The LPCVD Furnace Model offers two Transport formulation options for calculating diffusion coefficients. The multicomponent option provides greater accuracy at the expense of longer computing times. The mixture-averaged option is a good approximation when a carrier gas is present and is also computed more efficiently.

Equation 8–4 uses ordinary diffusion coefficients, , that are inexpensive combinations of binary diffusion coefficients. This formula is obtained by specifying DIFFUSION COEFFICIENTS = MIXTURE-AVERAGED (see Specify the Material Properties ). Equation 8–5 uses ordinary diffusion coefficients obtained from the Transport multicomponent option. It is specified by DIFFUSION COEFFICIENTS = MULTICOMPONENT.

Finally, if the LPCVD Furnace Model includes an equation of energy conservation, CONSERVE ENERGY = YES, then diffusion velocities may also include the effects of thermal diffusion as in the term:

This term is included by entering the keyword phrase INCLUDE THERMAL DIFFUSION = YES. Even though the regular diffusion coefficients may be averages, the thermal diffusion coefficients are always the ones predicted by the multicomponent transport option.

The equations are solved over the interior of an LPCVD reactor. This is a cylinder with wafers inside as shown in Figure 1.1: Schematic of a Multiwafer LPCVD Reactor, with the Important Dimensions Indicated . The LPCVD Furnace Model therefore applies the equations in cylindrical coordinates, where is the radial component of velocity in cm/sec, is the azimuthal component of velocity in rad/sec, and is the axial component of velocity in cm/sec. Moreover, the LPCVD Furnace Model supposes rotational symmetry and no azimuthal flow .

To reduce computing time, however, the LPCVD Furnace Model does not solve momentum equations, but instead assumes uniform pressure and reduces velocity to a scalar quantity by imposing the direction of flow. Specifically, the LPCVD Furnace Model supposes radial flow between wafers and axial flow elsewhere . This leaves equations to be solved for the species mass fractions, the temperature and the (signed) magnitude of velocity.

As a result of these assumptions and approximations, the equations solved by the LPCVD Furnace Model become these shown below (Equation 8–7 to Equation 8–10 ):

(8–7)

(8–8)

(8–9)

(8–10)