In addition to the gas, surface, and bulk species sensitivity coefficients, sensitivity coefficients for the growth (or etch) rates of the bulk phases with respect to the reaction rate coefficient parameters may also be computed where applicable. As the growth rates are derived quantities, the local sensitivity calculation method described in this section is used for both steady-state and for transient simulations.

First, the linear growth rate (units of cm/sec) of the bulk phase can be expressed by:

(17–12)

The derivative with respect to the parameters is then,

(17–13)

(17–14)

The vector, is the vector of raw sensitivity coefficients computed by solution of Equation 17–8 . is a matrix representing the derivative of the bulk species production rates from surface reaction with respect to the solution variables. and are the molecular weight and mass density of the k th bulk-phase species, respectively. The normalized growth rate sensitivity coefficients are computed as:

(17–15)

Note that, in general, can be either positive (growth) or negative (etch). Therefore, the absolute value of on the right-hand-side of Equation 17–15 is necessary to correctly normalize the sensitivity coefficients.