For some simple surface reaction mechanisms we have found it convenient to specify the surface reaction rate constant in terms of a "sticking coefficient" (probability), rather than an actual reaction rate. This approach is only allowed when there is exactly one gas-phase species reacting with a surface. Sticking-coefficient reactions may include any number of surface site or bulk-phase species as reactants, and any number of species of any phase as products

In such cases, one might have a measurement or intuition about the probability that a certain process takes place when a collision between a given gas-species occurs with the surface. For consistency in expressing each surface reaction in terms of a rate constant, we provide a conversion between this sticking coefficient form and the usual rate expression. The actual reaction rate (in moles/cm2/sec) is derived from this probability together with the physical gas-surface collision frequencies, as discussed further below.

The unitless sticking coefficients’ functional form has an "Arrhenius-like" form as follows:

(4–10)

In this case, , and are unitless and has units compatible with , the real-gas constant used for reaction activation energies multiplied by temperature. Surface Kinetics also allows for surface-coverage modification of a sticking coefficient, analogous to Equation 4–7 .

To illustrate the use of sticking coefficients, we give three successively complex examples of using sticking coefficients. First, to specify that SiH₂ (g) reacts with probability upon each collision with the surface, one could write the reaction

(4–11)

In this example, we have not explicitly included the surface in writing Equation 4–11 .

A somewhat more detailed way of using the sticking-coefficient specification would be to say that SiH₂ (g) reacts with probability upon each collision with a bare surface silicon atom, Si(s):

(4–12)

If the surface site fraction of Si(s) were unity, then a fraction of the collisions of SiH₂ with the surface would result in a reaction. However, for Si(s) coverages less than 1, the reaction rate decreases in proportion with the coverage of Si(s).

In a third (contrived) example, suppose there is a probability for a reaction to occur when SiH₂ collides with both a Si(s) and a C(s) reaction such as

(4–13)

The rate of this reaction would be proportional to both the coverage of Si(s) and C(s).

Conversion of a sticking coefficients to the usual mass-action kinetic rate constants uses the collision frequency of the gas species with the solid surface, as shown in Equation 4–14 .

(4–14)

Here, is the universal gas constant, is the molecular weight of the gas-phase species, is the total surface site concentration summed over all surface phases (number of moles of surface sites per unit area), and is the sum of all the stoichiometric coefficients of reactants that are surface species. The term involving raised to the power is needed to convert from the unitless sticking coefficient form to units appropriate for a rate constant, and the term in the square root accounts for the gas/surface collision frequency. In the third example given above, Equation 4–13 , the value of is 2, because there are two surface sites appearing as reactants, that is, Si(s) and C(s). The product term in Equation 4–14 is the product of the site-species occupancies, raised to a power equal to the reaction order for that species, for all site species that are reactants. Here, is the number of sites that the surface species occupies, and is the reaction order for that species. The product term will be equal to one when there are unity site occupancies for all of the surface species in the reaction.

Implicit in the sticking coefficient description just presented is an assumption that the sticking coefficient is relatively small, that is, much less than one. In this case the molecular motion in the vicinity of the solid surface is random and the collision frequency of gas-phase species with the surface is not affected by the surface itself. However, when the sticking coefficient is large, that is, close to one, then the velocity distribution becomes skewed. Species whose random motion carries them close to the surface have a high probability of staying there, which causes a non-Maxwellian velocity distribution that, in turn, alters the net species flux near the surface. Motz and Wise [26] analyzed this situation and suggested a correction factor that modified Equation 4–14 to become:

(4–15)

Goodwin and Gavillet [27] have incorporated this effect in their analysis of chemical vapor deposition of diamond films. However, in most cases sticking coefficients are derived from empirical data rather than theory, in which case it is usually inappropriate to apply the Motz-Wise correction. Users may turn this option on by including MWON in the REACTIONS line of their Surface Kinetics input file.

Using the kinetic rate constant derived from the sticking probability, the rate-of-progress is calculated using Equation 3–4 , as usual. The sticking coefficient specification is only allowed for the forward reaction. If the reaction is written as reversible, the reverse reaction rate constant would be calculated from Equation 3–6 to assure microscopic reversibility.