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| {{Underlinked|date=December 2013}}
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| '''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.<ref>[http://www.iupac.org/goldbook/S06012.pdf sticking coefficient] ''IUPAC Compendium of Chemical Terminology'' 2nd Edition (1997), Accessed 30 September 2008</ref> Sometimes the symbol '''S<sub>c</sub>''' is used to denote this coefficient, and its value is between 1 (all impinging atoms stick) and 0 (none of the 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.
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| ==Derivation==
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| When arriving at a site of a surface, an adatom has three options. There is a probability that it will adsorb to the surface (<math>P_a</math>), a probability that it will migrate to another site on the surface (<math>P_m</math>), and a probability that it will desorb from the surface and return to the bulk gas (<math>P_d</math>). For an empty site (θ=0) the sum of these three options is unity.
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| :<math> P_a + P_m + P_d=1 </math>
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| For a site already occupied by an adatom (θ>0), there is no probability of adsorbing, and so the probabilities sum as:
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| :<math> P_d'+P_m'=1 </math>
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| 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.
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| :<math> P_{m1}=P_m(1-\theta)+P_m'(\theta) </math>
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| :<math> P_{d1}=P_d(1-\theta)+P_d'(\theta) </math>
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| :<math> P_{a1}=P_m(1-\theta) </math>
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| 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.
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| :<math> P_{m2}=P_{m1} \times P_{m1}=P_{m1}^2 </math> | |
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| Thus the sticking probability (<math> s_c </math>) 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.
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| :<math> s=P_a(1-\theta)+P_{m1}P_a(1-\theta)+P_{m1}^2P_a(1-\theta)...</math>
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| :<math> s=P_a(1-\theta)\sum_{n=0}^{\infin} P_{m1}^n </math>
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| There is an identity we can make use of.
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| :<math>\sum_{n=0}^{\infin} x^n =\frac{1}{1-x}\forall x<1</math>
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| :<math>\therefore s=P_a(1-\theta)\frac{1}{1-P_{m1}}</math>
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| The sticking coefficient when the coverage is zero <math>s_0</math> can be obtained by simply setting <math>\theta=0</math>. We also remember that
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| :<math>1-P_{m1}=P_a+P_d</math>
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| :<math> s_0=\frac{P_a}{P_a+P_d} </math>
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| :<math> \frac{s}{s_0}=\frac{P_a(1-\theta)}{1-P_{m1}}\frac{P_a+P_d}{P_a} </math>
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| If we just look at the P of migration at the first site, we see that it is certainty minus all other possibilities.
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| :<math> P_m1=1-P_d(1-\theta)-P_d'(\theta)-P_a(1-\theta) </math>
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| Using this result, and rearranging, we find:
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| :<math> \frac{s}{s_0}=[1+\frac{P_d'\theta}{(P_a+P_d)(1-\theta)}]^{-1} </math>
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| :<math> \frac{s}{s_0}=[1+\frac{K\theta}{1-\theta}]^{-1} </math>
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| :<math> K\overset{\underset{\mathrm{def}}{}}{=}\frac{P_d'}{P_a+P_d} </math>
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| ==References==
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| {{reflist}}
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| *King-Ning Tu, James W. Mayer, and Leonard C. Feldman, in ''Electronic Thin Film Science for Electrical Engineers and Materials Scientists'', Macmillan, New York, 1992, pp. 101–102.
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| [[Category:Surface chemistry]]
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| [[Category:Materials science]]
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| [[Category:Dimensionless numbers]]
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