The boundary conditions for these differential equations account for the chemical deposition process due to surface chemistry. At the surface where chemistry occurs, the surface may be an inhomogeneous medium composed of different types of sites or phases. Several surface species may reside on a certain site type. A species may occupy more than one site.

The equations of production for surface species is given by:

(8–11)

where is the density of the n th site in mole/cm², is the index of a surface species, is the index of a surface site (phase), is the production rate of the k th species in mole/(cm² sec), is the occupancy factor for the k th species, and is the site fraction of the k th species.

The species fractions associated with each kind of site additionally must satisfy an algebraic constraint:

(8–12)

where is equal to 1, if species belongs to site and it is 0 otherwise. is the number of surface species.

As with gases, the LPCVD Furnace Model dynamically replaces one equation for surface species with an algebraic constraint as given in Equation 8–12 , for each surface site (phase). This leaves equations for surface fractions at each surface point.

The boundary conditions for the flow equations stipulate matching fluxes of energy and mass between the bounding surfaces and the gas.

Flows with reacting boundaries have non-zero velocities normal to the surface at the boundary. The boundary condition for overall mass conservation at reacting surface is given by:

(8–13)

The boundary condition for species conservation at a reacting surface is given by:

(8–14)

The energy balance is:

(8–15)

where is the coefficient of heat transfer in , is the interior unit normal vector in , is the production rate of the k th gas species by surface reactions in mole/(cm² sec), and is the temperature of the surface in . These flux boundary conditions ignore diffusion at the surface, hence only rather than appears in the left side of the second two equations. The gas affects surface composition because the production rates, , depend in part on the composition of the impinging gas.

The LPCVD Furnace Model's flow equations do not model injectors in detail, for example, as nozzles with boundary conditions on velocity. Instead, the LPCVD Furnace Model accounts for injected gases by adding source terms to its conservation equations. This is a reasonable simplification for the diffuse flows found in LPCVD reactors. The LPCVD Furnace Model adds the injector's mass, species, and energy flow rates, divided by the volume of the region over which injection occurs (which is determined by the grid), to the appropriate conservation equations.

Similarly, the LPCVD Furnace Model accounts for gas outflow by adding a sink term to the conservation equations throughout a certain region. The mass removed balances gains and losses throughout the reactor—mass inflow less mass deposition—-and must be determined by the simulation. The LPCVD Furnace Model adds this sink term, and allows outflow, at one end of the reactor called the "far end."

The fundamental unknowns or dependent variables in the equations are , , , and the mass outflow. The other quantities either are specified or are related to the unknowns by explicit formulas. The surface densities and factors, and , are specified with the chemical reactions in the Surface Kinetics Pre-processor input file. The heat transfer coefficient, , varies with surface location and temperature. The pressure, , is specified with the reactor operating conditions (PRESSURE in Specify the Operating Conditions ) and should be roughly in the range from 0.1 to 1.0 Torr. Surface temperatures, , also are specified with operating conditions. The LPCVD Furnace Model allows different temperatures for different reacting surfaces. The surfaces in the model are the reactor’s cylindrical sides, ends, and the wafers themselves. The same TEMPERATURE can be specified for all surfaces, or a TEMPERATURE FILE NAME can be specified that provides a list of temperatures for the reactor wall, and an array of temperatures for the wafer load (see Specify the Operating Conditions ). The formula for density, , is the equation of state for an ideal gas: , where is the pressure in dynes/cm², and is the universal gas constant, 8.314 ⋅ 10⁷ ergs/mole K.

The Ansys Chemkin libraries evaluate this formula, as well thermodynamic and transport properties based on local values of chemical species composition and thermodynamic state of the gas.