In modeling plasma systems, it is sometimes necessary to include reactions where the energy of the incident ion determines not only the reaction rate, but also the number of product species formed. For example, in physical etching the incident ion energy determines the number of species etched from the surface. Such surface reactions can be modeled in Surface Kinetics using a " yield enhancement" factor to account for the variable stoichiometry.

Consider the case in which a positive ion, I(g) hits a surface and knocks off a variable number of surface species, S(s). For each surface species S(s) destroyed, the example reaction produces two gas-phase products, P(g) and leaves behind some other surface species, O(s); another gas species Q(g) is produced by the reaction, but its stoichiometric coefficient is not dependent upon the number of surface species etched.

(4–31)

The coefficient is essentially a variable stoichiometric coefficient, which depends upon the energy of the positive ionic reactant I(g).

A reaction written like Equation 4–31 is required to satisfy mass, charge, and elemental balance (as is every reaction in a Surface Kinetics mechanism). For this always to be the case, the " sub-reaction"

(4–32)

consisting of all of the species in the original reaction that are multiplied by the coefficient , must also satisfy mass, charge, and elemental balance. In addition, unless the NONCON auxiliary keyword was declared on the REACTIONS line (described later), the sub-reaction must also conserve the number of surface sites.

An example of a reaction using the ion-enhanced yield option in the form accepted by the Surface Kinetics Pre-processor is

E + CL+ + #SICL3(S) + #SI(B) + SICL(S) => SICL2(S) + #SICL2 + #SICL(S)

The special character # identifies the energy-dependent multiplicative factor for the stoichiometric coefficient. Notice that the sub-reaction consisting of every species preceded by the # sign balances mass, elements, charge, and number of surface sites. The "yield" of this reaction (per incident CL+ ion) depends upon the energy of the ion.

We allow the following functional form for the yield enhancement:

(4–33)

The ion-enhanced yield can depend upon a threshold energy, , and the energy expressions can be raised to a specified power in two different ways through the use of the parameters and . Ion-enhanced-yield reactions can be declared through the Pre-processor input via the auxiliary keyword YIELD. An executable can find out which reactions were declared as ion-enhanced yield reactions and get an array of the parameters via a call to SKIYLD. Because the subroutines that evaluate rate constants in Surface Kinetics take temperature as an argument, and not species energy, subroutine SKRPAR must be called to input an array of ion energies, ENRGI, before the rate constant routine is called. Use of the YIELD keyword is only allowed for irreversible reactions.