The LPCVD Furnace Model is based on differential conservation equations for reacting fluid flow. The LPCVD Furnace Model solves conservation equations for mass, species, and (optionally) energy. For multi-component gases, the equation for mass conservation is:

(8–1)

where is the gas density in g/cm³, is the time in sec, and is the gas velocity (vector) in cm/sec.

The species conservation is:

(8–2)

Here, is the index of a gas species, is the diffusion velocity of k th species (vector) in cm/sec, is the molecular weight of k th species in g/mole, is the mass fraction of k th species, and is the production rate of k th species in mole/(cm³ sec).

The mass fractions in these equations satisfy a constraint

(8–3)

while the diffusion velocities are given as

(8–4)

for mixture-averaged formulation, or

(8–5)

for the multicomponent formulation. Here is the averaged diffusion coefficient for the k th species in cm² /sec, is the thermal diffusion coefficient for the k th species in g/(cm sec), is the multicomponent diffusion coefficient in cm² /sec, for the k th and j th species, is the number of gas species, is the temperature in , is the mean molecular weight in g/mole, and is the mole fraction of k th species.

Note that since pressure is assumed to be constant, these diffusion velocities neglect any effect of pressure gradient.

An optional equation for energy conservation, assuming no viscosity and uniform pressure, completes the set of conservation equations.

(8–6)

where is the mean enthalpy (mass units) of the gas mixture in ergs/g, is the enthalpy of the k th species (mass units) in ergs/g, and is the thermal conductivity in ergs/(cm K sec). Unless instructed otherwise (see CONSERVE ENERGY in Specify the Material Properties ), the LPCVD Furnace Model omits this equation and assumes the gas temperature is specified.

Equation 8–2 , Equation 8–4 , and Equation 8–5 do not satisfy the constraint that mass fractions sum to 1 (Equation 8–3 ). The LPCVD Furnace Model therefore balances equations and unknowns by dynamically discarding one species conservation equation, specifically, the one for the species with the largest mass fraction, and enforcing Equation 8–3 on this species.