Often, when modeling very low-pressure plasmas, it is reasonable to constrain the ion flux to a surface according to the Bohm criterion. This condition maintains that the maximum net flux of a particular ion to a surface is equal to the product of the ion density and the Bohm velocity, which is defined as:

(8–148)

For an electronegative gas, this expression must be modified to account for the presence of negative ions and their effect on the plasma sheath behavior. In the limit of a purely electronegative gas, the ion flux to a surface would be limited by the thermal speed of the ion.

To accommodate a large range of conditions, then, we use the correction to the Bohm velocity derived by Braithewaite and Allen, [77] as follows:

(8–149)

where is the sum over all negative ions of the product of the ion species’ concentration and its integer electronic charge.

The Plasma Reactor Models allow the user to specify this constraint in one of two ways. The first way is to use the Plasma Reactor "Bohm factor" setting. This keyword includes the input of a correction factor to the above Bohm velocity. When this option is included, the production rate of each ion by each surface reaction will be scaled, such that the net production rate of the ion on each material is given by

(8–150)

The second way to apply the modified Bohm criterion, is to use the Surface Kinetics BOHM auxiliary keyword. In this case, the individual reaction for which the auxiliary BOHM keyword is included, will have a rate of progress calculated in the Surface Kinetics routines as

(8–151)

where, in this case, the correction factor is the first reaction-rate coefficient specified on the reaction line in the Surface Kinetics input file. This rate-of-progress of the Bohm reaction will then be modified within the Plasma Reactor Model to account for the presence of any negative ions in the plasma; that is, each reaction with a BOHM auxiliary keyword ultimately has a rate of progress defined as:

(8–152)

The main difference between these two approaches arises when an ion participates in more than one surface reaction subject to the Bohm criterion. In the first approach, the net ion flux to the surface will be automatically scaled to the Bohm-limiting flux modified for electronegative gases and the user-defined correction factor . In the latter approach, each reaction will be subject to the Bohm limit independently. In that case, it is up to the user to make sure that the reaction coefficients add up to the desired overall correction factor, for all the reactions involving a particular ion. This overall correction factor is often used to account for spatial variations in ion density or transport limitations in the reactor being modeled. For example, the correction factor may be set equal to an estimation of the ratio of the ion density at the sheath edge to the ion density in the bulk of the plasma [73] , [74] , [75] .