = P m ( 1 − θ ) + P m ′ ( θ ) P d 1 = P d ( 1 − θ ) + P d ′ ( θ ) P a 1 = P a ( 1 − θ )

The P of migrating from the second site is the P of migrating from the first site and then migrating from the second site, and so we multiply the two values.

P m 2 = P m 1 × P m 1 = P m 1 2

Thus the sticking probability ( s c ) is the P of sticking of the first site, plus the P of migrating from the first site and then sticking to the second site, plus the P of migrating from the second site and then sticking at the third site etc.

s = P a ( 1 − θ ) + P m 1 P a ( 1 − θ ) + P m 1 2 P a ( 1 − θ ) . . . s = P a ( 1 − θ ) ∑ n = 0 ∞ P m 1 n

There is an identity we can make use of.

∑ n = 0 ∞ x n = 1 1 − x ∀ x < 1 ∴ s = P a ( 1 − θ ) 1 1 − P m 1

The sticking coefficient when the coverage is zero s 0 can be obtained by simply setting θ = 0 . We also remember that

1 − P m 1 = P a + P d s 0 = P a P a + P d s s 0 = P a ( 1 − θ ) 1 − P m 1 P a + P d P a

If we just look at the P of migration at the first site, we see that it is certainty minus all other possibilities.

P m 1 = 1 − P d ( 1 − θ ) − P d ′ ( θ ) − P a ( 1 − θ )

Using this result, and rearranging, we find:

s s 0 = [ 1 + P d ′ θ ( P a + P d ) ( 1 − θ ) ] − 1 s s 0 = [ 1 + K θ 1 − θ ] − 1 K = d e f P d ′ P a + P d

References

Sticking coefficient Wikipedia

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